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Tutorial Review Quality Management in Drug Analysis Anil C. Mehta Pharmacy Department, The General Infirmay, Leeds, UK LS1 3EX Summary of Contents Introduction Analytical Techniques Personnel Equipment and Chemicals Method Development Validation Ruggedness System Suitability Tests Method Comparison Solutions and Reagents Samples Analysis Internal Quality Control External Quality Control Accreditation Laboratory Audit Conclusion References Keywords: Review; drug analysis; method development; validation; quality; laboratory audit Introduction This paper provides a general outline of the issues that need to be addressed in order to obtain reliable data while performing drug analysis in a research environment.It is especially aimed at younger workers and laboratory managers wishing to introduce quality management systems into their laboratories. Quality management in drug analysis covers a wide range of quality improving activities designed to ensure the reliability of the analytical data.These activities include ensuring that the samples are properly collected and preserved prior to analysis, that the analysis is carried out using the appropriate technique and that the results are properly recorded and reported. This paper particularly focuses on the quality management needs of research laboratories where drug analysis is carried out on a non-routine basis. It provides guidelines on how to adopt a more systematic approach to laboratory management, method development and analysis.To assist younger workers, each section is provided with ample references. Guidelines on the quality management aspects of routine quality control (QC) work are already available from specialist texts related to industrial1–3 and hospital QC work.4 Analytical Techniques Drug analysis is undertaken during various phases of pharmaceutical development,5 such as formulation and stability studies, QC and toxicological and pharmacological testing in animals and man.6,7 In hospitals, drug analysis is performed on patients’ samples in support of clinical trials (bioavailability and pharmacokinetic studies) and in monitoring therapeutic drugs and drugs of abuse.8–11 All these investigations require reliable and validated analytical methods in order to measure drugs in complex media such as formulations and biofluids.Because of their selectivity, sensitivity and overall versatility, techniques such as GC, HPLC, supercritical fluid chromatography (SFC) and capillary electrophoresis (CE) coupled with selective detectors [diode-array detector (DAD) and MS] are frequently used to analyse multicomponent drug mixtures.Immunoassays [radioimmunoassay (RIA), enzyme multiplied immunoassay technique (EMIT)] because of their speed and simplicity are mainly used in drug monitoring in patients. Spectroscopic (UV, IR, AAS) and titrimetric techniques are routinely used in QC work, and TLC and more recently nearinfrared (NIR) spectrometry have been used for the rapid identification of impurities and degradation products in pharmaceuticals. Many other analytical techniques are used in product development and other applications.For example, thermal analysis techniques [thermogravimetric analysis (TGA), differential scanning calorimetry (DSC)] are used in investigating polymorphism and the presence of impurities in drug substances and radiochemical methods (administration of a radiolabelled drug in the body) are used in biodisposition studies.Since the individual enantiomers of a chiral drug can have different actions,12 emphasis is now placed upon stereospecific assays for the individual optical isomers of chiral drugs. These are mainly performed using HPLC with chiral mobile or stationary phases.13,14 Anil C. Mehta received his MSc in analytical chemistry from the University of London in 1967 and PhD in analytical chemistry from the University of Aberdeen in 1972.His PhD thesis was on the spectrofluorimetric analysis of alkaloids and their synthetic analogues. Following a postdoctoral year at the College of Pharmacy, University of Florida, he joined Leeds General Infirmary in 1974 in charge of the pharmacy quality control laboratory, continuing there as R & D manager until his recent retirement. His main interest has been the development of methods for drug analysis by GC and HPLC for solving pharmaceutical and biomedical problems. He has published (alone or with colleagues) over 70 research papers and reviews related to drug bioanalysis, quality control, method validation, sample treatment, dissolution and stability studies, pharmacokinetic and bioavailability studies, and therapeutic drug monitoring.Analyst, July 1997, Vol. 122 (83R–88R) 83ROver and above analytical techniques, robotic equipment is being increasingly employed in drug analysis for sample preparation to minimise monotonous tasks and avoid exposure to harmful chemicals.Robots used in conjunction with computer systems provide more reproducible and reliable results rapidly. Personnel The quality of analytical results depends on both instrument capability and the professional expertise of the user, and therefore for reliable results instruments must be used by an adequately qualified and trained operator using clearly written standard operating procedures (SOPs). A detailed job description should be available and the required level of qualifications and experience set for each post.Training should go beyond analytical measurement skills and should include laboratory safety (including COSHH regulations), sample handling, statistical analysis of data, documentation and report writing. Individual training records should be maintained for each member of staff. Deficiency in staff training, equipment handling and other laboratory matters can lead to the production of poor data.Equipment and Chemicals When choosing new equipment it is important to ensure that it is fit for its intended purpose and its performance is up to specificiations.15 Other things to be considered are cost, ease of use, quality of after-sales service and health and safety aspects. There should be clear, unambiguous, written procedures for the operation of the isntruments. They should give correct readings within their specified tolerance limits when checked at the appropriate intervals by standard procedures using reference materials.All standards and calibrators used must be traceable to nationally accepted standards. Minor preventative maintenance operations should be established and followed, such as keeping pH electrodes in a wet condition or storing chromatographic columns according to suppliers’ instructions. Once a year, a major equipment should be serviced by a qualified specialist under contract. This saves money in the long run.Computer controlled data processing systems such as laboratory information management system (LIMS) should be validated by a computer specialist to demonstrate that they are suitable for their intended use.16–18 Special attention should be given to the quality of laboratory glassware and reagents and standards. Reference standards should be prepared according to written procedures. For quantitative work, be sure to use good quality glassware (e.g., Class A volumetric glassware) and analytical-reagent or HPLC grade reagents and solvents, because other grades can contain impurities.If necessary, reagent and solvent blanks should be measured by GC or HPLC to check for potential interferences. If plastic ware is used, this must be checked for suitability for the analysis to avoid adsorption losses and contamination. Drug substances in pure form can be obtained from the suppliers such as British Pharmacopoeia Commission, London, or be requested from the drug manufacturer.Due consideration should be given to the safe storage and disposal of chemicals and solvents used in the laboratory. Finally, as a matter of good housekeeping, one should keep laboratories clean, with equipment uncluttered and benches tidy.19 Method Development Good planning is essential in the selection and development of the method for drug analysis. It is necessary to be able to quantify the active components in the samples rapidly with acceptable precision, accuracy and reliability within the cost and other constraints. It often happens that during product development or any other long term work, analytical methods evolve.As the nature of the sample changes (different dosage form or biological fluid), methods can be revised. Discussions between the laboratory staff and the request originator is necessary to reach agreement on why the analysis is required and how the results will be used. There should also be discussion on the sampling plan, documentation, report requirements and disposal of samples at the end of the project.In addition, other possible constraints, such as cost, time, safety and availability of trained staff will need to be considered. A logical and systematic approach is required in method selection and development. This can be outlined in four basic steps: (1) generate background data, (2) review the literature, (3) develop the method (optimise the experimental conditions) and (4) validate the performance of the method before using it routinely.Before starting any work, all the initial information on the drug (physico-chemical properties such as solubility, dissociation constant and UV absorption) and the dosage form or the intended dosage form (strength, presence of preservatives, type of container, stability, etc.) should be collected. For bioanalytical work, adequate information about the sample, subject and dosage, including co-administered drugs, should be obtained. All this information is very useful in setting up the analytical method, including sample clean-up.Some of the information mentioned above can be obtained from reference sources.20–27 Methods can be searched for (abstracts, journals, books, pharmacopoeias), recommended by colleagues or developed inhouse. The choice of the method depends on factors such as the nature of the drug, the complexity of the sample and the intended use.The choice of the method will also be governed by practical considerations such as the availability of equipment and specialist skills. If these are not available or prove costly then the work can be contracted out. For industrial products (bulk drugs), the regulatory guidelines for new drug substances require the identification of impurities at levels !0.1% for most compounds.28,29 Meeting this criterion requires careful consideration of the analytical techniques to be used in terms of limits of detection and determination and selectivity.To quantify a substance at the 0.1% level, a technique with a limit of determination of at least 0.05% will be required. Dissolution tests and stability assays require higher selectivity and sensitivity than routine QC assays. They require noninterference from excipients, process impurities and degradation products. They should be accurate, precise, rapid and capable of automation. Selectivity of the method is particularly important for dissolution testing as the final analytical step for dissolution samples is often a non-specific UV determination.Stability assays, on the other hand, should be robust and transferable. Bioanalytical methods for pharmacological and toxicological studies must be selective, i.e., free of interference from endogenous substances, co-administered drugs and metabolites, and sensitive enough to follow the absorption, distribution and elimination of the drug.Sensitivity is particularly important for paediatric or small animal samples since their availability may be limited to, say, 100 ml. Furthermore, biofluid assays must be accurate and precise in order to reveal differences between dosage forms or subjects (human volunteers, patients or animals). The analytical method used in drug monitoring in patients must be simple, reliable and rapid because results are needed urgently. It must be specific for the drug in question and free of interference from other drugs and metabolites.As therapeutic or toxicological drug monitoring is usually performed at compar- 84R Analyst, July 1997, Vol. 122atively high drug concentration, extreme sensitivity in the method is not often needed. Because most of the routinely monitored drugs have narrow therapeutic ranges (i.e., the difference between therapeutic and toxic concentrations is very small), it is essential that the method is accurate and precise since the imprecision of the method could lead to errors in interpretation and dose adjustment.If the method has been taken from the literature, it may not have been used for the matrix in question, and it is likely that some modification of the method will be required in order to make it suitable for the purpose. For reliable results it is better to use a technique with which one is familiar and choose the least complex method if this matches the requirements of the intended use.It is best to keep the number of operations to a minimum to reduce contamination possibilities and minimise losses of the analyte. For example, direct GC analysis is better than a method that involves derivatisation, provided that it is sensitive enough for the purpose and free from potential interferences. Although experience is required in method development work, guidance can be obtained from literature sources specialising in method development.30–37 These publications may serve as a starting point for the development of methods for drugs and/or metabolites.Alternatively, one can use one of the commercially available software packages (expert systems) to speed up chromatographic method development, particularly HPLC.38,39 These systems are developed to assist the chromatographer in the selection and optimisation of chromatographic conditions during method development. With the assistance of these systems, maximum information can be extracted from a minimum number of experiments.The main advantage of expert systems is that they provide immediate availability of an expert opinion through an inherent knowledge base, and respond to the user’s inquiry when presented with a problem. Validation Once the analytical method has been developed, it is validated before or during its use. Validation of the method establishes that its performance characteristics are adequate for the intended use. It builds quality and reliability into the method.In the pharmaceutical industry, validation of analytical method is required in support of product registration applications.40 Many of the principles, procedures and requirements of validation are common to the majority of analytical methods. Validation is performed by conducting a series of experiments using the specific conditions of the method and the same type of matrix as the intended samples. It entails evaluation of various parameters of the method such as accuracy, precision (reproducibility), linearity (concentration–detector response relationship), sensitivity, limits of detection and determination, recovery from the matrix and specificity (selectivity). The definitions and procedures used to calculate these parameters are adequately described in many publications related to pharmaceutical41 –50 and biomedical51–58 analysis.The International Conference on Harmonisation (ICH) has produced guidelines59 on the validation of analytical procedures for pharmaceutical product registration applications.One of the key aims of harmonisation is the mutual acceptance of data from different regulatory authorities. Carr et al.60 have reviewed in detail the validation requirements of various regulatory authorities and provided practical suggestions for satisfying these requirements. Validation does not imply that the method is free from errors. It only confirms that it is suitable for the purpose.Any modifications to a method during its use require its revalidation. For example, if a new instrument or a different type of chromatographic column is brought into use, or the method is applied to a different type of sample, it will require revalidation. The greater the modification, the greater the need for revalidation. Some revalidation may also be required when transferring the method between laboratories or when changes are made in the manufacturing process for the drug.Other factors which can be considered when validating a method are cost per analysis, ease and speed of operation and potential for automation. Once the method has been developed and validated, it is fully documented and approved for use. It should be described in sufficient detail to allow any analyst to use it without difficulty. Ruggedness In addition to the scientific parameters mentioned above, another useful parameter to consider during validation is the ruggedness or robustness of the analytical method.The ruggedness of a method is its ability to remain unaffected by small, unintentional changes in experimental conditions such as temperature, mobile phase composition and pH, or different sources of reagents and chromatographic columns. These can occur when a method is used over a long period or is transferred to another location. Since the drug development work can last for many years and be conducted at more than one site, the ruggedness of the method is critical so that it can be transferred between laboratories and used by different workers employing different instruments and reagents without any problems.System Suitability Tests Once the method is in routine use, check or system suitability tests (SSTs) should be run each time the method is used, to confirm that it is performing satisfactorily. Since instrument to instrument variations can have a significant effect on the assay, SSTs provide the added assurance that on a specific occasion the method is giving acceptable results.In chromatographic assays this is done by injecting a standard solution to check whether certain parameters such as retention time (RT), column efficiency (theoretical plates), tailing factor (peak asymmetry) or resolution between peaks are within preset limits. If so, the method is deemed satisfactory on that occasion. For example, in HPLC, if an SST based on RT passes, it should provide assurance that the HPLC pump and column are functioning satisfactorily. SSTs should not be confused with method validation.Validation is carried out at the method development stage. SSTs, on the other hand, check the performance of a given system (e.g., a particular chromatograph) on a given day prior to analysis. SSTs can detect normal changes (wear and tear) in the equipment (e.g., detector sensitivity) or supplies (e.g., chromatographic column) during normal usage. If the method is robust enough, it should not fail such tests.SSTs are particularly useful in routine QC work and stability studies. Further guidance on SSTs can be obtained from the literature61,62 or pharmacopoeias. 63.,64 Method Comparison The performance of a newly developed or modified method can be assessed by comparing the results obtained by it with those found with a reference (or comparison) method of known accuracy and precision using linear regression analysis.65–68 A reasonable number of samples (10–20) evenly spaced over a concentration range of interest are analysed by both the candidate method and the reference method.Results are plotted as points with one axis (usually the abscissa) for the reference method and the other for the candidate method. GLC and HPLC are often used as reference methods since they are less susceptible to interference from other substances. However, it is not always possible to conduct method comparison studies Analyst, July 1997, Vol. 122 85Rsimply because a suitable reference method is not routinely available or is costly, requiring special facilities.Simple linear regression is a widely used statistical approach for assessing systematic and random errors associated with the new method. It involves relatively simple calculations and provides reliable estimates of intercept and slope. However, if the appropriate computer program is available for statistical calculations, it is more appropriate to use weighted linear regression since this compensates for the change in variance across the concentration range.Solutions and Reagents Standard solutions of drugs in water or methanol are used during many stages of analysis such as calibration and validation. In bioanalytical work, although stock solutions can be prepared in water or methanol, standard solutions for calibration and other experiments should be prepared by dilution of the stock solution with a relevant biological fluid since aqueous solutions differ greatly from the biological matrix.Drug and reagent solutions are stored in such a way as to maintain their integrity. Prior to analysis, their stabilities should be tested by comparison with freshly prepared solutions. In general, solutions of drugs and chemicals are more stable at low temperature (4 or 220 °C) than at room temperature. All solutions must be clearly labelled with preparation and expiry dates. Stock solutions of photodecomposable substances should be stored in amber coloured containers and those of very unstable or volatile substances should be freshly prepared.Samples Sampling is often considered to be a weak link in the quality chain, particularly in drug bioanalysis, and is often the major contributor to measurement error. The importance of sampling is not often appreciated. Samples should be homogeneous and representative of the original material. A non-representative sample is of no value, however well the assay is carried out.The sample taking should be carried out in accordance with the approved procedures. It is essential that the samples are collected in a suitable container at the correct time in relation to the dose and correctly labelled and preserved under appropriate conditions.69–72 Sample identity should include the source of samples, dosage, sampling time in relation to the dose and date and the drug(s) to be assayed. In drug bioanalysis, as sampling frequently is not under the control of the analyst performing the assay, it is necessary to issue clear instructions to the sample provider for collection, storage and transport of samples.The biofluids most commonly analysed for drugs and/or metabolites are blood (plasma or serum) and urine. Blood (5–10 ml) should be centrifuged to retain either plasma, if an anticoagulant such as heparin is added to the sample, or serum, if the blood is coagulated.For urine, usually a midstream sample is collected for most analyses. However, in a urinary excretion study, sampling is performed quantitatively, i.e., the volume of urine is also measured at each collection. The samples should be sealed and packaged in such a way to avoid loss of contents during transport. To avoid potential health hazards, precautions (e.g., wearing of gloves) should be taken while handling them. They should be transported to the laboratory in accordance with legal requirements without delay.The laboratory must have a reliable system of documentation of samples from receipt in the laboratory to the disposal of the remainder. Samples must be unpacked in a suitable area taking into account any safety requirements. When a sample is received in poor condition, the analyst should check with the sender whether to proceed with the analysis. If the entire sample received by the laboratory is not initially required, it should be divided into subsamples, taking precautions to avoid contamination and losses through spillages.This practice is useful in case a repeat assay is required at a later stage. The stability of the analyte(s) in the sample during the collection and the storage should be known or assessed (temperature and duration), preferably before analysis. The lack of stability information may jeopardise subsequent investigations. In general, samples intended for immediate assay can be refrigerated, otherwise they are frozen at 220 °C until assayed.Unstable samples should be analysed without delay. Stability information on the samples may also be required during actual analysis, especially in the final extracts when they may be left in an autosampler awaiting final measurement. Once the analysis is over, unused samples should be retained at least until the final report is accepted. Analysis All analyses should be carried out in accordance with written procedures. Assays should preferably be performed in duplicate each time using a separate portion of the sample rather than a repeat determination on final solutions, e.g., a repeat injection into GC or HPLC system.A complete repeat analysis gives confidence in results and serves to check on the homogeneity of the sample and the random variation in the instrumental response.73 The laboratory should maintain records of the results as a matter of professional policy. The tests performed, results and relevant observations should be written down in a laboratory notebook and the corresponding copies of instrument traces stored.The notebook should serve as a record of each days work so that each step in the analysis can be traced at a later stage if required. A well kept notebook is also useful while preparing inhouse reports, regulatory submission or a paper for publication. Internal Quality Control Internal QC is usually applied to drug bioanalysis to monitor assay performance with regard to accuracy and precision.74 This is done by analysing specially prepared QC samples (or spiked samples) alongside a batch of samples and plotting the results of QC samples on a QC chart.75–77 Like calibration standards, QC samples are prepared by adding known amounts of drug to the biofluid.Usually, two concentrations of QC samples, one near the top and the other near the bottom of the calibration range, are used. For an assay with a wide calibration range, a third QC sample in the middle of the range can be tested.If the method is working satisfactorily, the results of the QC samples should fall within the pre-set limits, typically ±10% of the known values. External Quality Control If a laboratory offers drug analysis as part of a routine service (e.g., therapeutic monitoring), it is useful for such a laboratory to participate in an external QC scheme (proficiency testing scheme) involving many laboratories, provided that the drugs in question are included in such a scheme.77–79 In an external QC scheme, identical samples are periodically sent to the participants for assay, and the scheme coordinator after receiving the results reports that laboratory’s performance together with a summary of the results from all participants. Marked improvement in analytical standards over a period is a consistent finding with many quality assessment schemes.77 Only certain groups of drugs, such as anticonvulsants, antidepressants and benzodiazepines, are monitored by external quality assessment schemes.However, regular participation in such schemes is an effective way to measure the competence of the laboratory to undertake certain analyses. 86R Analyst, July 1997, Vol. 122Accreditation In addition to proficiency testing schemes, increasing attention is being given to external quality assessment schemes by which a laboratory has to prove its competence to an independent third party by participating in a recognised external quality assessment scheme.80–82 Laboratory accreditation is a formal recognition by an authorised body such as the National Measurement Accreditation Service (NAMAS) that the laboratory’s quality system is in place and meets the required standards to carry out specific tests or specific types of tests.83 First it should be decided for which methods, analytes, and/or analytical techniques (GC, HPLC, etc.) accreditation is sought.Accreditation is normally awarded following successful assessment of the laboratory’s quality system by a NAMAS officer and is subject to periodic review. Much emphasis is placed on documentation, calibration of equipment, staff competence and training and traceability of standard materials. Accreditation gives the laboratory and its customers added confidence in the quality of results. It should be mentioned that laboratories performing analyses related to toxicity testing in animals (toxicological safety studies) are required to comply with standards defined by Good Laboratory Practice (GLP).6,83 The principles of GLP were introduced by the US Food and Drug Administration (FDA) to ensure quality and integrity of the data generated during nonclinical testing of chemicals, including pharmaceuticals, for hazard and risk assessments.Laboratories doing such work would have to show that the studies had been carried out in accordance with GLP. The principles of GLP describe the organisational processes under which laboratory studies are planned, performed, monitored, recorded and reported to ensure the quality and integrity of laboratory data.Particular emphasis is placed on study design, record keeping and the role of the Study Director, who is appointed with overall responsibility for the study. The conduct of the study must be in accordance with the study plan and all data generated must be recorded, checked and signed and archived properly.GLP refers to all the operations of the laboratory pertaining to the study. This contrasts with the requirements of NAMAS, which is more concerned with the laboratory’s ability to carry out a particular test. Within the UK, GLP compliance is monitored by the Department of Health. Laboratory Audit Cost considerations may prevent laboratories from joining a proficiency or accreditation scheme. In this situation, it is useful to conduct an in-house audit of the laboratory’s quality management system at appropriate intervals say at least once a year.Auditors should preferably be independent of the activities of the laboratory that they are asked to audit. Large laboratories usually prefer to have separate auditing arrangements for some non-analytical aspects such as health and safety. Audits should cover all aspects of the laboratory practice from sample collection to reporting of results, and not just analytical performance.It should be sufficiently probing to highlight any drawback in the service. Corrective measures should be taken when a shortcoming is found in any aspect of the service. The use of audit is the most reliable way of identifying problems in the management of the laboratory. Laboratory audit is a subject in itself,83,84 the detailed discussion of which is beyond the scope of this paper. However a checklist of major areas to be audited is given in Table 1. Conclusion Quality management in drug analysis incorporates all measures taken to ensure the reliability of analytical data, starting from obtaining a satisfactory sample, analysing it correctly with a validated method, to reporting the results, with all procedures well documented and periodically reviewed.Responsibility for maintaining and improving the laboratory’s quality system lies with every member of the laboratory staff. By implementing an effective quality system, a significant improvement is made to the overall performance of the laboratory engaged in drug analysis.References 1 Medicines Control Agency, Rules and Guidance for Pharmaceutical Manufacturers, Stationery Office, London, 1997. 2 Artiges, A., Loulergue, M. H., and Reyneir, J. P., in International Pharmaceutical Product Registration, ed. Cartwright, A. C., and Matthews, B. R., Taylor and Francis, London, 1994, pp. 172–205. 3 Lee, C. R., Porziemsky, J. P., Gaspur, M., and Krstulovic, A. 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M., Ellis Horwood, Chichester, 1989. 14 Camilleri, P., Biasi, V., and Hutt, A., Chem.Br., 1994, 30, 43. 15 Burgess, C., and McDowall, R. D., LC–GC Int., 1997, 10, 87. 16 Huber, L., and Thomas, M., LC–GC Int., 1995, 8, 572. Table 1 A checklist for laboratory audit 1. Pre-analytical— (a) Documentation (request forms) (b) Sample management: collection, identification, processing and storage (c) Buying of correct grade of materials 2. Analytical— (a) Acquisition of material safety data sheets and risk assessment before commencing work (compliance with the COSHH regulations) (b) Procedures for the preparation of standards (c) Appropriate labelling and storage (with shelf-life) of standards (d) Validated analytical methods and standard operating procedures for the methods and the instruments (e) Internal quality control checks for the method.Corrective action if the results are outside the pre-set limits (f) Laboratory notebook for calibration data, results, calculations, instrument or computer outputs 3. Post-analytical— (a) Results report forms (b) Documentation: storage of results (c) Prompt communication with the request originator (e.g., comments on results) (d) Final report 4.Miscellaneous— (a) Staff training in all aspects of laboratory work (b) Maintenance of equipment and associated records (c) Health and safety aspects, including COSHH, fire precautions and disposal of laboratory waste (d) Existence of ‘Quality Manual’, i.e., all the above procedures (1–4) written down in sufficient detail for staff to refer to Analyst, July 1997, Vol. 122 87R17 Huber, L., LC–GC Int., 1996, 9, 564. 18 McDowall, R. D., LC–GC Int., 1996, 9, 202. 19 Horwitz, W., Anal. 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Sci., 1992, 81, 309. 52 Buick, A. R., Doig, M. V., Jeal, S. C., Land, G. S., and McDowall, R. D., J. Pharm. Biomed. Anal., 1990, 8, 629. 53 Phillips, L. J., Alexander, J., and Hill, H. M., in Analysis for Drugs and Metabolites Including Anti-infective Agents, ed. Reid, E., and Wilson, I. D., Royal Society of Chemistry, Cambridge, 1990, pp. 23–36. 54 Tanner, R. J. N., in Analysis for Drugs and Metabolites Including Anti-infective Agents, ed. Reid, E., and Wilson, I. D., Royal Society of Chemistry, Cambridge, 1990, pp. 57—63. 55 Mehta, A. C., Talanta, 1987, 34, 609. 56 Lang, J. R., and Bolton, S., J. Pharm. Biomed. Anal., 1991, 9, 357. 57 Lang, J. R., and Bolton, S., J. Pharm. Biomed. Anal., 1991, 9, 435. 58 Dadger, D., and Burnett, P. E., J. Pharm. Biomed. Anal., 1995, 14, 23. 59 International Conference on Harmonisation (ICH): Validation of Analytical Procedures, Note for Guidance, Commission of the European Communities, Brussels, 1995. 60 Carr, G. P. R., Wahlich, J. C., and Tanner, R. J. N., in International Pharmaceutical Product Registration, ed. Cartwright, A. C., and Matthews, B. R., Taylor and Francis, London, 1994, pp. 246–306. 61 Carr, G. P., and Wahlich, J., J. Pharm. Biomed. Anal., 1990, 8, 619. 62 McDowall, R. D., LC–GC Int., 1995, 8, 196. 63 British Pharmacopoeia 1993, HM Stationery office, London, 1993. 64 United States Pharmacopeia 1995, Mack, Easton, PA, 22nd revision, 1995. 65 Miller, J. C., and Miller, J. N., Analyst, 1988, 113, 1351. 66 Miller, J. N., Analyst, 1991, 116, 3. 67 Miller, J. C., and Miller, J. N., Statistics for Analytical Chemistry, Ellis Horwood, Chichester, 2nd edn., 1988. 68 Gilbert, M. T., Barinov-Colligon, I., and Miksic, J. R., J. Pharm. Biomed. Anal., 1995, 13, 385. 69 Toseland, P. A., in Clarke’s Isolation and Identification of Drugs, ed.Moffat, A. C., Pharmaceutical Press, London, 2nd edn., 1986, pp. 111–117. 70 Royal Pharmaceutical Society, Guidelines for a Pharmacy Based Pharmacokinetic Service, Pharm. 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Paper 7/00563F Received January 24, 1997 Accepted April 14, 1997 88R Analyst, July 1997, Vol. 122 Tutorial Review Quality Management in Drug Analysis Anil C.Mehta Pharmacy Department, The General Infirmay, Leeds, UK LS1 3EX Summary of Contents Introduction Analytical Techniques Personnel Equipment and Chemicals Method Development Validation Ruggedness System Suitability Tests Method Comparison Solutions and Reagents Samples Analysis Internal Quality Control External Quality Control Accreditation Laboratory Audit Conclusion References Keywords: Review; drug analysis; method development; validation; quality; laboratory audit Introduction This paper provides a general outline of the issues that need to be addressed in order to obtain reliable data while performing drug analysis in a research environment.It is especially aimed at younger workers and laboratory managers wishing to introduce quality management systems into their laboratories. Quality management in drug analysis covers a wide range of quality improving activities designed to ensure the reliability of the analytical data. These activities include ensuring that the samples are properly collected and preserved prior to analysis, that the analysis is carried out using the appropriate technique and that the results are properly recorded and reported.This paper particularly focuses on the quality management needs of research laboratories where drug analysis is carried out on a non-routine basis. It provides guidelines on how to adopt a more systematic approach to laboratory management, method development and analysis.To assist younger workers, each section is provided with ample references. Guidelines on the quality management aspects of routine quality control (QC) work are already available from specialist texts related to industrial1–3 and hospital QC work.4 Analytical Techniques Drug analysis is undertaken during various phases of pharmaceutical development,5 such as formulation and stability studies, QC and toxicological and pharmacological testing in animals and man.6,7 In hospitals, drug analysis is performed on patients’ samples in support of clinical trials (bioavailability and pharmacokinetic studies) and in monitoring therapeutic drugs and drugs of abuse.8–11 All these investigations require reliable and validated analytical methods in order to measure drugs in complex media such as formulations and biofluids.Because of their selectivity, sensitivity and overall versatility, techniques such as GC, HPLC, supercritical fluid chromatography (SFC) and capillary electrophoresis (CE) coupled with selective detectors [diode-array detector (DAD) and MS] are frequently used to analyse multicomponent drug mixtures.Immunoassays [radioimmunoassay (RIA), enzyme multiplied immunoassay technique (EMIT)] because of their speed and simplicity are mainly used in drug monitoring in patients. Spectroscopic (UV, IR, AAS) and titrimetric techniques are routinely used in QC work, and TLC and more recently nearinfrared (NIR) spectrometry have been used for the rapid identification of impurities and degradation products in pharmaceuticals. Many other analytical techniques are used in product development and other applications.For example, thermal analysis techniques [thermogravimetric analysis (TGA), differential scanning calorimetry (DSC)] are used in investigating polymorphism and the presence of impurities in drug substances and radiochemical methods (administration of a radiolabelled drug in the body) are used in biodisposition studies.Since the individual enantiomers of a chiral drug can have different actions,12 emphasis is now placed upon stereospecific assays for the individual optical isomers of chiral drugs. These are mainly performed using HPLC with chiral mobile or stationary phases.13,14 Anil C. Mehta received his MSc in analytical chemistry from the University of London in 1967 and PhD in analytical chemistry from the University of Aberdeen in 1972. His PhD thesis was on the spectrofluorimetric analysis of alkaloids and their synthetic analogues. Following a postdoctoral year at the College of Pharmacy, University of Florida, he joined Leeds General Infirmary in 1974 in charge of the pharmacy quality control laboratory, continuing there as R & D manager until his recent retirement.His main interest has been the development of methods for drug analysis by GC and HPLC for solving pharmaceutical and biomedical problems. He has published (alone or with colleagues) over 70 research papers and reviews related to drug bioanalysis, quality control, method validation, sample treatment, dissolution and stability studies, pharmacokinetic and bioavailability studies, and therapeutic drug monitoring.Analyst, July 1997, Vol. 122 (83R–88R) 83ROver and above analytical techniques, robotic equipment is being increasingly employed in drug analysis for sample preparation to minimise monotonous tasks and avoid exposure to harmful chemicals.Robots used in conjunction with computer systems provide more reproducible and reliable results rapidly. Personnel The quality of analytical results depends on both instrument capability and the professional expertise of the user, and therefore for reliable results instruments must be used by an adequately qualified and trained operator using clearly written standard operating procedures (SOPs). A detailed job description should be available and the required level of qualifications and experience set for each post.Training should go beyond analytical measurement skills and should include laboratory safety (including COSHH regulations), sample handling, statistical analysis of data, documentation and report writing. Individual training records should be maintained for each member of staff. Deficiency in staff training, equipment handling and other laboratory matters can lead to the production of poor data. Equipment and Chemicals When choosing new equipment it is important to ensure that it is fit for its intended purpose and its performance is up to specificiations.15 Other things to be considered are cost, ease of use, quality of after-sales service and health and safety aspects. There should be clear, unambiguous, written procedures for the operation of the isntruments.They should give correct readings within their specified tolerance limits when checked at the appropriate intervals by standard procedures using reference materials.All standards and calibrators used must be traceable to nationally accepted standards. Minor preventative maintenance operations should be established and followed, such as keeping pH electrodes in a wet condition or storing chromatographic columns according to suppliers’ instructions. Once a year, a major equipment should be serviced by a qualified specialist under contract. This saves money in the long run. Computer controlled data processing systems such as laboratory information management system (LIMS) should be validated by a computer specialist to demonstrate that they are suitable for their intended use.16–18 Special attention should be given to the quality of laboratory glassware and reagents and standards.Reference standards should be prepared according to written procedures. For quantitative work, be sure to use good quality glassware (e.g., Class A volumetric glassware) and analytical-reagent or HPLC grade reagents and solvents, because other grades can contain impurities.If necessary, reagent and solvent blanks should be measured by GC or HPLC to check for potential interferences. If plastic ware is used, this must be checked for suitability for the analysis to avoid adsorption losses and contamination. Drug substances in pure form can be obtained from the suppliers such as British Pharmacopoeia Commission, London, or be requested from the drug manufacturer.Due consideration should be given to the safe storage and disposal of chemicals and solvents used in the laboratory. Finally, as a matter of good housekeeping, one should keep laboratories clean, with equipment uncluttered and benches tidy.19 Method Development Good planning is essential in the selection and development of the method for drug analysis. It is necessary to be able to quantify the active components in the samples rapidly with acceptable precision, accuracy and reliability within the cost and other constraints. It often happens that during product development or any other long term work, analytical methods evolve.As the nature of the sample changes (different dosage form or biological fluid), methods can be revised. Discussions between the laboratory staff and the request originator is necessary to reach agreement on why the analysis is required and how the results will be used. There should also be discussion on the sampling plan, documentation, report requirements and disposal of samples at the end of the project.In addition, other possible constraints, such as cost, time, safety and availability of trained staff will need to be considered. A logical and systematic approach is required in method selection and development. This can be outlined in four basic steps: (1) generate background data, (2) review the literature, (3) develop the method (optimise the experimental conditions) and (4) validate the performance of the method before using it routinely.Before starting any work, all the initial information on the drug (physico-chemical properties such as solubility, dissociation constant and UV absorption) and the dosage form or the intended dosage form (strength, presence of preservatives, type of container, stability, etc.) should be collected. For bioanalytical work, adequate information about the sample, subject and dosage, including co-administered drugs, should be obtained. All this information is very useful in setting up the analytical method, including sample clean-up.Some of the information mentioned above can be obtained from reference sources.20–27 Methods can be searched for (abstracts, journals, books, pharmacopoeias), recommended by colleagues or developed inhouse. The choice of the method depends on factors such as the nature of the drug, the complexity of the sample and the intended use. The choice of the method will also be governed by practical considerations such as the availability of equipment and specialist skills.If these are not available or prove costly then the work can be contracted out. For industrial products (bulk drugs), the regulatory guidelines for new drug substances require the identification of impurities at levels !0.1% for most compounds.28,29 Meeting this criterion requires careful consideration of the analytical techniques to be used in terms of limits of detection and determination and selectivity.To quantify a substance at the 0.1% level, a technique with a limit of determination of at least 0.05% will be required. Dissolution tests and stability assays require higher selectivity and sensitivity than routine QC assays. They require noninterference from excipients, process impurities and degradation products. They should be accurate, precise, rapid and capable of automation. Selectivity of the method is particularly important for dissolution testing as the final analytical step for dissolution samples is often a non-specific UV determination.Stability assays, on the other hand, should be robust and transferable. Bioanalytical methods for pharmacological and toxicological studies must be selective, i.e., free of interference from endogenous substances, co-administered drugs and metabolites, and sensitive enough to follow the absorption, distribution and elimination of the drug. Sensitivity is particularly important for paediatric or small animal samples since their availability may be limited to, say, 100 ml.Furthermore, biofluid assays must be accurate and precise in order to reveal differences between dosage forms or subjects (human volunteers, patients or animals). The analytical method used in drug monitoring in patients must be simple, reliable and rapid because results are needed urgently. It must be specific for the drug in question and free of interference from other drugs and metabolites.As therapeutic or toxicological drug monitoring is usually performed at compar- 84R Analyst, July 1997, Vol. 122atively high drug concentration, extreme sensitivity in the method is not often needed. Because most of the routinely monitored drugs have narrow therapeutic ranges (i.e., the difference between therapeutic and toxic concentrations is very small), it is essential that the method is accurate and precise since the imprecision of the method could lead to errors in interpretation and dose adjustment.If the method has been taken from the literature, it may not have been used for the matrix in question, and it is likely that some modification of the method will be required in order to make it suitable for the purpose. For reliable results it is better to use a technique with which one is familiar and choose the least complex method if this matches the requirements of the intended use. It is best to keep the number of operations to a minimum to reduce contamination possibilities and minimise losses of the analyte.For example, direct GC analysis is better than a method that involves derivatisation, provided that it is sensitive enough for the purpose and free from potential interferences. Although experience is required in method development work, guidance can be obtained from literature sources specialising in method development.30–37 These publications may serve as a starting point for the development of methods for drugs and/or metabolites.Alternatively, one can use one of the commercially available software packages (expert systems) to speed up chromatographic method development, particularly HPLC.38,39 These systems are developed to assist the chromatographer in the selection and optimisation of chromatographic conditions during method development. With the assistance of these systems, maximum information can be extracted from a minimum number of experiments. The main advantage of expert systems is that they provide immediate availability of an expert opinion through an inherent knowledge base, and respond to the user’s inquiry when presented with a problem. Validation Once the analytical method has been developed, it is validated before or during its use.Validation of the method establishes that its performance characteristics are adequate for the intended use. It builds quality and reliability into the method. In the pharmaceutical industry, validation of analytical method is required in support of product registration applications.40 Many of the principles, procedures and requirements of validation are common to the majority of analytical methods.Validation is performed by conducting a series of experiments using the specific conditions of the method and the same type of matrix as the intended samples. It entails evaluation of various parameters of the method such as accuracy, precision (reproducibility), linearity (concentration–detector response relationship), sensitivity, limits of detection and determination, recovery from the matrix and specificity (selectivity).The definitions and procedures used to calculate these parameters are adequately described in many publications related to pharmaceutical41 –50 and biomedical51–58 analysis. The International Conference on Harmonisation (ICH) has produced guidelines59 on the validation of analytical procedures for pharmaceutical product registration applications.One of the key aims of harmonisation is the mutual acceptance of data from different regulatory authorities. Carr et al.60 have reviewed in detail the validation requirements of various regulatory authorities and provided practical suggestions for satisfying these requirements. Validation does not imply that the method is free from errors. It only confirms that it is suitable for the purpose. Any modifications to a method during its use require its revalidation.For example, if a new instrument or a different type of chromatographic column is brought into use, or the method is applied to a different type of sample, it will require revalidation. The greater the modification, the greater the need for revalidation. Some revalidation may also be required when transferring the method between laboratories or when changes are made in the manufacturing process for the drug. Other factors which can be considered when validating a method are cost per analysis, ease and speed of operation and potential for automation.Once the method has been developed and validated, it is fully documented and approved for use. It should be described in sufficient detail to allow any analyst to use it without difficulty. Ruggedness In addition to the scientific parameters mentioned above, another useful parameter to consider during validation is the ruggedness or robustness of the analytical method. The ruggedness of a method is its ability to remain unaffected by small, unintentional changes in experimental conditions such as temperature, mobile phase composition and pH, or different sources of reagents and chromatographic columns.These can occur when a method is used over a long period or is transferred to another location. Since the drug development work can last for many years and be conducted at more than one site, the ruggedness of the method is critical so that it can be transferred between laboratories and used by different workers employing different instruments and reagents without any problems.System Suitability Tests Once the method is in routine use, check or system suitability tests (SSTs) should be run each time the method is used, to confirm that it is performing satisfactorily. Since instrument to instrument variations can have a significant effect on the assay, SSTs provide the added assurance that on a specific occasion the method is giving acceptable results.In chromatographic assays this is done by injecting a standard solution to check whether certain parameters such as retention time (RT), column efficiency (theoretical plates), tailing factor (peak asymmetry) or resolution between peaks are within preset limits. If so, the method is deemed satisfactory on that occasion. For example, in HPLC, if an SST based on RT passes, it should provide assurance that the HPLC pump and column are functioning satisfactorily. SSTs should not be confused with method validation.Validation is carried out at the method development stage. SSTs, on the other hand, check the performance of a given system (e.g., a particular chromatograph) on a given day prior to analysis. SSTs can detect normal changes (wear and tear) in the equipment (e.g., detector sensitivity) or supplies (e.g., chromatographic column) during normal usage. If the method is robust enough, it should not fail such tests. SSTs are particularly useful in routine QC work and stability studies.Further guidance on SSTs can be obtained from the literature61,62 or pharmacopoeias. 63.,64 Method Comparison The performance of a newly developed or modified method can be assessed by comparing the results obtained by it with those found with a reference (or comparison) method of known accuracy and precision using linear regression analysis.65–68 A reasonable number of samples (10–20) evenly spaced over a concentration range of interest are analysed by both the candidate method and the reference method.Results are plotted as points with one axis (usually the abscissa) for the reference method and the other for the candidate method. GLC and HPLC are often used as reference methods since they are less susceptible to interference from other substances. However, it is not always possible to conduct method comparison studies Analyst, July 1997, Vol. 122 85Rsimply because a suitable reference method is not routinely available or is costly, requiring special facilities.Simple linear regression is a widely used statistical approach for assessing systematic and random errors associated with the new method. It involves relatively simple calculations and provides reliable estimates of intercept and slope. However, if the appropriate computer program is available for statistical calculations, it is more appropriate to use weighted linear regression since this compensates for the change in variance across the concentration range.Solutions and Reagents Standard solutions of drugs in water or methanol are used during many stages of analysis such as calibration and validation. In bioanalytical work, although stock solutions can be prepared in water or methanol, standard solutions for calibration and other experiments should be prepared by dilution of the stock solution with a relevant biological fluid since aqueous solutions differ greatly from the biological matrix.Drug and reagent solutions are stored in such a way as to maintain their integrity. Prior to analysis, their stabilities should be tested by comparison with freshly prepared solutions. In general, solutions of drugs and chemicals are more stable at low temperature (4 or 220 °C) than at room temperature. All solutions must be clearly labelled with preparation and expiry dates. Stock solutions of photodecomposable substances should be stored in amber coloured containers and those of very unstable or volatile substances should be freshly prepared.Samples Sampling is often considered to be a weak link in the quality chain, particularly in drug bioanalysis, and is often the major contributor to measurement error. The importance of sampling is not often appreciated. Samples should be homogeneous and representative of the original material. A non-representative sample is of no value, however well the assay is carried out.The sample taking should be carried out in accordance with the approved procedures. It is essential that the samples are collected in a suitable container at the correct time in relation to the dose and correctly labelled and preserved under appropriate conditions.69–72 Sample identity should include the source of samples, dosage, sampling time in relation to the dose and date and the drug(s) to be assayed. In drug bioanalysis, as sampling frequently is not under the control of the analyst performing the assay, it is necessary to issue clear instructions to the sample provider for collection, storage and transport of samples.The biofluids most commonly analysed for drugs and/or metabolites are blood (plasma or serum) and urine. Blood (5–10 ml) should be centrifuged to retain either plasma, if an anticoagulant such as heparin is added to the sample, or serum, if the blood is coagulated. For urine, usually a midstream sample is collected for most analyses.However, in a urinary excretion study, sampling is performed quantitatively, i.e., the volume of urine is also measured at each collection. The samples should be sealed and packaged in such a way to avoid loss of contents during transport. To avoid potential health hazards, precautions (e.g., wearing of gloves) should be taken while handling them. They should be transported to the laboratory in accordance with legal requirements without delay. The laboratory must have a reliable system of documentation of samples from receipt in the laboratory to the disposal of the remainder. Samples must be unpacked in a suitable area taking into account any safety requirements.When a sample is received in poor condition, the analyst should check with the sender whether to proceed with the analysis. If the entire sample received by the laboratory is not initially required, it should be divided into subsamples, taking precautions to avoid contamination and losses through spillages.This practice is useful in case a repeat assay is required at a later stage. The stability of the analyte(s) in the sample during the collection and the storage should be known or assessed (temperature and duration), preferably before analysis. The lack of stability information may jeopardise subsequent investigations. In general, samples intended for immediate assay can be refrigerated, otherwise they are frozen at 220 °C until assayed.Unstable samples should be analysed without delay. Stability information on the samples may also be required during actual analysis, especially in the final extracts when they may be left in an autosampler awaiting final measurement. Once the analysis is over, unused samples should be retained at least until the final report is accepted. Analysis All analyses should be carried out in accordance with written procedures. Assays should preferably be performed in duplicate each time using a separate portion of the sample rather than a repeat determination on final solutions, e.g., a repeat injection into GC or HPLC system.A complete repeat analysis gives confidence in results and serves to check on the homogeneity of the sample and the random variation in the instrumental response.73 The laboratory should maintain records of the results as a matter of professional policy. The tests performed, results and relevant observations should be written down in a laboratory notebook and the corresponding copies of instrument traces stored.The notebook should serve as a record of each days work so that each step in the analysis can be traced at a later stage if required. A well kept notebook is also useful while preparing inhouse reports, regulatory submission or a paper for publication. Internal Quality Control Internal QC is usually applied to drug bioanalysis to monitor assay performance with regard to accuracy and precision.74 This is done by analysing specially prepared QC samples (or spiked samples) alongside a batch of samples and plotting the results of QC samples on a QC chart.75–77 Like calibration standards, QC samples are prepared by adding known amounts of drug to the biofluid.Usually, two concentrations of QC samples, one near the top and the other near the bottom of the calibration range, are used. For an assay with a wide calibration range, a third QC sample in the middle of the range can be tested.If the method is working satisfactorily, the results of the QC samples should fall within the pre-set limits, typically ±10% of the known values. External Quality Control If a laboratory offers drug analysis as part of a routine service (e.g., therapeutic monitoring), it is useful for such a laboratory to participate in an external QC scheme (proficiency testing scheme) involving many laboratories, provided that the drugs in question are included in such a scheme.77–79 In an external QC scheme, identical samples are periodically sent to the participants for assay, and the scheme coordinator after receiving the results reports that laboratory’s performance together with a summary of the results from all participants. Marked improvement in analytical standards over a period is a consistent finding with many quality assessment schemes.77 Only certain groups of drugs, such as anticonvulsants, antidepressants and benzodiazepines, are monitored by external quality assessment schemes.However, regular participation in such schemes is an effective way to measure the competence of the laboratory to undertake certain analyses. 86R Analyst, July 1997, Vol. 122Accreditation In addition to proficiency testing schemes, increasing attention is being given to external quality assessment schemes by which a laboratory has to prove its competence to an independent third party by participating in a recognised external quality assessment scheme.80–82 Laboratory accreditation is a formal recognition by an authorised body such as the National Measurement Accreditation Service (NAMAS) that the laboratory’s quality system is in place and meets the required standards to carry out specific tests or specific types of tests.83 First it should be decided for which methods, analytes, and/or analytical techniques (GC, HPLC, etc.) accreditation is sought.Accreditation is normally awarded following successful assessment of the laboratory’s quality system by a NAMAS officer and is subject to periodic review.Much emphasis is placed on documentation, calibration of equipment, staff competence and training and traceability of standard materials. Accreditation gives the laboratory and its customers added confidence in the quality of results. It should be mentioned that laboratories performing analyses related to toxicity testing in animals (toxicological safety studies) are required to comply with standards defined by Good Laboratory Practice (GLP).6,83 The principles of GLP were introduced by the US Food and Drug Administration (FDA) to ensure quality and integrity of the data generated during nonclinical testing of chemicals, including pharmaceuticals, for hazard and risk assessments.Laboratories doing such work would have to show that the studies had been carried out in accordance with GLP. The principles of GLP describe the organisational processes under which laboratory studies are planned, performed, monitored, recorded and reported to ensure the quality and integrity of laboratory data.Particular emphasis is placed on study design, record keeping and the role of the Study Director, who is appointed with overall responsibility for the study. The conduct of the study must be in accordance with the study plan and all data generated must be recorded, checked and signed and archived properly. GLP refers to all the operations of the laboratory pertaining to the study.This contrasts with the requirements of NAMAS, which is more concerned with the laboratory’s ability to carry out a particular test. Within the UK, GLP compliance is monitored by the Department of Health. Laboratory Audit Cost considerations may prevent laboratories from joining a proficiency or accreditation scheme. In this situation, it is useful to conduct an in-house audit of the laboratory’s quality management system at appropriate intervals say at least once a year.Auditors should preferably be independent of the activities of the laboratory that they are asked to audit. Large laboratories usually prefer to have separate auditing arrangements for some non-analytical aspects such as health and safety. Audits should cover all aspects of the laboratory practice from sample collection to reporting of results, and not just analytical performance. It should be sufficiently probing to highlight any drawback in the service.Corrective measures should be taken when a shortcoming is found in any aspect of the service. The use of audit is the most reliable way of identifying problems in the management of the laboratory. Laboratory audit is a subject in itself,83,84 the detailed discussion of which is beyond the scope of this paper. However a checklist of major areas to be audited is given in Table 1. Conclusion Quality management in drug analysis incorporates all measures taken to ensure the reliability of analytical data, starting from obtaining a satisfactory sample, analysing it correctly with a validated method, to reporting the results, with all procedures well documented and periodically reviewed.Responsibility for maintaining and improving the laboratory’s quality system lies with every member of the laboratory staff. By implementing an effective quality system, a significant improvement is made to the overall performance of the laboratory engaged in drug analysis.References 1 Medicines Control Agency, Rules and Guidance for Pharmaceutical Manufacturers, Stationery Office, London, 1997. 2 Artiges, A., Loulergue, M. H., and Reyneir, J. P., in International Pharmaceutical Product Registration, ed. Cartwright, A. C., and Matthews, B. R., Taylor and Francis, London, 1994, pp. 172–205. 3 Lee, C. R., Porziemsky, J. P., Gaspur, M., and Krstulovic, A. M., LC– GC Int., 1996, 9, 414. 4 Sewell, G. J., J. Clin. Pharm.Ther., 1995, 20, 149. 5 Berridge, J. C., J. Pharm. Pharmacol., 1993, 45 (Suppl. 1), 361. 6 Chamberlain, J., The Analysis of Drugs in Biological Fluids, CRC Press, Boca Raton, FL, 2nd edn., 1995. 7 Baselt, R. C., and Cravey, R. H., Disposition of Toxic Drugs and Chemicals in Man, Chemical Toxicology Institute, Foster City, CA, USA, 4th edn., 1995. 8 Baselt, R. C., Analytical Procedures for Therapeutic Drug Monitoring and Emergency Toxicology, PSG, Littleton, MA, USA, 2nd edn., 1987. 9 Mehta, A. C., Anal. Proc., 1995, 32, 347. 10 Uges, D. R. A., Bouma, P., Pietersma, H., and Meijer-Koens, J., Eur. Hosp. Pharm., 1996, 2, 4. 11 Lai, C. K., Lee, T., Au, K. M., and Chan, A. Y. W., Clin. Chem., 1997, 43, 312. 12 Caldwell, J., J. Chromatogr., 1996, 719, 3. 13 Chiral Separations by HPLC: Applications to Pharmaceutical Compounds, ed. Krstulovic, A. M., Ellis Horwood, Chichester, 1989. 14 Camilleri, P., Biasi, V., and Hutt, A., Chem. Br., 1994, 30, 43. 15 Burgess, C., and McDowall, R.D., LC–GC Int., 1997, 10, 87. 16 Huber, L., and Thomas, M., LC–GC Int., 1995, 8, 572. Table 1 A checklist for laboratory audit 1. Pre-analytical— (a) Documentation (request forms) (b) Sample management: collection, identification, processing and storage (c) Buying of correct grade of materials 2. Analytical— (a) Acquisition of material safety data sheets and risk assessment before commencing work (compliance with the COSHH regulations) (b) Procedures for the preparation of standards (c) Appropriate labelling and storage (with shelf-life) of standards (d) Validated analytical methods and standard operating procedures for the methods and the instruments (e) Internal quality control checks for the method.Corrective action if the results are outside the pre-set limits (f) Laboratory notebook for calibration data, results, calculations, instrument or computer outputs 3. Post-analytical— (a) Results report forms (b) Documentation: storage of results (c) Prompt communication with the request originator (e.g., comments on results) (d) Final report 4.Miscellaneous— (a) Staff training in all aspects of laboratory work (b) Maintenance of equipment and associated records (c) Health and safety aspects, including COSHH, fire precautions and disposal of laboratory waste (d) Existence of ‘Quality Manual’, i.e., all the above procedures (1–4) written down in sufficient detail for staff to refer to Analyst, July 1997, Vol. 122 87R17 Huber, L., LC–GC Int., 1996, 9, 564. 18 McDowall, R. D., LC–GC Int., 1996, 9, 202. 19 Horwitz, W., Anal. Chem., 1978, 50, 521A. 20 Royal Pharmaceutical Society, British National Formulary, Pharmaceutical Press, Wallingford, 1997. 21 Association of British Pharmaceutical Industry, Data Sheet Compendium, Datapharm Publications, London, 1996. 22 Martindale, The Extra Pharmacopoeia, Pharmaceutical Press, Wallingford, 31st edn., 1996. 23 The Merck Index, an Encyclopedia of Chemicals, Merck, Rahway, NJ, 12th edn., 1996. 24 The Pharmaceutical Codex, ed. Lund, W., Pharmaceutical Press, London, 1994. 25 Handbook of Pharmaceutical Excipients, ed. Wade, A., and Weller, P. J., Pharmaceutical Press, London, 2nd edn., 1994. 26 Connors, K. A., Amidon, G. L., and Stella, V. J., Chemical Stability of Pharmaceuticals, Wiley, Chichester, 2nd edn., 1986. 27 Trissel, L. A., Handbook on Injectable Drugs, American Society of Hospital Pharmacists, Bethesda, MD, 9th edn., 1996. 28 Berridge, J. C., J. Pharm. Biomed. Anal., 1995, 14, 7. 29 International Conference on Harmonisation (ICH): Note for Guidance on Impurities in New Drug Substances, Commission of the European Communities, Brussels, 1995. 30 Clarke’s Isolation and Identification of Drugs, ed. Moffat, A. C., Pharmaceutical Press, London, 2nd edn., 1986. 31 Analytical Profiles of Drug Substances, ed. Florey, K., Academic Press, New York, 1972–91, vols. 1–20 (each volume contains a cumulative index). 32 Analytical Profiles of Drug Substances and Excipients, ed. Brittain, H. G., Academic Press, New York, 1992–94, vols. 21–23 (each volume contains a cumulative index). 33 Snyder, L. R., Glajch, J. L., and Kirkland, J. J., Practical HPLC Method Development, Wiley, Chichester, 2nd edn., 1997. 34 Boehlert, J. P., Drug Dev. Ind. Pharm., 1984, 10, 1343. 35 McNair, H. M., LC–GC Int., 1993, 6, 740. 36 Bowker, M. J., Analyst, 1996, 121, 91R. 37 Dolan, J. W., LC–GC Int., 1997, 10, 80. 38 Hamoir, T., and Massart, D. L., in Advances in Chromatography, ed. Brown, P. R., and Grushka, E., Marcel Dekker, New York, 1993, vol. 33, pp. 97–145. 39 Hamoir, T., Bourguignon, B., and Massart, D. L., Chromatographia, 1994, 39, 339. 40 Clarke, G. S., J. Pharm. Biomed. Anal., 1994, 12, 643. 41 Carr, G. P., and Wahlich, J. C., J. Pharm. Biomed. Anal., 1990, 8, 613. 42 Edwardson, P. A. D., Bhaskar, G., and Fairbrother, J. E., J. Pharm. Biomed. Anal., 1990, 8, 929. 43 Green, J. M., Anal. Chem., 1996, 68, 305A. 44 Wilson, T. D., J. Pharm., Biomed. Anal., 1990, 8, 389. 45 Jenke, D. R., J. Liq. Chromatogr. Relat. Technol., 1996, 19, 719. 46 Jenke, D. R., J. Liq. Chromatogr. Relat. Technol., 1996, 19, 737. 47 Jenke, D. R., J. Liq. Chromatogr. Relat. Technol., 1996, 19, 1873. 48 Mehta, A. C., J. Clin. Pharm. Ther., 1989, 14, 465. 49 Molnar, I., LC–GC Int., 1996, 9, 800. 50 Molnar, I., LC–GC Int., 1997, 10, 32. 51 Analytical Method Validation: Bioavailability, Bioequivalence, and Pharmacokinetic Studies, Conference Report, J. Pharm. Sci., 1992, 81, 309. 52 Buick, A. R., Doig, M. V., Jeal, S. C., Land, G. S., and McDowall, R. D., J. Pharm. Biomed. Anal., 1990, 8, 629. 53 Phillips, L. J., Alexander, J., and Hill, H. M., in Analysis for Drugs and Metabolites Including Anti-infective Agents, ed. Reid, E., and Wilson, I. D., Royal Society of Chemistry, Cambridge, 1990, pp. 23–36. 54 Tanner, R. J. N., in Analysis for Drugs and Metabolites Including Anti-infective Agents, ed. Reid, E., and Wilson, I. D., Royal Society of Chemistry, Cambridge, 1990, pp. 57—63. 55 Mehta, A. C., Talanta, 1987, 34, 609. 56 Lang, J. R., and Bolton, S., J. Pharm. Biomed. Anal., 1991, 9, 357. 57 Lang, J. R., and Bolton, S., J. Pharm. Biomed. Anal., 1991, 9, 435. 58 Dadger, D., and Burnett, P. E., J. Pharm. Biomed. Anal., 1995, 14, 23. 59 International Conference on Harmonisation (ICH): Validation of Analytical Procedures, Note for Guidance, Commission of the European Communities, Brussels, 1995. 60 Carr, G. P. R., Wahlich, J. C., and Tanner, R. J. N., in International Pharmaceutical Product Registration, ed. Cartwright, A. C., and Matthews, B. R., Taylor and Francis, London, 1994, pp. 246–306. 61 Carr, G. P., and Wahlich, J., J. Pharm. Biomed. Anal., 1990, 8, 619. 62 McDowall, R. D., LC–GC Int., 1995, 8, 196. 63 British Pharmacopoeia 1993, HM Stationery office, London, 1993. 64 United States Pharmacopeia 1995, Mack, Easton, PA, 22nd revision, 1995. 65 Miller, J. C., and Miller, J. N., Analyst, 1988, 113, 1351. 66 Miller, J. N., Analyst, 1991, 116, 3. 67 Miller, J. C., and Miller, J. N., Statistics for Analytical Chemistry, Ellis Horwood, Chichester, 2nd edn., 1988. 68 Gilbert, M. T., Barinov-Colligon, I., and Miksic, J. R., J. Pharm. Biomed. Anal., 1995, 13, 385. 69 Toseland, P. A., in Clarke’s Isolation and Identification of Drugs, ed. Moffat, A. C., Pharmaceutical Press, London, 2nd edn., 1986, pp. 111–117. 70 Royal Pharmaceutical Society, Guidelines for a Pharmacy Based Pharmacokinetic Service, Pharm. J., 1985, 234, 626. 71 Mehta, A. C., J. Clin. Pharm. Ther., 1989, 14, 285. 72 McDowall, R. D., LC–GC Int., 1995, 8, 384. 73 Crosby, N. T., Anal. Proc., 1991, 28, 138. 74 Causy, A. G., Hill, H. M., and Phillips, L. J., J. Pharm. Biomed. Anal., 1990, 8, 625. 75 Gardner, J. A., Coleman, S., and Farrow, S. G., Anal. Proc., 1993, 30, 292. 76 Mullins, E., Analyst, 1994, 119, 369. 77 Burnett, D., and Williams, J., in Clarke’s Isolation and Identification of Drugs, ed. Moffat, A. C., Pharmaceutical Press, London, 2nd edn., 1986, pp. 118–127. 78 Wilson, J. F., Tsanaclis, L. M., Perrett, J. E., Williams, J., Wicks, J. F. C., and Richens, A., Ther. Drug Monit., 1992, 14, 98. 79 Tsanaclis, L. M., and Wilson, J. F., Clin. Chem., 1993, 39, 851. 80 Huber, L., and Mandelatz, K., Int. Lab., 1994, 24, 19. 81 Huber, L., and Rogers, J. A., Int. Lab., 1995, 25, 10. 82 Huber, L., Int. Lab., 1995, 25, 9. 83 Quality in the Analytical Laboratory, ed. Newman, E. J., Wiley, Chichester, 1995. 84 Guidelines for Achieving Quality in Trace Analysis, ed. Sargent, M., and MacKay, G., Royal Society of Chemistry, Cambridge, 1995. Paper 7/00563F Received January 24, 1997 Accepted April 14, 1997 88R Analyst, July 1997, Vol. 122

ISSN:0003-2654    

DOI:10.1039/a700563f

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Visualisation of Confidence in Two-factor Designs Where Model, Replication and Star Points are Varied Pedro W. Araujo and Richard G. Brereton* School of Chemistry, University of Bristol, Cantock’s Close, Bristol, UK BS8 1TS Confidence in predictions over an experimental domain can be calculated using the known experimental error and a function that relates to the shape of the confidence bands, often called leverage. In this paper, leverage is calculated for two-factor designs based on the central composite design, changing the nature of the model, the position of the star points and the number of replicates in the centre.The shapes of the graphs of leverage are presented. Several conclusions can be deduced, for example, for many common arrangements of experiments, such as the case where three replicates are taken in the centre; confidence is not highest in the centre of experimentation. Keywords: Experimental design; leverage; confidence predictions; chemometrics There is a large literature on experimental design, stretching over more than 50 years.1–9 Many chemists employ multifactor designs in their experiments.The arrangements of experiments are often obtained by employing well established recipes; for example, star, factorial, central composite and face centred cube designs are frequently used. Many such designs are advocated by statisticians and have certain specific properties such as rotatability or equivariance that make the experimental arrangements useful under certain specific situations.However, the analytical chemist is often concerned with quantitative model building, especially in the case of multivariate calibration.10–11 In this, chemometric experiments differ somewhat from experiments in many other areas of science where the main aim might be to estimate qualitatively various trends or to optimise a system. In the area of linear calibration, there is a large literature on how confidence in a model can be estimated from experimental measurements,12–15 and this can be extended to multivariate and multifactor situations.There has, though, been much less work reported on how the number and position of experiments can influence the confidence in a model for two or more factors. Most traditional statistical literature was written before the advent of flexible personal computers (PCs), so it was a time-consuming process to perform calculations and visualise graphically confidence for new experimental arrangements.With the advent of easy-toprogram PCs with good graphics, it is now possible to visualise easily how changes in experimental arrangements and models can influence the confidence in quantitative predictions. It is essential to recognise that there is no sharply defined experimental region, even in the case of clear cut linear calibration. Experimentation simply results in a predicted model, whose confidence changes as independent variables are changed.Normally, the relative confidence in predictions is highest in the centre of experimentation, but, as is seen below, even this is not always the case. An analyst may have different reasons for developing a method. Some methods may be designed to work well only in a very narrowly defined region, so a design which predicts extremely well in the centre but very poorly outside a certain region is perfectly satisfactory. Under other circumstances, a method that predicts fairly evenly throughout a fairly large region but not so accurately may be more appropriate.In this paper, we use the concept of leverage16–18 to demonstrate how confidence varies over a design. The approaches outlined below can be extended to other designs fairly readily. Methodology Example In this section we illustrate the calculation and application of leverage using a simple design given in Table 1. The set of experiments involves measuring two coded variables x1 and x2, which may, for example, be equivalent to the true variables pH and temperature.Note that in this paper coded variables are employed—these are mathematical transforms of the true variables with certain properties such as orthogonality. Coding also allows the experimenter to look at data from different types of experiments using a common scale. Table 1 lists a series of experiments at N = 9 unique levels, there are q = 6 replicated points in the centre, so the total number of experiments in this case will be I = 14.Four points (often called star points) are positioned at p = ±1.5 units from the origin. The influence of changing the values of q and p is discussed later in this paper. Design Matrix and Model In this paper a model of the form �y b b x b x b xx k k k kkk k = + + + = = å å 0 1 2 2 12 1 2 1 2 (1) Table 1 General two-factor design used to study the influence of the number of replicates, the model and the relative positions of the experimental points on the leverage Part x1 x2 Central* 0 0 · · · · · · 0 0 Factorial 1 1 21 1 1 21 21 21 Star p 0 2p 0 0 p 0 2p * Repeated q times. Analyst, July 1997, Vol. 122 (621–630) 621will be used involving six coefficients. A design matrix X can be obtained from the experimental values (Table 2) where the 6 columns represent the values of the six parameters 1,x1,x2,x21 ,x22 and x1x2. The I = 14 rows represent the experiments. Uncertainty and Confidence Uncertainty19–21 measures how confidently a model predicts data in an experimental region; the greater the uncertainty the less the confidence in the predictions.For a given experiment, n, the uncertainty can be defined by u s n 2 2 1 1 = + ¢ - e[ ( ) ] x XX n A xn (2) where se is the root mean squared residual error over the total number of experiments I. The term xn(XAX)21xAn depends only on the design and not on the experimental response, so it is possible to predict a graph of uncertainty without performing any experiment by changing the levels of the variable xn across the domain of the factor space.When several replicates are monitored in the domain of the factor space (for instance q = six replicates in the centre of the design shown in Table 1) the uncertainty of prediction of the mean of q values defined here by u2q of response is given by u s q q 2 2 1 1 = + ¢ - e[ ( ) ] x x n n X XA (3) The statistical reliability of the model in the presence of error can be visualised by the confidence limits, which are calculated from the response data set. These confidence limits are a measure of how closely the model fits the data. For instance, 95% confidence means that we expect 95% of the responses to be within the region of this limit.Clearly, if the confidence limits are narrow, the scattering of the experimental responses will be small. The confidence limits are directly dependent on the uncertainty, through the expression y F u n m n ± - = � ( ) 1 2 , (4) Substituting eqn.(2) into eqn. (4) gives y s Fn m ± - - = �+ ¢ e 1 1 1 , [ ( ) ] x x n n X XA (5) where F has one degree of freedom in the numerator and n2m degrees of freedom in the denominator. In the same way taking into account eqn. (3), the confidence limit, when the replicates have been averaged, can be defined by y F u n m q ± - = � 1 2 , (6) Substituting eqn. (3) into eqn. (6) gives y s F q n m ± - - = � + ¢ e 1 1 1 , [ ( ) ] x x n n X XA (7) From eqn.(7) it is evident that if a large number of replicates are measured the confidence limits can be expressed by y S Fn m ± - - = � ¢ e 1 1 , ( ) x x n n X XA (8) When it is necessary to estimate the confidence limits of the entire predicted response surface instead of individual values, the Working and Hotelling22 confidence limits can be used y s m Fm n m ± - - = � � ¢ e , ( ) x x n n X XA 1 (9) Eqn.(9) is of the same form as eqn. (8); the only difference is the parameter m which represents the number of coefficients in the model and the value of F. Leverage In the previous section we introduced the term xn(XAX)21xAn which is a measure of the potential influence of an observation on the parameter estially called leverage, h. This parameter can be computed to demonstrate how confidence changes when the design or model is altered. The matrix H = X(XAX)21XA (10) is also called the hat matrix23,24 and has the following properties. Its diagonal elements equal the leverage at each experimental point.The leverage for the experimental points in the central composite design given in Table 1 (I = 14 experiments) for q = 6 replicates is calculated via the hat matrix whose diagonal Table 2 Design matrix used for the example described under Methodology. x0 x1 x2 x21 x22 x1x2 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 21 1 1 1 21 1 1 21 1 1 21 1 21 21 1 1 1 1 1.5 0 2.25 0 0 1 21.5 0 2.25 0 0 1 0 1.5 0 2.25 0 1 0 21.5 0 2.25 0 Fig. 1 Schematic representation of the algebraic expression for leverage h = x(XAX)21xA. 622 Analyst, July 1997, Vol. 122leverage values are 0.166 (central points), 0.596 (factorial points) and 0.655 (star points). These values show how, in this design, the leverage is smallest in the region where replicates have been recorded (central points) and in the region where the experimental points are close to the centre.The values of leverage in the factorial points to the star points should be compared. The sum of leverage over all experimental points equals the number of coefficients in the model. For instance, the model proposed in eqn. (1) involves six coefficients, so a design matrix of the form presented in Table 2 but with a different replication regime in the centre can be analysed and should demonstrate that no matter how many experiments are carried out, the summation over all the diagonal elements of the hat matrix will always be six.The summation of the diagonal leverage values obtained above is 6 3 0.166 + 4 3 0.596 + 4 3 0.655 = 6, whereas in Table 3, where there are no replicates in the centre, the summation is 1 3 0.973 + 4 3 0.599 + 4 3 0.657 = 6. Calculation of Leverage The approach of the previous section can be used to calculate leverage for an individual experimental point.However, confidence in a model can also be calculated over an entire experimental domain, not necessarily restricted to individual experiments. For example, confidence bands apply to an entire factor space. Equivalently, leverage can be used to explore how confidence varies when parameters are altered, even at points where the response is not measured. As such, leverage is a powerful tool for visualising how the design influences the confidence in a model. With modern methods for graphical display on PCs, the influence of the design on leverage, confidence and uncertainty can be readily visualised.Leverage for any experimental point can be calculated using the term (XAX)21. The vector x consists of the six coefficients and can be generalised for any experimental point x1 and x2. This vector (1 x1 x2 x21 x22 x1x2) can take on any value according to the experimental conditions. Multiplying x by (XAX)21 gives a new vector. Multiplying this new vector by xA then results in an algebraic expression for h given in Fig. 1.As an example in Fig. 2 we have selected the experimental point x1 = p = 1.5 and x2 = 0 of Table 1, so the vector x is (1 1.5 0 2.25 0 0) which when multiplying the term (XAX)21 gives the row vector designated by (a) in Fig. 2. Multiplying this row vector by xA gives a single scalar designated by (b) in Fig. 2. This is the value of leverage for the specific point (1.5, 0). However, it is also Fig. 2 Calculation of the expression h = x(XAX)21xA using the experimental points x1 = 1.5 and x2 = 0 of Table 1 (star part). Table 3 Computation of the hat matrix X(XAX)21 XA for the design matrix given in Table 2, except that only one measurement is taken at the centre point 0.973 0.060 0.599 0.060 20.136 0.599 0.060 20.136 0.129 0.599 0.060 0.129 20.136 20.136 0.599 20.054 0.297 20.056 0.297 20.056 0.657 20.054 20.056 0.297 20.056 0.297 0.128 0.657 20.054 0.297 0.297 20.056 20.056 20.107 20.107 0.657 20.054 20.056 20.056 0.297 0.297 20.107 20.107 0.128 0.657 ......................... . . . . . . . . . . . ........................ – – – – – – – – – – – | | | | | | | | – – – – – – – – – – –– – – – – – – – – – – | | | | | | | | – – – – – – – – – – –– – – – – – – – – – – | | | | | | | | – – – – – – – – – – –– – – – – – – – – – – | | | | | | | | – – – – – – – – – – – ...................... . . . . . . . . . . . . ...................... – – – – – – – – – – – | | | | | | | | – – – – – – – – – – – Central point leverage value.Factorial points leverage values. Star points leverage values. Fig. 3 Calculation of the coefficients of leverage. The broken arrows show the combination of rows and columns that have to be labelled and added to obtain the coefficient of x21 (20.078 + 0.118 2 0.078). Analyst, July 1997, Vol. 122 623possible to derive an equation for leverage as follows. The rows and columns of the matrix (XAX)21 are labelled according to the six corresponding terms of the vector x.The relevant values of each coefficient are then added together to give the terms of the derived equation as is shown in Fig. 3. For example, the coefficient of x21 is the sum of 20.078 (row 4, column 1), 0.118 (row 2, column 2) and 20.078 (row 1 , column 4), which equals 20.038. This procedure is equivalent to multiplying the vectors of coefficients (which consist of algebraic expressions rather than individual numbers) together with the matrix (XAX)21.Using this procedure the equation for leverage calculated from Fig. 3 is given by the expression: h = 0.166 2 0.038 (x21 + x22 ) + 0.113 (x41 + x42 ) + 0.279 x21 x22 (11) for the design of Table 1. Representation of Leverage The visualisation of the leverage values of the design presented in Table 1 can be computed using eqn. (11). A threedimensional plot as well as contour plot of leverage as a function of the whole experimental domain of the variables x1 and x2 can be produced (Fig. 4). The levels and grid lines of the contours can be varied, influencing the appearance of the contour plot. These kinds of plots are useful to explore how well the design predicts the model. The lower the leverage the higher the confidence in the model as is shown in eqn. (9), which is used to assess the confidence of the predicted surface or the contour plot. Furthermore, the graphical representation of leverage is a useful tool to envisage not only the behaviour at the experimental points of the design but also outside the experimental region.Designs A general central composite design for two factors given in Table 1 was selected for this work. This design is the result of combining a factorial and a star design, respectively. The distribution of the experimental points is given in Fig. 5, which shows clearly the superimposing of a factorial design on a star design. The number of factor combinations for this kind of design is given by N = 2k + 2k + 1 (12) With this number of unique experiments N, it is possible to fit the model described by the eqn.(1). The factorial and star part in the central composite design are used to estimate linear terms; the interaction term can only be estimated from the factorial part and the squared term only from the star part. Owing to this Fig. 4 Visualisation of leverage values of the design presented in Table 1 for q = 6 and p = ±1.5 (see colour key).Fig. 5 Central composite design studied. 624 Analyst, July 1997, Vol. 122versatility, this kind of design was chosen in order to study the influence of three factors on the leverage of a series of experiments, namely, (1) the number of replicates, (2) the model and (3) the relative positions of the experimental points. A schematic representation of the study performed is shown in Fig. 6. In all cases at least one central point at values of x1 and x2 of (0, 0) and four factorial points at values of (±1, ±1) are recorded.The position of the star points is varied between p = 0.5 and 1.5 at intervals of 0.25. The number of replicates in the centre is varied between 1 and 10. Various models can be employed to fit the data, namely: (a) linear, squared and interaction terms, (b) linear terms, (c) linear and interaction terms and (d) linear and squared terms. An advantage of the approach advocated in this work is that almost all possible designs can be compared, owing to the ability of PCs to produce results rapidly. Results The coefficients of the contour function for leverage were calculated as explained under Calculation of Leverage.The equations computed when the number of replicates, the model and the relative positions of the outliers are changed, respectively, are presented in Table 4. The contour plots used to study the influence on leverage when the number of replicates in the centre is increased from 1 to 10 are given in Fig. 7. In all cases a model of the form of eqn. (1) and star points at ±1 were employed. Fig. 8 represents the Fig. 6 Schematic representation of the study of the influence of three factors on the leverage, namely, number of replicates, the model and the relative positions of the experimental points. Table 4 Equations derived for leverage for the examples discussed in the text Centre p-value replicates Model* x0 x21 x22 x21 x22 x41 x42 1 1 a 0.556 20.500 20.500 0.250 0.500 0.500 2 0.357 20.262 20.262 0.107 0.429 0.429 3 0.263 20.149 20.149 0.039 0.395 0.395 4 0.208 20.083 20.083 0.000 0.375 0.375 5 0.172 20.040 20.040 20.026 0.362 0.362 6 0.147 20.010 20.010 20.044 0.353 0.353 7 0.128 0.013 0.013 20.058 0.346 0.346 8 0.114 0.030 0.030 20.068 0.341 0.341 9 0.102 0.044 0.044 20.077 0.337 0.337 10 0.093 0.056 0.056 20.083 0.333 0.333 1 6 b 0.071 0.167 0.167 0.000 0.000 0.000 c 0.071 0.167 0.167 0.250 0.000 0.000 d 0.147 20.010 20.010 20.294 0.353 0.353 0.5 6 a 0.111 0.099 0.099 27.559 4.096 4.096 0.75 0.126 0.045 0.045 21.125 0.893 0.893 1.25 0.163 20.040 20.040 0.233 0.191 0.191 1.5 0.166 20.038 20.038 0.279 0.113 0.113 *a: Linear, squared and interaction terms.b: Linear terms. c: Linear and interaction terms. d: Linear and squared terms. Analyst, July 1997, Vol. 122 625Fig. 7 Contour plots when the number of replicates in the centre of the design presented in Table 1 is increased. (a) 1 replicate, (b) 2 replicates and so on until (j) 10 replicates.Colour key as in Fig. 4. 626 Analyst, July 1997, Vol. 122case when the position of the star points is changed, using six replicates in the centre, a model of the form of eqn. (1) and varying the position of the star point from 0.5 to 1.5 at intervals of 0.25. The contour plots when the values of the model are altered are shown in Fig. 9. Influence of Replication Replication has a major influence on the shape of the leverage graph, as illustrated in Fig. 7, and the corresponding confidence bands. At low replication there is a low leverage at the corners of the square. The value of leverage then increases both towards the centre and the outside as the number of replicates increases. The region of the minimum decreases in size and the centre becomes flatter. The apparent loss of the small troughs from the graph using three replicates is simply a consequence of the chosen contour levels; in this paper the levels were kept constant for each graph for the sake of consistency.When more than two replicates are measured in the centre, the surface is fairly flat over a large region. By the time five replicates are included in the centre, there are no detectable local minima in the centre. This implies that five replicates are sufficient to produce a large flat region around the centre of the design where there is approximately equal confidence in prediction, which is an important feature of many experiments.The information relating to replication is summarised in Table 5. Along the bottom row of Table 5 are the values at points (±0.5, +0.5). As can be seen, leverage reduces dramatically up to about three replicates, and subsequently there is limited further change. The absolute minimum can be obtained using partial derivatives, here the change as extra replicates are taken is more even, being a 20% reduction from 1 to 2 replicates but 9% for increasing from 9 to 10 replicates.The position of the minimum moves towards the centre, being at (0, 0) for seven replicates. Another feature of Table 5 is that the leverage is higher in the centre than at the points (±0.5, 0.0), (0.0, ±0.5) and (±0.5, ±0.5) when less than four replicates are taken in the centre, suggesting that four replicates is the minimum requirement if confidence is to be best in the centre of the design. Interestingly, this minimum number of replicates may increase as the number of factors increase, reflecting the larger number of experiments performed away from the centre.Hence, there are important consequences for replication strategies if a method is to be developed that works best in the centre of the experimental region. The change in confidence can also be ascertained from the data in Table 5. For example, the confidence interval at the centre decreases by a factor of ABBBBBB (0.556/0.093), confidence being related to leverage by a square root relationship as discussed above, or under Leverage, as the number of replicates changes from 1 to 10, meaning a substantial tightening of the Fig. 8 Contour plots when the position of the star points (± p) of the design presented in Table 1 is changed.(a) 0.50, (b) 0.75, (c) 1.00, (d) 1.25 and (e) 1.50. Colour key as in Fig. 4. Analyst, July 1997, Vol. 122 627Fig. 9 Contours plots when the values of the model of the design presented in Table 1 are altered.(a) Linear, squared and interaction terms, (b) linear terms, (c) linear and interaction terms and (d) linear and squared terms. Colour key as in Fig. 4. Table 5 Summary of the main features observed when the centre is replicated. The top row represents the leverage values at (±0.50, ±0.00) or (±0.00, ±0.50), the diagonal numbers represent the leverage values at (0, 0), the bottom row represents the leverage values at (±0.50, ±0.50), the last column represents the minimum value of leverage found and its coordinate.The arrows represent the direction of increasing replication from 1 to 10 ? 0.462 0.318 0.251 0.211 0.185 0.167 0.153 0.143 0.134 0.127 0.556 0.356 (±0.63, ±0.63) 0.357 0.286 (±0.52, ±0.52) 0.263 0.236 (±0.42, ±0.42) 0.208 0.199 (±0.33, ±0.33) 0.172 0.170 (±0.24, ±0.24) 0.147 0.147 (±0.12, ±0.12) 0.128 0.128 (±0.00, ±0.00) 0.114 0.114 (±0.00, ±0.00) 0.102 0.102 (±0.00, ±0.00) 0.093 0.093 (±0.00, ±0.00) � 0.384 0.286 0.240 0.214 0.196 0.184 0.175 0.167 0.161 0.157 628 Analyst, July 1997, Vol. 122confidence intervals in the centre. The change in shape of the leverage graphs and confidence intervals can also be visualised by comparing Fig. 7(a) and (f) (one and six replicates, respectively, in the centre). The corners of the two contour plots at (±1, ±1) are virtually identical corresponding to leverage values of nearly 0.806 for one replicate and 0.784 for six replicates. The centre of the contour plot of Fig. 7(a) is at 0.556 but for Fig. 7(f) it is 0.147; this corresponds to differences in confidence between the centre and extreme corners of 20 for one replicate (i.e., very little difference) but 2.31 for six replicates, which is a substantial difference. By using the figures of Table 5, the equations and inspection of the contour plots, other trends can be observed. Influence of the Star Points Fig. 8 shows the influence of the position of the star points on the design, using six replicates. As can be seen, the shape of the graph is strongly influenced by the position of the star points.When the position is less than 1, the edges are squeezed towards the centre [Fig. 8(a) and (b)]. For a value of p = ±1, the leverage becomes roughly square [Fig. 8(c)]. Increasing the value of p results in a more circular graph for the model used here. At p = ±1.41, the contour plot will be exactly circular, corresponding to the rotatable central composite design. Table 6 summarises this information.Leverage is least in the centre up to p = ±0.75 but slightly greater at p = ±1.5. At p = ±1, the graph of leverage is exceptionally flat around the centre. Note that, about p = ±1, the centre point is not best predicted even when six replicates are employed. Hence, central composite design as normally applied with p = ±AB2 will not predict the data best in the centre. Influence of the Model The influence of the model is illustrated in Fig. 9 for the case of six replicates in the centre and a value of p = ±1. It is important to remember that the sum of coefficients for each model will be different, so the sum of leverage values over all experimental points will differ according to the model. The most dramatic effect relates to the shape of the contour plot. For linear terms and p = ±1, this plot is completely circular suggesting that confidence simply is a function of distance from the centre of the design.This behaviour, though, is also influenced by the position of the star points. When quadratic and interaction terms are added, a circular pattern emerges if the star point is at ±AB2 . The contour plot of the leverage for the full six terms and p = ±AB2 is given in Fig. 10(a). If the number of coefficients is reduced to three [Fig. 9(b)] the graph is no longer circular. Hence, both the model and the position of the star points influence the shape of the confidence surface. For comparison, the graph of leverage using only linear terms but p = ±AB2 is given in Fig. 10(b). Interestingly, this graph will always be circular in shape no matter what the values of p and Table 6 Summary of the main features observed when the influence of the position ±p is changed. The top row is of the leverage values at (±0.50, ±0.00) or (±0.00, ±0.50), the diagonal numbers represent the leverage values at (0, 0), the bottom row represents the leverage values at (±0.50, ±0.50), the last column represents the minimum value of leverage found and its coordinate.The arrows represent the direction of increasing the ±p values (0.5, 0.75, 1, 1.25 and 1.5, respectively) ? 0.392 0.193 0.167 0.165 0.164 0.111 0.111 (±0.00, ±0.00) 0.126 0.126 (±0.00, ±0.00) 0.147 0.147 (±0.12, ±0.12) 0.163 0.161 (±0.26, ±0.26) 0.166 0.163 (±0.27, ±0.27) � 0.200 0.190 0.184 0.181 0.179 Fig. 10 Contour plot when the position of the star points of the design presented in Table 6 is p =+AB2. (a) Linear, quadratic and interaction terms and (b) linear terms.Colour key as in Fig. 4. Analyst, July 1997, Vol. 122 629q, provided that the design is symmetrical. This is because the leverage equation consists of only three terms, namely, an intercept and the terms x21 and x22 . Adding interactions distorts the shape of the leverage graph, increasing it at the corners but not at the edges (or centre); this is because the edges represent the situation when the level of one factor is 0, and the other is ±1, so only one factor changes in level from the centre of the design, whereas the corners represent the situation when both factors are at p = ±1, i.e., both factors are changing, so there are interactions.A similar effect is observed when comparing the quadratic model with and without interactions. The edges always remain the same: for example, Fig. 9(d) can be obtained by stretching the corners of Figure 7(f). Conclusions Leverage is a powerful tool for exploring the confidence in predictions of regression models when experiments are designed in different ways. Graphical visualisation is useful.Although there is a large classical literature on experimental design, the emphasis is on certain fixed designs. In the case of quantitative model building in analytical science, the ability to change parameters gradually in an experiment is important. The aims of experimentation and method development often differ according to application, and it is vital, in advance, to look at how different arrangements relate to the quality of predictions.Some unexpected conclusions can come from using the type of analysis presented above, for example, cases where confidence is not highest in the centre of experimentation, which may be unexpected at first sight. An experimental design where, for example, three replicates are performed in the centre does not lead to highest confidence in the centre of the design.The importance of replicates, not only as a means for measurement of errors, but also as a means to change the shape of the confidence in a model, is emphasised in this study. We thank the Consejo Nacional de Investigaciones Cient�ýficas y Tecnol�ogicas de Venezuela (CONICIT) for finance (P.W.A.). Appendix List of Notations Used N Number of unique experiments I Total number of experiments q Number of replicates in the centre k Variable number xk Variable value p Outlier value i Experiment number (total) n Experiment number (unique) xki Value for each experiment hn Leverage for true experiment h Leverage as an equation X Design matrix H Hat matrix xn Vector of design for each experiment se Root mean squared residual error un Uncertainty for experiment n y Experimental response Y Response matrix y± Confidence limits m Number of coefficients in the model References 1 Box, G.E. P., and Wilson, K. B., J. R. Stat. Soc., 1951, 13, 1 2 Cochran, W.G., and Cox, G. M., Experimental Design, Wiley, New York, 1957. 3 Box, G. E. P., Hunter, W. G., and Hunter, J. S., Statistics for Experimenters, Wiley, New York, 1978. 4 Davies, O. L., The Design and Analysis of Industrial Experiments, Oliver and Boyd, London, 1984. 5 Steinberg, D. W., and Hunter, W. G., Technometrics, 1988, 26, 71. 6 Deming, S. N., and Morgan, S. L., Experimental Design: A Chemometric Approach, Elsevier, Amsterdam, 1987. 7 Morgan, E., Burton, K.W., and Church, P. A., Chemometr. Intell. Lab. Syst., 1989, 5, 283. 8 Brereton, R. G., Chemometrics Applications of Mathematics and Statistics to Laboratory Systems, Ellis Horwood, Chichester, 1993. 9 Bayne, C. K., and Rubin, I. B., Practical Experimental Designs and Optimization Methods for Chemists, VCH, Weinheim, 1986. 10 Martens, H., and Næs, T., Multivariate Calibration, Wiley, Chichester, 1989. 11 Sharaf, M. A., Illman, D. L., and Kowalski, B. R., Chemometrics, Wiley, New York, 1986. 12 Analytical Methods Committee, Analyst, 1994, 119, 2363. 13 Draper, N. R., and Smith, H., Applied Regression Analysis, Wiley, New York, 1966. 14 Miller, J. C., and Miller, J. N., Statistics for Analytical Chemistry, Ellis Horwood, Chichester, 1988. 15 Plackett, R. L., Regression Analysis, Oxford University Press, Oxford, 1960. 16 Velleman, P., and Welsch, R., Am. Stat., 1981, 35, 234. 17 Allus, M. A., Brereton, R. G., and Nickless, G., Chemometr. and Intell. Lab.Syst., 1989, 6, 65. 18 Araujo, P. W., and Brereton, R. G., Trends Anal. Chem., 1996, 15, 156. 19 Moore, D. S., Statistics. Concepts and Controversies, Freeman, San Francisco, CA, California, 1979. 20 Topping, J., Errors of Observation and Their Treatment, Chapman & Hall, London, 1962. 21 Davies O. L., and Goldsmith, P. L., Statistical Methods in Research and Production, Longmans, London, 22 Working, H., and Hotelling, H., J. Am. Stat. Assoc. Suppl. (Proc.), 1929, 24, 73. 23 Belsey, D. A., Kuh, E., and Welsch, R. E., Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Wiley, New York, 1980. 24 Anderson, V. L., and McLean, R. L., Design of Experiments: A Realistic Approach, Marcel Dekker, New York, 1974. Paper 7/00135E Received January 6, 1997 Accepted April 2, 1997 630 Analyst, July 1997, Vol. 122 Visualisation of Confidence in Two-factor Designs Where Model, Replication and Star Points are Varied Pedro W.Araujo and Richard G. Brereton* School of Chemistry, University of Bristol, Cantock’s Close, Bristol, UK BS8 1TS Confidence in predictions over an experimental domain can be calculated using the known experimental error and a function that relates to the shape of the confidence bands, often called leverage. In this paper, leverage is calculated for two-factor designs based on the central composite design, changing the nature of the model, the position of the star points and the number of replicates in the centre.The shapes of the graphs of leverage are presented. Several conclusions can be deduced, for example, for many common arrangements of experiments, such as the case where three replicates are taken in the centre; confidence is not highest in the centre of experimentation. Keywords: Experimental design; leverage; confidence predictions; chemometrics There is a large literature on experimental design, stretching over more than 50 years.1–9 Many chemists employ multifactor designs in their experiments. The arrangements of experiments are often obtained by employing well established recipes; for example, star, factorial, central composite and face centred cube designs are frequently used.Many such designs are advocated by statisticians and have certain specific properties such as rotatability or equivariance that make the experimental arrangements useful under certain specific situations. However, the analytical chemist is often concerned with quantitative model building, especially in the case of multivariate calibration.10–11 In this, chemometric experiments differ somewhat from experiments in many other areas of science where the main aim might be to estimate qualitatively various trends or to optimise a system.In the area of linear calibration, there is a large literature on how confidence in a model can be estimated from experimental measurements,12–15 and this can be extended to multivariate and multifactor situations.There has, though, been much less work reported on how the number and position of experiments can influence the confidence in a model for two or more factors. Most traditional statistical literature was written before the advent of flexible personal computers (PCs), so it was a time-consuming process to perform calculations and visualise graphically confidence for new experimental arrangements. With the advent of easy-toprogram PCs with good graphics, it is now possible to visualise easily how changes in experimental arrangements and models can influence the confidence in quantitative predictions.It is essential to recognise that there is no sharply defined experimental region, even in the case of clear cut linear calibration. Experimentation simply results in a predicted model, whose confidence changes as independent variables are changed. Normally, the relative confidence in predictions is highest in the centre of experimentation, but, as is seen below, even this is not always the case. An analyst may have different reasons for developing a method.Some methods may be designed to work well only in a very narrowly defined region, so a design which predicts extremely well in the centre but very poorly outside a certain region is perfectly satisfactory. Under other circumstances, a method that predicts fairly evenly throughout a fairly large region but not so accurately may be more appropriate.In this paper, we use the concept of leverage16–18 to demonstrate how confidence varies over a design. The approaches outlined below can be extended to other designs fairly readily. Methodology Example In this section we illustrate the calculation and application of leverage using a simple design given in Table 1. The set of experiments involves measuring two coded variables x1 and x2, which may, for example, be equivalent to the true variables pH and temperature.Note that in this paper coded variables are employed—these are mathematical transforms of the true variables with certain properties such as orthogonality. Coding also allows the experimenter to look at data from different types of experiments using a common scale. Table 1 lists a series of experiments at N = 9 unique levels, there are q = 6 replicated points in the centre, so the total number of experiments in this case will be I = 14. Four points (often called star points) are positioned at p = ±1.5 units from the origin.The influence of changing the values of q and p is discussed later in this paper. Design Matrix and Model In this paper a model of the form �y b b x b x b xx k k k kkk k = + + + = = å å 0 1 2 2 12 1 2 1 2 (1) Table 1 General two-factor design used to study the influence of the number of replicates, the model and the relative positions of the experimental points on the leverage Part x1 x2 Central* 0 0 · · · · · · 0 0 Factorial 1 1 21 1 1 21 21 21 Star p 0 2p 0 0 p 0 2p * Repeated q times.Analyst, July 1997, Vol. 122 (621–630) 621will be used involving six coefficients. A design matrix X can be obtained from the experimental values (Table 2) where the 6 columns represent the values of the six parameters 1,x1,x2,x21 ,x22 and x1x2. The I = 14 rows represent the experiments. Uncertainty and Confidence Uncertainty19–21 measures how confidently a model predicts data in an experimental region; the greater the uncertainty the less the confidence in the predictions.For a given experiment, n, the uncertainty can be defined by u s n 2 2 1 1 = + ¢ - e[ ( ) ] x XX n A xn (2) where se is the root mean squared residual error over the total number of experiments I. The term xn(XAX)21xAn depends only on the design and not on the experimental response, so it is possible to predict a graph of uncertainty without performing any experiment by changing the levels of the variable xn across the domain of the factor space.When several replicates are monitored in the domain of the factor space (for instance q = six replicates in the centre of the design shown in Table 1) the uncertainty of prediction of the mean of q values defined here by u2q of response is given by u s q q 2 2 1 1 = + ¢ - e[ ( ) ] x x n n X XA (3) The statistical reliability of the model in the presence of error can be visualised by the confidence limits, which are calculated from the response data set.These confidence limits are a measure of how closely the model fits the data. For instance, 95% confidence means that we expect 95% of the responses to be within the region of this limit. Clearly, if the confidence limits are narrow, the scattering of the experimental responses will be small. The confidence limits are directly dependent on the uncertainty, through the expression y F u n m n ± - = � ( ) 1 2 , (4) Substituting eqn. (2) into eqn.(4) gives y s Fn m ± - - = �+ ¢ e 1 1 1 , [ ( ) ] x x n n X XA (5) where F has one degree of freedom in the numerator and n2m degrees of freedom in the denominator. In the same way taking into account eqn. (3), the confidence limit, when the replicates have been averaged, can be defined by y F u n m q ± - = � 1 2 , (6) Substituting eqn. (3) into eqn. (6) gives y s F q n m ± - - = � + ¢ e 1 1 1 , [ ( ) ] x x n n X XA (7) From eqn. (7) it is evident that if a large number of replicates are measured the confidence limits can be expressed by y S Fn m ± - - = � ¢ e 1 1 , ( ) x x n n X XA (8) When it is necessary to estimate the confidence limits of the entire predicted response surface instead of individual varking and Hotelling22 confidence limits can be used y s m Fm n m ± - - = � � ¢ e , ( ) x x n n X XA 1 (9) Eqn.(9) is of the same form as eqn. (8); the only difference is the parameter m which represents the number of coefficients in the model and the value of F.Leverage In the previous section we introduced the term xn(XAX)21xAn which is a measure of the potential influence of an observation on the parameter estimated and is usually called leverage, h. This parameter can be computed to demonstrate how confidence changes when the design or model is altered. The matrix H = X(XAX)21XA (10) is also called the hat matrix23,24 and has the following properties. Its diagonal elements equal the leverage at each experimental point.The leverage for the experimental points in the central composite design given in Table 1 (I = 14 experiments) for q = 6 replicates is calculated via the hat matrix whose diagonal Table 2 Design matrix used for the example described under Methodology. x0 x1 x2 x21 x22 x1x2 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 21 1 1 1 21 1 1 21 1 1 21 1 21 21 1 1 1 1 1.5 0 2.25 0 0 1 21.5 0 2.25 0 0 1 0 1.5 0 2.25 0 1 0 21.5 0 2.25 0 Fig. 1 Schematic representation of the algebraic expression for leverage h = x(XAX)21xA. 622 Analyst, July 1997, Vol. 122leverage values are 0.166 (central points), 0.596 (factorial points) and 0.655 (star points). These values show how, in this design, the leverage is smallest in the region where replicates have been recorded (central points) and in the region where the experimental points are close to the centre. The values of leverage in the factorial points to the star points should be compared.The sum of leverage over all experimental points equals the number of coefficients in the model. For instance, the model proposed in eqn. (1) involves six coefficients, so a design matrix of the form presented in Table 2 but with a different replication regime in the centre can be analysed and should demonstrate that no matter how many experiments are carried out, the summation over all the diagonal elements of the hat matrix will always be six.The summation of the diagonal leverage values obtained above is 6 3 0.166 + 4 3 0.596 + 4 3 0.655 = 6, whereas in Table 3, where there are no replicates in the centre, the summation is 1 3 0.973 + 4 3 0.599 + 4 3 0.657 = 6. Calculation of Leverage The approach of the previous section can be used to calculate leverage for an individual experimental point. However, confidence in a model can also be calculated over an entire experimental domain, not necessarily restricted to individual experiments. For example, confidence bands apply to an entire factor space.Equivalently, leverage can be used to explore how confidence varies when parameters are altered, even at points where the response is not measured. As such, leverage is a powerful tool for visualising how the design influences the confidence in a model. With modern methods for graphical display on PCs, the influence of the design on leverage, confidence and uncertainty can be readily visualised. Leverage for any experimental point can be calculated using the term (XAX)21. The vector x consists of the six coefficients and can be generalised for any experimental point x1 and x2.This vector (1 x1 x2 x21 x22 x1x2) can take on any value according to the experimental conditions. Multiplying x by (XAX)21 gives a new vector. Multiplying this new vector by xA then results in an algebraic expression for h given in Fig. 1. As an example in Fig. 2 we have selected the experimental point x1 = p = 1.5 and x2 = 0 of Table 1, so the vector x is (1 1.5 0 2.25 0 0) which when multiplying the term (XAX)21 gives the row vector designated by (a) in Fig. 2. Multiplying this row vector by xA gives a single scalar designated by (b) in Fig. 2. This is the value of leverage for the specific point (1.5, 0). However, it is also Fig. 2 Calculation of the expression h = x(XAX)21xA using the experimental points x1 = 1.5 and x2 = 0 of Table 1 (star part).Table 3 Computation of the hat matrix X(XAX)21 XA for the design matrix given in Table 2, except that only one measurement is taken at the centre point 0.973 0.060 0.599 0.060 20.136 0.599 0.060 20.136 0.129 0.599 0.060 0.129 20.136 20.136 0.599 20.054 0.297 20.056 0.297 20.056 0.657 20.054 20.056 0.297 20.056 0.297 0.128 0.657 20.054 0.297 0.297 20.056 20.056 20.107 20.107 0.657 20.054 20.056 20.056 0.297 0.297 20.107 20.107 0.128 0.657 ........................ .. . . . . . . . . . . ........................ – – – – – – – – – – – | | | | | | | | – – – – – – – – – – –– – – – – – – – – – – | | | | | | | | – – – – – – – – – – –– – – – – – – – – – – | | | | | | | | – – – – – – – – – – –– – – – – – – – – – – | | | | | | | | – – – – – – – – – – – ...................... . . . . . . . . . . . . ...................... – – – – – – – – – – – | | | | | | | | – – – – – – – – – – – Central point leverage value. Factorial points leverage values.Star points leverage values. Fig. 3 Calculation of the coefficients of leverage. The broken arrows show the combination of rows and columns that have to be labelled and added to obtain the coefficient of x21 (20.078 + 0.118 2 0.078). Analyst, July 1997, Vol. 122 623possible to derive an equation for leverage as follows. The rows and columns of the matrix (XAX)21 are labelled according to the six corresponding terms of the vector x. The relevant values of each coefficient are then added together to give the terms of the derived equation as is shown in Fig. 3. For example, the coefficient of x21 is the sum of 20.078 (row 4, column 1), 0.118 (row 2, column 2) and 20.078 (row 1 , column 4), which equals 20.038. This procedure is equivalent to multiplying the vectors of coefficients (which consist of algebraic expressions rather than individual numbers) together with the matrix (XAX)21. Using this procedure the equation for leverage calculated from Fig. 3 is given by the expression: h = 0.166 2 0.038 (x21 + x22 ) + 0.113 (x41 + x42 ) + 0.279 x21 x22 (11) for the design of Table 1. Representation of Leverage The visualisation of the leverage values of the design presented in Table 1 can be computed using eqn. (11). A threedimensional plot as well as contour plot of leverage as a function of the whole experimental domain of the variables x1 and x2 can be produced (Fig. 4). The levels and grid lines of the contours can be varied, influencing the appearance of the contour plot.These kinds of plots are useful to explore how well the design predicts the model. The lower the leverage the higher the confidence in the model as is shown in eqn. (9), which is used to assess the confidence of the predicted surface or the contour plot. Furthermore, the graphical representation of leverage is a useful tool to envisage not only the behaviour at the experimental points of the design but also outside the experimental region.Designs A general central composite design for two factors given in Table 1 was selected for this work. This design is the result of combining a factorial and a star design, respectively. The distribution of the experimental points is given in Fig. 5, which shows clearly the superimposof a factorial design on a star design. The number of factor combinations for this kind of design is given by N = 2k + 2k + 1 (12) With this number of unique experiments N, it is possible to fit the model described by the eqn.(1). The factorial and star part in the central composite design are used to estimate linear terms; the interaction term can only be estimated from the factorial part and the squared term only from the star part. Owing to this Fig. 4 Visualisation of leverage values of the design presented in Table 1 for q = 6 and p = ±1.5 (see colour key). Fig. 5 Central composite design studied. 624 Analyst, July 1997, Vol. 122versatility, this kind of design was chosen in order to study the influence of three factors on the leverage of a series of experiments, namely, (1) the number of replicates, (2) the model and (3) the relative positions of the experimental points.A schematic representation of the study performed is shown in Fig. 6. In all cases at least one central point at values of x1 and x2 of (0, 0) and four factorial points at values of (±1, ±1) are recorded. The position of the star points is varied between p = 0.5 and 1.5 at intervals of 0.25.The number of replicates in the centre is varied between 1 and 10. Various models can be employed to fit the data, namely: (a) linear, squared and interaction terms, (b) linear terms, (c) linear and interaction terms and (d) linear and squared terms. An advantage of the approach advocated in this work is that almost all possible designs can be compared, owing to the ability of PCs to produce results rapidly. Results The coefficients of the contour function for leverage were calculated as explained under Calculation of Leverage. The equations computed when the number of replicates, the model and the relative positions of the outliers are changed, respectively, are presented in Table 4.The contour plots used to study the influence on leverage when the number of replicates in the centre is increased from 1 to 10 are given in Fig. 7. In all cases a model of the form of eqn. (1) and star points at ±1 were employed. Fig. 8 represents the Fig. 6 Schematic representation of the study of the influence of three factors on the leverage, namely, number of replicates, the model and the relative positions of the experimental points. Table 4 Equations derived for leverage for the examples discussed in the text Centre p-value replicates Model* x0 x21 x22 x21 x22 x41 x42 1 1 a 0.556 20.500 20.500 0.250 0.500 0.500 2 0.357 20.262 20.262 0.107 0.429 0.429 3 0.263 20.149 20.149 0.039 0.395 0.395 4 0.208 20.083 20.083 0.000 0.375 0.375 5 0.172 20.040 20.040 20.026 0.362 0.362 6 0.147 20.010 20.010 20.044 0.353 0.353 7 0.128 0.013 0.013 20.058 0.346 0.346 8 0.114 0.030 0.030 20.068 0.341 0.341 9 0.102 0.044 0.044 20.077 0.337 0.337 10 0.093 0.056 0.056 20.083 0.333 0.333 1 6 b 0.071 0.167 0.167 0.000 0.000 0.000 c 0.071 0.167 0.167 0.250 0.000 0.000 d 0.147 20.010 20.010 20.294 0.353 0.353 0.5 6 a 0.111 0.099 0.099 27.559 4.096 4.096 0.75 0.126 0.045 0.045 21.125 0.893 0.893 1.25 0.163 20.040 20.040 0.233 0.191 0.191 1.5 0.166 20.038 20.038 0.279 0.113 0.113 *a: Linear, squared and interaction terms.b: Linear terms. c: Linear and interaction terms. d: Linear and squared terms. Analyst, July 1997, Vol. 122 625Fig. 7 Contour plots when the number of replicates in the centre of the design presented in Table 1 is increased. (a) 1 replicate, (b) 2 replicates and so on until (j) 10 replicates. Colour key as in Fig. 4. 626 Analyst, July 1997, Vol. 122case when the position of the star points is changed, using six replicates in the centre, a model of the form of eqn. (1) and varying the position of the star point from 0.5 to 1.5 at intervals of 0.25. The contour plots when the values of the model are altered are shown in Fig. 9. Influence of Replication Replication has a major influence on the shape of the leverage graph, as illustrated in Fig. 7, and the corresponding confidence bands. At low replication there is a low leverage at the corners of the square.The value of leverage then increases both towards the centre and the outside as the number of replicates increases. The region of the minimum decreases in size and the centre becomes flatter. The apparent loss of the small troughs from the graph using three replicates is simply a consequence of the chosen contour levels; in this paper the levels were kept constant for each graph for the sake of consistency. When more than two replicates are measured in the centre, the surface is fairly flat over a large region. By the time five replicates are included in the centre, there are no detectable local minima in the centre.This implies that five replicates are sufficient to produce a large flat region around the centre of the design where there is approximately equal confidence in prediction, which is an important feature of many experiments. The information relating to replication is summarised in Table 5.Along the bottom row of Table 5 are the values at points (±0.5, +0.5). As can be seen, leverage reduces dramatically up to about three replicates, and subsequently there is limited further change. The absolute minimum can be obtained using partial derivatives, here the change as extra replicates are taken is more even, being a 20% reduction from 1 to 2 replicates but 9% for increasing from 9 to 10 replicates. The position of the minimum moves towards the centre, being at (0, 0) for seven replicates.Another feature of Table 5 is that the leverage is higher in the centre than at the points (±0.5, 0.0), (0.0, ±0.5) and (±0.5, ±0.5) when less than four replicates are taken in the centre, suggesting that four replicates is the minimum requirement if confidence is to be best in the centre of the design. Interestingly, this minimum number of replicates may increase as the number of factors increase, reflecting the larger number of experiments performed away from the centre.Hence, there are important consequences for replication strategies if a method is to be developed that works best in the centre of the experimental region. The change in confidence can also be ascertained from the data in Table 5. For example, the confidence interval at the centre decreases by a factor of ABBBBBB (0.556/0.093), confidence being related to leverage by a square root relationship as discussed above, or under Leverage, as the number of replicates changes from 1 to 10, meaning a substantial tightening of the Fig. 8 Contour plots when the position of the star points (± p) of the design presented in Table 1 is changed. (a) 0.50, (b) 0.75, (c) 1.00, (d) 1.25 and (e) 1.50. Colour key as in Fig. 4. Analyst, July 1997, Vol. 122 627Fig. 9 Contours plots when the values of the model of the design presented in Table 1 are altered. (a) Linear, squared and interaction terms, (b) linear terms, (c) linear and interaction terms and (d) linear and squared terms.Colour key as in Fig. 4. Table 5 Summary of the main features observed when the centre is replicated. The top row represents the leverage values at (±0.50, ±0.00) or (±0.00, ±0.50), the diagonal numbers represent the leverage values at (0, 0), the bottom row represents the leverage values at (±0.50, ±0.50), the last column represents the minimum value of leverage found and its coordinate. The arrows represent the direction of increasing replication from 1 to 10 ? 0.462 0.318 0.251 0.211 0.185 0.167 0.153 0.143 0.134 0.127 0.556 0.356 (±0.63, ±0.63) 0.357 0.286 (±0.52, ±0.52) 0.263 0.236 (±0.42, ±0.42) 0.208 0.199 (±0.33, ±0.33) 0.172 0.170 (±0.24, ±0.24) 0.147 0.147 (±0.12, ±0.12) 0.128 0.128 (±0.00, ±0.00) 0.114 0.114 (±0.00, ±0.00) 0.102 0.102 (±0.00, ±0.00) 0.093 0.093 (±0.00, ±0.00) � 0.384 0.286 0.240 0.214 0.196 0.184 0.175 0.167 0.161 0.157 628 Analyst, July 1997, Vol. 122confidence intervals in the centre.The change in shape of the leverage graphs and confidence intervals can also be vislised by comparing Fig. 7(a) and (f) (one and six replicates, respectively, in the centre). The corners of the two contour plots at (±1, ±1) are virtually identical corresponding to leverage values of nearly 0.806 for one replicate and 0.784 for six replicates. The centre of the contour plot of Fig. 7(a) is at 0.556 but for Fig. 7(f) it is 0.147; this corresponds to differences in confidence between the centre and extreme corners of 1.20 for one replicate (i.e., very little difference) but 2.31 for six replicates, which is a substantial difference.By using the figures of Table 5, the equations and inspection of the contour plots, other trends can be observed. Influence of the Star Points Fig. 8 shows the influence of the position of the star points on the design, using six replicates. As can be seen, the shape of the graph is strongly influenced by the position of the star points.When the position is less than 1, the edges are squeezed towards the centre [Fig. 8(a) and (b)]. For a value of p = ±1, the leverage becomes roughly square [Fig. 8(c)]. Increasing the value of p results in a more circular graph for the model used here. At p = ±1.41, the contour plot will be exactly circular, corresponding to the rotatable central composite design. Table 6 summarises this information. Leverage is least in the centre up to p = ±0.75 but slightly greater at p = ±1.5. At p = ±1, the graph of leverage is exceptionally flat around the centre.Note that, about p = ±1, the centre point is not best predicted even when six replicates are employed. Hence, central composite design as normally applied with p = ±AB2 will not predict the data best in the centre. Influence of the Model The influence of the model is illustrated in Fig. 9 for the case of six replicates in the centre and a value of p = ±1. It is important to remember that the sum of coefficients for each model will be different, so the sum of leverage values over all experimental points will differ according to the model.The most dramatic effect relates to the shape of the contour plot. For linear terms and p = ±1, this plot is completely circular suggesting that confidence simply is a function of distance from the centre of the design. This behaviour, though, is also influenced by the position of the star points. When quadratic and interaction terms are added, a circular pattern emerges if the star point is at ±AB2 .The contour plot of the leverage for the full six terms and p = ±AB2 is given in Fig. 10(a). If the number of coefficients is reduced to three [Fig. 9(b)] the graph is no longer circular. Hence, both the model and the position of the star points influence the shape of the confidence surface. For comparison, the graph of leverage using only linear terms but p = ±AB2 is given in Fig. 10(b).Interestingly, this graph will always be circular in shape no matter what the values of p and Table 6 Summary of the main features observed when the influence of the position ±p is changed. The top row is of the leverage values at (±0.50, ±0.00) or (±0.00, ±0.50), the diagonal numbers represent the leverage values at (0, 0), the bottom row represents the leverage values at (±0.50, ±0.50), the last column represents the minimum value of leverage found and its coordinate. The arrows represent the direction of increasing the ±p values (0.5, 0.75, 1, 1.25 and 1.5, respectively) ? 0.392 0.193 0.167 0.165 0.164 0.111 0.111 (±0.00, ±0.00) 0.126 0.126 (±0.00, ±0.00) 0.147 0.147 (±0.12, ±0.12) 0.163 0.161 (±0.26, ±0.26) 0.166 0.163 (±0.27, ±0.27) � 0.200 0.190 0.184 0.181 0.179 Fig. 10 Contour plot when the position of the star points of the design presented in Table 6 is p =+AB2. (a) Linear, quadratic and interaction terms and (b) linear terms. Colour key as in Fig. 4. Analyst, July 1997, Vol. 122 629q, provided that the design is symmetrical. This is because the leverage equation consists of only three terms, namely, an intercept and the terms x21 and x22 . Adding interactions distorts the shape of the leverage graph, increasing it at the corners but not at the edges (or centre); this is because the edges represent the situation when the level of one factor is 0, and the other is ±1, so only one factor changes in level from the centre of the design, whereas the corners represent the situation when both factors are at p = ±1, i.e., both factors are changing, so there are interactions.A similar effect is observed when comparing the quadratic model with and without interactions. The edges always remain the same: for example, Fig. 9(d) can be obtained by stretching the corners of Figure 7(f). Conclusions Leverage is a powerful tool for exploring the confidence in predictions of regression models when experiments are designed in different ways.Graphical visualisation is useful. Although there is a large classical literature on experimental design, the emphasis is on certain fixed designs. In the case of quantitative model building in analytical science, the ability to change parameters gradually in an experiment is important. The aims of experimentation and method development often differ according to application, and it is vital, in advance, to look at how different arrangements relate to the quality of predictions.Some unexpected conclusions can come from using the type of analysis presented above, for example, cases where confidence is not highest in the centre of experimentation, which may be unexpected at first sight. An experimental design where, for example, three replicates are performed in the centre does not lead to highest confidence in the centre of the design. The importance of replicates, not only as a means for measurement of errors, but also as a means to change the shape of the confidence in a model, is emphasised in this study.We thank the Consejo Nacional de Investigaciones Cient�ýficas y Tecnol�ogicas de Venezuela (CONICIT) for finance (P.W.A.). Appendix List of Notations Used N Number of unique experiments I Total number of experiments q Number of replicates in the centre k Variable number xk Variable value p Outlier value i Experiment number (total) n Experiment number (unique) xki Value for each experiment hn Leverage for true experiment h Leverage as an equation X Design matrix H Hat matrix xn Vector of design for each experiment se Root mean squared residual error un Uncertainty for experiment n y Experimental response Y Response matrix y± Confidence limits m Number of coefficients in the model References 1 Box, G. E. P., and Wilson, K. B., J. R. Stat. Soc., 1951, 13, 1 2 Cochran, W. G., and Cox, G. M., Experimental Design, Wiley, New York, 1957. 3 Box, G. E. P., Hunter, W. G., and Hunter, J. S., Statistics for Experimenters, Wiley, New York, 1978. 4 Davies, O. L., The Design and Analysis of Industrial Experiments, Oliver and Boyd, London, 1984. 5 Steinberg, D. W., and Hunter, W. G., Technometrics, 1988, 26, 71. 6 Deming, S. N., and Morgan, S. L., Experimental Design: A Chemometric Approach, Elsevier, Amsterdam, 1987. 7 Morgan, E., Burton, K. W., and Church, P. A., Chemometr. Intell. Lab. Syst., 1989, 5, 283. 8 Brereton, R. G., Chemometrics Applications of Mathematics and Statistics to Laboratory Systems, Ellis Horwood, Chichester, 1993. 9 Bayne, C. K., and Rubin, I. B., Practical Experimental Designs and Optimization Methods for Chemists, VCH, Weinheim, 1986. 10 Martens, H., and Næs, T., Multivariate Calibration, Wiley, Chichester, 1989. 11 Sharaf, M. A., Illman, D. L., and Kowalski, B. R., Chemometrics, Wiley, New York, 1986. 12 Analytical Methods Committee, Analyst, 1994, 119, 2363. 13 Draper, N. R., and Smith, H., Applied Regression Analysis, Wiley, New York, 1966. 14 Miller, J. C., and Miller, J. N., Statistics for Analytical Chemistry, Ellis Horwood, Chichester, 1988. 15 Plackett, R. L., Regression Analysis, Oxford University Press, Oxford, 1960. 16 Velleman, P., and Welsch, R., Am. Stat., 1981, 35, 234. 17 Allus, M. A., Br, R. G., and Nickless, G., Chemometr. and Intell. Lab. Syst., 1989, 6, 65. 18 Araujo, P. W., and Brereton, R. G., Trends Anal. Chem., 1996, 15, 156. 19 Moore, D. S., Statistics. Concepts and Controversies, Freeman, San Francisco, CA, California, 1979. 20 Topping, J., Errors of Observation and Their Treatment, Chapman & Hall, London, 1962. 21 Davies O. L., and Goldsmith, P. L., Statistical Methods in Research and Production, Longmans, London, 1982. 22 Working, H., and Hotelling, H., J. Am. Stat. Assoc. Suppl. (Proc.), 1929, 24, 73. 23 Belsey, D. A., Kuh, E., and Welsch, R. E., Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Wiley, New York, 1980. 24 Anderson, V. L., and McLean, R. L., Design of Experiments: A Realistic Approach, Marcel Dekker, New York, 1974. Paper 7/00135E Received January 6, 1997 Accepted April 2, 1997 630 Analyst, July 1997, Vol. 122

ISSN:0003-2654    

DOI:10.1039/a700135e

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Calibration of Gas Chromatography–Mass Spectrometry of Two-component Mixtures Using Univariate Regression and Two- and Three-Way Partial Least Squares Cevdet Demir and Richard G. Brereton* School of Chemistry, University of Bristol, Cantock’s Close, Bristol, UK BS8 1TS Univariate calibration and two-way and three-way partial least squares (PLS) were applied to a series of GC–MS results for 21 mixtures of two closely eluting compounds, salbutamol and clenbuterol. Steps in the analysis, including baseline correction, alignment of chromatograms, mass selection, unfolding (for three-way data), standardizing and centring, are described, appropriately modified for the problem in hand.Both mass spectral and, for three-way data, time dependent loadings can be calculated. The quality of quantitative predictions was determined using a leave one out cross validation method. For PLS slightly better predictions were obtained compared with the best predictions for univariate single ion monitoring.Three-way PLS provides a wealth of extra information. Keywords: Partial least squares; calibration; gas chromatography–mass spectrometry; chemometrics GC–MS is frequently employed as a quantitative technique.1,2 The traditional approach is to record a chromatogram of a mixture in the presence of a known concentration of one or more reference compounds,3 and then determine the ratio of the peak areas of each component in the mixture at a selected mass number to the peak area of the reference compound.This approach of using selective ion monitoring is then used to estimate concentrations, for example in environmental monitoring.4 However, GC–MS contains information over the entire mass range and, hence, is a multivariate technique. Single masses provide only univariate information, whereas using a range of masses allows multivariate approaches such as partial least squares (PLS).5–8 There are two ways in which PLS could be employed. The first, or two-way, method simply involves performing PLS on a set of masses simultaneously, for example, selecting 20 masses, and then doing calibration. However, GC– MS can also be considered as a candidate for three-way calibration. Rather than sum the masses up over all points in time, the intensity at each point in time and each mass number can be recorded to give a two-way matrix for each experimental mixture, and a three-way matrix (tensor)9,10 when a series of mixtures are analysed.Although PLS supposedly should provide better results than univariate methods, key problems have to be overcome first. For example, the majority of masses in GC–MS are redundant, containing no useful information. In this respect GC–MS differs crucially from, for example, HPLC with diode-array detection, where each wavelength contains some useful information. Hence mass selection11,12 is a key step. For three-way data, chromatograms have to be aligned, since the true offset of each chromatogram differs slightly according to run.Scaling or standardization13 has an important role to play in multivariate calibration, as each mass may have different significance, especially if the spectrum of one component in a mixture is dominant by a prominent ion. In this paper, we propose approaches for multivariate calibration of GC–MS data and look at the effectiveness in relation to univariate methods. In addition, multivariate calibration can reveal extra trends and information about the data.Experimental Previous studies established a mixture of salbutamol and clenbuterol as good reference standards because both peaks are partially overlapping and each compound has several ions in common.11 A mixture design resulting in 21 chromatograms at six concentration levels was used for the study in this paper. Salbutamol and clenbuterol were purchased from Sigma (Poole, Dorset, UK) and quinine from Fluka (Gillingham, Dorset, UK).In order to improve volatility, trimethylsilyl (TMS) derivatives were prepared by adding N,O-bis(trimethylsilyl)trifluoroacetamide (BSTFA) (Sigma) to the standard samples. The samples were heated at 80 °C for 1 h. Reagents were removed under nitrogen (40 °C). The derivatized samples were redissolved in toluene–MSTFA (99 + 1 v/v). Stock standard solutions of salbutamol, clenbuterol and quinine were prepared at concentrations of 4.22, 4.04 and 4.10 mg ml21, respectively.From these solutions a 153.75 mg ml21 quinine solution was prepared and for salbutamol and clenbuterol six working standard solutions were prepared by diluting 20, 10, 6.667, 5, 4 and 3.333 times. The theoretical mixture design is given in Table 1, and the concentrations in Table 2. A typical chromatogram is illustrated in Fig. 1. Mass spectra recorded on a Fisons (Loughborough, UK) MD800 mass spectrometer were obtained at a scan rate of 200 min21 for the datasets.The GC–MS conditions were the same as in previous studies.12 The region where clenbuterol and salbutamol elute was reduced to 18 datapoints in time. The spectra of pure salbutamol and clenbuterol are given in Figs. 2 and 3 for reference. Table 1 Mixture design for salbutamol and clenbuterol. The numbers 0.5, 1, etc., refer to relative concentrations Experiment No.* Salbutamol Clenbuterol 1 0.5 0.5 2(a) and (b) 1.0 1.0 3(a) and (b) 1.0 2.0 4(a) and (b) 1.0 3.0 5 1.5 1.5 6(a) and (b) 2.0 1.0 7(a) and (b) 2.0 2.0 8(a) and (b) 2.0 3.0 9 2.5 2.5 10(a) and (b) 3.0 1.0 11(a) and (b) 3.0 2.0 12(a) and (b) 3.0 3.0 * (a) and (b) represent replicates; 21 experiments were performed in total.Analyst, July 1997, Vol. 122 (631–638) 631Preprocessing, Selection of Significant Masses and Ratioing to Internal Standard Before performing any data analysis, it is important to preprocess the data to obtain useful information. The first step is to perform baseline correction.A baseline region which represents only noise can be selected visually or by plotting the logarithm of the sum of squares of the data. After the selection of noise regions, the mean intensity at each mass number is calculated, and these means are subtracted from the data to give a baseline corrected dataset. Owing to the variability of GC conditions, the compounds may not elute at exactly the same time for each run. Therefore, it is necessary to adjust the elution time for all the samples so that the salbutamol and clenbuterol peaks are centred at the same datapoint.After shifting the elution time the clusters of peaks for each chromatogram are aligned. The next step is to select a number of significant masses for calibration. Of the mass numbers between 100 and 400 only certain diagnostic masses are useful. The majority of masses are either not detected or represent noise. Previously we described a method for the selection of masses in an individual chromatogram, using the variance/mean ratio for each mass.In this study, however, there are 21 chromatograms, each of which results in different diagnostic masses. For each of the 21 chromatograms, the 50 most significant masses ranked by the variance/mean ratio over the cluster containing salbutamol and clenbuterol are computed, using the procedure described previously. Masses that are common to all 21 sets of significant masses are then selected, resulting in 20 significant masses, 10 of which primarily arise from salbutamol and 10 from clenbuterol.Using significantly fewer than 20 masses results in a distribution biased towards salbutamol, presumably because the spectrum of salbutamol dominates in intensity. The order of these masses is determined as follows. If kij is the rank of mass j in chromatogram i (with rank 1 being most significant), the total rank over all chromatograms is given by K k j ij i I = = å1 The smaller this number, the more significant is the mass.For the internal standard (quinine), the total peak area is an indication of the amount of quinine present; since an equal amount of quinine standard was introduced into each mixture, this number acts as an internal calibrant. The total integral over the quinine peak and all masses (not just the 20 significant masses) was determined and is given, for chromatogram i, by qi. Because this varies, the ratio dijn = zijn/qi, where zijn is the intensity at mass j over the salbutamol and clenbuterol cluster at time n in chromatogram i was calculated as an indicator of intensity as ratioed to an internal standard at each mass.Calibration was performed relative to z rather than the raw data in all cases. Univariate Calibration The simplest method of regression is univariate calibration,14 in which peak areas at selected masses are calibrated to concentrations. In order to carry out a univariate calibration, a single mass would be chosen which measures the response that corresponds to the concentration of a compound in a sample.The choice of Table 2 Injected amounts of salbutamol and clenbuterol Experiment Salbutamol/ Clenbuterol/ No.* ng ml21 ng ml21 1 52.75 50.5 2(a) and (b) 105.5 101 3(a) and (b) 105.5 202 4(a) and (b) 105.5 303 5 158.25 151.5 6(a) and (b) 211 101 7(a) and (b) 211 202 8(a) and (b) 211 303 9 263.75 252.5 10(a) and (b) 316.5 101 11(a) and (b) 316.5 202 12(a) and (b) 316.5 303 * (a) and (b) represent replicates; 21 experiments were performed in total.Fig. 1 A typical mixture chromatogram of (A) salbutamol and (B) clenbuterol. Fig. 2 Mass spectrum of pure salbutamol. Fig. 3 Mass spectrum of pure clenbuterol. 632 Analyst, July 1997, Vol. 122the mass is important and represents the compound with no interference from other masses that may be present. For mass j, the total peak area (ratioed to quinine) is given by xij: x d ij ijn n N N = = å1 2 Integrating over the region of salbutamol/clenbuterol gives a total area at mass j.A model of the form �yil = b0jl + b1jlxij where b0jl is an intercept term, b1jl is the slope, xij is the total integrated ratioed peak area at mass j, �yil is the predicted concentration of a standard l and i is the sample number, is then computed, using inverse regression,15 where the two terms are given by b x x y y x x b y b x jl ij j ij l i I ij i I jl l jl j 1 1 2 1 0 1 = - - - = - = = å å ( )( ) ( ) This approach assumes all errors are in the measurement of intensity by GC–MS, which is probably the main source of error in this study.The quality of calibration for compound l can then be determined using the root mean square error of prediction: R I y y l il il i I = - = å1 2 1 (� ) where yil is the known concentration of compound l for sample i. This error term is used for comparisons among significant masses and calibration models for compound l. PLS Calibration Notation In this paper three-way matrices are denoted by uppercase bold italic underlined characters, two-way matrices by uppercase bold italics, vectors by lowercase bold italics and scalars by normal italics.For three-way PLS, the raw data matrix D– – has dimensions I 3 J 3 N0 with I samples, J masses and N0 (N2 2 N1 + 1) points in time. The matrix D arises from this when unfolded, having dimensions I 3 JN0 as described below. For two-way PLS, the raw data matrix is X having dimensions I 3 J.Each column corresponds to the total integrated intensity between times N1 and N2 for each of the J masses. N1 and N2 were estimated as the elution times at the beginning and end of the peak cluster. No compounds are eluted before and after these times. Note that the two-way matrix X is different from the matrix D. PLS can be three-way or two-way, and to distinguish this a superscript w (2 or 3) is placed above the appropriate scores, loadings and error matrices, vectors and scalars.The left-hand side superscript l (1 or 2) refers to compound number. Concentration vectors are denoted by y with an appropriate left-hand side superscript. Further details are given in the Appendix. Unfolding There are many possible three-way calibration methods in the literature. An easy way of performing three-way calibration is to unfold the three-way data matrix into a two-way matrix.16–20 This is performed by concatenating the rows of a matrix to give a row vector.If the objects for one sample form a I 3 N matrix, it becomes a length IN row vector. The two-way matrix is established by performing the same operation for all the samples. Fig. 4 shows the unfolding of a three-way data matrix D with I (21) rows and N0 3 J (360 = 18 3 20) columns. PLS is then used to calculate the matrices lT and lP for component l. The concentration vector ly is the same for both two- and three way PLS.Standardization In this paper we consider the influence of standardization on PLS predictions. Standardizing is a form of scaling. For twoway PLS this process is simple and involves the transformation s ij ij j ij j i I x x x x x I = - - - = å ( ) ( ) 2 1 1 For three-way PLS, the procedure is somewhat more complex than in the two-way case. The aim of standardization in this study is to ensure that all masses have equal influence over the calibration problem. The mass at m/z 369 is very intense and would dominate the analysis, so salbutamol would be predicted much better than clenbuterol in the absence of standardization.However, it is still important to retain the relative influence of readings between samples as per two-way data; if the data are standardized after unfolding, the variation in intensity in different times is lost; each time and mass is independently standardized. The aim of standardization should not be to weight each time equally but only to weight each mass equally.Therefore, the procedure involves standardizing the entire mass readings at all times over all samples prior to unfolding. Standardizing for three-way PLS analysis can be described as follows: d d IN d d d IN j ijn i I n N N s ijn ijn j i I n N N = = - = = = = å å å å 1 0 2 1 0 1 2 1 2 ( ) Note that this procedure is nevertheless different from that for two-way data, since there will be 378 ( = 18 3 21) datapoints arising from each mass, rather than only 21 datapoints.The scaled (standardized) samples are then unfolded. Note that the unfolded data will no longer be mean centred, which operation has to take place again after unfolding. Fig. 4 Unfolding a three-way data matrix into a two-way data matrix to prepare for the PLS analysis. Analyst, July 1997, Vol. 122 633Centring Mean centring the data is the second important operation for PLS calibration. For two-way PLS, it involves subtracting the column mean from each element: cxij = xij 2 �xj or c ij ijn n N N ijn i I n N N x d d IN = - = = = å åå 1 2 1 2 1 0 Note that for three-way data, the process of standardization as described above does not result in mean centring at each point in time.Mean centring can be carried out by unfolding the three-way matrix to a two-way, I3JN0, matrix, and then centre this matrix as in ordinary PLS. For three-way PLS, the data are mean centred as follows: cdijn = dijn 2 – djn PLS An application of two- and three-way PLS is presented using GC–MS data.The methods are well described in the literature. For two-way data, PLS is performed on the X matrix with dimension I 3 J so that X = lTBl PB+ lEB ly = luBl qB+ lfB where B denotes two-way scores and loadings. If there are K components lT, for example, will have I rows and K columns. The corresponding unfolded PLS estimates the following model: D = lTò lPò + lEò ly = luòl qò + lfò For two-way PLS, each mass has a corresponding loading for each component and each compound.The magnitude of these loadings can be presented graphically as a function of mass number. Although some loadings are negative, in order to be consistent with the result for three-way PLS, they are presented as absolute values. The interpretation of loadings for three-way data is more complex. PLS is performed on the unfolded data matrix. The resulting loadings are folded back to form a loadings matrix for each component.These loadings can be plotted as a function of time for each mass, i.e., graphs of lPòjn,m versus n for each j and m. Another way is to plot a graph of the root mean square loadings: l j m l jn m n N N N ¢¢¢ = ¢¢¢ = å P p , , 1 2 1 2 which shows howdings are influenced by mass number. These graphs can be compared with graphs for the corresponding two-way data. Cross Validation An important aspect is to evaluate how well the calibration model predicts unknown samples.Finding a minimum root mean square error can be used for this purpose. Cross validation is frequently used to determine the optimum number of principal components for multivariate calibration. 21,22 Increasing the number of PLS components will always result in a closer fit to the data. However, this does not imply that the later components are significant. There are several methods for testing the significance of each component, but most are based on cross validation.In this paper, we use the method of taking one sample out at a time.23 Each of the 21 samples is removed in turn and the two errors are calculated by v s s s m s i i g f y y f y y I s = - = - - ' å ( �) ( �) ( ) 2 2 1 where s is the sample removed, gs is the group of 20 samples excluding sample s, vf is the validation error and mf is the modelling error. Over all 21 samples, there will be 21 values of vf and mf, so the overall root mean square validation and modelling errors are given by v v s s I m m s s I F I f F I f = = = = å å 1 1 1 1 The prediction error, without cross validation, is given by f2 = fA f, where f is the vector of prediction errors for each sample.The cross validation error is likely to be considerably larger than the modelling error, which in turn is of the same approximate size as the prediction error. The prediction error will reduce according to the number of PLS components used but, if the data behave well, the validation error should decrease until the true number of components is found, and then increase, since the latter components are simply noise and so do not correctly model the validation samples.To perform cross validation correctly, it is necessary to centre and, where appropriate, scale the 20 samples separately each time, i.e., if standardization is required, this is performed 21 times. The transformation on the 20 samples is then repeated on the 21st. It is not correct to standardize and/or centre the entire dataset of 21 samples and then model the remaining 20 samples, as the components will be neither centred nor standardized.Results and Discussion Univariate Calibration The univariate calibration errors for the 20 selected masses are given in Table 3. In addition, a crude form of validation is performed by constructing a model using 20 samples and determining the prediction error on the 21st. This is repeated leaving one sample out each time.As can be seen from Table 3, the prediction, modelling and validation errors are comparable in size for this example. Interestingly, some masses result in substantial errors. For clenbuterol, all masses are relatively low in intensity compared with m/z 369 for salbutamol and so result in high errors. It would be hard to predict from first principles that m/z 166 results in a low error. Only four masses result in errors around 15 ng ml21. This suggests that using selective ion monitoring as a means of univariate calibration is risky and highly dependent on the chosen mass, and it would be hard to predict which mass is best 634 Analyst, July 1997, Vol. 122from first principles. For each component, the 10 masses are ranked in descending order of significance as suggested by the ranking criterion in the third section. For clenbuterol, it is clear that the more significant masses do not necessarily lead to better calibration predictions. PLS Predictions The two-way PLS errors for prediction, modelling and validation are given in Tables 4 and 5.A large number of conclusions may be drawn. The first relates to the number of significant PLS components in the model. Although the prediction error reduces dramatically in all cases, this does not imply that the later components are real. One criterion for significance is that the true number of components is reached when the validation error is a minimum. Extending the calculations to 10 components for clenbuterol suggests that this is reached at around four components (Table 6).However, a flat graph of validation errors often indicates that the safest result is at the beginning of the plateau, suggesting two components for the standardized data and four for the unstandardized data. The difference between the results for standardized and unstandardized data is striking, especially for clenbuterol. A reason is that the salbutamol peak at m/z 369 dominates the analysis so that the clenbuterol peaks are relatively minor in size, meaning a poor fit if only a few components are used. This is also reflected in the univariate calibration models since the less intense peaks are dominated by noise.Standardizing results in comparable predictions for both salbutamol and clenbuterol provided two components are used for salbutamol and four for clenbuterol as suggested by the validation errors. It is interesting that standardizing results in a worse model for salbutamol if only one PLS component is used.This is because m/z 369 is very intense and diagnostic, but if there is standardization this advantage is removed. Three-way PLS predictions of the unstandardized data (Tables 7 and 8) result in errors comparable in size for both salbutamol and clenbuterol. In some cases the models are actually slightly worse. This probably is because of the problems of exactly aligning data. Because there is an unpredictable offset when a chromatogram is run, the precise position of a peak will change relative to the beginning of acquisition for an intense peak.This change may be significant for two-way data; the intensities are simply summed for each mass, so this offset is irrelevant. When the data are standardized this problem apparently disappears, presumably because the intense tops of peaks have less influence on the model. The predictions for clenbuterol are now fairly good, even for one component. Loadings A great deal of information can come from the loadings plot.The easiest to interpret are the loadings plotted as a function of time using three way analysis. The loadings for the first two PLS components are given in Figs. 5 and 6. For the Table 3 Root mean square errors of univariate calibration (ng ml21). Prediction error refers to the error when the entire 21 samples are used; validation and modelling errors are the average errors when the data set is split into 1 test and 20 training samples Salbutamol Clenbuterol Mass Prediction Modelling Validation Mass Prediction Modelling Validation 369 14.51201 14.5034 15.2465 262 52.9003 52.3151 54.7844 370 15.9678 15.9253 16.7844 243 45.523 45.5224 46.6973 147 23.5113 20.5732 24.1903 264 42.2964 42.042 43.8859 207 13.8473 13.8339 14.5452 186 31.8329 28.9176 33.644 265 60.5821 60.5802 61.4897 173 26.4489 26.103 27.2311 133 28.4676 27.4523 29.2518 212 36.0138 35.4542 38.0682 294 24.1052 24.0685 24.6289 166 14.0452 13.1963 14.8421 281 24.8886 24.813 26.2671 188 34.3321 33.4795 35.831 220 20.2818 20.2816 21.2602 245 23.7456 21.4552 24.4513 177 51.3573 50.8283 52.6191 277 40.8727 40.2014 42.5105 Table 4 Root mean square error of two-way PLS calibration of salbutamol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 14.5 14.7907 15.5489 30.0977 29.218 34.3195 2 13.8364 14.1351 15.459 10.8668 10.705 12.454 3 12.6539 12.8975 15.0545 8.8071 8.4721 12.3484 4 10.3475 10.2772 14.7892 6.8891 6.5467 11.2131 Table 5 Root mean square error of two-way PLS calibration of clenbuterol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 65.8421 65.6303 69.8464 30.7642 30.7846 34.4136 2 29.2507 29.0469 31.1823 20.6712 20.9968 22.7378 3 22.6302 23.023 28.2061 13.2479 12.4302 22.1795 4 13.1725 13.2623 19.4711 11.8193 10.9652 19.1694 Analyst, July 1997, Vol. 122 635unstandardized data there is little difference for the first PLS component between salbutamol and clenbuterol, except a slightly larger maximum at fast elution time, reflecting the position of clenbuterol. This is presumably bee the ion at m/z 369 dominates no matter which component is used for calibration. Even though m/z 369 is not well correlated with clenbuterol, it will, nevertheless, exhibit a small correlation because of the design as chromatograms 1, 5 and 9 are correlated for both components so there will be a slight correlation between salbutamol and clenbuterol concentrations which is picked up. The second component is necessary for a good model, particularly for clenbuterol, as can be seen from Tables 7 and 8.Here there is a dramatic difference, the earlier eluting salbutamol having a negative influence on clenbuterol calibration. The reverse is the case, but less strongly, for salbutamol. The standardized time-dependent loadings show a much more obvious trend, the maxima for both salbutamol and clenbuterol being in the correct place.The second loadings provide an appropriate negative balancing effect. These are in good agreement with the expectations from the prediction error. The influence of standardization is especially obvious from the first PLS component of Fig. 6. Note that the small correlation with the second compound is almost certainly a result of the design used, demonstrating the special importance of design when doing calibration experiments.This is likely to disappear if an orthogonal design is employed. The mass spectral loadings are harder to interpret primarily because they are displayed in the absolute value mode. Only the three-way spectral loadings are illustrated for sake of brevity (Figs. 7 and 8) but similar conclusions also come from two-way analysis. The root mean square loadings over all points in time are illustrated for this purpose.For example, the loadings for unstandardized salbutamol show maxima at peaks for salbuta- Table 6 Root mean square error of two-way PLS cross validation of clenbuterol for 10 PLS components (ng ml21) Component Unstandardized Standardized 1 69.8464 34.4136 2 31.1823 22.7378 3 28.2061 22.1795 4 19.4711 19.1694 5 22.1532 21.9661 6 23.258 22.7049 7 24.7529 24.1972 8 26.2817 26.6376 9 27.2957 27.1828 10 30.8872 28.1535 Fig. 5 Time-dependent loadings for the first two components of three-way PLS data for salbutamol.The top figures represent the unstandardized data and the bottom figures the standardized data. Table 7 Root mean square error of three-way PLS calibration of salbutamol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 15.3467 15.5379 21.7641 16.7973 15.7835 22.202 2 14.3254 14.5242 19.9991 14.0457 14.0227 20.3149 3 12.3116 12.1632 18.6847 10.9006 10.1287 18.8127 4 9.4362 9.5854 16.4184 7.414 7.0539 17.0949 Table 8 Root mean square error of three-way PLS calibration of clenbuterol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 57.4241 55.2667 65.7378 17.8093 17.7842 23.1488 2 25.6571 26.7913 31.1776 15.8925 15.9249 22.1179 3 17.7387 17.832 23.8823 9.7123 10.0147 21.119 4 11.9961 11.6328 22.3824 5.7637 5.6139 19.7164 Fig. 6 Time-dependent loadings for the first two components of three-way PLS data for clenbuterol.The top figures represent the unstandardized data and the bottom figures the standardized data. 636 Analyst, July 1997, Vol. 122mol in the first PLS component, being a good reconstruction of the salbutamol spectrum since the time-dependent loadings also suggest that the first component primarily picks up salbutamol. The second component is influenced more by clenbuterol, although in negative manner, so the loadings primarily relate to the clenbuterol spectrum with a more prominent maximum at m/z 262, although some salbutamol (m/z 369) still remains.Standardizing the data distorts the relative mass spectral intensities but the trends are still there. For example, the timedependent loadings for the first standardized component for clenbuterol and second for salbutamol are dominated by clenbuterol and the equivalent mass spectral loadings show low intensity at m/z 369 and 370 but relatively high intensities at m/z 262.Visually the loadings for the three-way first standardized PLS components of salbutamol and clenbuterol can be divided into two groups, those of value around 0.07 and 0.02. These are given in Table 9. Remarkably, the high value loadings all arise primarily from the calibrant and the low value loadings from the second component. There is a high degree of correspondence between the order of these loadings and the order of univariate calibration errors as given in Table 3.For example, the m/z 265 and 177 ions have the highest calibration errors for salbutamol and, therefore, appear intermediate between the salbutamol and clenbuterol group in clenbuterol (0.0542 and 0.0413). The m/z 166 and 245 ions have lowest univariate calibration errors for clenbuterol (and are the only two ions that could be employed to provide an estimate of clenbuterol concentration with a high degree of confidence in the univariate models) and both have the highest loadings.The results for salbutamol are slightly less clear, but the ion with the highest univariate calibration error (m/z 265) has, nevertheless, the lowest value of the loadings for the salbutamol first component. A graph of the time-dependent loadings for salbutamol explains this. The second component is not as well defined as it is for clenbuterol. Conclusions This paper has described two methods for PLS calibration of GC–MS data. The improvement in prediction error is small but significant over univariate calibration if PLS is properly performed.However, the major advantage of PLS is that 20 masses can be used, and the prediction error is better than the best single mass. The difficulty with single ion approaches is that a correct choice of mass must be made. For at least one of the components, it is not clear, from first principles, which mass is most suitable, so selective ion monitoring risks poor results unless great care is taken to select a range of ions, some of which may not be obvious to the mass spectrometrists at first glance.Three-way PLS does not have major advantages over twoway methods as far as prediction errors are concerned. One problem is correctly aligning chromatograms. If digital resolution is not very high (typically a peak is defined by around 10 datapoints in GC–MS), small shifts in detector offsets can result in difficulties exactly aligning chromatograms, so introducing extra errors into the calibration24 which counterbalance the advantages of using the extra dimension.However, three-way analysis does result in more diagnostic information such as time-dependent loadings and, certainly for more complex problems of three or four components eluting at slightly different times, will reveal much more than two-way procedures. The absolute importance of data scaling such as standardizing and mean centring at the correct step in the procedure has been discussed.In this paper, we have only reported meaningful results. Incorrectly applying data preprocessing methods results in meaningless output, so the user of such approaches must take great care. We thank Dr. F. Burden for helpful discussions relating to cross validation and P. Hindmarch for writing the program for Fig. 7 Spectral loadings of three-way PLS data for salbutamol. The top figures represent the unstandardized data and the bottom figures the standardized data.Fig. 8 Spectral loadings of three-way PLS data for clenbuterol. The top figures represent the unstandardized data and the bottom figures the standardized data. Table 9 Root mean square loadings of the first standardized three-way PLS component of salbutamol and clenbuterol and their assignments (C and S) Corre- Corresponding sponding Salbutamol m/z compound Clenbuterol m/z compound 0.0769 133 S 0.0713 245 C 0.0740 207 S 0.0713 166 C 0.0739 220 S 0.0705 277 C 0.0719 147 S 0.0705 186 C 0.0713 177 S 0.0702 243 C 0.0695 281 S 0.0700 264 C 0.0694 369 S 0.0661 173 C 0.0692 370 S 0.0649 262 C 0.0658 294 S 0.0640 212 C 0.0626 265 S 0.0635 188 C 0.0341 186 C 0.0542 265 S 0.0270 188 C 0.0413 177 S 0.0266 262 C 0.0278 220 S 0.0257 173 C 0.0274 133 S 0.0232 277 C 0.0247 281 S 0.0224 212 C 0.0235 207 S 0.0224 166 C 0.0206 370 S 0.0196 243 C 0.0201 369 S 0.0176 264 C 0.0198 294 S 0.0165 245 C 0.0190 147 S Analyst, July 1997, Vol. 122 637decoding GC–MS data.We are grateful for support from Uludag University (Bursa, Turkey). Appendix List of Notations Used D–– Three-way GC–MS data matrix D Unfolded GC–MS data matrix X Two-way GC–MS data matrix i Sample number I Total number of samples j Mass number l Compound number Kj Total rank over all chromatograms kij Rank of mass j qi Quinine peak area for sample i summed over time and all masses zijn Intensity for mass j, sample i and time n dijn Peak area ratio for mass j, sample i and time n n Time N1 Point in time at the beginning of a cluster of peaks N2 Point in time at the end of a cluster of peaks xij Peak area ratio for mass j and sample i summed over all time sxij Standardized data matrix for two-way PLS cxij Mean centred data matrix for two-way PLS sdijn Standardised data matrix for three-way PLS cdijn Mean centred data matrix for three-way PLS �yil Predicted concentration yil Concentration of compound l �yl Mean concentration of compound l �xj Mean peak area ratio of mass j summed over time bojl Intercept of univariate calibration line b1jl Slope of univariate calibration line Rl Root mean square error of compound l ly Concentration vector for compound l lTw PLS scores matrix for compound l ltw m PLS scores vector for compound l ltw im PLS scores for sample i, component m and compound l lPw PLS loadings matrix for compound l lpw m PLS loadings vector for component m and compound l w Order of PLS (2 or 3) lpw mj Loadings for mass j for two-way PLS lpw mjn Loadings for mass j and time n for three-way PLS lPw mj Sum of loadings for mass j over all time for threeway PLS m Component number M Total number of components N0 Number of data points in time over significant peaks (N2 2 N1 + 1) lEB Error matrix of X for two-way PLS and compound l lEAAA Error matrix of D for three-way PLS and compound l lfB Error vector of y for two-way PLS and compound l s Removed sample vf Validation error mf Modelling error gs Group of samples excluding sample s vF Root mean square validation error mF Root mean square modelling error References 1 Boqu�e, R., and Rius, F.X., Chemom. 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W., Cirovic, D. A., and Brereton, R. G., Analyst, 1996, 121, 581. 16 Henrion, R., Chemom. Intell. Lab. Syst., 1994, 25, 1. 17 Ståhle, L., Chemom. Intell. Lab. Syst., 1989, 7, 95. 18 Smilde, A. K., and Doornbos, D. A., J. Chemom., 1991, 5, 345. 19 Bro, R., J. Chemom., 1996, 10, 47. 20 Geladi, P., Chemom.Intell. Lab. Syst., 1989, 7, 11. 21 Zhang, P., and Littlejohn, D., Chemom. Intell. Lab. Syst., 1996, 34, 203. 22 Sharaf, M., Illman, D. L., and Kowalski, B. R., Chemometrics, Wiley, New York, 1986. 23 Gemperline, P. J., J. Chemom., 1989, 3, 549. 24 Cirovic, D. A., Jacobsen, R. M., and Brereton, R. G., Anal. Commun., 1996, 33, 231. Paper 6/08245I Received December 6, 1996 Accepted March 10, 1997 638 Analyst, July 1997, Vol. 122 Calibration of Gas Chromatography–Mass Spectrometry of Two-component Mixtures Using Univariate Regression and Two- and Three-Way Partial Least Squares Cevdet Demir and Richard G.Brereton* School of Chemistry, University of Bristol, Cantock’s Close, Bristol, UK BS8 1TS Univariate calibration and two-way and three-way partial least squares (PLS) were applied to a series of GC–MS results for 21 mixtures of two closely eluting compounds, salbutamol and clenbuterol. Steps in the analysis, including baseline correction, alignment of chromatograms, mass selection, unfolding (for three-way data), standardizing and centring, are described, appropriately modified for the problem in hand.Both mass spectral and, for three-way data, time dependent loadings can be calculated. The quality of quantitative predictions was determined using a leave one out cross validation method. For PLS slightly better predictions were obtained compared with the best predictions for univariate single ion monitoring.Three-way PLS provides a wealth of extra information. Keywords: Partial least squares; calibration; gas chromatography–mass spectrometry; chemometrics GC–MS is frequently employed as a quantitative technique.1,2 The traditional approach is to record a chromatogram of a mixture in the presence of a known concentration of one or more reference compounds,3 and then determine the ratio of the peak areas of each component in the mixture at a selected mass number to the peak area of the reference compound. This approach of using selective ion monitoring is then used to estimate concentrations, for example in environmental monitoring.4 However, GC–MS contains information over the entire mass range and, hence, is a multivariate technique. Single masses provide only univariate information, whereas using a range of masses allows multivariate approaches such as partial least squares (PLS).5–8 There are two ways in which PLS could be employed.The first, or two-way, method simply involves performing PLS on a set of masses simultaneously, for example, selecting 20 masses, and then doing calibration.However, GC– MS can also be considered as a candidate for three-way calibration. Rather than sum the masses up over all points in time, the intensity at each point in time and each mass number can be recorded to give a two-way matrix for each experimental mixture, and a three-way matrix (tensor)9,10 when a series of mixtures are analysed.Although PLS supposedly should provide better results than univariate methods, key problems have to be overcome first. For example, the majority of masses in GC–MS are redundant, containing no useful information. In this respect GC–MS differs crucially from, for example, HPLC with diode-array detection, where each wavelength contains some useful information. Hence mass selection11,12 is a key step. For three-way data, chromatograms have to be aligned, since the true offset of each chromatogram differs slightly according to run. Scaling or standardization13 has an important role to play in multivariate calibration, as each mass may have different significance, especially if the spectrum of one component in a mixture is dominant by a prominent ion.In this paper, we propose approaches for multivariate calibration of GC–MS data and look at the effectiveness in relation to univariate methods. In addition, multivariate calibration can reveal extra trends and information about the data.Experimental Previous studies established a mixture of salbutamol and clenbuterol as good reference standards because both peaks are partially overlapping and each compound has several ions in common.11 A mixture design resulting in 21 chromatograms at six concentration levels was used for the study in this paper. Salbutamol and clenbuterol were purchased from Sigma (Poole, Dorset, UK) and quinine from Fluka (Gillingham, Dorset, UK).In order to improve volatility, trimethylsilyl (TMS) derivatives were prepared by adding N,O-bis(trimethylsilyl)trifluoroacetamide (BSTFA) (Sigma) to the standard samples. The samples were heated at for 1 h. Reagents were removed under nitrogen (40 °C). The derivatized samples were redissolved in toluene–MSTFA (99 + 1 v/v). Stock standard solutions of salbutamol, clenbuterol and quinine were prepared at concentrations of 4.22, 4.04 and 4.10 mg ml21, respectively.From these solutions a 153.75 mg ml21 quinine solution was prepared and for salbutamol and clenbuterol six working standard solutions were prepared by diluting 20, 10, 6.667, 5, 4 and 3.333 times. The theoretical mixture design is given in Table 1, and the concentrations in Table 2. A typical chromatogram is illustrated in Fig. 1. Mass spectra recorded on a Fisons (Loughborough, UK) MD800 mass spectrometer were obtained at a scan rate of 200 min21 for the datasets. The GC–MS conditions were the same as in previous studies.12 The region where clenbuterol and salbutamol elute was reduced to 18 datapoints in time.The spectra of pure salbutamol and clenbuterol are given in Figs. 2 and 3 for reference. Table 1 Mixture design for salbutamol and clenbuterol. The numbers 0.5, 1, etc., refer to relative concentrations Experiment No.* Salbutamol Clenbuterol 1 0.5 0.5 2(a) and (b) 1.0 1.0 3(a) and (b) 1.0 2.0 4(a) and (b) 1.0 3.0 5 1.5 1.5 6(a) and (b) 2.0 1.0 7(a) and (b) 2.0 2.0 8(a) and (b) 2.0 3.0 9 2.5 2.5 10(a) and (b) 3.0 1.0 11(a) and (b) 3.0 2.0 12(a) and (b) 3.0 3.0 * (a) and (b) represent replicates; 21 experiments were performed in total.Analyst, July 1997, Vol. 122 (631–638) 631Preprocessing, Selection of Significant Masses and Ratioing to Internal Standard Before performing any data analysis, it is important to preprocess the data to obtain useful information. The first step is to perform baseline correction. A baseline region which represents only noise can be selected visually or by plotting the logarithm of the sum of squares of the data.After the selection of noise regions, the mean intensity at each mass number is calculated, and these means are subtracted from the data to give a baseline corrected dataset. Owing to the variability of GC conditions, the compounds may not elute at exactly the same time for each run. Therefore, it is necessary to adjust the elution time for all the samples so that the salbutamol and clenbuterol peaks are centred at the same datapoint.After shifting the elution time the clusters of peaks for each chromatogram are aligned. The next step is to select a number of significant masses for calibration. Of the mass numbers between 100 and 400 only certain diagnostic masses are useful. The majority of masses are either not detected or represent noise. Previously we described a method for the selection of masses in an individual chromatogram, using the variance/mean ratio for each mass.In this study, however, there are 21 chromatograms, each of which results in different diagnostic masses. For each of the 21 chromatograms, the 50 most significant masses ranked by the variance/mean ratio over the cluster containing salbutamol and clenbuterol are computed, using the procedure described previously. Masses that are common to all 21 sets of significant masses are then selected, resulting in 20 significant masses, 10 of which primarily arise from salbutamol and 10 from clenbuterol.Using significantly fewer than 20 masses results in a distribution biased towards salbutamol, presumably because the spectrum of salbutamol dominates in intensity. The order of these masses is determined as follows. If kij is the rank of mass j in chromatogram i (with rank 1 being most significant), the total rank over all chromatograms is given by K k j ij i I = = å1 The smaller this number, the more significant is the mass.For the internal standard (quinine), the total peak area is an indication of the amount of quinine present; since an equal amount of quinine standard was introduced into each mixture, this number acts as an internal calibrant. The total integral over the quinine peak and all masses (not just the 20 significant masses) was determined and is given, for chromatogram i, by qi. Because this varies, the ratio dijn = zijn/qi, where zijn is the intensity at mass j over the salbutamol and clenbuterol cluster at time n in chromatogram i was calculated as an indicator of intensity as ratioed to an internal standard at each mass.Calibration was performed relative to z rather than the raw data in all cases. Univariate Calibration The simplest method of regression is univariate calibration,14 in which peak areas at selected masses are calibrated to concentrations. In order to carry out a univariate calibration, a single mass would be chosen which measures the response that corresponds to the concentration of a compound in a sample.The choice of Table 2 Injected amounts of salbutamol and clenbuterol Experiment Salbutamol/ Clenbuterol/ No.* ng ml21 ng ml21 1 52.75 50.5 2(a) and (b) 105.5 101 3(a) and (b) 105.5 202 4(a) and (b) 105.5 303 5 158.25 151.5 6(a) and (b) 211 101 7(a) and (b) 211 202 8(a) and (b) 211 303 9 263.75 252.5 10(a) and (b) 316.5 101 11(a) and (b) 316.5 202 12(a) and (b) 316.5 303 * (a) and (b) represent replicates; 21 experiments were performed in total.Fig. 1 A typical mixture chromatogram of (A) salbutamol and (B) clenbuterol. Fig. 2 Mass spectrum of pure salbutamol. Fig. 3 Mass spectrum of pure clenbuterol. 632 Analyst, July 1997, Vol. 122the mass is important and represents the compound with no interference from other masses that may be present. For mass j, the total peak area (ratioed to quinine) is given by xij: x d ij ijn n N N = = å1 2 Integrating over the region of salbutamol/clenbuterol gives a total area at mass j.A model of the form �yil = b0jl + b1jlxij where b0jl is an intercept term, b1jl is the slope, xij is the total integrated ratioed peak area at mass j, �yil is the predicted concentration of a standard l and i is the sample number, is then computed, using inverse regression,15 where the two terms are given by b x x y y x x b y b x jl ij j ij l i I ij i I jl l jl j 1 1 2 1 0 1 = - - - = - = = å å ( )( ) ( ) This approach assumes all errors are in the measurement of intensity by GC–MS, which is probably the main source of error in this study.The quality of calibration for compound l can then be determined using the root mean square error of prediction: R I y y l il il i I = - = å1 2 1 (� ) where yil is the known concentration of compound l for sample i. This error term is used for comparisons among significant masses and calibration models for compound l.PLS Calibration Notation In this paper three-way matrices are denoted by uppercase bold italic underlined characters, two-way matrices by uppercase bold italics, vectors by lowercase bold italics and scalars by normal italics. For three-way PLS, the raw data matrix D– – has dimensions I 3 J 3 N0 with I samples, J masses and N0 (N2 2 N1 + 1) points in time. The matrix D arises from this when unfolded, having dimensions I 3 JN0 as described below. For two-way PLS, the raw data matrix is X having dimensions I 3 J.Each column corresponds to the total integrated intensity between times N1 and N2 for each of the J masses. N1 and N2 were estimated as the elution times at the beginning and end of the peak cluster. No compounds are eluted before and after these times. Note that the two-way matrix X is different from the matrix D. PLS can be three-way or two-way, and to distinguish this a superscript w (2 or 3) is placed above the appropriate scores, loadings and error matrices, vectors and scalars.The left-hand side superscript l (1 or 2) refers to compound number. Concentration vectors are denoted by y with an appropriate left-hand side superscript. Further details are given in the Appendix. Unfolding There are many possible three-way calibration methods in the literature. An easy way of performing three-way calibration is to unfold the three-way data matrix into a two-way matrix.16–20 This is performed by concatenating the rows of a matrix to give a row vector.If the objects for one sample form a I 3 N matrix, it becomes a length IN row vector. The two-way matrix is established by performing the seration for all the samples. Fig. 4 shows the unfolding of a three-way data matrix D with I (21) rows and N0 3 J (360 = 18 3 20) columns. PLS is then used to calculate the matrices lT and lP for component l. The concentration vector ly is the same for both two- and three way PLS. Standardization In this paper we consider the influence of standardization on PLS predictions.Standardizing is a form of scaling. For twoway PLS this process is simple and involves the transformation s ij ij j ij j i I x x x x x I = - - - = å ( ) ( ) 2 1 1 For three-way PLS, the procedure is somewhat more complex than in the two-way case. The aim of standardization in this study is to ensure that all masses have equal influence over the calibration problem. The mass at m/z 369 is very intense and would dominate the analysis, so salbutamol would be predicted much better than clenbuterol in the absence of standardization.However, it is still important to retain the relative influence of readings between samples as per two-way data; if the data are standardized after unfolding, the variation in intensity in different times is lost; each time and mass is independently standardized. The aim of standardization should not be to weight each time equally but only to weight each mass equally. Therefore, the procedure involves standardizing the entire mass readings at all times over all samples prior to unfolding.Standardizing for three-way PLS analysis can be described as follows: d d IN d d d IN j ijn i I n N N s ijn ijn j i I n N N = = - = = = = å å å å 1 0 2 1 0 1 2 1 2 ( ) Note that this procedure is nevertheless different from that for two-way data, since there will be 378 ( = 18 3 21) datapoints arising from each mass, rather than only 21 datapoints.The scaled (standardized) samples are then unfolded. Note that the unfolded data will no longer be mean centred, which operation has to take place again after unfolding. Fig. 4 Unfolding a three-way data matrix into a two-way data matrix to prepare for the PLS analysis. Analyst, July 1997, Vol. 122 633Centring Mean centring the data is the second important operation for PLS calibration. For two-way PLS, it involves subtracting the column mean from each element: cxij = xij 2 �xj or c ij ijn n N N ijn i I n N N x d d IN = - = = = å åå 1 2 1 2 1 0 Note that for three-way data, the process of standardization as described above does not result in mean centring at each point in time.Mean centring can be carried out by unfolding the three-way matrix to a two-way, I3JN0, matrix, and then centre this matrix as in ordinary PLS. For three-way PLS, the data are mean centred as follows: cdijn = dijn 2 – djn PLS An application of two- and three-way PLS is presented using GC–MS data.The methods are well described in the literature. For two-way data, PLS is performed on the X matrix with dimension I 3 J so that X = lTBl PB+ lEB ly = luBl qB+ lfB where B denotes two-way scores and loadings. If there are K components lT, for example, will have I rows and K columns. The corresponding unfolded PLS estimates the following model: D = lTò lPò + lEò ly = luòl qò + lfò For two-way PLS, each mass has a corresponding loading for each component and each compound. The magnitude of these loadings can be presented graphically as a function of mass number.Although some loadings are negative, in order to be consistent with the result for three-way PLS, they are presented as absolute values. The interpretation of loadings for three-way data is more complex. PLS is performed on the unfolded data matrix. The resulting loadings are folded back to form a loadings matrix for each component. These loadings can be plotted as a function of time for each mass, i.e., graphs of lPòjn,m versus n for each j and m.Another way is to plot a graph of the root mean square loadings: l j m l jn m n N N N ¢¢¢ = ¢¢¢ = å P p , , 1 2 1 2 which shows how the loadings are influenced by mass number. These graphs can be compared with graphs for the corresponding two-way data. Cross Validation An important aspect is to evaluate how well the calibration model predicts unknown samples. Finding a minimum root mean square error can be used for this purpose.Cross validation is frequently used to determine the optimum number of principal components for multivariate calibration. 21,22 Increasing the number of PLS components will always result in a closer fit to the data. However, this does not imply that the later components are significant. There are several methods for testing the significance of each component, but most are based on cross validation. In this paper, we use the method of taking one sample out at a time.23 Each of the 21 samples is removed in turn and the two errors are calculated by v s s s m s i i g f y y f y y I s = - = - - ' å ( �) ( �) ( ) 2 2 1 where s is the sample removed, gs is the group of 20 samples excluding sample s, vf is the validation error and mf is the modelling error.Over all 21 samples, there will be 21 values of vf and mf, so the overall root mean square validation and modelling errors are given by v v s s I m m s s I F I f F I f = = = = å å 1 1 1 1 The prediction error, without cross validation, is given by f2 = fA f, where f is the vector of prediction errors for each sample.The cross validation error is likely to be considerably larger than the modelling error, which in turn is of the same approximate size as the prediction error. The prediction error will reduce according to the number of PLS components used but, if the data behave well, the validation error should decrease until the true number of components is found, and then increase, since the latter components are simply noise and so do not correctly model the validation samples.To perform cross validation correctly, it is necessary to centre and, where appropriate, scale the 20 samples separately each time, i.e., if standardization is required, this is performed 21 times. The transformation on the 20 samples is then repeated on the 21st. It is not correct to standardize and/or centre the entire dataset of 21 samples and then model the remaining 20 samples, as the components will be neither centred nor standardized.Results and Discussion Univariate Calibration The univariate calibration errors for the 20 selected masses are given in Table 3. In addition, a crude form of validation is performed by constructing a model using 20 samples and determining the prediction error on the 21st. This is repeated leaving one sample out each time. As can be seen from Table 3, the prediction, modelling and validation errors are comparable in size for this example.Interestingly, some masses result in substantial errors. For clenbuterol, all masses are relatively low in intensity compared with m/z 369 for salbutamol and so result in high errors. It would be hard to predict from first principles that m/z 166 results in a low error. Only four masses result in errors around 15 ng ml21. This suggests that using selective ion monitoring as a means of univariate calibration is risky and highly dependent on the chosen mass, and it would be hard to predict which mass is best 634 Analyst, July 1997, Vol. 122from first principles. For each component, the 10 masses are ranked in descending order of significance as suggested by the ranking criterion in the third section. For clenbuterol, it is clear that the more significant masses do not necessarily lead to better calibration predictions. PLS Predictions The two-way PLS errors for prediction, modelling and validation are given in Tables 4 and 5.A large number of conclusions may be drawn. The first relates to the number of significant PLS components in the model. Although the prediction error reduces dramatically in all cases, this does not imply that the later components are real. One criterion for significance is that the true number of components is reached when the validation error is a minimum. Extending the calculations to 10 components for clenbuterol suggests that this is reacheround four components (Table 6).However, a flat graph of validation errors often indicates that the safest result is at the beginning of the plateau, suggesting two components for the standardized data and four for the unstandardized data. The difference between the results for standardized and unstandardized data is striking, especially for clenbuterol. A reason is that the salbutamol peak at m/z 369 dominates the analysis so that the clenbuterol peaks are relatively minor in size, meaning a poor fit if only a few components are used.This is also reflected in the univariate calibration models since the less intense peaks are dominated by noise. Standardizing results in comparable predictions for both salbutamol and clenbuterol provided two components are used for salbutamol and four for clenbuterol as suggested by the validation errors. It is interesting that standardizing results in a worse model for salbutamol if only one PLS component is used.This is because m/z 369 is very intense and diagnostic, but if there is standardization this advantage is removed. Three-way PLS predictions of the unstandardized data (Tables 7 and 8) result in errors comparable in size for both salbutamol and clenbuterol. In some cases the models are actually slightly worse. This probably is because of the problems of exactly aligning data. Because there is an unpredictable offset when a chromatogram is run, the precise position of a peak will change relative to the beginning of acquisition for an intense peak.This change may be significant for two-way data; the intensities are simply summed for each mass, so this offset is irrelevant. When the data are standardized this problem apparently disappears, presumably because the intense tops of peaks have less influence on the model. The predictions for clenbuterol are now fairly good, even for one component.Loadings A great deal of information can come from the loadings plot. The easiest to interpret are the loadings plotted as a function of time using three way analysis. The loadings for the first two PLS components are given in Figs. 5 and 6. For the Table 3 Root mean square errors of univariate calibration (ng ml21). Prediction error refers to the error when the entire 21 samples are used; validation and modelling errors are the average errors when the data set is split into 1 test and 20 training samples Salbutamol Clenbuterol Mass Prediction Modelling Validation Mass Prediction Modelling Validation 369 14.51201 14.5034 15.2465 262 52.9003 52.3151 54.7844 370 15.9678 15.9253 16.7844 243 45.523 45.5224 46.6973 147 23.5113 20.5732 24.1903 264 42.2964 42.042 43.8859 207 13.8473 13.8339 14.5452 186 31.8329 28.9176 33.644 265 60.5821 60.5802 61.4897 173 26.4489 26.103 27.2311 133 28.4676 27.4523 29.2518 212 36.0138 35.4542 38.0682 294 24.1052 24.0685 24.6289 166 14.0452 13.1963 14.8421 281 24.8886 24.813 26.2671 188 34.3321 33.4795 35.831 220 20.2818 20.2816 21.2602 245 23.7456 21.4552 24.4513 177 51.3573 50.8283 52.6191 277 40.8727 40.2014 42.5105 Table 4 Root mean square error of two-way PLS calibration of salbutamol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 14.5 14.7907 15.5489 30.0977 29.218 34.3195 2 13.8364 14.1351 15.459 10.8668 10.705 12.454 3 12.6539 12.8975 15.0545 8.8071 8.4721 12.3484 4 10.3475 10.2772 14.7892 6.8891 6.5467 11.2131 Table 5 Root mean square error of two-way PLS calibration of clenbuterol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 65.8421 65.6303 69.8464 30.7642 30.7846 34.4136 2 29.2507 29.0469 31.1823 20.6712 20.9968 22.7378 3 22.6302 23.023 28.2061 13.2479 12.4302 22.1795 4 13.1725 13.2623 19.4711 11.8193 10.9652 19.1694 Analyst, July 1997, Vol. 122 635unstandardized data there is little difference for the first PLS component between salbutamol and clenbuterol, except a slightly larger maximum at fast elution time, reflecting the position of clenbuterol. This is presumably because the ion at m/z 369 dominates no matter which component is used for calibration. Even though m/z 369 is not well correlated with clenbuterol, it will, nevertheless, exhibit a small correlation because of the design as chromatograms 1, 5 and 9 are correlated for both components so there will be a slight correlation between salbutamol and clenbuterol concentrations which is picked up.The second component is necessary for a good model, particularly for clenbuterol, as can be seen from Tables 7 and 8. Here there is a dramatic difference, the earlier eluting salbutamol having a negative influence on clenbuterol calibration. The reverse is the case, but less strongly, for salbutamol. The standardized time-dependent loadings show a much more obvious trend, the maxima for both salbutamol and clenbuterol being in the correct place.The second loadings provide an appropriate negative balancing effect. These are in good agreement with the expectations from the prediction error. The influence of standardization is especially obvious from the first PLS component of Fig. 6. Note that the small correlation with the second compound is almost certainly a result of the design used, demonstrating the special importance of design when doing calibration experiments. This is likely to disappear if an orthogonal design is employed.The mass spectral loadings are harder to interpret primarily because they are displayed in the absolute value mode. Only the three-way spectral loadings are illustrated for sake of brevity (Figs. 7 and 8) but similar conclusions also come from two-way analysis. The root mean square loadings over all points in time are illustrated for this purpose.For example, the loadings for unstandardized salbutamol show maxima at peaks for salbuta- Table 6 Root mean square error of two-way PLS cross validation of clenbuterol for 10 PLS components (ng ml21) Component Unstandardized Standardized 1 69.8464 34.4136 2 31.1823 22.7378 3 28.2061 22.1795 4 19.4711 19.1694 5 22.1532 21.9661 6 23.258 22.7049 7 24.7529 24.1972 8 26.2817 26.6376 9 27.2957 27.1828 10 30.8872 28.1535 Fig. 5 Time-dependent loadings for the first two components of three-way PLS data for salbutamol. The top figures represent the unstandardized data and the bottom figures the standardized data.Table 7 Root mean square error of three-way PLS calibration of salbutamol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 15.3467 15.5379 21.7641 16.7973 15.7835 22.202 2 14.3254 14.5242 19.9991 14.0457 14.0227 20.3149 3 12.3116 12.1632 18.6847 10.9006 10.1287 18.8127 4 9.4362 9.5854 16.4184 7.414 7.0539 17.0949 Table 8 Root mean square error of three-way PLS calibration of clenbuterol (ng ml21) Unstandardized Standardized Component Prediction Modelling Validation Prediction Modelling Validation 1 57.4241 55.2667 65.7378 17.8093 17.7842 23.1488 2 25.6571 26.7913 31.1776 15.8925 15.9249 22.1179 3 17.7387 17.832 23.8823 9.7123 10.0147 21.119 4 11.9961 11.6328 22.3824 5.7637 5.6139 19.7164 Fig. 6 Time-dependent loadings for the first two components of three-way PLS data for clenbuterol.The top figures represent the unstandardized data and the bottom figures the standardized data. 636 Analyst, July 1997, Vol. 122mol in the first PLS component, being a good reconstruction of the salbutamol spectrum since the time-dependent loadings also suggest that the first component primarily picks up salbutamol. The second component is influenced more by clenbuterol, although in negative manner, so the loadings primarily relate to the clenbuterol spectrum with a more prominent maximum at m/z 262, although some salbutamol (m/z 369) still remains.Standardizing the data distorts the relative mass spectral intensities but the trends are still there. For example, the timedependent loadings for the first standardized component for clenbuterol and second for salbutamol are dominated by clenbuterol and the equivalent mass spectral loadings show low intensity at m/z 369 and 370 but relatively high intensities at m/z 262.Visually the loadings for the three-way first standardized PLS components of salbutamol and clenbuterol can be divided into two groups, those of value around 0.07 and 0.02. These are given in Table 9. Remarkably, the high value loadings all arise primarily from the calibrant and the low value loadings from the second component. There is a high degree of correspondence between the order of these loadings and the order of univariate calibration errors as given in Table 3. For example, the m/z 265 and 177 ions have the highest calibration errors for salbutamol and, therefore, appear intermediate between the salbutamol and clenbuterol group in clenbuterol (0.0542 and 0.0413). The m/z 166 and 245 ions have lowest univariate calibration errors for clenbuterol (and are the only two ions that could be employed to provide an estimate of clenbuterol concentration with a high degree of confidence in the univariate models) and both have the highest loadings.The results for salbutamol are slightly less clear, but the ion with the highest univariate calibration error (m/z 265) has, nevertheless, the lowest value of the loadings for the salbutamol first component.A graph of the time-dependent loadings for salbutamol explains this. The second component is not as well defined as it is for clenbuterol. Conclusions This paper has described two methods for PLS calibration of GC–MS data. The improvement in prediction error is small but significant over univariate calibration if PLS is properly performed.However, the major advantage of PLS is that 20 masses can be used, and the prediction error is better than the best single mass. The difficulty with single ion approaches is that a correct choice of mass must be made. For at least one of the components, it is not clear, from first principles, which mass is most suitable, so selective ion monitoring risks poor results unless great care is taken to select a range of ions, some of which may not be obvious to the mass spectrometrists at first glance. Three-way PLS does not have major advantages over twoway methods as far as prediction errors are concerned.One problem is correctly aligning chromatograms. If digital resolution is not very high (typically a peak is defined by around 10 datapoints in GC–MS), small shifts in detector offsets can result in difficulties exactly aligning chromatograms, so introducing extra errors into the calibration24 which counterbalance the advantages of using the extra dimension. However, three-way analysis does result in more diagnostic information such as time-dependent loadings and, certainly for more complex problems of three or four components eluting at slightly different times, will reveal much more than two-way procedures.The absolute importance of data scaling such as standardizing and mean centring at the correct step in the procedure has been discussed. In this paper, we have only reported meaningful results.Incorrectly applying data preprocessing methods results in meaningless output, so the user of such approaches must take great care. We thank Dr. F. Burden for helpful discussions relating to cross validation and P. Hindmarch for writing the program for Fig. 7 Spectral loadings of three-way PLS data for salbutamol. The top figures represent the unstandardized data and the bottom figures the standardized data. Fig. 8 Spectral loadings of three-way PLS data for clenbuterol.The top figures represent the unstandardized data and the bottom figures the standardized data. Table 9 Root mean square loadings of the first standardized three-way PLS component of salbutamol and clenbuterol and their assignments (C and S) Corre- Corresponding sponding Salbutamol m/z compound Clenbuterol m/z compound 0.0769 133 S 0.0713 245 C 0.0740 207 S 0.0713 166 C 0.0739 220 S 0.0705 277 C 0.0719 147 S 0.0705 186 C 0.0713 177 S 0.0702 243 C 0.0695 281 S 0.0700 264 C 0.0694 369 S 0.0661 173 C 0.0692 370 S 0.0649 262 C 0.0658 294 S 0.0640 212 C 0.0626 265 S 0.0635 188 C 0.0341 186 C 0.0542 265 S 0.0270 188 C 0.0413 177 S 0.0266 262 C 0.0278 220 S 0.0257 173 C 0.0274 133 S 0.0232 277 C 0.0247 281 S 0.0224 212 C 0.0235 207 S 0.0224 166 C 0.0206 370 S 0.0196 243 C 0.0201 369 S 0.0176 264 C 0.0198 294 S 0.0165 245 C 0.0190 147 S Analyst, July 1997, Vol. 122 637decoding GC–MS data. We are grateful for support from Uludag University (Bursa, Turkey).Appendix List of Notations Used D–– Three-way GC–MS data matrix D Unfolded GC–MS data matrix X Two-way GC–MS data matrix i Sample number I Total number of samples j Mass number l Compound number Kj Total rank over all chromatograms kij Rank of mass j qi Quinine peak area for sample i summed over time and all masses zijn Intensity for mass j, sample i and time n dijn Peak area ratio for mass j, sample i and time n n Time N1 Point in time at the beginning of a cluster of peaks N2 Point in time at the end of a cluster of peaks xij Peak area ratio for mass j and sample i summed over all time sxij Standardized data matrix for two-way PLS cxij Mean centred data matrix for two-way PLS sdijn Standardised data matrix for three-way PLS cdijn Mean centred data matrix for three-way PLS �yil Predicted concentration yil Concentration of compound l �yl Mean concentration of compound l �xj Mean peak area ratio of mass j summed over time bojl Intercept of univariate calibration line b1jl Slope of univariate calibration line Rl Root mean square error of compound l ly Concentration vector for compound l lTw PLS scores matrix for compound l ltw m PLS scores vector for compound l ltw im PLS scores for sample i, component m and compound l lPw PLS loadings matrix for compound l lpw m PLS loadings vector for component m and compound l w Order of PLS (2 or 3) lpw mj Loadings for mass j for two-way PLS lpw mjn Loadings for mass j and time n for three-way PLS lPw mj Sum of loadings for mass j over all time for threeway PLS m Component number M Total number of components N0 Number of data points in time over significant peaks (N2 2 N1 + 1) lEB Error matrix of X for two-way PLS and compound l lEAAA Error matrix of D for three-way PLS and compound l lfB Error vector of y for two-way PLS and compound l s Removed sample vf Validation error mf Modelling error gs Group of samples excluding sample s vF Root mean square validation error mF Root mean square modelling error References 1 Boqu�e, R., and Rius, F. X., Chemom. Intell. Lab. Syst., 1996, 32, 11. 2 Practical Mass Spectrometry, ed. Middleditch, B. S., Plenum Press, New York, 1979. 3 Millard, B. J., Quantitative Mass Spectrometry, Heyden, London, 1978. 4 Cirovic, D. A., Brereton, R. G., Walsh, P. T., Ellwood, J. A., and Scobbie, E., Analyst, 1996, 121, 575. 5 H�oskuldsson, A., J. Chemom., 1988, 2, 211. 6 Wold, S., Geladi, P., Esbensen, K., and Ohman, J., J. Chemom., 1987, 1, 41. 7 Kowalski, B. R., and Seasholtz, M. B., J. Chemom., 1991, 5, 129. 8 Martens, H., and Naes, T., Multivariate Calibration, Wiley, New York, 1989. 9 Sanchez, E., and Kowalski, B. R., J. Chemom., 1988, 2, 247. 10 Sanchez, E., and Kowalski, B. R., J. Chemom., 1988, 2, 265. 11 Demir, C., Hindmarch, P., and Brereton, R. G., Analyst, 1996, 121, 1443. 12 Hindmarch, P., Demir, C., and Brereton, R. G., Analyst, 1996, 121, 993. 13 Smilde, A. K., Chemom. Intell. Lab. Syst., 1992, 15, 143. 14 Booksh, K. S., and Kowalski, B. R., Anal. Chem., 1994, 66, 782A. 15 Araujo, P. W., Cirovic, D. A., and Brereton, R. G., Analyst, 1996, 121, 581. 16 Henrion, R., Chemom. Intell. Lab. Syst., 1994, 25, 1. 17 Ståhle, L., Chemom. Intell. Lab. Syst., 1989, 7, 95. 18 Smilde, A. K., and Doornbos, D. A., J. Chemom., 1991, 5, 345. 19 Bro, R., J. Chemom., 1996, 10, 47. 20 Geladi, P., Chemom. Intell. Lab. Syst., 1989, 7, 11. 21 Zhang, P., and Littlejohn, D., Chemom. Intell. Lab. Syst., 1996, 34, 203. 22 Sharaf, M., Illman, D. L., and Kowalski, B. R., Chemometrics, Wiley, New York, 1986. 23 Gemperline, P. J., J. Chemom., 1989, 3, 549. 24 Cirovic, D. A., Jacobsen, R. M., and Brereton, R. G., Anal. Commun., 1996, 33, 231. Paper 6/08245I Received December 6, 1996 Accepted March 10, 1997 638 Analyst, July 1997

ISSN:0003-2654    

DOI:10.1039/a608245i

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Simultaneous Spectrophotometric Determination of Calcium and Magnesium in Mineral Waters by Means of Multivariate Partial Least-squares Regression F. Blascoa, M. J. Medina-Hern�andeza, S. Sagrado*a and F. M. Fern�andezb a Departamento de Qu�ýmica Anal�ýtica, Facultad de Farmacia, Universidad de Valencia, C/Vicente Andr�es Estell�es s/n, 46100 Burjassot, Valencia, Spain b Laboratorio de An�alisis de Trazas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina A method for simultaneous spectrophotometric determination of calcium and magnesium in mineral waters using multivariate calibration methods is proposed.The method is based on the development of the reaction between the analytes and Methylthymol Blue at pH 11. Two operational modes were used: static (spectral information) and flow injection (FI) (spectral and kinetic information). The selection of variables was studied. A series of synthetic solutions containing different concentrations of calcium and magnesium were used to check the prediction ability of the partial least-squares models.The method was applied to the analysis of mineral waters and the results were compared with those obtained by complexometry. No significant differences at the 95% confidence level were found. The proposed method is simple, accurate and reproducible, and it could be easily adapted as a portable (static mode) or automatic (FI) method. Keywords: Partial least-squares regression; multicomponent analysis; calcium; magnesium; flow injection; mineral waters Calcium and magnesium are two of the most commonly determined cations in drinking waters.From a physiological point of view, calcium and magnesium, along with sodium and potassium, are the most important ions affecting cardiology, owing to their role in nervous impulse conduction and cell contraction. From an industrial point of view, the main problem is related to the formation of deposits of their carbonates.The traditional method in quality control of calcium and magnesium in water and waste water is complexometry using EDTA as titrant.1 Although this is an inexpensive method, it requires some skill. The main disadvantage of complexometric methods is that they are time consuming and subject to operational errors. Several instrumental approaches, including FAAS and ICPAES, 1 have been proposed for determining these analytes individually in water.Adaptations of highly selective techniques to a continuous-flow scheme, e.g., FAAS2 and potentiometry using ion-selective electrodes,3,4 make it easier to automate the analysis. UV/VIS spectrophotometric methods have the advantage of simplicity, speed and low cost. Some UV/VIS methods have been reported that use different chromogenic reagents in flow schemes.5–12 The main drawback of UV/VIS spectrophotometry is its poor selectivity. In some cases, a change in the pH allows the determination of both analytes in a sequential way.5–6 In other cases, multivariate analysis of data permits the treatment of the non-specific data obtained with UV/VIS detectors.This strategy allows the simultaneous determination of calcium and magnesium and avoids the previous separation required, for instance, using multiple linear regression (MLR).729 G�omez et al.9 used 4-(2-pyridylazo)resorcinol (PAR) as a chromogenic reagent in a sequential injection (SI) analysis.However, this reagent presents a too high molar absorptivity in relation to that of the CaII and MgII complexes in the working wavelength range, and it offers a narrow spectral window from a multivariate perspective. In addition, some disadvantages of the MLR method have been reported,13 mainly related to collinearity problems in the signal matrix. These problems are frequent in spectrophotometric analysis, i.e., the near linear relationships between absorbances at adjacent frequencies.Recently, soft algorithms such as partial least squares (PLS), which avoids the collinearity problems, have been used for simultaneous determination of the analytes. Novikov and Shpigun10 used the difference in the analyte signal profiles at one wavelength in a flow injection (FI) system based on the reaction of calcium and magnesium with Chlorophosphonazo III. Ruis�anchez et al.11 used an SI system to form the derivative between the analytes and Arsenazo III and to carry it to the flow cell.In the latter case, spectral information was used for the PLS model construction, and commercial samples (mineral waters) were used as a calibration set to include the interference effects in the calibration process. However, a limited predictive ability of the model performance was reported (85% of the MgII concentration variance and 66.3% of the CaII concentration variance). In this paper, a method for the simultaneous spectrophotometric determination of calcium and magnesium in mineral waters using multivariate calibration methods is proposed.The method is based on the reaction between the analytes and Methylthymol Blue (MTB) at pH 11. The quality of the information obtained using static (spectral) or FI (spectral/ kinetic) strategies was compared by principal component analysis (PCA) and PLS models. The selection of the variables to be used in the model was examined. The models were evaluated by data structure in the latent variables space and the prediction capability in terms of the percentage of crossvalidated explained variance.The optimized method was applied to the analysis of mineral waters and the results were compared with those obtained by complexometry. A comparison between the reproducibility of the proposed method, the complexometric method and an ICP-AES method was performed. This study is a preliminary step for further applications to the routine determination of CaII and MgII in water samples.Experimental Reagents and Standards Individual stock solutions of CaII and MgII containing 0.1 g l21 of each metal were made by dissolving the appropriate amounts of CaCO3 and MgNO3, respectively. The reagent solution was 1 3 1024 m in MTB and 1 3 1022 m in NH4 +–NH3 buffer (pH 11). All chemicals were of analytical-reagent grade. E-pure de- Analyst, July 1997, Vol. 122 (639–643) 639ionized water (Barnstead Sybron, IA, USA) was used throughout to prepare the solutions.Apparatus and Manifold The spectra were obtained with a Model 8452A diode-array spectrophotometer (Hewlett-Packard, Palo Alto, CA, USA) connected to a Vectra (ES/12) computer via an HPIB protocol (Hewlett-Packard). The FI assembly was built using a peristaltic pump (Minipuls 2, Gilson, Middleton, WI, USA), an injection valve (Model 5020, Rheodyne, Cotati, CA, USA), an 18 ml flow cell (Model 178012-QS, Hellma, M�ulheim/Baden, Germany) and 0.5 mm id PTFE tubes.A monochannel manifold was used. To produce extensive mixing between the sample and the reagent, a Tygon tube (38 cm 3 3 mm id) was used as a reactor, prior to detection. Other FI conditions were flow rate 2.5 ml min21 and sample volume 100 ml. Data processing was performed with a 100 MHz Pentium personal computer. Procedure Calibration sets Two calibration sets were used. In one case, the calibration set consisted of 14 solutions containing various amounts of each metal in the range of concentrations between 10 and100 mg l21 of CaII and 0 and 40 mg l21 of MgII (see Fig. 1).These solutions were obtained by appropiate dilution of stock standard solutions. In the other case, the calibration set was obtained from eight commercial waters and ten binary or ternary mixtures of these samples. The calcium and magnesium contents of the solutions were checked by complexometry with EDTA and these data were used as reference values. In each case, the concentration data were used as the Y-block (concentration matrix).Operational modes and data acquisition Samples or synthetic standards were assayed in two operational modes. In one (static mode), 100 ml of the solutions were mixed with 10 ml of the indicator solution and the absorbance values of each mixture were measured between 300 and 800 nm at 2 nm intervals. In the second mode (FI mode), 100 ml of the solutions were injected into the indi as the carrier reagent stream, and the absorbance values of the sample– reagent bolus were measured between 300 and 800 nm at 2 nm intervals, from 20 to 150 s after injection at 2 s intervals.Software and Data Processing The incorporated software of the HP Vectra ES/12 computer (HP 89531A) was used to select the data acquisition conditions and to produce files in ASCII code. Multivariate calibration was performed using a PLS2 algorithm written in our laboratory in QBASIC 4.5.Linear regression analysis was performed using STATGRAPHICS 7.0. All data were column centred prior to the application of the PLS algorithm. The percentage of explained variance in cross-validation (%EVCV) was used as a measure of the quality of the model. The cross-validation process was the ‘full validation’ strategy14 using four deletion groups. Results and Discussion Selection of the Method The experimental design was conditioned by the intended future application of the method to the routine quality control of diverse samples of water.Different aspects of the problem were therefore considered. First, the method has to be flexible, i.e., easily adaptable as a portable or automatic method.Therefore, two operational modes were chosen: static and FI modes. The former makes use of spectral information and could be adapted as a portable test. The FI mode permits easy automation of the method and may increase its selectivity by incorporating unique kinetic information.The SI methodology previously reported 9,11 presents aspects common to the static and FI methodologies, but it does not present their advantages. Second, the method has to make it possible to perform the analysis on the sample without previous manipulation and must be able to determine CaII and MgII in the range of concentrations found in mineral commercial waters. Figure 1 shows the calcium and magnesium concentration distributions of the samples (in capital letters).A similar experimental design of synthetic standards (numbers in Fig. 1) was adopted to optimize the method. Another aspect studied was the selection of the chromogenic reagent. MTB was tested for the simultaneous determination of CaII and MgII in order to overcome the limitations of other reagents used previously, e.g., PAR9 and Arsenazo III.11 The complexes of CaII and MgII with MTB presented, at pH 11, a high molar absorptivity compared with that of the reagent.Fig. 2 shows the spectra of the MTB complexes corresponding to Fig. 1 Calcium and magnesium concentrations in mineral waters (capital letters) and their mixtures (lower case letters) and experimental design of synthetic standards (numbers). Fig. 2 UV/VIS spectra of some synthetic standard solutions corresponding to the calibration set obtained by the static mode. +, Standard number 1; 8, standard number 10; 2, standard number 8; and ½, standard number 14. 640 Analyst, July 1997, Vol. 122four synthetic standards (points 1, 8, 10 and 14 in Fig. 1). The spectral changes indicate the existence of two relevant zones (I and II in Fig. 2) and reveal severe spectral overlapping. On the other hand, when the FI mode is used, the signal matrix corresponding to each solution is formed by the absorbance values obtained as a function of the wavelength and the time from injection. The information on the kinetic profiles was considered. Table 1 shows the different situations studied throughout the optimization process using the static mode (models S1–S3) and the FI mode (models F1–F4).Exploratory Data Analysis Prior to the study of the PLS models, an exploratory data analysis of the signal matrix (X-block) was carried out. In order to compare the influence of the static and FI modes on the quality of the spectral data, PCA was applied to the data corresponding to the models S1 and F1 (Table 1). In both cases, 50 spectral variables were used.In model F1, the spectrum at 42 s (time corresponding to the FI peak maxima) was used. Fig. 3 shows the PCA score plots. The samples (not used in the PCA model construction) were also included in the plots. In both the S1 and F1 PCA models, the first principal component may relate to the total CaII and MgII concentration in the solutions. The second principal component may relate to the relative content of calcium (objects 1, 4, 7, 10 and 13) and magnesium (objects 2, 5, 8 and 14) in the solutions.In general, both plots reproduce well the experimental design shown in Fig. 1. However, sample h (prepared by mixing samples R, L and V) appears as an outlier in Fig. 3(a) but not in Fig. 3(b). This reflects an error due to the manipulation of this sample using the static mode. On the other hand, solutions with high CaII and MgII concentrations [points 11–14 in Fig. 3(b)] show similar score values on the first principal component. This could indicate non-linearities between the signal obtained in flow conditions and the analyte concentration, thereby suggesting a lack of reagent in the central region of the sample bolus.Fig. 4 shows the correspondence factor analysis (CFA) plot corresponding to the model S1. This plot reveals the relationships between the objects and the original variables (wavelengths). As can be observed, the objects with a high CaII content, i.e., points 4, 7, 10 and 13, are related to the wavelength ranges 400–442 and 616–700 nm (variables 1–8 and 37–50 in Fig. 4). In contrast, the objects with a high MgII content, i.e., 2, 5, 8 and 14, are related to the wavelength range 466–598 nm (variables 12–34 in Fig. 4). Analysis of PLS Models In the previous section, the quality of the data obtained from the static and FI modes, models S1 and F1, respectively, was discussed. Now the usefulness of this information in predicting CaII and MgII concentrations is considered. For this purpose, the concentration values of the 14 synthetic standards were used as the Y-block in combination with the X-block data to construct the PLS models. Table 1 shows the %EVCV for all the models studied.The necessity for wavelength selection in ill-conditioned situations has recently been proposed.15 In order to select the relevant spectral information, two different strategies were used: (a) The plot (not shown) of the B coefficients corresponding to the equation Y = XB + E, for each analyte, versus the original wavelengths16 and (b) the genetic algorithm methodology, 14 in which the frequency of appearance of each variable versus the original variables was plotted (not shown).Large absolute B values and large frequency values, respectively, reveal the importance of the original spectral variables in predicting the analyte concentrations. In both cases, two main conclusions were obtained: first, that zone II of the spectra in Fig. 2 is more important than zone I, and second, that the wavelengths preceding the absorption maximum (606–610 nm) are related to the MgII concentration, while the subsequent wavelengths are related to the CaII concentration. These conclusions agree with those derived from Figure 4.In model S2, 50 wavelengths in the spectral zone II were used. The %EVCV values obtained using this model were larger than those obtained with model S1 (see Table 1). In order to observe the influence of data reduction in zone II, six wavelengths were selected to built model S3.The results using this model were similar to those obtained with model S2, which suggests that a reduction in the number of wavelengths in this spectral zone does not imply a loss of the model prediction ability. This conclusion encourages the use of the time profiles at a small number of wavelengths, in order to improve the %EVCV for the analytes. In models F2 and F3, full kinetic information at one discrete wavelength was used. At 634 nm (model F2), the CaII concentration is well explained, while the MgII concentration is poorly described.In contrast, at 562 nm (model F3), the prediction for MgII increased. The modelling power17 of the time variables was calculated for models F2 and F3. The plot Table 1 Features of the models studied during optimization and explained variance in cross-validation by PLS models. The number of latent variables (LVs) corresponds to the first local %EVCV maximum. X-block %EVCV (LVs) Analysis Spectral Wavelength/ Model mode zone nm Time/s Calcium Magnesium S1 Static I + II 400–694 — 93.2 (2) 96.3 (4) D = 6 S2 Static II 560–660 — 97.3 (2) 98.4 (4) D = 2 S3 Static II 580–630 — 96.2 (2) 98.6 (3) D = 10 F1 FI I + II 400–694 42 84.7 (1) 92.3 (3) D = 6 F2 FI II 634 34–150 93.2 (1) 73.3 (3) D = 2 F3 FI II 562 34–150 77.5 (1) 87.1 (2) D = 2 F4 FI II 526–670 48–98 98.8 (3) 99.6 (3) D = 18 D = 2 Analyst, July 1997, Vol. 122 641(not shown) of modelling power versus time revealed a decrease in the values corresponding to the peak maximum (42 s).This confirms the non-linearities suggested by Fig. 3(b). The maximum modelling power was obtained in the range 48–98 s. The above results suggest that an adequate combination of spectral and kinetic information may improve the ability of the PLS model to make predictions from the FI data. Model F4 was constructed with a 9 3 26 data matrix, as indicated in Table 1.A significant improvement in the %EVCV values with respect to the previous models studied was obtained. Analysis of Mineral Waters The best validation of a predictive model is its use in the prediction of reference samples. The CaII and MgII contents of 18 mineral waters (original and mixtures) were predicted by means of the PLS models S2 and F4, and the results were compared with the complexometric reference values. Fig. 5 shows the results for model F4. The predictions obtained with model F4 were better than those obtained with model S2.In addition, as expected from the PCA score plot [Fig. 3(a)], sample h was incorrectly predicted with model S2. Table 2 gives linear regression statistics for the prediction results. For models S2 and F4 an intercept significantly equal to zero and a slope significantly equal to unity were achieved (95% confidence level). However, model F4 is more reliable (smaller confidence intervals and larger r and F ratio values) than model S2.Fig. 3 PCA analysis corresponding to the models: (a) S1 and (b) F1 (see Table 1 for details). Fig. 4 CFA analysis corresponding to model S1. Fig. 5 Predicted concentrations using model F4 versus the reference values: (top, calcium; and bottom, magnesium). Table 2 Regression statistics for predicted versus declared CaII and MgII values Slope ± Intercept ± Analyte Model CI* CI r† F-ratio‡ CaII S2§ 0.88 ± 0.17 4 ± 9 0.94 117 F4 1.00 ± 0.10 0.73 ± 5 0.98 491 MGII S2§ 1.04 ± 0.12 20.4 ± 1.7 0.98 365 F4 1.08 ± 0.1 21.5 ± 1.5 0.99 503 * Confidence interval (95% confidence level).† Correlation coefficient. ‡ Variance modelled by regression to residual variance ratio. § Sample h was excluded from the regression. 642 Analyst, July 1997, Vol. 122In order to compare the reproducibility of the proposed method (PLS model F4) with that obtained by complexometric and ICP methods, seven independent analyses of sample C were performed by the three methods.The RSDs found with the proposed method were 2.6 and 1.6% for CaII and MgII, respectively, and were statistically comparable (95% confidence level) to those obtained by complexometry (1.3 and 2.3%) or ICP (1.4 and 1.5%). Finally, the samples were used instead of the synthetic standards as the calibration set under the same conditions as in models S2 and F4. The %EVCV (and latent variables) values obtained for CaII and MgII were 81.8(3) and 92.3(2) using the static mode and 95.1(3) and 96.1(4) using the FI mode.In both operational modes, the use of real samples led to lower %EVCV values than those obtained using synthetic standards. This suggests the presence of interference effects in samples, and therefore a reduction in the prediction ability is obtained. On the other hand, the %EVCV values found with the FI mode are adequate for predicting future samples. The results of this preliminary study allow us to extrapolate some conclusions relevant to the use of this method in routine analysis in the future.MTB seems to be an adequate chromogenic reagent for the simultaneous determination of CaII and MgII by spectrophotometry in combination with multivariate calibration techniques, such as PLS. FI measurements seem to provide more reliable results than those obtained by means of the static operational mode. However, the results of the static mode may permit its use as a rapid portable test.The use of real samples (i.e., reference samples) is recommended for obtaining more robust and reliable models, but synthetic standards also seem to be useful and could be employed when no reference concentration values for samples are available. F. M. Fern�andez thanks the Instituto de Cooperaci�on Iberoamericana for a grant that made possible his collaboration in these studies. The authors express their gratitude to E. Bonet (Gamaser S. A., Valencia, Spain) for his help with the ICP measurements.References 1 Franson, M. A. H., Standard Methods for the Examination of Water and Wastewater, American Public Health Association and Water Polution Control Federation, Washington, DC, 18th edn., 1992. 2 Basson, W. P., and Van Staden, J. F., Fresenius’ Z. Anal. Chem., 1980, 302, 370. 3 Wada, H., Ozawa, T., Nakagawa, G., Asano, Y., and Ito, S., Anal. Chim. Acta, 1988, 211, 213. 4 Foster, R. J., and Diamond, D., Anal. Chem., 1992, 64, 1721. 5 Yuan, Y., Anal.Chim. Acta, 1988, 212, 291. 6 Ca�nete, F., R�ýos, A., Luque de Castro, M. D., and Valc�arcel, M., Analyst, 1987, 112, 262. 7 Blanco, M., Coello, J., Gen�e, J., Iturriaga, H., and Maspoch, S., Anal. Chim. Acta, 1989, 224, 23. 8 G�omez, E., Estela, J. M., and Cerd�a, V., Anal. Chim. Acta, 1991, 249, 513. 9 G�omez, E., Tom�as, C., Cladera, A., Estela, J. M., and Cerd�a, V., Analyst, 1995, 120, 1181. 10 Novikov, E. A., and Shpigun, L. K., Zh. Anal. Khim., 1993, 48, 1326. 11 Ruis�anchez, I., Rius, A., Larrechi, M.S., Callao, M. P. and Rius, F. X., Chemom. Intell. Lab. Syst., 1994, 24, 55. 12 Rius, A., Callao, M. P., and Rius, F. X., Anal. Chim. Acta, 1995, 316, 27. 13 Haaland, D. M., and Thomas, E. V., Anal. Chem., 1988, 60, 1193. 14 Leardi, R., J. Chemom., 1994, 8, 65. 15 Xu, L., and Schechter, I., Anal. Chem. 1996, 68, 2392. 16 Garrido Frenich, A., Jouan-Rimbaud, D., Massart, D. L., Kuttatharmmakul, S., Martinez Galera, M., and Martinez Vidal, J. L., Analyst, 1995, 120, 2787. 17 Cela, R., Avances en Quimiometria Pr�actica, Universidad de Santiago de Compostela, Santiago de Compostela, 1994. Paper 6/08244K Received December 6, 1996 Accepted April 10, 1997 Analyst, July 1997, Vol. 122 643 Simultaneous Spectrophotometric Determination of Calcium and Magnesium in Mineral Waters by Means of Multivariate Partial Least-squares Regression F. Blascoa, M. J. Medina-Hern�andeza, S. Sagrado*a and F. M. Fern�andezb a Departamento de Qu�ýmica Anal�ýtica, Facultad de Farmacia, Universidad de Valencia, C/Vicente Andr�es Estell�es s/n, 46100 Burjassot, Valencia, Spain b Laboratorio de An�alisis de Trazas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina A method for simultaneous spectrophotometric determination of calcium and magnesium in mineral waters using multivariate calibration methods is proposed.The method is based on the development of the reaction between the analytes and Methylthymol Blue at pH 11.Two operational modes were used: static (spectral information) and flow injection (FI) (spectral and kinetic information). The selection of variables was studied. A series of synthetic solutions containing different concentrations of calcium and magnesium were used to check the prediction ability of the partial least-squares models. The method was applied to the analysis of mineral waters and the results were compared with those obtained by complexometry. No significant differences at the 95% confidence level were found.The proposed method is simple, accurate and reproducible, and it could be easily adapted as a portable (static moPartial least-squares regression; multicomponent analysis; calcium; magnesium; flow injection; mineral waters Calcium and magnesium are two of the most commonly determined cations in drinking waters. From a physiological point of view, calcium and magnesium, along with sodium and potassium, are the most important ions affecting cardiology, owing to their role in nervous impulse conduction and cell contraction. From an industrial point of view, the main problem is related to the formation of deposits of their carbonates.The traditional method in quality control of calcium and magnesium in water and waste water is complexometry using EDTA as titrant.1 Although this is an inexpensive method, it requires some skill.The main disadvantage of complexometric methods is that they are time consuming and subject to operational errors. Several instrumental approaches, including FAAS and ICPAES, 1 have been proposed for determining these analytes individually in water. Adaptations of highly selective techniques to a continuous-flow scheme, e.g., FAAS2 and potentiometry using ion-selective electrodes,3,4 make it easier to automate the analysis. UV/VIS spectrophotometric methods have the advantage of simplicity, speed and low cost.Some UV/VIS methods have been reported that use different chromogenic reagents in flow schemes.5–12 The main drawback of UV/VIS spectrophotometry is its poor selectivity. In some cases, a change in the pH allows the determination of both analytes in a sequential way.5–6 In other cases, multivariate analysis of data permits the treatment of the non-specific data obtained with UV/VIS detectors. This strategy allows the simultaneous determination of calcium and magnesium and avoids the previous separation required, for instance, using multiple linear regression (MLR).729 G�omez et al.9 used 4-(2-pyridylazo)resorcinol (PAR) as a chromogenic reagent in a sequential injection (SI) analysis.However, this reagent presents a too high molar absorptivity in relation to that of the CaII and MgII complexes in the working wavelength range, and it offers a narrow spectral window from a multivariate perspective.In addition, some disadvantages of the MLR method have been reported,13 mainly related to collinearity problems in the signal matrix. These problems are frequent in spectrophotometric analysis, i.e., the near linear relationships between absorbances at adjacent frequencies. Recently, soft algorithms such as partial least squares (PLS), which avoids the collinearity problems, have been used for simultaneous determination of the analytes. Novikov and Shpigun10 used the difference in the analyte signal profiles at one wavelength in a flow injection (FI) system based on the reaction of calcium and magnesium with Chlorophosphonazo III.Ruis�anchez et al.11 used an SI system to form the derivative between the analytes and Arsenazo III and to carry it to the flow cell. In the latter case, spectral information was used for the PLS model construction, and commercial samples (mineral waters) were used as a calibration set to include the interference effects in the calibration process. However, a limited predictive ability of the model performance was reported (85% of the MgII concentration variance and 66.3% of the CaII concentration variance).In this paper, a method for the simultaneous spectrophotometric determination of calcium and magnesium in mineral waters using multivariate calibration methods is proposed. The method is based on the reaction between the analytes and Methylthymol Blue (MTB) at pH 11. The quality of the information obtained using static (spectral) or FI (spectral/ kinetic) strategies was compared by principal component analysis (PCA) and PLS models.The selection of the variables to be used in the model was examined. The models were evaluated by data structure in the latent variables space and the prediction capability in terms of the percentage of crossvalidated explained variance. The optimized method was applied to the analysis of mineral waters and the results were compared with those obtained by complexometry.A comparison between the reproducibility of the proposed method, the complexometric method and an ICP-AES method was performed. This study is a preliminary step for further applications to the routine determination of CaII and MgII in water samples. Experimental Reagents and Standards Individual stock solutions of CaII and MgII containing 0.1 g l21 of each metal were made by dissolving the appropriate amounts of CaCO3 and MgNO3, respectively.The reagent solution was 1 3 1024 m in MTB and 1 3 1022 m in NH4 +–NH3 buffer (pH 11). All chemicals were of analytical-reagent grade. E-pure de- Analyst, July 1997, Vol. 122 (639–643) 639ionized water (Barnstead Sybron, IA, USA) was used throughout to prepare the solutions. Apparatus and Manifold The spectra were obtained with a Model 8452A diode-array spectrophotometer (Hewlett-Packard, Palo Alto, CA, USA) connected to a Vectra (ES/12) computer via an HPIB protocol (Hewlett-Packard).The FI assembly was built using a peristaltic pump (Minipuls 2, Gilson, Middleton, WI, USA), an injection valve (Model 5020, Rheodyne, Cotati, CA, USA), an 18 ml flow cell (Model 178012-QS, Hellma, M�ulheim/Baden, Germany) and 0.5 mm id PTFE tubes. A monochannel manifold was used. To produce extensive mixing between the sample and the reagent, a Tygon tube (38 cm 3 3 mm id) was used as a reactor, prior to detection. Other FI conditions were flow rate 2.5 ml min21 and sample volume 100 ml. Data processing was performed with a 100 MHz Pentium personal computer.Procedure Calibration sets Two calibration sets were used. In one case, the calibration set consisted of 14 solutions containing various amounts of each metal in the range of concentrations between 10 and100 mg l21 of CaII and 0 and 40 mg l21 of MgII (see Fig. 1). These solutions were obtained by appropiate dilution of stock standard solutions. In the other case, the calibration set was obtained from eight commercial waters and ten binary or ternary mixtures of these samples. The calcium and magnesium contents of the solutions were checked by complexometry with EDTA and these data were used as reference values.In each case, the concentration data were used as the Y-block (concentration matrix). Operational modes and data acquisition Samples or synthetic standards were assayed in two operational modes. In one (static mode), 100 ml of the solutions were mixed with 10 ml of the indicator solution and the absorbance values of each mixture were measured between 300 and 800 nm at 2 nm intervals.In the second mode (FI mode), 100 ml of the solutions were injected into the indicator solution, used as the carrier reagent stream, and the absorbance values of the sample– reagent bolus were measured between 300 and 800 nm at 2 nm intervals, from 20 to 150 s after injection at 2 s intervals. Software and Data Processing The incorporated software of the HP Vectra ES/12 computer (HP 89531A) was used to select the data acquisition conditions and to produce files in ASCII code.Multivariate calibration was performed using a PLS2 algorithm written in our laboratory in QBASIC 4.5. Linear regression analysis was performed using STATGRAPHICS 7.0. All data were column centred prior to the application of the PLS algorithm. The percentage of explained variance in cross-validation (%EVCV) was used as a measure of the quality of the model.The cross-validation process was the ‘full validation’ strategy14 using four deletion groups. Results and Discussion Selection of the Method The experimental design was conditioned by the intended future application of the method to the routine quality control of diverse samples of water. Different aspects of the problem were therefore considered. First, the method has to be flexible, i.e., easily adaptable as a portable or automatic method.Therefore, two operational modes were chosen: static and FI modes.The former makes use of spectral information and could be adapted as a portable test. The FI mode permits easy automation of the method and may increase its selectivity by incorporating kinetic information. The SI methodology previously reported 9,11 presents aspects common to the static and FI methodologies, but it does not present their advantages. Second, the method has to make it possible to perform the analysis on the sample without previous manipulation and must be able to determine CaII and MgII in the range of concentrations found in mineral commercial waters.Figure 1 shows the calcium and magnesium concentration distributions of the samples (in capital letters). A similar experimental design of synthetic standards (numbers in Fig. 1) was adopted to optimize the method. Another aspect studied was the selection of the chromogenic reagent. MTB was tested for the simultaneous determination of CaII and MgII in order to overcome the limitations of other reagents used previously, e.g., PAR9 and Arsenazo III.11 The complexes of CaII and MgII with MTB presented, at pH 11, a high molar absorptivity compared with that of the reagent. Fig. 2 shows the spectra of the MTB complexes corresponding to Fig. 1 Calcium and magnesium concentrations in mineral waters (capital letters) and their mixtures (lower case letters) and experimental design of synthetic standards (numbers). Fig. 2 UV/VIS spectra of some synthetic standard solutions corresponding to the calibration set obtained by the static mode. +, Standard number 1; 8, standard number 10; 2, standard number 8; and ½, standard number 14. 640 Analyst, July 1997, Vol. 122four synthetic standards (points 1, 8, 10 and 14 in Fig. 1). The spectral changes indicate the existence of two relevant zones (I and II in Fig. 2) and reveal severe spectral overlapping. On the other hand, when the FI mode is used, the signal matrix corresponding to each solution is formed by the absorbance values obtained as a function of the wavelength and the time from injection.The information on the kinetic profiles was considered. Table 1 shows the different situations studied throughout the optimization process using the static mode (models S1–S3) and the FI mode (models F1–F4). Exploratory Data Analysis Prior to the study of the PLS models, an exploratory data analysis of the signal matrix (X-block) was carried out.In order to compare the influence of the static and FI modes on the quality of the spectral data, PCA was applied to the data corresponding to the models S1 and F1 (Table 1). In both cases, 50 spectral variables were used. In model F1, the spectrum at 42 s (time corresponding to the FI peak maxima) was used. Fig. 3 shows the PCA score plots. The samples (not used in the PCA model construction) were also included in the plots. In both the S1 and F1 PCA models, the first principal component may relate to the total CaII and MgII concentration in the solutions. The second principal component may relate to the relative content of calcium (objects 1, 4, 7, 10 and 13) and magnesium (objects 2, 5, 8 and 14) in the solutions.In general, both plots reproduce well the experimental design shown in Fig. 1. However, sample h (prepared by mixing samples R, L and V) appears as an outlier in Fig. 3(a) but not in Fig. 3(b).This reflects an error due to the manipulation of this sample using the static mode. On the other hand, solutions with high CaII and MgII concentrations [points 11–14 in Fig. 3(b)] show similar score values on the first principal component. This could indicate non-linearities between the signal obtained in flow conditions and the analyte concentration, thereby suggesting a lack of reagent in the central region of the sample bolus. Fig. 4 shows the correspondence factor analysis (CFA) plot corresponding to the model S1.This plot reveals the relationships between the objects and the original variables (wavelengths). As can be observed, the objects with a high CaII content, i.e., points 4, 7, 10 and 13, are related to the wavelength ranges 400–442 and 616–700 nm (variables 1–8 and 37–50 in Fig. 4). In contrast, the objects with a high MgII content, i.e., 2, 5, 8 and 14, are related to the wavelength range 466–598 nm (variables 12–34 in Fig. 4). Analysis of PLS Models In the previous section, the quality of the data obtained from the static and FI modes, models S1 and F1, respectively, was discussed.Now the usefulness of this information in predicting CaII and MgII concentrations is considered. For this purpose, the concentration values of the 14 synthetic standards were used as the Y-block in combination with the X-block data to construct the PLS models. Table 1 shows the %EVCV for all the models studied. The necessity for wavelength selection in ill-conditioned situations has recently been proposed.15 In order to select the relevant spectral information, two different strategies were used: (a) The plot (not shown) of the B coefficients corresponding to the equation Y = XB + E, for each analyte, versus the original wavelengths16 and (b) the genetic algorithm methodology, 14 in which the frequency of appearance of each variable versus the original variables was plotted (not shown).Large absolute B values and large frequency values, respectively, reveal the importance of the original spectral variables in predicting the analyte concentrations.In both cases, two main conclusions were obtained: first, that zone II of the spectra in Fig. 2 is more important than zone I, and second, that the wavelengths preceding the absorption maximum (606–610 nm) are related to the MgII concentration, while the subsequent wavelengths are related to the CaII concentration. These conclusions agree with those derived from Figure 4.In model S2, 50 wavelengths in the spectral zone II were used. The %EVCV values obtained using this model were larger than those obtained with model S1 (see Table 1). In order to observe the influence of data reduction in zone II, six wavelengths were selected to built model S3. The results using this model were similar to those obtained with model S2, which suggests that a reduction in the number of wavelengths in this spectral zone does not imply a loss of the model prediction ability.This conclusion encourages the use of the time profiles at a small number of wavelengths, in order to improve the %EVCV for the analytes. In models F2 and F3, full kinetic information at one discrete wavelength was used. At 634 nm (model F2), the CaII concentration is well explained, while the MgII concentration is poorly described. In contrast, at 562 nm (model F3), the prediction for MgII increased. The modelling power17 of the time variables was calculated for models F2 and F3.The plot Table 1 Features of the models studied during optimization and explained variance in cross-validation by PLS models. The number of latent variables (LVs) corresponds to the first local %EVCV maximum. X-block %EVCV (LVs) Analysis Spectral Wavelength/ Model mode zone nm Time/s Calcium Magnesium S1 Static I + II 400–694 — 93.2 (2) 96.3 (4) D = 6 S2 Static II 560–660 — 97.3 (2) 98.4 (4) D = 2 S3 Static II 580–630 — 96.2 (2) 98.6 (3) D = 10 F1 FI I + II 400–694 42 84.7 (1) 92.3 (3) D = 6 F2 FI II 634 34–150 93.2 (1) 73.3 (3) D = 2 F3 FI II 562 34–150 77.5 (1) 87.1 (2) D = 2 F4 FI II 526–670 48–98 98.8 (3) 99.6 (3) D = 18 D = 2 Analyst, July 1997, Vol. 122 641(not shown) of modelling power versus time revealed a decrease in the values corresponding to the peak maximum (42 s). This confirms the non-linearities suggested by Fig. 3(b). The maximum modelling power was obtained in the range 48–98 s.The above results suggest that an adequate combination of spectral and kinetic information may improve the ability of the PLS model to make predictions from the FI data. Model F4 was constructed with a 9 3 26 data matrix, as indicated in Table 1. A significant improvement in the %EVCV values with respect to the previous models studied was obtained. Analysis of Mineral Waters The best validation of a predictive model is its use in the prediction of reference samples.The CaII and MgII contents of 18 mineral waters (original and mixtures) were predicted by means of the PLS models S2 and F4, and the results were compared with the complexometric reference values. Fig. 5 shows the results for model F4. The predictions obtained with model F4 were better than those obtained with model S2. In addition, as expected from the PCA score plot [Fig. 3(a)], sample h was incorrectly predicted with model S2. Table 2 gives linear regression statistics for the prediction results.For models S2 and F4 an intercept significantly equal to zero and a slope significantly equal to unity were achieved (95% confidence level). However, model F4 is more reliable (smaller confidence intervals and larger r and F ratio values) than model S2. Fig. 3 PCA analysis corresponding to the models: (a) S1 and (b) F1 (see Table 1 for details). Fig. 4 CFA analysis corresponding to model S1. Fig. 5 Predicted concentrations using model F4 versus the reference values: (top, calcium; and bottom, magnesium).Table 2 Regression statistics for predicted versus declared CaII and MgII values Slope ± Intercept ± Analyte Model CI* CI r† F-ratio‡ CaII S2§ 0.88 ± 0.17 4 ± 9 0.94 117 F4 1.00 ± 0.10 0.73 ± 5 0.98 491 MGII S2§ 1.04 ± 0.12 20.4 ± 1.7 0.98 365 F4 1.08 ± 0.1 21.5 ± 1.5 0.99 503 * Confidence interval (95% confidence level). † Correlation coefficient. ‡ Variance modelled by regression to residual variance ratio. § Sample h was excluded from the regression. 642 Analyst, July 1997, Vol. 122In order to compare the reproducibility of the proposed method (PLS model F4) with that obtained by complexometric and ICP methods, seven independent analyses of sample C were performed by the three methods. The RSDs found with the proposed method were 2.6 and 1.6% for CaII and MgII, respectively, and were statistically comparable (95% confidence level) to those obtained by complexometry (1.3 and 2.3%) or ICP (1.4 and 1.5%).Finally, the samples were used instead of the synthetic standards as the calibration set under the same conditions as in models S2 and F4. The %EVCV (and latent variables) values obtained for CaII and MgII were 81.8(3) and 92.3(2) using the static mode and 95.1(3) and 96.1(4) using the FI mode. In both operational modes, the use of real samples led to lower %EVCV values than those obtained using synthetic standards. This suggests the presence of interference effects in samples, and therefore a reduction in the prediction ability is obtained.On the other hand, the %EVCV values found with the FI mode are adequate for predicting future samples. The results of this preliminary study allow us to extrapolate some conclusions relevant to the use of this method in routine analysis in the future. MTB seems to be an adequate chromogenic reagent for the simultaneous determination of CaII and MgII by spectrophotometry in combination with multivariate calibration techniques, such as PLS. FI measurements seem to provide more reliable results than those obtained by means of the static operational mode. However, the results of the static mode may permit its use as a rapid portable test. The use of real samples (i.e., reference samples) is recommended for obtaining more robust and reliable models, but synthetic standards also seem to be useful and could be employed when no reference concentration values for samples are available. F. M. Fern�andez thanks the Instituto de Cooperaci�on Iberoamericana for a grant that made possible his collaboration in these studies. The authors express their gratitude to E. Bonet (Gamaser S. A., Valencia, Spain) for his help with the ICP measurements. References 1 Franson, M. A. H., Standard Methods for the Examination of Water and Wastewater, American Public Health Association and Water Polution Control Federation, Washington, DC, 18th edn., 1992. 2 Basson, W. P., and Van Staden, J. F., Fresenius’ Z. Anal. Chem., 1980, 302, 370. 3 Wada, H., Ozawa, T., Nakagawa, G., Asano, Y., and Ito, S., Anal. Chim. Acta, 1988, 211, 213. 4 Foster, R. J., and Diamond, D., Anal. Chem., 1992, 64, 1721. 5 Yuan, Y., Anal. Chim. Acta, 1988, 212, 291. 6 Ca�nete, F., R�ýos, A., Luque de Castro, M. D., and Valc�arcel, M., Analyst, 1987, 112, 262. 7 Blanco, M., Coello, J., Gen�e, J., Iturriaga, H., and Maspoch, S., Anal. Chim. Acta, 1989, 224, 23. 8 G�omez, E., Estela, J. M., and Cerd�a, V., Anal. Chim. Acta, 1991, 249, 513. 9 G�omez, E., Tom�as, C., Cladera, A., Estela, J. M., and Cerd�a, V., Analyst, 1995, 120, 1181. 10 Novikov, E. A., and Shpigun, L. K., Zh. Anal. Khim., 1993, 48, 1326. 11 Ruis�anchez, I., Rius, A., Larrechi, M. S., Callao, M. P. and Rius, F. X., Chemom. Intell. Lab. Syst., 1994, 24, 55. 12 Rius, A., Callao, M. P., and Rius, F. X., Anal. Chim. Acta, 1995, 316, 27. 13 Haaland, D. M., and Thomas, E. V., Anal. Chem., 1988, 60, 1193. 14 Leardi, R., J. Chemom., 1994, 8, 65. 15 Xu, L., and Schechter, I., Anal. Chem. 1996, 68, 2392. 16 Garrido Frenich, A., Jouan-Rimbaud, D., Massart, D. L., Kuttatharmmakul, S., Martinez Galera, M., and Martinez Vidal, J. L., Analyst, 1995, 120, 2787. 17 Cela, R., Avances en Quimiometria Pr�actica, Universidad de Santiago de Compostela, Santiago de Compostela, 1994. Paper 6/08244K Received December 6, 1996 Accepted April 10, 1997 Analys

ISSN:0003-2654    

DOI:10.1039/a608244k

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Wavelet Denoising of Infrared Spectra Bjørn K. Alsberg*a, Andrew M. Woodwarda, Michael K. Winsona, Jem Rowlandb and Douglas B. Kella a Institute of Biological Sciences, University of Wales, Aberystwyth, Ceredigion, UK SY23 3DA. E-mail: bka@aber.ac.uk b Department of Computer Science, University of Wales, Aberystwyth, Ceredigion, UK SY23 3DA The application of wavelet denoising to infrared spectra was investigated. Six different wavelet denoising methods (SURE, VISU, HYBRID, MINMAX, MAD and WAVELET PACKETS) were applied to pure infrared spectra with various added levels of homo- and heteroscedastic noise.The performances of the wavelet denoising methods were compared with the standard Fourier and moving mean filtering in terms of root mean square errors between the pure and denoised spectra and visual quality of the denoised spectrum. The use of predictive ability as a possible objective criterion for denoising performance was also investigated. The main conclusion is that for very low signal-to-noise ratios (S/N) the standard denoising methods (Fourier and moving mean) are comparable to the more sophisticated methods.At higher S/N levels the wavelet denoising methods, in particular the HYBRID and VISU methods, are better. Wavelet methods are also better in restoring the visual quality of the denoised infrared spectra. Keywords: Wavelets; wavelet packets; denoising; infrared spectra; homoscedastic noise; heteroscedastic noise; chemometrics; rapid screening The rapid quantitative and qualitative information obtained from applying multivariate methods to spectra (e.g., IR, Raman, UV) has been a very popular way of replacing slow wet chemical analyses.We are interested in particular in the determination of the concentrations of important compounds produced by industrially relevant bacteria and yeasts. In order to extract reliable information from any kind of data vector such as those in IR spectra,1,2 unwanted noise has to be dealt with.3–6 There are several ways of reducing the effect of noise in spectra, taking the mean of several co-added spectra being the most common. Unfortunately, co-adding of spectra is a timeconsuming method when a large number of spectra are to be recorded.In particular, we are interested in cases of highthroughput analyses where FTIR spectra are recorded at numerous locations on 2D surfaces, e.g., TLC plates, in biological tissues and in bacterial colonies.It is true that when a very small number of FTIR spectra are to be recorded, it is relatively rapid to use the appropriate number of co-adds to ensure a satisfactory signal-to-noise ratio, (S/N). However, when only a small number of co-adds is desired, mathematical techniques for removing the noise after recording of the spectra are more attractive. The theory of convolutions and filter theory have been applied to a wide range of problems. However, there are certain types of problem where the frequency-domain methods are not optimal for removing noise.The traditional filtering methods in most cases rely on the frequencies obtained in the power spectrum being stationary. The theory of wavelets promises several improvements to the traditional filtering methods. The major difference is the fact that wavelet methods can much better resolve frequencies varying in time (or along a pseudotime axis such as that representing wavenumbers).Theory Introduction to Wavelets and Wavelet Packets Wavelets are becoming an increasingly important tool in image and signal processing.7–10 Wavelets are effective in extracting both time- and frequency-like information from a time-varying signal. The short-time Fourier transform performs a constant bandwidth splitting of the signal whereas the wavelet transform has a proportional (octave) bandwidth splitting of the frequency domain. Unlike the Fourier transform, the wavelet transform can use a variety of different basis functions with different properties.Non-orthogonal wavelet bases are referred to as frames,11–13 but will not be discussed here. The more popular orthogonal wavelet bases have several interesting properties that make them a suitable basis for tools in signal analysis and compression. One important property of many wavelet basis functions is their localisation of both time and frequency domains simultaneously. A continuous wavelet decomposition can be written as w s b t b f t t s ( , ) ( ) ( ) = - -• •Ú Y d (1) where ys(x) is the wavelet function at a particular scale s, i.e., the same wavelet function is dilated or contracted according to the scale, and f(t) is function to be analysed; b signifies the translation of the wavelet at scale s.Eqn. (1) can be expressed as a convolution: w(s,b) = ys(t)Ûf(t)?F[w(s,b)] = F[ys(t )]F[f(t )] (2) Eqn. (1) is really a convolution of the signal f with the wavelet function in the time domain and we have emphasised this in eqn.(2) by using the convolution operator symbol Û. The equation to the right of the arrow is the convolution in the time domain expressed in the frequency domain by straightforward application of the convolution theorem;14 F indicates the Fourier transform operator. The scale can be interpreted as a measure of frequency. A short scale contains high-frequency components whereas a long scale contains low-frequency components. An intuitive way of looking at the wavelet transform is to interpret it as a sequence of combinations of bandpass filters.The wavelet function y(t ) (also referred to as the ‘mother wavelet’) can be interpreted as a high-pass filter acting on the original signal; the scaling function f(t) (also referred to as the ‘father wavelet’), on the other hand, behaves as a low-pass filter. The wavelet function y(t) can be written as a linear combination of the scaling function. The scaling function has the property that it can be written in terms of scaled versions of itself: f(x) = ckf(2x - k) k = 0 N (3) Analyst, July 1997, Vol. 122 (645–652) 645In this paper, only the discrete wavelet transform will be used. This means that we restrict the choice of scale s and translations b; in general, we set s = a0 j, b = kb0a0 j (4) where a0 = 2 and b0 = 1 is the most common choice; j is an index that can be any natural number. A common algorithm for calculating discrete wavelet coefficients is the so-called Mallat algorithm.15–17 At each scale, high- (H) and low- (L) pass filters are applied to the input signal.The actual shapes of these filters are determined by the kind of wavelet function used. The output from the high-pass filter at each scale is recorded as the wavelet coefficients. The low-pass filter extracts the low-frequency components for the next scale where another set of high- and low-pass filters is employed. At each successive scale (n 2 1) the length of the vector upon which the filters operate is halved; this is referred to as decimation.Thus, the number of scales is log2(n). The corresponding vector of wavelet coefficients for a scale j is written as w(j). Wavelet reconstruction, i.e., going from wavelet coefficients back into the original domain, is simply a multiplication of a vector w containing the coefficients for all scales with a matrix consisting of all time shifted wavelet functions for all scales: f = wBT (5) where BT is the transposed matrix of wavelet functions for all scales. The structure of the vector w is w = [w(0)w(1)w(2)···w(J)] (6) The tree structure of the Mallat algorithm can be extended such that the filters are also used on the output from the highpass filter.Such a decomposition of the data is encompased in the theory of wavelet packets.18–30 The wavelet packets form a superset of the traditional wavelet coefficients, which corresponds to the leftmost branch of the tree.Because of this algorithmic tree structure, it is possible to prune branches in the tree to optimise some fitting criterion. Denoising Using Wavelets Noise is a phenomenon that affects all frequencies, whereas the signal of interest is most likely to occupy a small part of the frequency domain. Since the signal will tend to dominate the low-frequency components, it is expected that the majority of high-frequency components above a certain level are due to noise.This is the underlying philosophy for traditional Fourier filtering where low-pass filters cut off the high-frequency components. Similarly, we can expect small wavelet coefficients at short scales to be mainly noise components. The procedure for wavelet denoising will therefore be as follows: (i) apply a wavelet transform to signal fnoisy and obtain the vector w of wavelet coefficients; (ii) suppress or remove those elements in w that are thought to be attributed to noise; and (iii) apply the cognate inverse wavelet transform to w to obtain a function f denoised.In this paper, we use eight different denoising techniques. Two of them (Fourier filtering and moving average) are used as references for the performance of the wavelet methods. All the methods presented are part of the WaveLab package for MATLAB,31 which was used in all experiments presented. Wavelet denoising methods in general32–36 use two different approaches, hard and soft thresholding.The hard thresholding philosophy is simply to set all the wavelet coefficients below a certain threshold to zero. Soft thresholding, on the other hand, reduces the value of wavelet coefficients towards zero if they are above a certain value (referred to as ‘shrinking’). For a certain wavelet coefficient at scale j we have wk = sign(wk)(õwkõ2l)+ (7) where sign returns the sign of the wavelet coefficient wk and the parentheses represent the threshold value.We will sometimes refer to this function as SOFT (w,t), where t is the threshold and w the vector to be thresholded. Methods for Denoising SURE This denoising method is based on Stein’s Unbiased Risk Estimate37 and is applied to the whole wavelet coefficient vector, i.e., the thresholding is performed on each scale j. The SURE method is a hard thresholding approach where the major work is invested in finding the right threshold for the different scales. First, we need to sort the squared wavelet coefficients {ak = [wk (j)]2} in ascending order.The cumulative total of ak is computed: bi = ak k =1 i (8) Further, a vector c is needed which has the same size as the number of elements in the current scale j. The first element in c is nj 2 1, where nj is the number of elements in the wavelet coefficient vector at scale j, and decreases linearly for successive vector elements to 0 (the last element). A risk value, ri, is computed for every wavelet coefficient: ri = (nj - 2i) + bi + aici nj (9) The wavelet coefficient that has the minimum ri is selected as the threshold value for that scale j.Note that the absolute value of the coefficient is used as the threshold. If the coefficient õwi (j)õ is chosen as the threshold, all coefficients with absolute values below will be set to zero. We will refer to this threshold as t = SURE [w(j)]. VISU For some of the denoising methods we need to specify L, which is the longest scale used in the thresholding.In this method we apply the denoising only on the coefficients in the index interval [2L + 1, n] where n is the number of wavelet coefficients. The L parameter must be much smaller than J where n = 2J. We define the threshold parameter t = (2 log n)1 2, which is used in the soft thresholding scheme described above. HYBRID This is a soft threshold method where in some cases the soft threshold tA = (2 log nj)1 2 is used, and in other cases tB = SURE [w(j)] is used, depending on the parameter e, defined as follows: e n n j j j = - w( ) 2 (10) such that (11) if then else A A B e J n SOFT t SOFT t t j j j < 3 2 / ( ) ( ) [ , ] ( ,min( , )] w w 646 Analyst, July 1997, Vol. 122where J is the total number of scales and nj is the number of elements in scale j. MEDIAN ABSOLUTE DEVIATION (MAD) Here the soft thresholding method is applied to the individual scales j. The threshold used for each scale j is s j = median[w(j) ] . 0 6745 (12) Each wavelet coefficient scale is divided by sj, v(j) = w(j)/sj, and we use the threshold t = (2 log nj)1 2. The thresholding is then done by SOFT [v(j), t]. MINIMAX This procedure finds ‘optimum’ thresholds tn such that the risk R(f denoised, f), given by R( f denoised , f ) = 1 n ( f i denoised - f i )2 i =1 n (13) between the estimated wavelet coefficient qest and the true wavelet coefficient q satisfy R(qest,q)@L(e2+Ropt) (14) where L is a constant which is related to the optimum risk Ropt if we had an oracle that could tell us what wavelet coefficients are larger than the noise level e.A set of thresholds tn are used that satisfy tn @ (2 log n)1 2. For very large n the optimum threshold values will approach (2 log n)1 2. The thresholds are subsequently used in a soft thresholding scheme. Fourier This is the classical Fourier denoising approach where the components with high frequencies are assumed to represent noise only and are therefore removed. In this case we use a soft thresholding technique which is dependent on input from the user.A region in the power spectrum of the signal is specified which most likely contains noise; this is usually located in the upper region of the power spectrum. The maximum amplitude value in this region is used as a cut-off level. At the located cutoff frequency a sigmoid function is used to implement a soft threshold. Moving mean filter A simple moving average filter was chosen as the ‘baseline’ method with which to compare the other, more complicated methods.A sliding window of size w is selected. For each step in the sliding process we find the mean of the curve points inside the window. This mean value is used as the output of the filter at each step. The window size is chosen to reflect the frequency content of the true signal by making sure the cut-off frequency of the filter is slightly larger than the bandwidth of the true signal.WAVELET PACKETS (WP) The WP denoising method used here has two significant steps: estimation of the best WP basis for denoising followed by proper selection of the denoising threshold. To select a basis, the Coifman–Wickerhauser ‘best basis’ algorithm is used.38 This algorithm is based on finding the basis that gives rise to the minimum entropy of the signal energy distribution. The energy of a signal is the sum of the squares of its elements. This energy will be the same for different choices of bases, but the distribution will be different over its coordinates.To quantify this distribution, the entropy of the squares of the coordinates of the signal is used. From a data compression viewpoint it is advantageous to find a distribution with a low entropy. This means the signal can be described by a small number of bits. After finding the best basis the WP method uses Stein’s Unbiased Risk Estimate in the calculation of hard denoising thresholds.Heteroscedastic and Homoscedastic Noise Definitions and properties Let us assume we have a signal, h(t), that contains only homoscedastic noise. In general, we write this as h(t) = an(t) + s(t) (15) where a is a scalar that determines the size of the noise n(t) and s(t) is the pure signal. This Fourier transforms to H(w) = aN(w) + S(w) (16) such that the signal is independent of the noise and is concentrated only in the region defined by S(w). For heteroscedastic noise, however, the noise correlates in intensity with the amplitude of the signal h(t) = af[s(t )] n(t) + s(t) (17) where f (s) is the dependence of the noise on this signal.A Fourier transform of the noisy signal h(t) produces H(w) = aF[s(t )]ÛN(w) + S(w) (18) where Û is the convolution operator and upper case letters signify the corresponding Fourier transform of the functions in the time domain (written in lower case letters). The spectrum of the heteroscedastic noise can thus be regarded as the convolution of the spectrum of the homoscedastic noise with that of the signal.Accordingly, all frequencies in the spectrum will contain information related directly to the signal, s(t ). Constructing heteroscedastic noise When constructing heteroscedastic noise for the purpose of assessing different denoising methods, it is necessary to decide on the structure of the function f described in the previous section. The easiest choice is to let it be a constant such that the heteroscedastic noise is h(t) = a s(t ) n(t) + s(t) (19) In this paper, however, we decided to formulate f such that it is in accordance with the type of heteroscedastic noise that is normally present in absorbance spectra.It has been demonstrated39 that the non-linear transform from transmittance to absorbance spectra itself converts homoscedastic noise into heteroscedasticity. It should be stressed that other phenomena can contribute to the observed heteroscedasticity. For instance, irreproducibility of transmitter offsets may also have an influence.We have, however, in order to simplify, assumed that the heteroscedasticity observed is caused only by the conversion from transmittance to absorbance. We note that the Beer transform is A = log(I0/I) = 2log T (20) where A is the absorbance, I0 is the original intensity of the incident beam, I is the reduced intensity of the beam after passing through the sample and T is the transmittance.Homoscedastic noise in a transmittance spectrum will be converted into heteroscedasticity after the transformation into Analyst, July 1997, Vol. 122 647absorbance units. This means that our observed signal s(t ) is the result of a Beer transform s(t) = 2log[q(t )] (21) where q(t) is the transmittance signal. Adding homoscedastic noise n(t) to the transmittance signal q(t) now gives z(t) = 2log[a q(t) + n(t)] = log{1/[a q(t) + n(t)]} (22) In order to see that the noise becomes related to the size of the signal, we will use an intuitive rather than a mathematical argument.Assume that we have a large peak in the transmittance region with a small perturbation from noise. The 2log (large number + small perturbation) corresponds to a region in the 2log function that is relatively flat, i.e., the small perturbations from the noise will not change the output significantly (which now becomes an absorbance). If we have a small signal that has a size comparable to the noise, then we will have a situation where the fluctuation in the signal + noise will be comparable in size with the noise.Now, the 2log (small number + small perturbation) will be in a very steep region of the non-linear function and therefore any small changes will correspond to a large change in the output (absorbance). This means that the standard deviation (which is a measure of change in value) will be higher for regions containing small transmittance intensities (i.e., high absorbance) and low for regions containing high transmittance intensities (i.e., low absorbance).In this paper we make use of this fact and therefore convert from absorbance to transmittance units and add homoscedastic noise with a certain S/N. The S/N values in all the experiments are obtained from the following equation S / N = sj j n (sj - nj )2 j n (23) where sj and nj are the jth true signal and noise element, respectively. The noisy transmittance spectrum is subsequently transformed back into the absorbance domain where the noise is now heteroscedastic.In general, any non-linear transform of a signal will convert homoscedastic into heteroscedastic noise. Experimental Assessment of Denoising Performance We shall use two different ways of assessing the performance of the different denoising methods. The first method is based on the use of the root mean square (rms) difference between the denoised noisy spectrum and noise-free spectrum as a measure of the performance of the different methods. Since the denoising process can often introduce offsets and scalings that can influence the rms values, we employed the technique of multiplicative scatter correction (MSC)40–45 on the denoised spectra before calculating the rms differences.In MSC it is assumed that the observed spectrum y can be written in terms of the reference spectrum s as y = as + b. The MSC operation on y is therefore yh = (y 2 b)/a.In this paper y is a spectrum that has been denoised using one of the methods described and s is the noise-free spectrum. Values of a and b are constructed for every denoised spectrum for each denoising method. The rms difference is calculated between yh and s. The second method of assessing denoising preformance used in this paper is to measure the rms error of prediction on an unseen validation set using the denoised data set. All the data sets used in this paper (data sets 1–4) are such that we know the true underlying noise-free spectrum.This will, of course, not normally be the case in real applications and in general the investigator is left with visual inspection of the denoised signal as a way of determining the appropriateness of the denoising method for the data set. However, in the case of FTIR spectrometry noisy spectra will approach the ‘true’ noisefree spectra as the number of co-adds (followed by averaging) is increased.Description of Experimental Conditions Infrared spectra for data sets 2, 3 and 4 were recorded in the wavenumber interval 4000–600 cm21 using a Bruker IFS28 FTIR spectrometer (Bruker Spectrospin, Coventry, UK) equipped with a liquid nitrogen cooled MCT (mercury cadmium telluride) detector and a diffuse-reflectance absorbance TLC accessory (4 cm21 resolution, spectra collected at 20 s21). ASCII data were exported from the Opus software used to control the FTIR instrument and imported into MATLAB.Data set 1 This data set consists of an artificially generated IR absorbance spectrum to which is subsequently added homoscedastic noise and heteroscedastic noise with S/N = 1, 2, . . ., 30. Data set 2 Homoscedastic or heteroscedastic noise (S/N = 1,2, . . ., 30) was added to the pure diffuse reflectance spectrum of sodium succinate. Data set 3 To improve the S/N it is standard procedure in all instruments to take the mean of several spectra of the same sample.The S/N will improve as the square root of the number of co-added spectra that are used in the mean calculation for homoscedastic noise. This square root dependence is approximately true for heteroscedastic noise up to about 300–400 co-adds. Above this number of co-adds the S/N improves almost linearly (not shown). Unfortunately, taking the mean of a sufficiently large number of spectra is too slow a process when rapid screening of thousands of samples is necessary. Here we want to use denoising methods to improve the accuracy in the estimation of the profile of the ‘true’ spectrum (i.e., a mean spectrum of many co-adds that has a high S/N) from single co-add spectra (i.e., with low S/N).Our choice of compound in this experiment was glucose at a 20 mm concentration. The reference, and estimate of the ‘true’ spectrum, was the mean of 300 co-adds. Our data matrix was a set of 300 single co-add spectra. When we plotted the mean vector versus the standard deviation vector of this data set we observed a clear linear relationship.This confirms our knowledge about absorbance IR spectra that the standard deviation of the absorbance is proportional to the mean value of the absorbance. Unfortunately, some regions in the spectra were significantly different from the glucose regions and thus removed from the data set. These regions were 4000–3619 and 1186–600 cm21, which constituted the first and the last part of the spectra.Each of these spectra was subjected to the eight denoising methods described above and the rms difference was calculated between the denoised spectrum and the ‘true’ spectrum. The mean value of this rms difference over all the 300 spectra for all the eight methods was used to give an indication of the best method. 648 Analyst, July 1997, Vol. 122Data set 4 Data set 4 consists of 40 diffuse reflectance FTIR spectra of a developed culture of the bacterium Staphylococcus aureus containing the antibiotic ampicillin at different concentrations (0.5–20 mm).Infrared spectra (256 co-adds) for each of these samples were recorded. ASCII data were exported from the Opus software used to control the FTIR instrument and imported into MATLAB. The samples were separated into calibration and validation sets, each containing 20 objects, using the DUPLEX method.46 PLS with leave-one-out cross-validation was used for finding the optimum model for the calibration data.In order to demonstrate the denoising effect at different noise levels, we added heteroscedastic noise to the data set with S/N in the region [1, 20]. Calculation and Presentation Details All the data were reconstructed using the Symmlet 8 wavelet, which we have found to be a very good wavelet for modelling spectra. One of the reasons for this is that the Symmlet 8 basis resembles to some extent the shape of peaks found in IR spectra. The low-frequency cut-off for shrinkage was set to L = 5.Denoising of the spectra was also performed using a threshold of L = 0 but it had a tendency to produce reconstructed spectra that were judged not to be sufficiently smooth. L was also used as the branch depth in the wavelet packet transform. The rms difference between the reconstructed and the true spectrum (i.e., that with very little noise) was calculated for each method at each S/N. The resulting matrix for each denoising method contained the rms differences from the true spectrum for each denoised spectrum at each S/N level.We summarise the results of these matrices by taking the mean and the standard deviation for all the spectra in the data sets. For convenience, we will sometimes refer to the different denoising methods by numbers: 1 = VISU, 2 = SURE, 3 = HYBRID, 4 = MINMAX, 5 = MAD, 6 = FOURIER, 7 = PACKETS, 8 = MOVING MEAN and 9 = NOISY SIGNAL (i.e., the untreated signal containing noise). Results Data Set 1, Homoscedastic Noise Homoscedastic noise (S/N from 1.61 to 30.00) was added to this spectrum and the results obtained by applying the various denoising methods to the noisy spectrum are given in Table 1.The best methods over the whole S/N range are the wavelet HYBRID (3) and Fourier (6) methods. The HYBRID method is slightly better than the Fourier method for low S/N ( < 7.5). At very low S/N levels the HYBRID and the Fourier methods together with the moving average converge to almost identical performance.The mean rms for the HYBRID method is 6.21 (median 3.67) and the mean for the Fourier method is 6.70 (median 4.59). To obtain a visual impression of the denoising process, we inspected the reconstruction results of four methods, HYBRID, Fourier, PACKETS and moving mean, at S/N = 4.69. The visualisation (not shown) seems to confirm the rms differences in that the denoised spectrum from the HYBRID method is better than the results from the Fourier and moving average methods.The PACKETS denoised spectrum, however, seems visually to be better than the reported rms values would suggest. In the Fourier denoised spectrum we observe unwanted ringing effects from aliasing. Similar ringing effects can be seen in the wavelet reconstructions at lower frequencies. Data Set 1, Heteroscedastic Noise Heteroscedastic noise was added to the noise-free data set 1. The results of applying the eight different denoising methods to the noisy spectrum is shown in Fig. 1. Again, the HYBRID denoising method (3) is slightly better for almost all the S/N levels, with the Fourier (6) next, equalling the HYBRID over most of the S/N range. The PACKETS method performs almost as well in this data set. The mean rms difference produced by the HYBRID method is 6.27 compared with 7.14 for the Fourier method. Reconstructed denoised spectra for methods 3, 6, 7 and 9 at a noise level S/N = 4.67 are displayed in Fig. 2. The Fourier, HYBRID and moving average methods all show similar ringing effects which are absent in the PACKETS reconstruction.Table 1 Rms differences between the ideal spectrum and the denoised spectrum for eight denoising methods applied to data set 1 to which has been added homoscedastic noise. The column headed S/N contains the signal-to-noise ratio used for each of the 20 experiments. The methods are indicated by numbers: 1 = VISU, 2 = SURE, 3 = HYBRID, 4 = MINMAX, 5 = MAD, 6 = Fourier, 7 = WAVELET PACKETS, 8 = Moving mean and 9 = NOISY SIGNAL S/N 1 2 3 4 5 6 7 8 9 1.61 31.34 32.05 30.14 41.44 30.55 27.61 30.34 81.69 27.52 3.27 17.96 17.17 12.74 23.90 17.50 13.22 20.11 40.15 13.12 4.69 17.09 13.69 11.07 16.55 14.59 12.29 14.02 27.97 12.70 6.05 12.79 15.46 9.38 14.96 13.24 13.18 11.79 21.68 10.57 7.98 10.23 10.84 6.84 10.25 11.10 6.64 7.31 16.44 9.38 9.08 10.56 8.53 8.51 9.35 11.96 10.64 9.12 14.46 9.25 10.68 8.84 9.12 5.54 9.03 9.48 5.43 6.94 12.29 9.25 12.50 7.09 6.93 4.78 7.60 8.62 4.89 6.11 10.50 8.54 13.56 6.79 5.76 3.95 6.26 6.52 6.38 5.11 9.68 7.86 15.02 6.46 5.51 3.71 5.90 8.43 5.53 4.83 8.74 8.45 17.43 5.76 4.08 3.64 5.26 7.37 3.73 4.13 7.53 8.08 18.69 5.60 3.46 2.95 4.42 6.99 3.06 3.87 7.02 7.77 20.92 5.39 4.58 3.35 4.45 8.04 4.29 3.65 6.27 8.43 21.45 5.60 3.91 3.09 3.98 7.59 3.06 3.29 6.12 8.17 22.88 5.08 3.46 2.79 3.81 7.17 2.84 3.51 5.74 7.91 24.80 4.50 4.37 2.42 3.81 6.60 2.42 3.20 5.29 7.93 26.79 4.46 3.70 2.47 3.58 6.12 2.33 3.24 4.90 7.99 28.10 4.39 2.96 2.37 3.12 6.30 2.20 3.30 4.67 7.87 29.28 4.16 2.59 2.29 2.97 6.16 2.25 2.76 4.48 7.78 30.00 4.22 2.97 2.24 2.87 5.90 2.10 2.61 4.37 7.88 Mean 8.92 8.06 6.21 9.18 10.01 6.70 7.46 15.00 9.82 Median 6.11 5.05 3.67 5.58 7.81 4.59 4.48 8.13 8.30 Analyst, July 1997, Vol. 122 649Data Set 2, Homoscedastic Noise The effect of the different denoising methods on data set 2 (to which are added various levels of homoscedastic noise) is shown in Table 2.Again, using the rms difference criterion, HYBRID (3) is the best method overall, followed very closely by both the Fourier and PACKETS methods, which behave very similarly to each other. The denoised spectrum for the four methods HYBRID, moving mean, Fourier and PACKET at noise level S/N = 4.97 was computed (not shown). We observe that the visual quality of the WAVELET PACKET denoised spectrum is better than that of the Fourier method, although this is not reflected in the trend observed in the rms difference values.The PACKET method in general produces smooth spectra but can be erroneous in larger detail. Data Set 2, Heteroscedastic Noise Fig. 3 shows the effect of the different denoising methods on data set 2, to which are added various levels of heteroscedastic noise. The HYBRID method is again best at mid and high S/N but the Fourier method performs better at low S/N. The most interesting feature from the analysis is the far superior performance of the moving mean over all the other methods for mid to low S/N.Surprisingly, the moving mean (8) method gives much lower rms values than any of the spectral methods. Is this trend also observed in the denoised spectrum for the different methods (S/ N = 3.67)? Visual inspection of the reconstructions does not reflect the rms values above (see Fig. 4). This is presumably due to the eye favouring smoothness such that a smooth signal with large scale errors would be seen as better than a slightly noisier trace which is actually more representative of the true signal.Data Set 3 The eight different denoising methods described above were used on each of the single co-adds and the rms difference was calculated between the denoised co-adds and the ‘true’ signal. The mean and the standard deviation values for all the rms values were calculated as a measure of ranking the denoising Fig. 1 Result of denoising using six wavelet methods, Fourier and median filter denoising on data set 1.Heteroscedastic noise. Only four of the applied methods are shown. Fig. 2 Reconstructed noisy spectra of data set 1 containing heteroscedastic noise. Table 2 Rms differences between the ideal spectrum and the denoised spectrum for eight denoising methods applied to data set 2 to which has been added homoscedastic noise. The column headed S/N contains the signal-to-noise ratio used for each of the 20 experiments. The methods are indicated by numbers: 1 = VISU, 2 = SURE, 3 = HYBRID, 4 = MINMAX, 5 = MAD, 6 = Fourier, 7 = WAVELET PACKETS, 8 = Moving mean and 9 = NOISY SIGNAL S/N 1 2 3 4 5 6 7 8 9 1.34 62.95 100.10 51.66 80.51 64.78 62.61 59.25 58.00 121.68 2.52 48.99 39.54 33.86 38.65 51.93 45.73 42.53 33.18 64.58 3.86 36.21 27.41 22.51 26.45 43.20 27.29 28.91 26.50 42.21 4.97 32.82 20.76 19.79 18.61 38.38 24.07 24.40 23.62 32.76 6.71 25.60 15.37 16.42 14.34 29.15 16.47 19.84 20.30 24.24 7.68 20.52 17.87 11.48 14.10 31.78 16.28 14.17 20.10 21.19 8.92 20.62 12.41 10.59 11.89 27.57 13.24 13.47 19.38 18.24 10.60 18.21 10.40 9.47 9.49 26.66 11.16 12.89 18.71 15.36 11.26 16.45 11.36 8.83 9.76 23.77 11.51 10.60 18.68 14.45 12.66 15.34 10.54 8.27 8.72 24.53 10.47 10.80 18.42 12.86 13.77 13.52 10.01 7.88 8.70 23.44 9.59 9.14 18.31 11.82 15.56 13.80 7.88 7.34 7.20 22.58 8.37 8.56 18.12 10.46 16.27 12.20 8.57 7.14 7.48 21.69 8.28 7.73 18.06 10.00 17.55 12.03 8.03 6.42 6.82 22.09 7.59 7.55 17.91 9.27 19.04 11.50 6.95 6.08 5.94 19.97 8.11 7.46 17.86 8.55 20.37 11.31 6.56 6.00 5.76 20.02 6.93 7.14 18.03 7.99 21.48 10.54 6.75 5.59 5.55 20.53 6.66 6.60 17.79 7.58 24.02 9.67 5.30 5.13 5.17 22.67 6.06 5.95 17.72 6.77 23.96 9.55 6.04 5.22 5.14 21.76 6.30 6.05 17.95 6.79 24.98 9.23 5.73 5.02 4.72 21.10 6.15 6.46 17.65 6.51 Mean 20.55 16.88 12.74 14.75 28.98 15.64 15.47 22.67 21.81 Median 14.57 10.21 8.07 8.71 23.60 10.03 9.87 18.37 12.34 650 Analyst, July 1997, Vol. 122methods.The measured S/N of the data set was fairly high, 107 ± 5. The mean rms values for the different methods were 0.85 ± 0.05 for VISU, 1.07 ± 0.05 for SURE, 1.04 ± 0.05 for HYBRID, 1.06 ± 0.05 for MINMAX, 2.8 ± 0.1 for MAD, 1.75 ± 0.03 for Fourier, 1.03 ± 0.05 for PACKETS, 1.07 ± 0.05 for moving mean and 3.88 ± 0.03 for NOISY SIGNAL.All the wavelet methods [except for method 5 (MAD)] have a lower rms than the Fourier and moving mean methods. Again, using visual inspection of the reconstructions (not shown), we see that the Fourier and moving mean methods have a tendency for oversmoothing of certain regions.The wavelet methods seem to be better at capturing significant spikes in the spectra. Data Set 4 The noise-free and untreated data set was first analysed with the partial least squares (PLS) method. A five factor PLS model was formed using full cross-validation. When this model was applied to an unseen validation set, an rms prediction error of 9.7% was achieved.Further denoising on this data set will improve the prediction error by approximately 2%. In order to observe the performance for different noise levels, heteroscedastic noise was added to the data set (S/N = 1–20). For each noise level, all the denoising methods described earlier were used prior to PLS modelling (five factors extracted). The results of the rms errors of prediction are shown in Fig. 5. As shown before, the traditional methods such as Fourier and moving average perform better than or as well as all the wavelet methods for noise levels lower than S/N = 7.Above this noise level one of the wavelet denoising methods (VISU) performs better. None of the denoising methods can achieve an rms error in prediction lower than 10% in the noise level range. Discussion and Conclusions One important implication of improved denoising techniques in IR spectrometry is that we can improve the S/N with a significantly reduced number of co-adds. This will be of particular importance for experiments in which we wish to record the IR spectra with rapidity, such as in screening for metabolite overproduction and 2D surface mappings.Under such conditions, the benefit of higher throughput is essentially in proportion to the reduction in the number of co-adds. Other experimental methods that may be expected to benefit from wavelet denoising techniques are the group of coupled methods (GC–IR, LC–IR, etc.).When the location of smaller peaks in coupled methods is necessary, heteroscedastic noise can have a devastating effect on the correctness of the results.47–49 In addition, denoising applied to spectra in general will be of importance in any kind of multivariate modelling performed on the spectra. Examples of popular methods that are often used in the analysis of spectra are PLS50–60 and neural networks.61–65 In this case it is possible to construct objective criteria that can be used to optimise denoising of spectra.For instance, it is possible to use the predictive ability or classification error to find the optimum choice of threshold in the wavelet denoising process. The need for such objective criteria is emphasised by the disparity, shown by some of the results in this paper, between the ‘quality’ of denoised spectra as assessed by rms difference values and by visual assessment of the denoised spectra. Although the wavelet approach allows greater freedom than traditional filtering methods, this also requires appropriate selection of more parameters by the user in order to optimise the denoising process.The wavelet transform allows a greater degree of compression into a smaller proportion of coefficients than the Fourier transform, and should therefore allow a greater rejection of noise with optimum parameter selection. The major improvement in the wavelet denoising methods compared with the standard filtering methods is the possibility of localising the frequency information to selected parts of the spectrum.For instance, in IR spectra we have the complex fingerprint regions in the 1000–400 cm21 range which will contain sharper peaks than in the 4000–3000 cm21 region. This means that we do not want to apply the same frequency cut-off for these two regions. A standard Fourier filtering approach will look at the whole power spectrum for both regions and apply the frequency cutoff for the whole spectrum.Accordingly, wavelets can be better in such cases because they are localised in both the ‘time’ (here wavenumber) and frequency domains. The comparison of the transform methods with our ‘baseline’ method of a moving mean filter is instructive. It can be seen Fig. 3 Result of denoising using six wavelet methods, Fourier and median filter denoising on data set 2. Heteroscedastic noise. Only four of the applied methods are shown. Fig. 4 Reconstruction comparison for data set 2 containing heteroscedastic noise.Fig. 5 The rms error of prediction when using the eight denoising methods. Here only the best wavelet method is shown (VISU), together with the comparable classical methods (Fourier and moving mean). Analyst, July 1997, Vol. 122 651above that, with the filter length chosen as indicated, the moving mean filter is just as efficient as any of the more advanced methods at low S/N, but at the cost of poor performance at high S/N.It should be noted that shortening the length of this filter allows it to perform better than the rest at high S/N, but now at the cost of poor performance at low S/N. The advantage of the adaptive methods such as HYBRID is that they automatically produce performance close to the optimum across the whole range of noise levels studied. We thank the Chemicals and Pharmaceuticals Directorate of the UK BBSRC, GlaxoWellcome and Bruker/Spectrospin for financial support. References 1 Stark, P.B., Herron, M. M., and Matteson, A., Applied Spectrosc., 1993, 47, 1820. 2 Walczak, B., van den Bogaert, B., and Massart, D. L., Anal. Chem., 1996, 68, 1742. 3 Berger, J., Coifman, R. R., and Goldberg, M. J., J. Audio-Eng. Soc., 1994, 42, 808. 4 Coifman, R. 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Notes Math., 1983, 973, 286. 58 Wold, S., Ruhe, A., Wold, H., and Dunn, W. J., SIAM J. Sci. Stat. Comput., 1984, 5, 735. 59 Wold, S., Technometrics, 1993, 35, 136. 60 Zhu, E. Y., and Barnes, R. M., J. Chemom., 1995, 9, 363. 61 Bulsari, A. B., Neural Networks for Chemical Engineers, Elsevier, Amsterdam, 1995. 62 Bishop, C. M., Neural Networks for Pattern Recognition, Clarendon Press, Oxford, 1995. 63 Cheng, B., and Titterington, D.M., Stat. Sci., 1994, 9, 2. 64 Haykin, S., Neural Networks, Macmillan, New York, 1994. 65 Goodacre, R., Neal, M. J., and Kell, D. B., Zbl. Bakteriol., 1996, 284, 516. Paper 6/08255F Received December 9, 1996 Accepted April 21, 1997 652 Analyst, July 1997, Vol. 122 Wavelet Denoising of Infrared Spectra Bjørn K. Alsberg*a, Andrew M. Woodwarda, Michael K. Winsona, Jem Rowlandb and Douglas B.Kella a Institute of Biological Sciences, University of Wales, Aberystwyth, Ceredigion, UK SY23 3DA. E-mail: bka@aber.ac.uk b Department of Computer Science, University of Wales, Aberystwyth, Ceredigion, UK SY23 3DA The application of wavelet denoising to infrared spectra was investigated. Six different wavelet denoising methods (SURE, VISU, HYBRID, MINMAX, MAD and WAVELET PACKETS) were applied to pure infrared spectra with various added levels of homo- and heteroscedastic noise.The performances of the wavelet denoising methods were compared with the standard Fourier and moving mean filtering in terms of root mean square errors between the pure and denoised spectra and visual quality of the denoised spectrum. The use of predictive ability as a possible objective criterion for denoising performance was also investigated. The main conclusion is that for very low signal-to-noise ratios (S/N) the standard denoising methods (Fourier and moving mean) are comparable to the more sophisticated methods.At higher S/N levels the wavelet denoising methods, in particular the HYBRID and VISU methods, are better. Wavelet methods are also better in restoring the visual quality of the denoised infrared spectra. Keywords: Wavelets; wavelet packets; denoising; infrared spectra; homoscedastic noise; heteroscedastic noise; chemometrics; rapid screening The rapid quantitative and qualitative information obtained from applying multivariate methods to spectra (e.g., IR, Raman, UV) has been a very popular way of replacing slow wet chemical analyses.We are interested in particular in the determination of the concentrations of important compounds produced by industrially relevant bacteria and yeasts. In order to extract reliable information from any kind of data vector such as those in IR spectra,1,2 unwanted noise has to be dealt with.3–6 There are several ways of reducing the effect of noise in spectra, taking the mean of several co-added spectra being the most common. Unfortunately, co-adding of spectra is a timeconsuming method when a large number of spectra are to be recorded.In particular, we are interested in cases of highthroughput analyses where FTIR spectra are recorded at numerous locations on 2D surfaces, e.g., TLC plates, in biological tissues and in bacterial colonies. It is true that when a very small number of FTIR spectra are to be recorded, it is relatively rapid to use the appropriate number of co-adds to ensure a satisfactory signal-to-noise ratio, (S/N).However, when only a small number of co-adds is desired, mathematical techniques for removing the noise after recording of the spectra are more attractive. The theory of convolutions and filter theory have been applied to a wide range of problems. However, there are certain types of problem where the frequency-domain methods are not optimal for removing noise. The traditional filtering methods in most cases rely on the frequencies obtained in the power spectrum being stationary.The theory of wavelets promises several improvements to the traditional filtering methods. The major difference is the fact that wavelet methods can much better resolve frequencies varying in time (or along a pseudotime axis such as that representing wavenumbers). Theory Introduction to Wavelets and Wavelet Packets Wavelets are becoming an increasingly important tool in image and signal processing.7–10 Wavelets are effective in extracting both time- and frequency-like information from a time-varying signal.The short-time Fourier transform performs a constant bandwidth splitting of the signal whereas the wavelet transform has a proportional (octave) bandwidth splitting of the frequency domain. Unlike the Fourier transform, the wavelet transform can use a variety of different basis functions with different properties. Non-orthogonal wavelet bases are referred to as frames,11–13 but will not be discussed here.The more popular orthogonal wavelet bases have several interesting properties that make them a suitable basis for tools in signal analysis and compression. One important property of many wavelet basis functions is their localisation of both time and frequency domains simultaneously. A continuous wavelet decomposition can be written as w s b t b f t t s ( , ) ( ) ( ) = - -• •Ú Y d (1) where ys(x) is the wavelet function at a particular scale s, i.e., the same wavelet function is dilated or contracted according to the scale, and f(t) is function to be analysed; b signifies the translation of the wavelet at scale s.Eqn. (1) can be expressed as a convolution: w(s,b) = ys(t)Ûf(t)?F[w(s,b)] = F[ys(t )]F[f(t )] (2) Eqn. (1) is really a convolution of the signal f with the wavelet function in the time domain and we have emphasised this in eqn. (2) by using the convolution operator symbol Û.The equation to the right of the arrow is the convolution in the time domain expressed in the frequency domain by straightforward application of the convolution theorem;14 F indicates the Fourier transform operator. The scale can be interpreted as a measure of frequency. A short scale contains high-frequency components whereas a long scale contains low-frequency components. An intuitive way of looking at the wavelet transform is to interpret it as a sequence of combinations of bandpass filters.The wavelet function y(t ) (also referred to as the ‘mother wavelet’) can be interpreted as a high-pass filter acting on the original signal; the scaling function f(t) (also referred to as the ‘father wavelet’), on the other hand, behaves as a low-pass filter. The wavelet function y(t) can be written as a linear combination of the scaling function. The scaling function has the property that it can be written in terms of scaled versions of itself: f(x) = ckf(2x - k) k = 0 N (3) Analyst, July 1997, Vol. 122 (645–652) 645In this paper, only the discrete wavelet transform will be used. This means that we restrict the choice of scale s and translations b; in general, we set s = a0 j, b = kb0a0 j (4) where a0 = 2 and b0 = 1 is the most common choice; j is an index that can be any natural number. A common algorithm for calculating discrete wavelet coefficients is the so-called Mallat algorithm.15–17 At each scale, high- (H) and low- (L) pass filters are applied to the input signal.The actual shapes of these filters are determined by the kind of wavelet function used. The output from the high-pass filter at each scale is recorded as the wavelet coefficients. The low-pass filter extracts the low-frequency components for the next scale where another set of high- and low-pass filters is employed. At each successive scale (n 2 1) the length of the vector upon which the filters operate is halved; this is referred to as decimation.Thus, the number of scales is log2(n). The corresponding vector of wavelet coefficients for a scale j is written as w(j). Wavelet reconstruction, i.e., going from wavelet coefficients back into the original domain, is simply a multiplication of a vector w containing the coefficients for all scales with a matrix consisting of all time shifted wavelet functions for all scales: f = wBT (5) where BT is the transposed matrix of wavelet functions for all scales. The structure of the vector w is w = [w(0)w(1)w(2)···w(J)] (6) The tree structure of the Mallat algorithm can be extended such that the filters are also used on the output from the highpass filter.Such a decomposition of the data is encompased in the theory of wavelet packets.18–30 The wavelet packets form a superset of the traditional wavelet coefficients, which corresponds to the leftmost branch of the tree. Because of this algorithmic tree structure, it is possible to prune branches in the tree to optimise some fitting criterion.Denoising Using Wavelets Noise is a phenomenon that affects all frequencies, whereas the signal of interest is most likely to occupy a small part of the frequency domain. Since the signal will tend to dominate the low-frequency components, it is expected that the majority of high-frequency components above a certain level are due to noise. This is the underlying philosophy for traditional Fourier filtering where low-pass filters cut off the high-frequency components. Similarly, we can expect small wavelet coefficients at short scales to be mainly noise components.The procedure for wavelet denoising will therefore be as follows: (i) apply a wavelet transform to signal fnoisy and obtain the vector w of wavelet coefficients; (ii) suppress or remove those elements in w that are thought to be attributed to noise; and (iii) apply the cognate inverse wavelet transform to w to obtain a function f denoised.In this paper, we use eight different denoising techniques. Two of them (Fourier filtering and moving average) are used as references for the performance of the wavelet methods. All the methods presented are part of the WaveLab package for MATLAB,31 which was used in all experiments presented. Wavelet denoising methods in general32–36 use two different approaches, hard and soft thresholding. The hard thresholding philosophy is simply to set all the wavelet coefficients below a certain threshold to zero.Soft thresholding, on the other hand, reduces the value of wavelet coefficients towards zero if they are above a certain value (referred to as ‘shrinking’). For a certain wavelet coefficient at scale j we have wk = sign(wk)(õwkõ2l)+ (7) where sign returns the sign of the wavelet coefficient wk and the parentheses represent the threshold value. We will sometimes refer to this function as SOFT (w,t), where t is the threshold and w the vector to be thresholded. Methods for Denoising SURE This denoising method is based on Stein’s Unbiased Risk Estimate37 and is applied to the whole wavelet coefficient vector, i.e., the thresholding is performed on each scale j.The SURE method is a hard thresholding approach where the major work is invested in finding the right threshold for the different scales. First, we need to sort the squared wavelet coefficients {ak = [wk (j)]2} in ascending order. The cumulative total of ak is computed: bi = ak k =1 i (8) Further, a vector c is needed which has the same size as the number of elements in the current scale j.The first element in c is nj 2 1, where nj is the number of elements in the wavelet coefficient vector at scale j, and decreases linearly for successive vector elements to 0 (the last element). A risk value, ri, is computed for every wavelet coefficient: ri = (nj - 2i) + bi + aici nj (9) The wavelet coefficient that has the minimum ri is selected as the threshold value for that scale j.Note that the absolute value of the coefficient is used as the threshold. If the coefficient õwi (j)õ is chosen as the threshold, all coefficients with absolute values below will be set to zero. We will refer to this threshold as t = SURE [w(j)]. VISU For some of the denoising methods we need to specify L, which is the longest scale used in the thresholding. In this method we apply the denoising only on the coefficients in the index interval [2L + 1, n] where n is the number of wavelet coefficients.The L parameter must be much smaller than J where n = 2J. We define the threshold parameter t = (2 log n)1 2, which is used in the soft thresholding scheme described above. HYBRID This is a soft threshold method where in some cases the soft threshold tA = (2 log nj)1 2 is used, and in other cases tB = SURE [w(j)] is used, depending on the parameter e, defined as follows: e n n j j j = - w( ) 2 (10) such that (11) if then else A A B e J n SOFT t SOFT t t j j j < 3 2 / ( ) ( ) [ , ] ( ,min( , )] w w 646 Analyst, July 1997, Vol. 122where J is the total number of scales and nj is the number of elements in scale j. MEDIAN ABSOLUTE DEVIATION (MAD) Here the soft thresholding method is applied to the individual scales j. The threshold used for each scale j is s j = median[w(j) ] . 0 6745 (12) Each wavelet coefficient scale is divided by sj, v(j) = w(j)/sj, and we use the threshold t = (2 log nj)1 2. The thresholding is then done by SOFT [v(j), t].MINIMAX This procedure finds ‘optimum’ thresholds tn such that the risk R(f denoised, f), given by R( f denoised , f ) = 1 n ( f i denoised - f i )2 i =1 n (13) between the estimated wavelet coefficient qest and the true wavelet coefficient q satisfy R(qest,q)@L(e2+Ropt) (14) where L is a constant which is related to the optimum risk Ropt if we had an oracle that could tell us what wavelet coefficients are larger than the noise level e.A set of thresholds tn are used that satisfy tn @ (2 log n)1 2. For very large n the optimum threshold values will approach (2 log n)1 2. The thresholds are subsequently used in a soft thresholding scheme. Fourier This is the classical Fourier denoising approach where the components with high frequencies are assumed to represent noise only and are therefore removed. In this case we use a soft thresholding technique which is dependent on input from the user.A region in the power spectrum of the signal is specified which most likely contains noise; this is usually located in the upper region of the power spectrum. The maximum amplitude value in this region is used as a cut-off level. At the located cutoff frequency a sigmoid function is used to implement a soft threshold. Moving mean filter A simple moving average filter was chosen as the ‘baseline’ method with which to compare the other, more complicated methods.A sliding window of size w is selected. For each step in the sliding process we find the mean of the curve points inside the window. This mean value is used as the output of the filter at each step. The window size is chosen to reflect the frequency content of the true signal by making sure the cut-off frequency of the filter is slightly larger than the bandwidth of the true signal. WAVELET PACKETS (WP) The WP denoising method used here has two significant steps: estimation of the best WP basis for denoising followed by proper selection of the denoising threshold.To select a basis, the Coifman–Wickerhauser ‘best basis’ algorithm is used.38 This algorithm is based on finding the basis that gives rise to the minimum entropy of the signal energy distribution. The energy of a signal is the sum of the squares of its elements. This energy will be the same for different choices of bases, but the distribution will be different over its coordinates. To quantify this distribution, the entropy of the squares of the coordinates of the signal is used.From a data compression viewpoint it is advantageous to find a distribution with a low entropy. This means the signal can be described by a small number of bits. After finding the best basis the WP method uses Stein’s Unbiased Risk Estimate in the calculation of hard denoising thresholds. Heteroscedastic and Homoscedastic Noise Definitions and properties Let us assume we have a signal, h(t), that contains only homoscedastic noise.In general, we write this as h(t) = an(t) + s(t) (15) where a is a scalar that determines the size of the noise n(t) and s(t) is the pure signal. This Fourier transforms to H(w) = aN(w) + S(w) (16) such that the signal is independent of the noise and is concentrated only in the region defined by S(w). For heteroscedastic noise, however, the noise correlates in intensity with the amplitude of the signal h(t) = af[s(t )] n(t) + s(t) (17) where f (s) is the dependence of the noise on this signal.A Fourier transform of the noisy signal h(t) produces H(w) = aF[s(t )]ÛN(w) + S(w) (18) where Û is the convolution operator and upper case letters signify the corresponding Fourier transform of the functions in the time domain (written in lower case letters). The spectrum of the heteroscedastic noise can thus be regarded as the convolution of the spectrum of the homoscedastic noise with that of the signal.Accordingly, all frequencies in the spectrum will contain information related directly to the signal, s(t ). Constructing heteroscedastic noise When constructing heteroscedastic noise for the purpose of assessing different denoising methods, it is necessary to decide on the structure of the function f described in the previous section. The easiest choice is to let it be a constant such that the heteroscedastic noise is h(t) = a s(t ) n(t) + s(t) (19) In this paper, however, we decided to formulate f such that it is in accordance with the type of heteroscedastic noise that is normally present in absorbance spectra.It has been demonstrated39 that the non-linear transform from transmittance to absorbance spectra itself converts homoscedastic noise into heteroscedasticity. It should be stressed that other phenomena can contribute to the observed heteroscedasticity. For instance, irreproducibility of transmitter offsets may also have an influence. We have, however, in order to simplify, assumed that the heteroscedasticity observed is caused only by the conversion from transmittance to absorbance.We note that the Beer transform is A = log(I0/I) = 2log T (20) where A is the absorbance, I0 is the original intensity of the incident beam, I is the reduced intensity of the beam after passing through the sample and T is the transmittance. Homoscedastic noise in a transmittance spectrum will be converted into heteroscedasticity after the transformation into Analyst, July 1997, Vol. 122 647absorbance units. This means that our observed signal s(t ) is the result of a Beer transform s(t) = 2log[q(t )] (21) where q(t) is the transmittance signal. Adding homoscedastic noise n(t) to the transmittance signal q(t) now gives z(t) = 2log[a q(t) + n(t)] = log{1/[a q(t) + n(t)]} (22) In order to see that the noise becomes related to the size of the signal, we will use an intuitive rather than a mathematical argument.Assume that we have a large peak in the transmittance region with a small perturbation from noise. The 2log (large number + small perturbation) corresponds to a region in the 2log function that is relatively flat, i.e., the small perturbations from the noise will not change the output significantly (which now becomes an absorbance). If we have a small signal that has a size comparable to the noise, then we will have a situation where the fluctuation in the signal + noise will be comparable in size with the noise.Now, the 2log (small number + small perturbation) will be in a very steep region of the non-linear function and therefore any small changes will correspond to a large change in the output (absorbance). This means that the standard deviation (which is a measure of change in value) will be higher for regions containing small transmittance intensities (i.e., high absorbance) and low for regions containing high transmittance intensities (i.e., low absorbance).In this paper we make use of this fact and therefore convert from absorbance to transmittance units and add homoscedastic noise with a certain S/N. The S/N values in all the experiments are obtained from the following equation S / N = sj j n (sj - nj )2 j n (23) where sj and nj are the jth true signal and noise element, respectively. The noisy transmittance spectrum is subsequently transformed back into the absorbance domain where the noise is now heteroscedastic.In general, any non-linear transform of a signal will convert homoscedastic into heteroscedastic noise. Experimental Assessment of Denoising Performance We shall use two different ways of assessing the performance of the different denoising methods. The first method is based on the use of the root mean square (rms) difference between the denoised noisy spectrum and noise-free spectrum as a measure of the performance of the different methods. Since the denoising process can often introduce offsets and scalings that can influence the rms values, we employed the technique of multiplicative scatter correction (MSC)40–45 on the denoised spectra before calculating the rms differences.In MSC it is assumed that the observed spectrum y can be written in terms of the reference spectrum s as y = as + b. The MSC operation on y is therefore yh = (y 2 b)/a. In this paper y is a spectrum that has been denoised using one of the methods described and s is the noise-free spectrum.Values of a and b are constructed for every denoised spectrum for each denoising method. The rms difference is calculated between yh and s. The second method of assessing denoising preformance used in this paper is to measure the rms error of prediction on an unseen validation set using the denoised data set. All the data sets used in this paper (data sets 1–4) are such that we know the true underlying noise-free spectrum. This will, of course, not normally be the case in real applications and in general the investigator is left with visual inspection of the denoised signal as a way of determining the appropriateness of the denoising method for the data set.However, in the case of FTIR spectrometry noisy spectra will approach the ‘true’ noisefree spectra as the number of co-adds (followed by averaging) is increased. Description of Experimental Conditions Infrared spectra for data sets 2, 3 and 4 were recorded in the wavenumber interval 4000–600 cm21 using a Bruker IFS28 FTIR spectrometer (Bruker Spectrospin, Coventry, UK) equipped with a liquid nitrogen cooled MCT (mercury cadmium telluride) detector and a diffuse-reflectance absorbance TLC accessory (4 cm21 resolution, spectra collected at 20 s21).ASCII data were exported from the Opus software used to control the FTIR instrument and imported into MATLAB. Data set 1 This data set consists of an artificially generated IR absorbance spectrum to which is subsequently added homoscedastic noise and heteroscedastic noise with S/N = 1, 2, .. ., 30. Data set 2 Homoscedastic or heteroscedastic noise (S/N = 1,2, . . ., 30) was added to the pure diffuse reflectance spectrum of sodium succinate. Data set 3 To improve the S/N it is standard procedure in all instruments to take the mean of several spectra of the same sample. The S/N will improve as the square root of the number of co-added spectra that are used in the mean calculation for homoscedastic noise.This square root dependence is approximately true for heteroscedastic noise up to about 300–400 co-adds. Above this number of co-adds the S/N improves almost linearly (not shown). Unfortunately, taking the mean of a sufficiently large number of spectra is too slow a process when rapid screening of thousands of samples is necessary. Here we want to use denoising methods to improve the accuracy in the estimation of the profile of the ‘true’ spectrum (i.e., a mean spectrum of many co-adds that has a high S/N) from single co-add spectra (i.e., with low S/N).Our choice of compound in this experiment was glucose at a 20 mm concentration. The reference, and estimate of the ‘true’ spectrum, was the mean of 300 co-adds. Our data matrix was a set of 300 single co-add spectra. When we plotted the mean vector versus the standard deviation vector of this data set we observed a clear linear relationship. This confirms our knowledge about absorbance IR spectra that the standard deviation of the absorbance is proportional to the mean value of the absorbance.Unfortunately, some regions in the spectra were significantly different from the glucose regions and thus removed from the data set. These regions were 4000–3619 and 1186–600 cm21, which constituted the first and the last part of the spectra. Each of these spectra was subjected to the eight denoising methods described above and the rms difference was calculated between the denoised spectrum and the ‘true’ spectrum.The mean value of this rms difference over all the 300 spectra for all the eight methods was used to give an indication of the best method. 648 Analyst, July 1997, Vol. 122Data set 4 Data set 4 consists of 40 diffuse reflectance FTIR spectra of a developed culture of the bacterium Staphylococcus aureus containing the antibiotic ampicillin at different concentrations (0.5–20 mm). Infrared spectra (256 co-adds) for each of these samples were recorded.ASCII data were exported from the Opus software used to control the FTIR instrument and imported into MATLAB. The samples were separated into calibration and validation sets, each containing 20 objects, using the DUPLEX method.46 PLS with leave-one-out cross-validation was used for finding the optimum model for the calibration data. In order to demonstrate the denoising effect at different noise levels, we added heteroscedastic noise to the data set with S/N in the region [1, 20].Calculation and Presentation Details All the data were reconstructed using the Symmlet 8 wavelet, which we have found to be a very good wavelet for modelling spectra. One of the reasons for this is that the Symmlet 8 basis resembles to some extent the shape of peaks found in IR spectra. The low-frequency cut-off for shrinkage was set to L = 5. Denoising of the spectra was also performed using a threshold of L = 0 but it had a tendency to produce reconstructed spectra that were judged not to be sufficiently smooth.L was also used as the branch depth in the wavelet packet transform. The rms difference between the reconstructed and the true spectrum (i.e., that with very little noise) was calculated for each method at each S/N. The resulting matrix for each denoising method contained the rms differences from the true spectrum for each denoised spectrum at each S/N level. We summarise the results of these matrices by taking the mean and the standard deviation for all the spectra in the data sets.For convenience, we will sometimes refer to the different denoising methods by numbers: 1 = VISU, 2 = SURE, 3 = HYBRID, 4 = MINMAX, 5 = MAD, 6 = FOURIER, 7 = PACKETS, 8 = MOVING MEAN and 9 = NOISY SIGNAL (i.e., the untreated signal containing noise). Results Data Set 1, Homoscedastic Noise Homoscedastic noise (S/N from 1.61 to 30.00) was added to this spectrum and the results obtained by applying the various denoising methods to the noisy spectrum are given in Table 1.The best methods over the whole S/N range are the wavelet HYBRID (3) and Fourier (6) methods. The HYBRID method is slightly better than the Fourier method for low S/N ( < 7.5). At very low S/N levels the HYBRID and the Fourier methods together with the moving average converge to almost identical performance. The mean rms for the HYBRID method is 6.21 (median 3.67) and the mean for the Fourier method is 6.70 (median 4.59).To obtain a visual impression of the denoising process, we inspected the reconstruction results of four methods, HYBRID, Fourier, PACKETS and moving mean, at S/N = 4.69. The visualisation (not shown) seems to confirm the rms differences in that the denoised spectrum from the HYBRID method is better than the results from the Fourier and moving average methods. The PACKETS denoised spectrum, however, seems visually to be better than the reported rms values would suggest.In the Fourier denoised spectrum we observe unwanted ringing effects from aliasing. Similar ringing effects can be seen in the wavelet reconstructions at lower frequencies. Data Set 1, Heteroscedastic Noise Heteroscedastic noise was added to the noise-free data set 1. The results of applying the eight different denoising methods to the noisy spectrum is shown in Fig. 1. Again, the HYBRID denoising method (3) is slightly better for almost all the S/N levels, with the Fourier (6) next, equalling the HYBRID over most of the S/N range.The PACKETS method performs almost as well in this data set. The mean rms difference produced by the HYBRID method is 6.27 compared with 7.14 for the Fourier method. Reconstructed denoised spectra for methods 3, 6, 7 and 9 at a noise level S/N = 4.67 are displayed in Fig. 2. The Fourier, HYBRID and moving average methods all show similar ringing effects which are absent in the PACKETS reconstruction.Table 1 Rms differences between the ideal spectrum and the denoised spectrum for eight denoising methods applied to data set 1 to which has been added homoscedastic noise. The column headed S/N contains the signal-to-noise ratio used for each of the 20 experiments. The methods are indicated by numbers: 1 = VISU, 2 = SURE, 3 = HYBRID, 4 = MINMAX, 5 = MAD, 6 = Fourier, 7 = WAVELET PACKETS, 8 = Moving mean and 9 = NOISY SIGNAL S/N 1 2 3 4 5 6 7 8 9 1.61 31.34 32.05 30.14 41.44 30.55 27.61 30.34 81.69 27.52 3.27 17.96 17.17 12.74 23.90 17.50 13.22 20.11 40.15 13.12 4.69 17.09 13.69 11.07 16.55 14.59 12.29 14.02 27.97 12.70 6.05 12.79 15.46 9.38 14.96 13.24 13.18 11.79 21.68 10.57 7.98 10.23 10.84 6.84 10.25 11.10 6.64 7.31 16.44 9.38 9.08 10.56 8.53 8.51 9.35 11.96 10.64 9.12 14.46 9.25 10.68 8.84 9.12 5.54 9.03 9.48 5.43 6.94 12.29 9.25 12.50 7.09 6.93 4.78 7.60 8.62 4.89 6.11 10.50 8.54 13.56 6.79 5.76 3.95 6.26 6.52 6.38 5.11 9.68 7.86 15.02 6.46 5.51 3.71 5.90 8.43 5.53 4.83 8.74 8.45 17.43 5.76 4.08 3.64 5.26 7.37 3.73 4.13 7.53 8.08 18.69 5.60 3.46 2.95 4.42 6.99 3.06 3.87 7.02 7.77 20.92 5.39 4.58 3.35 4.45 8.04 4.29 3.65 6.27 8.43 21.45 5.60 3.91 3.09 3.98 7.59 3.06 3.29 6.12 8.17 22.88 5.08 3.46 2.79 3.81 7.17 2.84 3.51 5.74 7.91 24.80 4.50 4.37 2.42 3.81 6.60 2.42 3.20 5.29 7.93 26.79 4.46 3.70 2.47 3.58 6.12 2.33 3.24 4.90 7.99 28.10 4.39 2.96 2.37 3.12 6.30 2.20 3.30 4.67 7.87 29.28 4.16 2.59 2.29 2.97 6.16 2.25 2.76 4.48 7.78 30.00 4.22 2.97 2.24 2.87 5.90 2.10 2.61 4.37 7.88 Mean 8.92 8.06 6.21 9.18 10.01 6.70 7.46 15.00 9.82 Median 6.11 5.05 3.67 5.58 7.81 4.59 4.48 8.13 8.30 Analyst, July 1997, Vol. 122 649Data Set 2, Homoscedastic Noise The effect of the different denoising methods on data set 2 (to which are added various levels of homoscedastic noise) is shown in Table 2. Again, using the rms difference criterion, HYBRID (3) is the best method overall, followed very closely by both the Fourier and PACKETS methods, which behave very similarly to each other.The denoised spectrum for the four methods HYBRID, moving mean, Fourier and PACKET at noise level S/N = 4.97 was computed (not shown). We observe that the visual quality of the WAVELET PACKET denoised spectrum is better than that of the Fourier method, although this is not reflected in the trend observed in the rms difference values. The PACKET method in general produces smooth spectra but can be erroneous in larger detail.Data Set 2, Heteroscedastic Noise Fig. 3 shows the effect of the different denoising methods on data set 2, to which are added various levels of heteroscedastic noise. The HYBRID method is again best at mid and high S/N but the Fourier method performs better at low S/N. The most interesting feature from the analysis is the far superior performance of the moving mean over all the other methods for mid to low S/N. Surprisingly, the moving mean (8) method gives much lower rms values than any of the spectral methods.Is this trend also observed in the denoised spectrum for the different methods (S/ N = 3.67)? Visual inspection of the reconstructions does not reflect the rms values above (see Fig. 4). This is presumably due to the eye favouring smoothness such that a smooth signal with large scale errors would be seen as better than a slightly noisier trace which is actually more representative of the true signal.Data Set 3 The eight different denoising methods described above were used on each of the single co-adds and the rms difference was calculated between the denoised co-adds and the ‘true’ signal. The mean and the standard deviation values for all the rms values were calculated as a measure of ranking the denoising Fig. 1 Result of denoising using six wavelet methods, Fourier and median filter denoising on data set 1. Heteroscedastic noise. Only four of the applied methods are shown.Fig. 2 Reconstructed noisy spectra of data set 1 containing heteroscedastic noise. Table 2 Rms differences between the ideal spectrum and the denoised spectrum for eight denoising methods applied to data set 2 to which has been added homoscedastic noise. The column headed S/N contains the signal-to-noise ratio used for each of the 20 experiments. The methods are indicated by numbers: 1 = VISU, 2 = SURE, 3 = HYBRID, 4 = MINMAX, 5 = MAD, 6 = Fourier, 7 = WAVELET PACKETS, 8 = Moving mean and 9 = NOISY SIGNAL S/N 1 2 3 4 5 6 7 8 9 1.34 62.95 100.10 51.66 80.51 64.78 62.61 59.25 58.00 121.68 2.52 48.99 39.54 33.86 38.65 51.93 45.73 42.53 33.18 64.58 3.86 36.21 27.41 22.51 26.45 43.20 27.29 28.91 26.50 42.21 4.97 32.82 20.76 19.79 18.61 38.38 24.07 24.40 23.62 32.76 6.71 25.60 15.37 16.42 14.34 29.15 16.47 19.84 20.30 24.24 7.68 20.52 17.87 11.48 14.10 31.78 16.28 14.17 20.10 21.19 8.92 20.62 12.41 10.59 11.89 27.57 13.24 13.47 19.38 18.24 10.60 18.21 10.40 9.47 9.49 26.66 11.16 12.89 18.71 15.36 11.26 16.45 11.36 8.83 9.76 23.77 11.51 10.60 18.68 14.45 12.66 15.34 10.54 8.27 8.72 24.53 10.47 10.80 18.42 12.86 13.77 13.52 10.01 7.88 8.70 23.44 9.59 9.14 18.31 11.82 15.56 13.80 7.88 7.34 7.20 22.58 8.37 8.56 18.12 10.46 16.27 12.20 8.57 7.14 7.48 21.69 8.28 7.73 18.06 10.00 17.55 12.03 8.03 6.42 6.82 22.09 7.59 7.55 17.91 9.27 19.04 11.50 6.95 6.08 5.94 19.97 8.11 7.46 17.86 8.55 20.37 11.31 6.56 6.00 5.76 20.02 6.93 7.14 18.03 7.99 21.48 10.54 6.75 5.59 5.55 20.53 6.66 6.60 17.79 7.58 24.02 9.67 5.30 5.13 5.17 22.67 6.06 5.95 17.72 6.77 23.96 9.55 6.04 5.22 5.14 21.76 6.30 6.05 17.95 6.79 24.98 9.23 5.73 5.02 4.72 21.10 6.15 6.46 17.65 6.51 Mean 20.55 16.88 12.74 14.75 28.98 15.64 15.47 22.67 21.81 Median 14.57 10.21 8.07 8.71 23.60 10.03 9.87 18.37 12.34 650 Analyst, July 1997, Vol. 122methods.The measured S/N of the data set was fairly high, 107 ± 5. The mean rms values for the different methods were 0.85 ± 0.05 for VISU, 1.07 ± 0.05 for SURE, 1.04 ± 0.05 for HYBRID, 1.06 ± 0.05 for MINMAX, 2.8 ± 0.1 for MAD, 1.75 ± 0.03 for Fourier, 1.03 ± 0.05 for PACKETS, 1.07 ± 0.05 for moving mean and 3.88 ± 0.03 for NOISY SIGNAL.All the wavelet methods [except for method 5 (MAD)] have a lower rms than the Fourier and moving mean methods. Again, using visual inspection of the reconstructions (not shown), we see that the Fourier and moving mean methods have a tendency for oversmoothing of certain regions. The wavelet methods seem to be better at capturing significant spikes in the spectra.Data Set 4 The noise-free and untreated data set was first analysed with the partial least squares (PLS) method. A five factor PLS model was formed using full cross-validation. When this model was applied to an unseen validation set, an rms prediction error of 9.7% was achieved. Further denoising on this data set will improve the prediction error by approximately 2%.In order to observe the performance for different noise levels, heteroscedastic noise was added to the data set (S/N = 1–20). For each noise level, all the denoising methods described earlier were used prior to PLS modelling (five factors extracted). The results of the rms errors of prediction are shown in Fig. 5. As shown before, the traditional methods such as Fourier and moving average perform better than or as well as all the wavelet methods for noise levels lower than S/N = 7.Above this noise level one of the wavelet denoising methods (VISU) performs better. None of the denoising methods can achieve an rms error in prediction lower than 10% in the noise level range. Discussion and Conclusions One important implication of improved denoising techniques in IR spectrometry is that we can improve the S/N with a significantly reduced number of co-adds. This will be of particular importance for experiments in which we wish to record the IR spectra with rapidity, such as in screening for metabolite overproduction and 2D surface mappings.Under such conditions, the benefit of higher throughput is essentially in proportion to the reduction in the number of co-adds. Other experimental methods that may be expected to benefit from wavelet denoising techniques are the group of coupled methods (GC–IR, LC–IR, etc.). When the location of smaller peaks in coupled methods is necessary, heteroscedastic noise can have a devastating effect on the correctness of the results.47–49 In addition, denoising applied to spectra in general will be of importance in any kind of multivariate modelling performed on the spectra.Examples of popular methods that are often used in the analysis of spectra are PLS50–60 and neural networks.61–65 In this case it is possible to construct objective criteria that can be used to optimise denoising of spectra. For instance, it is possible to use the predictive ability or classification error to find the optimum choice of threshold in the wavelet denoising process.The need for such objective criteria is emphasised by the disparity, shown by some of the results in this paper, between the ‘quality’ of denoised spectra as assessed by rms difference values and by visual assessment of the denoised spectra. Although the wavelet approach allows greater freedom than traditional filtering methods, this also requires appropriate selection of more parameters by the user in order to optimise the denoising process.The wavelet transform allows a greater degree of compression into a smaller proportion of coefficients than the Fourier transform, and should therefore allow a greater rejection of noise with optimum parameter selection. The major improvement in the wavelet denoising methods compared with the standard filtering methods is the possibility of localising the frequency information to selected parts of the spectrum.For instance, in IR spectra we have the complex fingerprint regions in the 1000–400 cm21 range which will contain sharper peaks than in the 4000–3000 cm21 region. This means that we do not want to apply the same frequency cut-off for these two regions. A standard Fourier filtering approach will look at the whole power spectrum for both regions and apply the frequency cutoff for the whole spectrum. Accordingly, wavelets can be better in such cases because they are localised in both the ‘time’ (here wavenumber) and frequency domains.The comparison of the transform methods with our ‘baseline’ method of a moving mean filter is instructive. It can be seen Fig. 3 Result of denoising using six wavelet methods, Fourier and median filter denoising on data set 2. Heteroscedastic noise. Only four of the applied methods are shown. Fig. 4 Reconstruction comparison for data set 2 containing heteroscedastic noise. Fig. 5 The rms error of prediction when using the eight denoising methods.Here only the best wavelet method is shown (VISU), together with the comparable classical methods (Fourier and moving mean). Analyst, July 1997, Vol. 122 651above that, with the filter length chosen as indicated, the moving mean filter is just as efficient as any of the more advanced methods at low S/N, but at the cost of poor performance at high S/N. It should be noted that shortening the length of this filter allows it to perform better than the rest at high S/N, but now at the cost of poor performance at low S/N.The advantage of the adaptive methods such as HYBRID is that they automatically produce performance close to the optimum across the whole range of noise levels studied. We thank the Chemicals and Pharmaceuticals Directorate of the UK BBSRC, GlaxoWellcome and Bruker/Spectrospin for financial support. References 1 Stark, P. B., Herron, M. M., and Matteson, A., Applied Spectrosc., 1993, 47, 1820. 2 Walczak, B., van den Bogaert, B., and Massart, D. L., Anal. Chem., 1996, 68, 1742. 3 Berger, J., Coifman, R. R., and Goldberg, M. J., J. Audio-Eng. Soc., 1994, 42, 808. 4 Coifman, R. R., and Wickerhauser, M. V., Opt. Eng., 1994, 33, 2170. 5 Donoho, D. L., and Johnstone, I. M., C.R. Acad. Sci., Ser. I., 1994, 319, 1317. 6 Healy, D. M., Lu, J., and Weaver, J. B., Ann. Biomed. Eng., 1995, 23, 637. 7 Paternot, X., Signal Processing via Wavelet and Identification, Massachusetts Institute of Technology Laboratory for Information and Decision Systems, Cambridge, MA, 1996. 8 Wavelet Transform Applications to Data, Signal, Image, and Video Processing: September 11–15, 1995, Engineering 867.121, University of California Los Angeles University Extension Department of Engineering Information Systems and Technical Management Short Course Program, Los Angeles, CA, 1995. 9 Wavelet Applications in Signal and Image Processing II: 27–29 July 1994, San Diego, California, SPIE, Bellingham, WA, 1994. 10 Young, R. K., Wavelet Theory and its Applications, Kluwer, Boston, 1993. 11 Daubechies, I., Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992. 12 Daubechies, I., and Grossmann, A., Commun. Pure Appl. Math., 1988, 41, 151. 13 Teolis, A., and Benedetto, J. J., Signal Process., 1995, 45, 369. 14 Cartwright, M., Fourier Methods for Mathematicians, Scientists and Engineers, Ellis Horwood, New York, 1990. 15 Mallat, S., IEEE Trans.Pattern Anal. Machine Intell., 1989, 11, 674. 16 Mallat, S., Trans. Am. Math. Soc., 1989, 315, 69 and 18 215. 17 Davis, G., Mallat, S., and Zhang, Z. F., Opt. Eng., 1994, 33, 2183. 18 Cody, M. A., Dr. Dobbs J., 1994, 19, 44. 19 Berger, J., Coifman, R. R., and Goldberg, M. J., J. Audio-Eng. Soc., 1994, 42, 808. 20 Chu, C. H. H., Opt. Eng., 1994, 33, 2136. 21 Chui, C. K., and Li, C., SIAM J. Math. Anal., 1993, 24, 712. 22 Donoho, D. L., in Different Perspectives on Wavelets, ed. Daubechies, I., American Mathematical Society, Providence, RI, 1993, pp. 173–205. 23 Jawerth, B., and Sweldens, W., SIAM Rev., 1994, 36, 377. 24 Laine, A., and Fan, J., IEEE Trans. Pattern Anal. Machine Intell., 1993, 15, 1186. 25 Lambrecht, C. V., and Karrakchou, M., Signal Process., 1995, 47, 135. 26 Learned, R. E., and Willsky, A. S., Appl. Comput. Harmonic Anal., 1995, 2, 265. 27 Park, D., and Lee, M. H., IEEE Trans. Consumer Electron., 1994, 40, 527. 28 Wickerhauser, M. V., in Different Perspectives on Wavelets, ed. Daubechies, I., American Mathematical Society, Providence, RI, 1993, pp. 155–171. 29 Yen, N.-C., J. Am. Stat. Assoc., 1994, 95, 889. 30 Yoshida, H., Doi, K., Nishikawa, R. M., and Giger, M. L., Radiology, 1995, 197, 393. 31 Buckheit, J., Chen, S., Crutchfield, J., Donoho, D., Gao, H., Johnstone, I., Kolaczyk, E., Scargle, J., Young, K., and Yu, T., http://playfair.Stanford.EDU:80/ ~ wavelab/, 1966. 32 Donoho, D. L., and Johnstone, I. M., Biometrika, 1994, 81, 425. 33 Donoho, D. L., and Johnstone, I. M., C.R. Acad. Sci., Seri. I, 1994, 319, 1317. 34 Donoho, D. L., and Johnstone, I. M., J. Am. Stat. Assoc., 1995, 90, 1200. 35 Donoho, D. L., IEEE Trans. Inf. Theory, 1995, 41, 613. 36 Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., and Picard, D., R. Stat. Soc., Ser. B, 1995, 57, 301. 37 Donoho, D. L., and Johnstone, I. M., J. Am. Stat. Assoc., 1995, 90, 1200. 38 Coifman, R. R., and Wickerhauser, M. V., IEEE Trans. Inf. Theory, 1992, 38, 713. 39 Toft, J., and Kvalheim, O. M., Chemom. Intell. Lab. Syst., 1993, 19, 65. 40 Iversen, A. J., and Palm, T., Appl. Spectrosc., 1985, 39, 641. 41 Isaksson, T., and Næs, T., Appl. Spectrosc., 1988, 42, 1273. 42 Sorvaniemi, J., Kinnunen, A., Tsados, A., and Malkki, Y., Food Sci. Technol. Lebensm.-Wiss. Technol., 1993, 26, 251. 43 Isaksson, T., and Kowalski, B., Appl. Spectrosc., 1993, 47, 702. 44 Carlsson, A. E., and Janne, K. L. R., Appl. Spectrosc., 1995, 49, 1037. 45 Helland, I. S., Næs, T., and Isaksson, T., Chemom. Intell. Lab. Syst., 1995, 29, 233. 46 Snee, R. D., Technometrics, 1977, 19, 415. 47 Keller, H. R., Massart, D. L., Liang, Y. Z., and Kvalheim, O. M., Anal. Chim. Acta, 1992, 263, 29. 48 Kvalheim, O. M., Brakstad, F., and Liang, Y. Z., Anal. Chem., 1994, 66, 43. 49 Ritter, C., Gilliard, J. A., Cumps, J., and Tilquin, B., Anal. Chim. Acta, 1996, 318, 125. 50 Clementi, S., Alunni, S., Bisani, M. L., Bonelli, d., Chiocchini, D., Cruciani, G., Giulietti, G., Johansson, E., and Wold, S., Chim. Ind. (Milan), 1988, 70, 78. 51 DeJong, S., J. Chemom., 1993, 7, 551. 52 Frank, I. E., Chemom. Intell. Lab. Syst., 1990, 8, 109. 53 Geladi, P., Chemom. Intell. Lab. Syst., 1987, 2, 257. 54 Geladi, P., Chemom. Intell. Lab. Syst., 1992, 15 R7. 55 Holcomb, T. R., and Morari, M., Comput. Chem. Eng., 1992, 16, 393. 56 Wakeling, I. N., and Macfie, H. J. H., J. Chemom., 1992, 6, 189. 57 Wold, S., Martens, H., and Wold, H., Lect. Notes Math., 1983, 973, 286. 58 Wold, S., Ruhe, A., Wold, H., and Dunn, W. J., SIAM J. Sci. Stat. Comput., 1984, 5, 735. 59 Wold, S., Technometrics, 1993, 35, 136. 60 Zhu, E. Y., and Barnes, R. M., J. Chemom., 1995, 9, 363. 61 Bulsari, A. B., Neural Networks for Chemical Engineers, Elsevier, Amsterdam, 1995. 62 Bishop, C. M., Neural Networks for Pattern Recognition, Clarendon Press, Oxford, 1995. 63 Cheng, B., and Titterington, D. M., Stat. Sci., 1994, 9, 2. 64 Haykin, S., Neural Networks, Macmillan, New York, 1994. 65 Goodacre, R., Neal, M. J., and Kell, D. B., Zbl. Bakteriol., 1996, 284, 516. Paper 6/08255F Received December 9, 1996 Accepted April 21, 1997 652 Analyst, July 1997, Vol. 122

ISSN:0003-2654    

DOI:10.1039/a608255f

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Probability for Detecting Hot Particles in Environmental Samples by Sample Splitting K. Bunzl GSF-National Research Center for Environment and Health, Institute of Radiation Protection, Neuherberg, 85764, Germany The presence of radioactive hot particles in environmental samples (e.g., soil, vegetation, sediments) is frequently detected by observing significant differences in the activities of sub-samples, which are otherwise alike. The probabilities for detecting hot particles in this way were calculated by using Monte Carlo methods as a function of the number of hot particles in the original sample, the number of sub-samples used, the frequency distribution of the activities of the hot particles, and the precision with which the activities of the sub-samples are determined. Assuming, for example, (i) a log-normal distribution of the activities of the hot particles with a relative standard deviation h � 1, and (ii) that a difference of > 30% between the activities of the sub-sample with the largest and that with the smallest activity can be detected, splitting the original sample into three sub-samples will be sufficient to detect the presence of up to five hot particles with a probability of > 95%.If four sub-samples are used, the presence of up to 20 hot particles can be detected with this probability. In general, it will not be effective to increase the precision of the activity measurements of the sub-samples at the expense of the number of sub-samples investigated.Keywords: Hot particles; fallout; environmental samples; sample preparation; sub-sampling; probability estimates; Monte Carlo calculations Radionuclides released into the air can be present as gases, aerosols and particulate matter. In this context, particles which exhibit a point-like, very high specific activity are usually called ‘hot particles’. They may be produced by atmospheric nuclear weapon tests or nuclear reactor accidents and can be formed by two processes: disintegration of the nuclear fuel mass, or condensation of evaporated products.In particular, during the Chernobyl accident a large amount of radioactive material was released as hot particles and spread over wide areas. The largest particles (up to 150 mm) were deposited close to the release point, but smaller particles (up to a few micrometres) were found in many countries outside the former USSR, e.g., in Poland, Germany, Greece and the Scandinavian countries (for an excellent review see, e.g., ref. 1). As a result of the presence of hot particles, environmental samples (e.g., soil, vegetation, sediments and air filters) will not only be contaminated fairly uniformly owing to the dry and wet deposition of radioactive aerosols, but may also contain one or more hot particles. Failure to recognize the presence of hot particles in a sample will, however, have serious consequences: (i) The activity of the sample is no longer representative for other samples which are not contaminated by hot particles; (ii) investigations on the speciation or availability of the radionuclides for ecological processes (e.g., migration in the soil2 or plant uptake3) will produce results that are misleading; and (iii) if hot particles penetrate the human respiratory tract, the resulting very high local radiation doses have to be taken into account.Various methods exist to detect the presence of hot particles in samples.For flat surfaces, scanning devices or autoradiography are useful techniques. Bulky samples, however, such as soils, vegetation or food, are usually first mechanically well homogenized, and subsequently split into a given number of equal sub-samples (e.g., according to mass). If the activities of these sub-samples are not all alike within a given experimental error, one has to consider seriously that one or more hot particles were present in the original sample.The inverse conclusion, however, that no hot particles are present in the sample if the activities of all sub-samples are alike is not justified, because it cannot be excluded that each sub-sample contains by chance the same number of identical hot particles, or that the sum of the activities of different hot particles in each sub-sample is indistinguishable. As a result, one can detect the presence of hot particles by dividing a sample into a given number of samples only with a certain probability, which depends on the number of hot particles in the original sample, the number of sub-samples measured, and the frequency distribution of the activities of the hot particles.The purpose of this paper was, therefore, to calculate the probabilities for detecting the presence of hot particles by sample splitting as a function of these variables. This can be achieved by using Monte Carlo methods. The probabilities thus obtained can be used, e.g., to estimate the number of sub-samples required to detect the presence of hot particles in a sample with a given probability (e.g., 95 or 99%).The results are, of course, not restricted to the detection of radioactive hot particles, but can be applied to any sample, in which a chemical (e.g., a pollutant) is distributed inhomogeneously. Method Let us assume that the original sample contains a total of k hot particles. After homogenizing the sample mechanically as far as possible, it is divided into n sub-samples of equal size (e.g., for a soil sample according to mass, for an air filter according to area).Each sub-sample will then contain a certain number of hot particles between 0 and k. The resulting total activity (or the activity of a particular radionuclide), Asub-sample, of each subsample will then depend on the corresponding number and the activities, Ahp, of the hot particles. The simplest case would be to assume that all hot particles in the original sample have the same activities.This case, however, would be extremely unlikely. Experimental investigations on the frequency distribution of the activities of hot particles in the Chernobyl fallout demonstrated repeatedly the presence of log-normal distributions of Ahp.4–9 For this reason we will assume throughout the following a log-normal distribution for the activities. As will be seen later, the calculated probabilities for the detection of hot particles will not depend on the geometric mean or median activity but only on the relative width (relative standard deviation) of the frequency distribution.Analyst, July 1997, Vol. 122 (653–656) 653The two-parameter log-normal distribution shall be defined as10 f x x x y y y ( ) exp (ln ) = - - é ë êê ù û úú 1 2 1 22 2 s p s m (1) where my and sy 2 are the true mean and the variance, respectively, of the transformed random variable Y = ln X. The geometric mean, mg, and the geometric standard deviation sg, are then given as mg = exp(my); sg = exp(sy) (2) and the relative standard deviation is, in this notation 10 h s = - exp( ) y 2 1 (3) Because the width of the frequency distribution of the hot particles can vary (depending on the type of hot particles and distance from the release point), h will be a variable in the following calculations.Finally, we have to specify to what extent the activities of the n sub-samples of equal size have to differ, before we can conclude that this difference is the result of hot particles.In general, and if no hot particles are present, it will be possible to homogenize a sample by mixing to an extent that the activities of the sub-samples agree within about 10–20% relative. Therefore, when the difference between the sub-sample with the largest and that with the smallest activity is significantly larger than this value, i.e., if DAsub-samples = (Asub-sample, max 2 Asub-sample, min)/ (Asub-sample, max) (4) exceeds a given value, DA* sub-samples, we will conclude that such an observation is due to the presence of hot particles.The choice of a value for DA* sub-samples depends on the degree of mixing and on the precision of the activity measurement. In the following, values of 30 and 50% will be used for this quantity. Because the distribution of the hot particles among the subsamples can be assumed be a purely random process, the probabilities for detecting the presence of hot particles by sample splitting can be calculated by using Monte Carlo methods.Outline of Routines (1) Inputs the following data: Total number, k, of hot particles in the original sample. Number, n, of sub-samples. Relative standard deviation, h, of the log-normal distribution of the activities of the hot particles. Percentage difference, DA* sub-samples, between the activities of the sub-samples, which has to be exceeded, before the presence of hot particles in the original sample is accepted.(2) Sets the initial activities, Asub-sample, i (i = 1, 2, ..., n), of all n sub-samples to zero. (3) Draws a value for the activity, Ahp, of a hot particle at random from the selected frequency distribution. [An arbitrary value for the mean can be selected; the value of sy is obtained from the selected value of the relative standard deviation according to eqn. (3)]. The value of Ahp is then added to the activity, Asub-sample, i (1 @ i @ n), of a sub-sample, where the value of i is selected by using a random number generator, which produces integer numbers between 1 and n.Step (3) is repeated k-times. (4) Tests whether the resulting activities of the sub-samples are sufficiently different to be detectable. For that, Asub-sample, max and Asub-sample, min are found, and DAsub-samples is calculated using eqn.(4). If DAsub-samples ! DA* sub-samples, this will be counted as a positive event. (5) Repeats steps (3) and (4) z-times, where z is a large number (e.g., 1 3 105–1 3 106).(6) Calculates the probability, p, for detecting k hot particles by measuring the activities of n sub-samples as p = sum of all positive events divided by z. All calculations were performed using a log-normal frequency distribution with a geometric mean of 1 and given relative standard deviation. Repetition of a calculation using a different value for the geometric mean but with the same relative standard deviation did not change the result.Results and Discussion As mentioned, the frequency distributions observed for the activities of hot particles from the Chernobyl fallout or from other nuclear power plants are obviously in most cases lognormal4 –9 and exhibit a fairly large relative standard deviation. Mandjukov et al.7 reported, e.g., for the activity distribution of 38 hot particles (fuel fragments) a geometric mean of 12 kBq and a geometric standard deviation of 6.5.According to eqn. (4), this yields a relative standard deviation, h, of 5.7. For 85 activation (metallic) particles they observed a log-normal distribution with h = 2.45. To be conservative when calculating the probabilities for detecting hot particles we assumed the following log-normal distributions: (1) h = 0.3 and DA* sub-samples = 30%; (2) h = 1 and DA* sub-samples = 30%; (3) h = 1 and DA* sub-samples = 50%. The results are given in Tables 1–3. The errors of the calculated probabilities correspond to the number of significant digits given for these values. If we assume a fairly narrow log-normal distribution (h = 0.3) and are able to discriminate experimentally at least a difference of 30% between the largest and smallest activity of the sub-samples (DA* sub-samples = 30%), it is evident (Table 1) that splitting the original sample into only two sub-samples will not be very reliable for detecting the presence of hot particles.The resulting probabilities are, even if only a few hot particles are present in the original sample, always less than 90%.Splitting the sample into three sub-samples will yield much higher probabilities: e.g., > 90% if @10 particles are present in the original sample. If the number of sub-samples is increased to four, the probabilities are > 95% for @20 hot particles. To detect the presence of up to 20 hot particles in the original Table 1 Probabilities (in %) for detecting the presence of hot particles by sample splitting as a function of the number of hot particles in the original sample and the number of sub-samples. Prerequisites: log-normal distribution for the activities of the hot particles with a relative standard deviation h = 0.3.Minimum detectable value for differences between the activities of the sub-samples: DA* sub-samples = 30%. * ( > 95%), ** ( > 99%), *** ( > 99.9%). Number Number of sub-samples of hot particles 2 3 4 5 6 7 8 9 10 2 70 *** *** *** *** *** *** *** *** 3 88 93 *** *** *** *** *** *** *** 4 70 * * *** *** *** *** *** *** 5 74 * ** ** *** *** *** *** *** 10 60 91 * ** *** *** *** *** *** 20 46 82 * ** ** *** *** *** *** 50 24 59 84 94 * ** ** *** *** 100 9 35 63 82 93 * ** ** *** 654 Analyst, July 1997, Vol. 122sample with a probability of > 99%, at least five sub-samples are necessary. The probabilities given in Table 2 were calculated using a somewhat broader log-normal distribution of the activities of the hot particles, namely h = 1.The value of DA* sub-samples was again set to 30%. As can be seen, the probabilities obtained for the detection of hot particles will then increase. Three subsamples are already sufficient for the detection of up to five hot particles with a probability of > 95%, and four sub-samples are adequate to detect with this probability up to 20 particles. By using five sub-samples, up to ten hot particles can be found with a probability of > 99.9%, and even up to 50 with a probability of > 95%.It seems likely that most frequency distributions of the activities of the hot particles are even wider than those considered above (see e.g., ref. 8). Increasing the relative standard deviation of the frequency distribution will in general, as shown above, increase substantially the probabilities for the detection of hot particles. This can also be understood intuitively, because the chance of finding different activities of the sub-samples after distributing, e.g., three hot particles on three sub-samples, will become larger as the difference between the activities of the hot particles becomes greater.Thus, if wider frequency distributions are present than those considered here, the probabilities given in Tables 1 and 2 are lower estimates. Finally, we will examine the effect of the value used for DA* sub-samples. In the above calculations we assumed that it would be possible to detect a difference of at least 30% between the activities of the sub-sample with the largest and the smallest activity.In emergency cases, however, when, e.g., only short counting times of the samples can be employed, the error of the activity measurements might be larger, and a value of DA* sub-samples = 50% might be more realistic. Using this value and assuming again a relative standard deviation, h, of 1 for the log-normal distribution of the activities of the hot particles, the resulting probabilities are given in Table 3.As expected, these values become smaller. Three sub-samples are now sufficient only for the detection of up to three particles with a probability of > 95%. To detect the presence of up to ten hot particles with a probability > 95%, four sub-samples will be required. To detect up to five hot particles in the sample with a probability > 99.9%, five sub-samples will be necessary. Nevertheless, the data in Tables 2 and 3 show that it might not be worthwhile to measure the activities of the sub-samples with a very high precision (e.g., by using long counting times).This time might be better spent to rather increase the number of sub-samples investigated. It would, for example, be more effective to measure five sub-samples with a precision corresponding to DA* sub-samples = 50% than only three sub-samples but with a precision corresponding to DA* sub-samples = 30% (see Tables 2 and 3).Conclusions The presence of hot particles in environmental samples by determining the activity of sub-samples can be detected with a fairly high probability. The wider the frequency distribution of the activities of the hot particles (large relative standard deviation), the smaller the number of sub-samples necessary to detect the presence of hot particles with a given probability will be. Unless there is a strong indication of the presence of a large number of hot particles in the original sample (i.e., n < 5), these will usually be detected with a probability > 95% by assessing 3–4 sub-samples.In general, it will not be effective to increase the precision of the activity measurements of the sub-samples at the expense of the number of sub-samples investigated. This project was supported by the Bundesminister f�ur Umwelt, Naturschutz und Reaktorsicherheit under contract St.Sch. 4090. Its contents are solely the responsibility of the author. References 1 Sandalls, F.J., Segal, M. G., and Victorova. N., J. Environ. Radioact., 1993, 18, 5. 2 Bunzl, K., Schimmack, W., Krouglov, S. V., and Alexakhin, R. M., Sci. Total Environ., 1995, 175, 49. 3 Salbu, B., in Proceedings of an International Workshop on Hot Particles from the Chernobyl Fallout, ed. von Philipsborn, H., and Steinh�ausler, F., Schriftenreihe des Bergbau und Industriemuseums Ostbayerns, Band 16, Theuern, 1987, pp. 83–84. 4 Akopova, A. B., Viktorova, N.V., Krishchian, V. M, Magradze, N. V., Ovnanian, K. M., Tumanian, K. I., and Chalabian, T. S., Nucl. Tracks, Radiat. Meas., 1993, 21, 323. 5 Kashparov, V. A., Ivanov, Y. I., Zvarisch, S. I., Protsak, V. P., Khomutinin, Y. V., Kurepin, A. D., and Pazukhin, E. M., Radioact. Waste Manage., 1996, 114, 246. 6 Osuch, S., Dabrowska, M., Jaracz, P., Kaczanowski, J., Van Kho, L., Mirowski. S., Piasecki, E., Szeflinska, G., Szeflinski. Z., Tropilo, J., Wilhelmi, Z., Jastrzebski, J., and Pienkowski, L., Health Phys., 1989, 57, 707. 7 Mandjukov, I. G., Mandjukova, B. V., Alexiev, A., and Andreev, Ts., Radiat. Prot. Dosimetry, 1994, 54, 133. 8 Georgi, B., Helmeke, H. J., Hietel, B., and Tschiersch, J., in Proceedings of an International Workshop on Hot Particles from the Chernobyl Fallout. ed. von Philipsborn, H., and Steinh�ausler, F., Table 2 Probabilities (in %) for detecting the presence of hot particles by sample splitting as a function of the number of hot particles in the original sample and the number of sub-samples.Prerequisites: log-normal distribution for the activities of the hot particles with a relative standard deviation h = 1. Minimum detectable value for differences between the activities of the sub-samples: DA* sub-samples = 30%. * ( > 95%), ** ( > 99%), *** ( > 99.9%). Number Number of sub-samples of hot particles 2 3 4 5 6 7 8 9 10 2 88 *** *** *** *** *** *** *** *** 3 85 * *** *** *** *** *** *** *** 4 82 * *** *** *** *** *** *** *** 5 80 * ** *** *** *** *** *** *** 10 69 94 ** *** *** *** *** *** *** 20 58 89 * ** *** *** *** *** *** 50 37 75 92 * ** *** *** *** *** 100 20 56 82 93 * ** ** *** *** Table 3 Probabilities (in %) for detecting the presence of hot particles by sample splitting as a function of the number of hot particles in the original sample and the number of sub-samples.Prerequisites: log-normal distribution for the activities of the hot particles with a relative standard deviation h = 1.Minimum detectable value for differences between the activities of the sub-samples: DA* sub-samples = 50%. * ( > 95%), ** ( > 99%), *** ( > 99.9%). Number Number of sub-samples of hot particles 2 3 4 5 6 7 8 9 10 2 78 *** *** *** *** *** *** *** *** 3 72 * *** *** *** *** *** *** *** 4 67 94 ** *** *** *** *** *** *** 5 62 92 * *** *** *** *** *** *** 10 46 82 * ** ** *** *** *** *** 20 28 66 88 * ** ** *** *** *** 50 9 34 62 82 92 * ** ** ** 100 2 12 32 54 73 86 93 * * Analyst, July 1997, Vol. 122 655Schriftenreihe des Bergbau und Industriemuseums Ostbayerns. Band 16, Theuern, 1987, pp. 39–52. 9 Ivanov, Y., Kashparov, V., Sandalls, J., Laptev, G., Victorova, N., Kruglov, S., Salbu, B., Oughton, D., and Arkhipov, N., in The Radiological Consequences of the Chernobyl Accident. Proceedings of the First International Conference, ed. Karaoglou, A., Desmet, G., Kelley, G. N., and Menzel, H. G., European Commission, Brussels, 1996, pp. 173-177. 10 Gilbert, R. O., Statistical Methods for Environmental Pollution Monitoring, Van Nostrand Reinhold, New York, 1987, pp. 152– 157. Paper 7/00252A Received January 10, 1997 Accepted April 3, 1997 656 Analyst, July 1997, Vol. 122 Probability for Detecting Hot Particles in Environmental Samples by Sample Splitting K. Bunzl GSF-National Research Center for Environment and Health, Institute of Radiation Protection, Neuherberg, 85764, Germany The presence of radioactive hot particles in environmental samples (e.g., soil, vegetation, sediments) is frequently detected by observing significant differences in the activities of sub-samples, which are otherwise alike.The probabilities for detecting hot particles in this way were calculated by using Monte Carlo methods as a function of the number of hot particles in the original sample, the number of sub-samples used, the frequency distribution of the activities of the hot particles, and the precision with which the activities of the sub-samples are determined.Assuming, for example, (i) a log-normal distribution of the activities of the hot particles with a relative standard deviation h � 1, and (ii) that a difference of > 30% between the activities of the sub-sample with the largest and that with the smallest activity can be detected, splitting the original sample into three sub-samples will be sufficient to detect the presence of up to five hot particles with a probability of > 95%.If four sub-samples are used, the presence of up to 20 hot particles can be detected with this probability. In general, it will not be effective to increase the precision of the activity measurements of the sub-samples at the expense of the number of sub-samples investigated. Keywords: Hot particles; fallout; environmental samples; sample preparation; sub-sampling; probability estimates; Monte Carlo calculations Radionuclides released into the air can be present as gases, aerosols and particulate matter. In this context, particles which exhibit a point-like, very high specific activity are usually called ‘hot particles’.They may be produced by atmospheric nuclear weapon tests or nuclear reactor accidents and can be formed by two processes: disintegration of the nuclear fuel mass, or condensation of evaporated products. In particular, during the Chernobyl accident a large amount of radioactive material was released as hot particles and spread over wide areas. The largest particles (up to 150 mm) were deposited close to the release point, but smaller particles (up to a few micrometres) were found in many countries outside the former USSR, e.g., in Poland, Germany, Greece and the Scandinavian countries (for an excellent review see, e.g., ref. 1). As a result of the presence of hot particles, environmental samples (e.g., soil, vegetation, sediments and air filters) will not only be contaminated fairly uniformly owing to the dry and wet deposition of radioactive aerosols, but may also contain one or more hot particles.Failure to recognize the presence of hot particles in a sample will, however, have serious consequences: (i) The activity of the sample is no longer representative for other samples which are not contaminated by hot particles; (ii) investigations on the speciation or availability of the radionuclides for ecological processes (e.g., migration in the soil2 or plant uptake3) will produce results that are misleading; and (iii) if hot particles penetrate the human respiratory tract, the resulting very high local radiation doses have to be taken into account.Various methods exist to detect the presence of hot particles in samples. For flat surfaces, scanning devices or autoradiography are useful techniques. Bulky samples, however, such as soils, vegetation or food, are usually first mechanically well homogenized, and subsequently split into a given number of equal sub-samples (e.g., according to mass).If the activities of these sub-samples are not all alike within a given experimental error, one has to consider seriously that one or more hot particles were present in the original sample. The inverse conclusion, however, that no hot particles are present in the sample if the activities of all sub-samples are alike is not ju because it cannot be excluded that each sub-sample contains by chance the same number of identical hot particles, or that the sum of the activities of different hot particles in each sub-sample is indistinguishable. As a result, one can detect the presence of hot particles by dividing a sample into a given number of samples only with a certain probability, which depends on the number of hot particles in the original sample, the number of sub-samples measured, and the frequency distribution of the activities of the hot particles.The purpose of this paper was, therefore, to calculate the probabilities for detecting the presence of hot particles by sample splitting as a function of these variables. This can be achieved by using Monte Carlo methods. The probabilities thus obtained can be used, e.g., to estimate the number of sub-samples required to detect the presence of hot particles in a sample with a given probability (e.g., 95 or 99%). The results are, of course, not restricted to the detection of radioactive hot particles, but can be applied to any sample, in which a chemical (e.g., a pollutant) is distributed inhomogeneously.Method Let us assume that the original sample contains a total of k hot particles. After homogenizing the sample mechanically as far as possible, it is divided into n sub-samples of equal size (e.g., for a soil sample according to mass, for an air filter according to area). Each sub-sample will then contain a certain number of hot particles between 0 and k.The resulting total activity (or the activity of a particular radionuclide), Asub-sample, of each subsample will then depend on the corresponding number and the activities, Ahp, of the hot particles. The simplest case would be to assume that all hot particles in the original sample have the same activities. This case, however, would be extremely unlikely. Experimental investigations on the frequency distribution of the activities of hot particles in the Chernobyl fallout demonstrated repeatedly the presence of log-normal distributions of Ahp.4–9 For this reason we will assume throughout the following a log-normal distribution for the activities.As will be seen later, the calculated probabilities for the detection of hot particles will not depend on the geometric mean or median activity but only on the relative width (relative standard deviation) of the frequency distribution. Analyst, July 1997, Vol. 122 (653–656) 653The two-parameter log-normal distribution shall be defined as10 f x x x y y y ( ) exp (ln ) = - - é ë êê ù û úú 1 2 1 22 2 s p s m (1) where my and sy 2 are the true mean and the variance, respectively, of the transformed random variable Y = ln X.The geometric mean, mg, and the geometric standard deviation sg, are then given as mg = exp(my); sg = exp(sy) (2) and the relative standard deviation is, in this notation 10 h s = - exp( ) y 2 1 (3) Because the width of the frequency distribution of the hot particles can vary (depending on the type of hot particles and distance from the release point), h will be a variable in the following calculations. Finally, we have to specify to what extent the activities of the n sub-samples of equal size have to differ, before we can conclude that this difference is the result of hot particles.In general, and if no hot particles are present, it will be possible to homogenize a sample by mixing to an extent that the activities of the sub-samples agree within about 10–20% relative.Therefore, when the difference between the sub-sample with the largest and that with the smallest activity is significantly larger than this value, i.e., if DAsub-samples = (Asub-sample, max 2 Asub-sample, min)/ (Asub-sample, max) (4) exceeds a given value, DA* sub-samples, we will conclude that such an observation is due to the presence of hot particles. The choice of a value for DA* sub-samples depends on the degree of mixing and on the precision of the activity measurement. In the following, values of 30 and 50% will be used for this quantity.Because the distribution of the hot particles among the subsamples can be assumed to be a purely random process, the probabilities for detecting the presence of hot particles by sample splitting can be calculated by using Monte Carlo methods. Outline of Routines (1) Inputs the following data: Total number, k, of hot particles in the original sample.Number, n, of sub-samples. Relative standard deviation, h, of the log-normal distribution of the activities of the hot particles. Percentage difference, DA* sub-samples, between the activities of the sub-samples, which has to be exceeded, before the presence of hot particles in the original sample is accepted. (2) Sets the initial activities, Asub-sample, i (i = 1, 2, ..., n), of all n sub-samples to zero. (3) Draws a value for the activity, Ahp, of a hot particle at random from the selected frequency distribution.[An arbitrary value for the mean can be selected; the value of sy is obtained from the selected value of the relative standard deviation according to eqn. (3)]. The value of Ahp is then added to the activity, Asub-sample, i (1 @ i @ n), of a sub-sample, where the value of i is selected by using a random number generator, which produces integer numbers between 1 and n. Step (3) is repeated k-times. (4) Tests whether the resulting activities of the sub-samples are sufficiently different to be detectable.For that, Asub-sample, max and Asub-sample, min are found, and DAsub-samples is calculated using eqn.(4). If DAsub-samples ! DA* sub-samples, this will be counted as a positive event. (5) Repeats steps (3) and (4) z-times, where z is a large number (e.g., 1 3 105–1 3 106). (6) Calculates the probability, p, for detecting k hot particles by measuring the activities of n sub-samples as p = sum of all positive events divided by z.All calculations were performed using a log-normal frequency distribution with a geometric mean of 1 and given relative standard deviation. Repetition of a calculation using a different value for the geometric mean but with the same relative standard deviation did not change the result. Results and Discussion As mentioned, the frequency distributions observed for the activities of hot particles from the Chernobyl fallout or from other nuclear power plants are obviously in most cases lognormal4 –9 and exhibit a fairly large relative standard deviation.Mandjukov et al.7 reported, e.g., for the activity distribution of 38 hot particles (fuel fragments) a geometric mean of 12 kBq and a geometric standard deviation of 6.5. According to eqn. (4), this yields a relative standard deviation, h, of 5.7. For 85 activation (metallic) particles they observed a log-normal distribution with h = 2.45. To be conservative when calculating the probabilities for detecting hot particles we assumed the following log-normal distributions: (1) h = 0.3 and DA* sub-samples = 30%; (2) h = 1 and DA* sub-samples = 30%; (3) h = 1 and DA* sub-samples = 50%.The results are given in Tables 1–3. The errors of the calculated probabilities correspond to the number of significant digits given for these values. If we assume a fairly narrow log-normal distribution (h = 0.3) and are able to discriminate experimentally at least a difference of 30% between the largest and smallest activity of the sub-samples (DA* sub-samples = 30%), it is evident (Table 1) that splitting the original sample into only two sub-samples will not be very reliable for detecting the presence of hot particles.The resulting probabilities are, even if only a few hot particles are present in the original sample, always less than 90%. Splitting the sample into three sub-samples will yield much higher probabilities: e.g., > 90% if @10 particles are present in the original sample.If the number of sub-samples is increased to four, the probabilities are > 95% for @20 hot particles. To detect the presence of up to 20 hot particles in the original Table 1 Probabilities (in %) for detecting the presence of hot particles by sample splitting as a function of the number of hot particles in the original sample and the number of sub-samples. Prerequisites: log-normal distribution for the activities of the hot particles with a relative standard deviation h = 0.3.Minimum detectable value for differences between the activities of the sub-samples: DA* sub-samples = 30%. * ( > 95%), ** ( > 99%), *** ( > 99.9%). Number Number of sub-samples of hot particles 2 3 4 5 6 7 8 9 10 2 70 *** *** *** *** *** *** *** *** 3 88 93 *** *** *** *** *** *** *** 4 70 * * *** *** *** *** *** *** 5 74 * ** ** *** *** *** *** *** 10 60 91 * ** *** *** *** *** *** 20 46 82 * ** ** *** *** *** *** 50 24 59 84 94 * ** ** *** *** 100 9 35 63 82 93 * ** ** *** 654 Analyst, July 1997, Vol. 122sample with a probability of > 99%, at least five sub-samples are necessary. The probabilities given in Table 2 were calculated using a somewhat broader log-normal distribution of the activities of the hot particles, namely h = 1. The value of DA* sub-samples was again set to 30%. As can be seen, the probabilities obtained for the detection of hot particles will then increase. Three subsamples are already sufficient for the detection of up to five hot particles with a probability of > 95%, and four sub-samples are adequate to detect with this probability up to 20 particles.By using five sub-samples, up to ten hot particles can be found with a probability of > 99.9%, and even up to 50 with a probability of > 95%. It seems likely that most frequency distributions of the activities of the hot particles are even wider than those considered above (see e.g., ref. 8). Increasing the relative standard deviation of the frequency distribution will in general, as shown above, increase substantially the probabilities for the detection of hot particles. This can also be understood intuitively, because the chance of finding different activities of the sub-samples after distributing, e.g., three hot particles on three sub-samples, will become larger as the difference between the activities of the hot particles becomes greater. Thus, if wider frequency distributions are present than those considered here, the probabilities given in Tables 1 and 2 are lower estimates.Finally, we will examine the effect of the value used for DA* sub-samples. In the above calculations we assumed that it would be possible to detect a difference of at least 30% between the activities of the sub-sample with the largest and the smallest activity. In emergency cases, however, when, e.g., only short counting times of the samples can be employed, the error of the activity measurements might be larger, and a value of DA* sub-samples = 50% might be more realistic.Using this value and assuming again a relative standard deviation, h, of 1 for the log-normal distribution of the activities of the hot particles, the resulting probabilities are given in Table 3. As expected, these values become smaller. Three sub-samples are now sufficient only for the detection of up to three particles with a probability of > 95%.To detect the presence of up to ten hot particles with a probability > 95%, four sub-samples will be required. To detect up to five hot particles in the sample with a probability > 99.9%, five sub-samples will be necessary. Nevertheless, the data in Tables 2 and 3 show that it might not be worthwhile to measure the activities of the sub-samples with a very high precision (e.g., by using long counting times). This time might be better spent to rather increase the number of sub-samples investigated.It would, for example, be more effective to measure five sub-samples with a precision corresponding to DA* sub-samples = 50% than only three sub-samples but with a precision corresponding to DA* sub-samples = 30% (see Tables 2 and 3). Conclusions The presence of hot particles in environmental samples by determining the activity of sub-samples can be detected with a fairly high probability. The wider the frequency distribution of the activities of the hot particles (large relative standard deviation), the smaller the number of sub-samples necessary to detect the presence of hot particles with a given probability will be.Unless there is a strong indication of the presence of a large number of hot particles in the original sample (i.e., n < 5), these will usually be detected with a probability > 95% by assessing 3–4 sub-samples. In general, it will not be effective to increase the precision of the activity measurements of the sub-samples at the expense of the number of sub-samples investigated.This project was supported by the Bundesminister f�ur Umwelt, Naturschutz und Reaktorsicherheit under contract St.Sch. 4090. Its contents are solely the responsibility of the author. References 1 Sandalls, F. J., Segal, M. G., and Victorova. N., J. Environ. Radioact., 1993, 18, 5. 2 Bunzl, K., Schimmack, W., Krouglov, S. V., and Alexakhin, R. M., Sci. Total Environ., 1995, 175, 49. 3 Salbu, B., in Proceedings of an International Workshop on Hot Particles from the Chernobyl Fallout, ed.von Philipsborn, H., and Steinh�ausler, F., Schriftenreihe des Bergbau und Industriemuseums Ostbayerns, Band 16, Theuern, 1987, pp. 83–84. 4 Akopova, A. B., Viktorova, N. V., Krishchian, V. M, Magradze, N. V., Ovnanian, K. M., Tumanian, K. I., and Chalabian, T. S., Nucl. Tracks, Radiat. Meas., 1993, 21, 323. 5 Kashparov, V. A., Ivanov, Y. I., Zvarisch, S. I., Protsak, V. P., Khomutinin, Y.V., Kurepin, A. D., and Pazukhin, E. M., Radioact. Waste Manage., 1996, 114, 246. 6 Osuch, S., Dabrowska, M., Jaracz, P., Kaczanowski, J., Van Kho, L., Mirowski. S., Piasecki, E., Szeflinska, G., Szeflinski. Z., Tropilo, J., Wilhelmi, Z., Jastrzebski, J., and Pienkowski, L., Health Phys., 1989, 57, 707. 7 Mandjukov, I. G., Mandjukova, B. V., Alexiev, A., and Andreev, Ts., Radiat. Prot. Dosimetry, 1994, 54, 133. 8 Georgi, B., Helmeke, H. J., Hietel, B., and Tschiersch, J., in Proceedings of an International Workshop on Hot Particles from the Chernobyl Fallout. ed.von Philipsborn, H., and Steinh�ausler, F., Table 2 Probabilities (in %) for detecting the presence of hot particles by sample splitting as a function of the number of hot particles in the original sample and the number of sub-samples. Prerequisites: log-normal distribution for the activities of the hot particles with a relative standard deviation h = 1. Minimum detectable value for differences between the activities of the sub-samples: DA* sub-samples = 30%. * ( > 95%), ** ( > 99%), *** ( > 99.9%). Number Number of sub-samples of hot particles 2 3 4 5 6 7 8 9 10 2 88 *** *** *** *** *** *** *** *** 3 85 * *** *** *** *** *** *** *** 4 82 * *** *** *** *** *** *** *** 5 80 * ** *** *** *** *** *** *** 10 69 94 ** *** *** *** *** *** *** 20 58 89 * ** *** *** *** *** *** 50 37 75 92 * ** *** *** *** *** 100 20 56 82 93 * ** ** *** *** Table 3 Probabilities (in %) for detecting the presence of hot particles by sample splitting as a function of the number of hot particles in the original sample and the number of sub-samples. Prerequisites: log-normal distribution for the activities of the hot particles with a relative standard deviation h = 1. Minimum detectable value for differences between the activities of the sub-samples: DA* sub-samples = 50%. * ( > 95%), ** ( > 99%), *** ( > 99.9%). Number Number of sub-samples of hot particles 2 3 4 5 6 7 8 9 10 2 78 *** *** *** *** *** *** *** *** 3 72 * *** *** *** *** *** *** *** 4 67 94 ** *** *** *** *** *** *** 5 62 92 * *** *** *** *** *** *** 10 46 82 * ** ** *** *** *** *** 20 28 66 88 * ** ** *** *** *** 50 9 34 62 82 92 * ** ** ** 100 2 12 32 54 73 86 93 * * Analyst, July 1997, Vol. 122 655Schriftenreihe des Bergbau und Industriemuseums Ostbayerns. Band 16, Theuern, 1987, pp. 39–52. 9 Ivanov, Y., Kashparov, V., Sandalls, J., Laptev, G., Victorova, N., Kruglov, S., Salbu, B., Oughton, D., and Arkhipov, N., in The Radiological Consequences of the Chernobyl Accident. Proceedings of the First International Conference, ed. Karaoglou, A., Desmet, G., Kelley, G. N., and Menzel, H. G., European Commission, Brussels, 1996, pp. 173-177. 10 Gilbert, R. O., Statistical Methods for Environmental Pollution MonitoVan Nostrand Reinhold, New York, 1987, pp. 152– 157. Paper 7/00252A Received January 10, 1997 Accepted April 3, 1997 656 Analyst, July 1997, Vol. 122

ISSN:0003-2654    

DOI:10.1039/a700252a

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Simultaneous Determination of Potassium and Sodium by Optode Spectra and an Artificial Neural Network Algorithm Wing Hong Chan*a, Albert W. M. Leea, Daniel W. J. Kwonga, Yi-Zeng Liangb and Ke-Min Wangb a Department of Chemistry, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong b Department of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, China An optode device that contains two optical ion-selective membranes for potassium and sodium was used to obtain optode spectra of mixtures of these two ions. Such spectra are a non-linear function of the concentrations of the two ions. A back-propagation artificial neural network (BP-ANN) model was used to analyse these mixture optode spectra.The results showed that the BP-ANN technique is satisfactory for treating such non-linearity embedded in the data. In addition, an index for addressing the quality of the model approximation was defined and shown to be highly effective in controlling over-fitting in BP-ANN training. Keywords: Optode spectrum; potassium and sodium determination; non-linear multivariate calibration; neural network; over-fitting The development of detection methods for some clinically important ions, such as potassium and sodium, has received much attention recently.Several sodium- and potassiumselective optode membranes have been reported.1–4 These optode membranes combine the well established cationselective neutral carriers together with the neutral chromoionophores which change their absorption spectra in the visible region on protonation in the same membrane phase.Although these optode membranes have been successfully applied in optical determinations of sodium and potassium ions in human blood samples,1,2,4 their selectivities are not sufficiently adequate when the concentration of the primary ion is lower than those of the interfering ions. In addition, one cannot achieve the simultaneous determination of both sodium and potassium ions with only one kind of optode membrane.To solve these problems, an optode device that contains two kinds of optical ion-selective membranes was developed in this work. This optode device can produce an optode spectrum corresponding to a mixture of these two ions. Such spectra, however, were found to depend on the concentrations of the two ions in a non-linear fashion. A back-propagation artificial neural network (BP-ANN) algorithm was used to handle such non-linear spectral data.The results showed that the BP-ANN technique is quite satisfactory for treating the non-linearity embedded in the data. Further an index for addressing the model approximation quality was defined and was shown to be highly effective in controlling over-fitting in BP-ANN training. Principle and Algorithm Optode Device and Mixture Optode Spectrum Since an optode membrane can furnish a spectrum of an analyte, one can therefore in principle conduct multicomponent analysis with multivariate calibration techniques developed in chemometrics.In order to determine potassium and sodium ions simultaneously, the optode device shown in Fig. 1 was designed. This device incorporates ion-selective membranes for potassium and sodium in a single cell, with one side for the Na+- selective membrane, which contains the tetraester of calix[4]arene as the Na+-selective neutral carrier and ETH 5294 as the H+- selective membrane chromo-ionophore, and the other side for the K+-selective membrane, which contains the hexaester of calix[6]arene as the K+-selective neutral carrier and ETH 2439 as the H+-selective membrane chromo-ionophore. Since the two chromo-ionophores, ETH 5294 and ETH 2439, exhibit different optical absorption spectra for the fully and partially protonated forms, represented by curves A and B, respectively, in Fig. 2, this optode device can in principle furnish a spectrum containing information from both the sodium and potassium ions.Our measurements using this device indeed support such a notion. In Fig. 2 (a), when only one selective membrane for either potassium ion or sodium ion was used, the optode spectrum obtained corresponded to that due to that particular (major) ion. However, when both types of ion-selective membranes are present in the device, the mixture spectrum obtained, shown in Fig. 2 (b), gives information corresponding to both ions.This result suggests that it might be possible to determine both ions simultaneously from the obtained spectrum using multivariate calibration techniques. However, it should be pointed out that the optode spectrum obtained using this device is different from the absorption spectrum obtained in conventional spectrophotometry. Previous study3 has shown that linear relationships between the concentrations of the two ions and the apparent absorbance might not be realized. Consequently, techniques Fig. 1. Schematic diagram of the optode measurement cell with two different ion-sensing membranes: 1, polypropylene support with sample inlet and outlet; 2, O-ring seal; 3, quartz glass support; 4, Na+-selective optode membrane; 5, Plexiglas cell wall; 6, fixing screw; 7, K+-selective optode membrane. Analyst, July 1997, Vol. 122 (657–661) 657based on linear models commonly used in multivariate calibration, such as multiple linear regression (MLR), principal component regression (PCR) and partial least-squares (PLS) analysis, might not be applicable.This problem therefore calls for a technique capable of dealing with non-linear calibration. BP-ANN Algorithm and Index for Model Approximation The BP-ANN technique is a powerful non-linear mapping technique5,6 and has recently been applied in the multivariate non-linear calibration of some fluorimetric data.7 Certainly there are other techniques capable of dealing with non-linearity in data when a non-linear model which can adequately describe such data is available.8 However, the existence of such a model for data obtained from this kind of optode device is by no means assured.Therefore, a non-linear mapping technique, which requires no assumed mathematical model, was used in our data treatment and the BP-ANN technique was chosen for this purpose. Assume that C = f(A) + E (1) where An3p represents the measurement spectral matrix, in which each row denotes one of the n mixture spectra obtained from the optode device at p different wavelengths, Cn3m denotes the corresponding concentration matrix with each row expressing the concentration vector for one known mixture sample containing m distinct components in the training set.The task for the BP-ANN technique is to find a non-linear mapping, denoted by f in eqn. (1), which specifies the mathematical relationship between matrix C and A. This procedure is known as supervised training in BP-ANN in which the network is trained to generate correct outputs from inputs.After this mathematical relationship f has been determined, one can easily find the concentration matrix of an unknown sample, Cunknown,k3m, from the corresponding measurement spectral matrix, Aunknown,k3p, according to the following equation: Cunknown,k3m = f(Aunknown,k3p) (2) This procedure, defined by eqn. (2), is known as the prediction step in BP-ANN. The training procedure, defined by eqn.(1), is achieved by supervised learning, which corrects weights after one sample spectrum (a multivariate signal) passes through the network. The correction of weights is based on the error (difference) between the desired target and the actual output. Since the basic theory of the BP-ANN technique has been well described in the literature,5,9–11 we shall only give the equation for the correction of weights here: Dwji l = hdj louti l21 + mDwji l(previous) (3) The weights Dwji l on the lth layer of neurons are corrected by two terms: the d rule and the momentum term.The coefficient h is known as the learning rate constant, which determines the speed at which the weights change, and is usually set at a certain value. If the learning rate is set too low, the calculation will be slow because only small changes in weights are allowed. If the learning rate is high, the weights may change too quickly and the possibility that the weights will overshoot desirable values (i.e., the calculation will end up in a local minimum instead of a global minimum) will increase.In our calculation, the learning rate constant h was set at 0.5. The coefficient m of the previous iteration step is referred to as the momentum constant because it opposes a change in direction between successive iteration steps, just as inertia opposes a change in direction of of physical motion. With a large momentum value, the network changes direction slowly even in response to significant changes in the gradient of the error, thus allowing it to deal with oscillations due to changing input patterns or conflicting examples.However, too large a momentum value will not allow the effects of previous steps to decay and smaller values may not have sufficient stabilizing effect. In this work, through trial and error, m was set at 0.4. dj l is the error obtained on the jth neuron at the lth layer. The term outi l21 is the output from the ith neuron on the (l-1)th layer, i.e., the input to all neurons on the lth layer.Dwji l(previous) is the correction of the same weight wji l on the same level l in the previous iteration step. Thus, the problem of finding the nonlinear mapping f in eqn. (1) is now transformed into an optimization problem which can be solved by the deepest gradient descent optimization method to obtain the correction of weights [in eqn. (3)] iteratively. The most serious problem in BP-ANN is perhaps overfitting. 5 A common form of over-fitting in regression analysis is illustrated in Fig. 3. In this figure, although the curve of the best- Fig. 2. Optode spectra of A, TRIS–HCl buffer solutions at pH 7 and B, a solution containing both Na+ (146 mmol l21) and K+ (4.3 mmol l21) ions obtained from the optode device shown in Fig. 1. (a) Optode spectrum obtained with only the Na+- selective membrane (upper part) or K+- selective membrane (lower part) on one side of the measurement cell. (b) Optode spectrum obtained with the Na+-selective optode membrane mounted on one side and the K+-selective optode membrane on the other side of the measurement cell.Fig. 3. Illustration of the problem of over-fitting in regression analysis. +; Data points in control set; and o, data points in the training set. Solid line, over-fit modelling; and, dotted line, correct modelling. 658 Analyst, July 1997, Vol. 122fit model (represented by the dotted line) does not pass through all the data points in both the training and the control set, it does reflect the general trend of the data.The data points in the training set, however, can be fitted very well by an over-fitted model (shown as the solid line in Fig. 3), but the prediction errors of the data points outside of the training set are then huge. The over-fitting problem can usually be overcome by a crossvalidation technique in regression analysis.12 However in BPANN, the over-fitting problem is different from that in regression analysis.In regression analysis, the problem arises from the use of an excessive number of parameters in the model. In BP-ANN, since the network topology is already established, the over-fitting problem is really a problem of fitting the values of the parameters (i.e., the weights) and not their number. Hence, cross-validation techniques commonly used in regression analysis, such as PLSR, PCA and MLR, cannot be directly applied here.In fact, the over-fitting problem in BP-ANN is derived mainly from over-learning.5 In order to prevent the network from over-fitting, controlling the learning procedure in BP-ANN becomes paramount. A new index for monitoring the learning procedure was therefore developed in this work. To evaluate the quality of fitting, the samples are divided into two subsets, one for training and the other for control. They are called the training set and the control (test) set, respectively.In the learning procedure, error information from the training set is back-propagated to adjust the weights in the network according to eqn. (3), whereas the error information from the control set is only recorded without back-propagation. The total error information, which is called the model error in this work, is used to control the learning procedure. The model error can be defined as follows: em = (nt/n)et + (nc/n)ec + Iet-ecI = (ntet + ncec)/n + Iet-ecI (4) where et is the mean (root-mean-square) prediction error of the training set and ec is the mean (root-mean-square) prediction error of the control set during the learning procedure. The total number of samples is denoted by n, and nt and nc denote the numbers of samples in the training and the control set, respectively.Note that the model error defined in eqn. (4) consists essentially of two terms: a weighted error for all the samples and an absolute difference between the errors from the training and the control set.The first term is the weighted errors for all the samples. The errors from the training set data will decrease monotonously with an increasing number of iterations in the learning procedure. Thus, with an increasing number of iterations, the prediction errors for the data in the training set should become smaller. However, the prediction errors for the data in the control set can behave differently. In general, the prediction errors in the control set data become larger if there is over-fitting in the learning procedure.Hence, there should be a point during the learning process at which the model error reaches a minimum value. To find this optimum point in the learning procedure in BP-ANN, an index, Indappr, is defined based on the model error, em: Indappr = d/em (5) where d is a constant and was taken as 100 for convenience in this work. From eqn. (5), one can easily see that the best model approximation, with a minimized model error em, is reached when Indappr becomes a maximum in the learning procedure.Inclusion of the Iet - ecI term in the calculation of em is also used for monitoring the over-fitting problem. If Iet - ecI is large, it means that at least one of the root-mean-squared prediction errors (i.e., et or ec) must be large, therefore suggesting the occurrence of over-fitting during the learning procedure because the two prediction errors should be of comparable values.Experimental Materials In preparing the optode membrane, the following compounds were used as received: high relative molecular mass poly(vinyl chloride) (PVC) and bis(2-ethylhexyl) sebacate (BOS) from Aldrich (Milwaukee, WI, USA) and ETH 5294, ETH 2439, potassium tetrakis(4-chlorophenyl)borate (KTpClPB) from Fluka (Buchs, Switzerland). For the synthesis of the calixarene derivatives, calix[4]arene and calix[6]arene and ethyl bromoacetate were obtained from Aldrich.The hexaester and tetraester of calixarene were prepared according to literature procedures. 13,14 TRIS base for preparing buffer solutions was obtained from Sigma (St. Louis, MO, USA). Optode Membrane Preparation The Na+-selective optode membrane was prepared from a mixture of 50 mg of PVC, 100 mg of BOS, 1.02 mg of KTpClPB, 1.2 mg (0.0108 mmol) of ETH 5294 and 1.78 mg of tetraester of calix[4]arene. The K+-selective optode membrane was prepared from a mixture of 50 mg of PVC, 100 mg of BOS, 0.675 mg of KTpClPB, 1 mg (0.0108 mmol) of ETH 2439 and 1.25 mg of hexaester of calix[6]arene. The two mixtures were dissolved in 1.0 ml of tetrahydrofuran.By using a spin-on device, each membrane was cast on to a quartz plate. Two quartz plates with the two different ion-selective membranes were then mounted on the measurement cell as shown in Fig. 1. The optode device was placed in an OLIS Cary 15 UV/VIS spectrophotometer (On-line Instrument Systems Inc., Bogart, GA, USA) and the absorption spectrum (i.e., the optode spectrum) was measured.In order to cover the common range of concentrations of potassium and sodium ions in human blood, the experimental design for the training set and the control set of mixtures of the two ions is shown in Table 1. The corresponding optode spectra of these mixture samples are shown in Fig. 4. All solutions were prepared with distilled water. All inorganic chemicals were of analytical-reagent grade and were used as received.TRIS–HCl buffer solutions (0.1 mol l21) of suitable pH were used in obtaining the response curves for the optode membrane. Results and Discussion Different detection ranges of analyte concentration may be defined by adjusting the pH of the solution.3,4 However, with regard to the chromo-ionophores, ETH 5294 works better in an alkaline medium whereas ETH 2439 performs well in a slightly Table 1 Experimental design for mixtures of potassium and sodium ions Na+/mmol l21 K+/mmol l21 Samples of training set— 52.80 1.90 69.60 2.53 86.40 3.16 103.20 3.79 120.00 4.42 136.80 5.05 153.60 5.68 170.40 6.31 187.20 6.94 204.00 7.57 Samples of control set— 94.80 3.48 111.60 4.11 128.40 4.74 Analyst, July 1997, Vol. 122 659acidic medium. For the simultaneous determination of sodium and potassium, pH 7 was selected as a reasonable compromise for the sensitive use of both chromo-ionophores. As shown in Fig. 5, at pH 7, the working dynamic range for both potassium and sodium ions covers at least three orders of magnitude, which is superior to that at other pH values studied.Hence the optode spectral measurements were made at pH 7. Unlike multivariate calibration in conventional absorption spectrophotometry, in optode spectral measurements there is no simple linear relationship between the absorbance and the concentration of the analyte as described by the Lambert–Beer law.3 The relationship between the concentrations of the components and the optode spectra, f, is essentially a non-linear one.The results obtained by PCR, a linear multivariate calibration technique, confirmed this conclusion. The PCR calibration results are given in Table 2. In principle, two principal components should be sufficient for this twocomponent system. However, it is apparent from Table 2 that the results cannot be analysed by PCR using only two principal components. Slight improvements were obtained when four and five principal components were included, but the resultant errors were >10%, which is unacceptable in any quantitative chemical analysis.A non-linear multivariate calibration technique is therefore necessary. The results from BP-ANN with five principal components as inputs and seven hidden nodes are given in Table 3. From this table, we can see that the best model approximation (curve A in Fig. 6), obtained with just over 900 Fig. 4. Measured optode spectra for 13 samples with different concentrations of Na+ and K+ as listed in Table 1.Fig. 5. Response curves for the two optode membranes at pH 7. Curve a is the response curve of the K+-selective optode membrane and curve b is the response curve for the Na+-selective optode membrane. Table 2 Results from PCR with different numbers of principal components. N denotes the number of principal components included in regression. Relative error (%) N = 2 N = 4 N = 5 Set Na+ K+ Na+ K+ Na+ K+ Training set 224.24 225.20 214.90 215.47 23.86 24.00 0.07 0.04 2.34 2.38 22.01 22.10 3.04 3.12 0.20 0.20 26.11 26.24 3.60 3.67 23.70 3.78 23.45 23.53 11.74 11.95 11.45 11.65 11.18 11.38 11.30 11.47 13.17 13.37 12.38 12.55 3.63 3.68 1.44 1.46 1.77 1.80 1.25 1.27 0.65 0.66 2.42 2.44 26.81 26.88 28.73 28.82 27.42 27.50 28.97 29.06 24.44 4.49 25.45 25.51 Test set 3.13 3.20 2.00 2.05 21.72 21.75 20.49 20.50 26.22 26.34 26.66 26.79 12.76 12.97 10.84 11.01 12.48 12.67 Table 3 Relative prediction errors (%) from BP-ANN with five input and seven hidden nodes Results for best model approximation (965 iterations) Results with 3000 iterations in learning procedure Set Na+ K+ Na+ K+ Training set 2.32 3.51 0.01 0.05 23.44 23.86 20.07 20.09 2.67 2.27 0.04 20.01 21.37 21.30 0.00 0.04 21.76 21.61 20.09 20.12 2.48 2.05 0.10 0.13 0.61 1.07 0.07 0.06 20.60 20.63 20.10 20.10 21.66 21.45 20.03 20.04 0.28 20.18 0.02 20.01 Test set 23.74 23.94 25.59 25.66 0.84 0.39 21.17 21.11 1.29 1.44 3.51 3.51 Fig. 6. Mean relative prediction errors for the training set and the control set and model approximation in BP-ANN learning procedure. A, Model approximation defined in eqn. (5); B, mean relative prediction errors for the control set; and C, mean relative prediction errors for the training set. 660 Analyst, July 1997, Vol. 122iterations in the learning procedure, was satisfactory. With an increasing number of iterations in the learning procedure, the over-fitting problem emerges. The results from BP-ANN with 3000 iterations in the learning procedure illustrate this point (see Table 3).The relative prediction errors are very low ( < 0.1%), for the training set, but fairly high for the control set, with a maximum of 5.7% obtained. This is characteristic of over-fitting in BP-ANN, as illustrated previously in Fig. 3. Another problem in BP-ANN is the proper choice of the numbers of input and hidden nodes in the neural network.In order to reduce the number of input nodes, PCA was used to preprocess our data.15 In this procedure, sample scores representing the spectral data were used instead of the actual sample spectra themselves. By using a combination of these two techniques, the number of input data (i.e., input nodes) can be reduced to a small number of principal components without losing any information in the original spectral data. Consequently, the training time is dramatically reduced. Table 4 gives the prediction errors of BP-ANN modelling with different numbers of input and hidden nodes in the neural network.In this study, the best result was obtained with five input and seven hidden nodes in the network. Conclusion An optode device that contains two optical ion-selective membranes was constructed for the simultaneous determination of mixtures of sodium and potassium ions. The BP-ANN model, recently developed in chemometrics, proved to be a useful tool for handling the non-linear optode spectral data obtained using this device.An index for addressing the model over-fitting problem in BP-ANN was also defined and proved effective in controlling over-fitting in the BP-ANN learning procedure. Financial support from the Hong Kong Research Grant Council (grant number HKBC 143/95P) is gratefully acknowledged. References 1 Seiler, K., Wang, K., Bakker, E., Morf, W. E., Rusterholz, B., Sprichiger, U. E., and Simon, W., Clin. Chem. (Winston-Salem, N.C.), 1991, 37, 1350. 2 Wang, K, Seiler, K., Morf, W. E., Sprichiger, U. E., Simon, W., Lindner, E., and Pungor, E., Anal. Sci., 1990, 6, 715. 3 Chan, W. H., Lee, A. W. M., Lee, C. M., Yau, K. W., and Wang, K., Analyst, 1995, 120, 1963. 4 Chan, W. H., Lee, A. W. M., Kwong, D. W. J., Tam, W. L., and Wang, K. M., Analyst, 1996, 121, 531. 5 Simits, J. R. M., Melssen, W. J., Buydens, L. M. C., and Kateman, G., Chemom. Intell. Lab. Syst., 1994, 22, 165. 6 Simits, J.R. M., Melssen, W. J., Buydens, L. M. C., and Kateman, G., Chemom. Intell. Lab. Syst., 1994, 23, 267. 7 Liu, P., Liang, Y., Wang, S., Seng, X., and Yu, R., Chem. J. Chin. Univ., 1995, 16, 456. 8 Frank, I. E., Chemom. Intell. Lab. Syst., 1995, 27, 1. 9 Zupan, J., and Gasteiger, J., Neural Networks for Chemists: an Introduction, VCH, Weinheim, 1993. 10 Burns, J. A., and Whitesides, G. M., Chem. Rev., 1993, 93, 2583. 11 Withoff, B. J., Chemom. Intell. Lab. Syst., 1993, 18, 115. 12 Wold, S., Technometrics, 1978, 20, 397. 13 McKervey, M. A., Seward, E. M., Ferguson, G., Ruhl, B., and Harris, S. J., J. Chem. Soc., Chem. Commun., 1985, 8. 14 Iwamoto, K., Araki, K., and Shinkai, S., J. Org. Chem., 1993, 56, 4955. 15 Gemperline, P. J., Long, J. R., and Gregoriou, V. G., Anal. Chem., 1991, 63, 2313. Paper 6/08541E Received December 23, 1996 Accepted March 20, 1997 Table 4 Mean relative prediction errors (%) for BP-ANN with different numbers of input and hidden nodes (input : hidden) in network 3:5 4:5 4:8 4:9 5:7 6:8 6:9 7:8 7:9 6.61 2.65 2.76 2.60 1.78 1.93 1.81 4.36 4.09 Analyst, July 1997, Vol. 122 661 Simultaneous Determination of Potassium and Sodium by Optode Spectra and an Artificial Neural Network Algorithm Wing Hong Chan*a, Albert W. M. Leea, Daniel W. J. Kwonga, Yi-Zeng Liangb and Ke-Min Wangb a Department of Chemistry, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong b Department of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, China An optode device that contains two optical ion-selective membranes for potassium and sodium was used to obtain optode spectra of mixtures of these two ions.Such spectra are a non-linear function of the concentrations of the two ions. A back-propagation artificial neural network (BP-ANN) model was used to analyse these mixture optode spectra. The results showed that the BP-ANN technique is satisfactory for treating such non-linearity embedded in the data.In addition, an index for addressing the quality of the model approximation was defined and shown to be highly effective in controlling over-fitting in BP-ANN training. Keywords: Optode spectrum; potassium and sodium determination; non-linear multivariate calibration; neural network; over-fitting The development of detection methods for some clinically important ions, such as potassium and sodium, has received much attention recently. Several sodium- and potassiumselective optode membranes have been reported.1–4 These optode membranes combine the well established cationselective neutral carriers together with the neutral chromoionophores which change their absorption spectra in the visible region on protonation in the same membrane phase.Although these optode membranes have been successfully applied in optical determinations of sodium and potassium ions in human blood samples,1,2,4 their selectivities are not sufficiently adequate when the concentration of the primary ion is lower than those of the interfering ions. In addition, one cannot achieve the simultaneous determination of both sodium and potassium ions with only one kind of optode membrane.To solve these problems, an optode device that contains two kinds of optical ion-selective membranes was developed in this work. This optode device can produce an optode spectrum corresponding to a mixture of these two ions. Such spectra, however, were found to depend on the concentrations of the two ions in a non-linear fashion. A back-propagation artificial neural network (BP-ANN) algorithm was used to handle such non-linear spectral data.The results showed that the BP-ANN technique is quite satisfactory for treating the non-linearity embedded in the data. Further an index for addressing the model approximation quality was defined and was shown to be highly effective in controlling over-fitting in BP-ANN training. Principle and Algorithm Optode Device and Mixture Optode Spectrum Since an optode membrane can furnish a spectrum of an analyte, one can therefore in principle conduct multicomponent analysis with multivariate calibration techniques developed in chemometrics.In order to determine potassium and sodium ions simultaneously, the optode device shown in Fig. 1 was designed. This device incorporates ion-selective membranes for potassium and sodium in a single cell, with one side for the Na+- selective membrane, which contains the tetraester of calix[4]arene as the Na+-selective neutral carrier and ETH 5294 as the H+- selective membrane chromo-ionophore, and the other side for the K+-selective membrane, which contains the hexaester of calix[6]arene as the K+-selective neutral carrier and ETH 2439 as the H+-selective membrane chromo-ionophore.Since the two chromo-ionophores, ETH 5294 and ETH 2439, exhibit different optical absorption spectra for the fully and partially protonated forms, represented by curves A and B, respectively, in Fig. 2, this optode device can in principle furnish a spectrum containing information from both the sodium and potassium ions. Our measurements using this device indeed support such a notion. In Fig. 2 (a), when only one selective membrane for either potassium ion or sodium ion was used, the optode spectrum obtained corresponded to that due to that particular (major) ion. However, when both types of ion-selective membranes are present in the device, the mixture spectrum obtained, shown in Fig. 2 (b), gives information corresponding to both ions. This result suggests that it might be possible to determine both ions simultaneously from the obtained spectrum using multivariate calibration techniques. However, it should be pointed out that the optode spectrum obtained using this device is different from the absorption spectrum obtained in conventional spectrophotometry. Previous study3 has shown that linear relationships between the concentrations of the two ions and the apparent absorbance might not be realized.Consequently, techniques Fig. 1. Schematic diagram of the optode measurement cell with two different ion-sensing membranes: 1, polypropylene support with sample inlet and outlet; 2, O-ring seal; 3, quartz glass support; 4, Na+-selective optode membrane; 5, Plexiglas cell wall; 6, fixing screw; 7, K+-selective optode membrane. Analyst, July 1997, Vol. 122 (657–661) 657based on linear models commonly used in multivariate calibration, such as multiple linear regression (MLR), principal component regression (PCR) and partial least-squares (PLS) analysis, might not be applicable. This problem therefore calls for a technique capable of dealing with non-linear calibration. BP-ANN Algorithm and Index for Model Approximation The BP-ANN technique is a powerful non-linear mapping technique5,6 and has recently been applied in the multivariate non-linear calibration of some fluorimetric data.7 Certainly there are other techniques capable of dealing with non-linearity in data when a non-linear model which can adequately describe such data is available.8 However, the existence of such a model for data obtained from this kind of optode device is by no means assured.Therefore, a non-linear mapping technique, which requires no assumed mathematical model, was used in our data treatment and the BP-ANN technique was chosen for this purpose.Assume that C = f(A) + E (1) where An3p represents the measurement spectral matrix, in which each row denotes one of the n mixture spectra obtained from the optode device at p different wavelengths, Cn3m denotes the corresponding concentration matrix with each row expressing the concentration vector for one known mixture sample containing m distinct components in the training set. The task for the BP-ANN technique is to find a non-linear mapping, denoted by f in eqn.(1), which specifies the mathematical relationship between matrix C and A. This procedure is known as supervised training in BP-ANN in which the network is trained to generate correct outputs from inputs. After this mathematical relationship f has been determined, one can easily find the concentration matrix of an unknown sample, Cunknown,k3m, from the corresponding measurement spectral matrix, Aunknown,k3p, according to the following equation: Cunknown,k3m = f(Aunknown,k3p) (2) This procedure, defined by eqn.(2), is known as the prediction step in BP-ANN. The training procedure, defined by eqn. (1), is achieved by supervised learning, which corrects weights after one sample spectrum (a multivariate signal) passes through the network. The correction of weights is based on the error (difference) between the desired target and the actual output. Since the basic theory of the BP-ANN technique has been well described in the literature,5,9–11 we shall only give the equation for the correction of weights here: Dwji l = hdj louti l21 + mDwji l(previous) (3) The weights Dwji l on the lth layer of neurons are corrected by two terms: the d rule and the momentum term. The coefficient h is known as the learning rate constant, which determines the speed at which the weights change, and is usually set at a certain value.If the learning rate is set too low, the calculation will be slow because only small changes in weights are allowed.If the learning rate is high, the weights may change too quickly and the possibility that the weights will overshoot desirable values (i.e., the calculation will end up in a local minimum instead of a global minimum) will increase. In our calculation, the learning rate constant h was set at 0.5. The coefficient m of the previous iteration step is referred to as the momentum constant because it opposes a change in direction between successive iteration steps, just as inertia opposes a change in direction of of physical motion.With a large momentum value, the network changes direction slowly even in response to significant changes in the gradient of the error, thus allowing it to deal with oscillations due to changing input patterns or conflicting examples. However, too large a momentum value will not allow the effects of previous steps to decay and smaller values may not have sufficient stabilizing effect. In this work, through trial and error, m was set at 0.4. dj l is the error obtained on the jth neuron at the lth layer.The term outi l21 is the output from the ith neuron on the (l-1)th layer, i.e., the input to all neurons on the lth layer. Dwji l(previous) is the correction of the same weight wji l on the same level l in the previous iteration step. Thus, the problem of finding the nonlinear mapping f in eqn. (1) is now transformed into an optimization problem which can be solved by the deepest gradient descent optimization method to obtain the correction of weights [in eqn.(3)] iteratively. The most serious problem in BP-ANN is perhaps overfitting. 5 A common form of over-fitting in regression analysis is illustrated in Fig. 3. In this figure, although the curve of the best- Fig. 2. Optode spectra of A, TRIS–HCl buffer solutions at pH 7 and B, a solution containing both Na+ (146 mmol l21) and K+ (4.3 mmol l21) ions obtained from the optode device shown in Fig. 1. (a) Optode spectrum obtained with only the Na+- selective membrane (upper part) or K+- selective membrane (lower part) on one side of the measurement cell. (b) Optode spectrum obtained with the Na+-selective optode membrane mounted on one side and the K+-selective optode membrane on the other side of the measurement cell. Fig. 3. Illustration of the problem of over-fitting in regression analysis. +; Data points in control set; and o, data points in the training set. Solid line, over-fit modelling; and, dotted line, correct modelling. 658 Analyst, July 1997, Vol. 122fit model (represented by the dotted line) does not pass through all the data points in both the training and the control set, it does reflect the general trend of the data. The data points in the training set, however, can be fitted very well by an over-fitted model (shown as the solid line in Fig. 3), but the prediction errors of the data points outside of the training set are then huge.The over-fitting problem can usually be overcome by a crossvalidation technique in regression analysis.12 However in BPANN, the over-fitting problem is different from that in regression analysis. In regression analysis, the problem arises from the use of an excessive number of parameters in the model. In BP-ANN, since the network topology is already established, the over-fitting problem is really a problem of fitting the values of the parameters (i.e., the weights) and not their number.Hence, cross-validation techniques commonly used in regression analysis, such as PLSR, PCA and MLR, cannot be directly applied here. In fact, the over-fitting problem in BP-ANN is derived mainly from over-learning.5 In order to prevent the network from over-fitting, controlling the learning procedure in BP-ANN becomes paramount. A new index for monitoring the learning procedure was therefore developed in this work. To evaluate the quality of fitting, the samples are divided into two subsets, one for training and the other for control.They are called the training set and the control (test) set, respectively. In the learning procedure, error information from the training set is back-propagated to adjust the weights in the network according to eqn. (3), whereas the error information from the control set is only recorded without back-propagation. The total error information, which is called the model error in this work, is used to control the learning procedure. The model error can be defined as follows: em = (nt/n)et + (nc/n)ec + Iet-ecI = (ntet + ncec)/n + Iet-ecI (4) where et is the mean (root-mean-square) prediction error of the training set and ec is the mean (root-mean-square) prediction error of the control set during the learning procedure.The total number of samples is denoted by n, and nt and nc denote the numbers of samples in the training and the control set, respectively. Note that the model error defined in eqn.(4) consists essentially of two terms: a weighted error for all the samples and an absolute difference between the errors from the training and the control set. The first term is the weighted errors for all the samples. The errors from the training set data will decrease monotonously with an increasing number of iterations in the learning procedure. Thus, with an increasing number of iterations, the prediction errors for the data in the training set should become smaller.However, the prediction errors for the data in the control set can behave differently. In general, the prediction errors in the control set data become larger if there is over-fitting in the learning procedure. Hence, there should be a point during the learning process at which the model error reaches a minimum value. To find this optimum point in the learning procedure in BP-ANN, an index, Indappr, is defined based on the model error, em: Indappr = d/em (5) where d is a constant and was taken as 100 for convenience in this work.From eqn. (5), one can easily see that the best model approximation, with a minimized model error em, is reached when Indappr becomes a maximum in the learning procedure. Inclusion of the Iet - ecI term in the calculation of em is also used for monitoring the over-fitting problem. If Iet - ecI is large, it means that at least one of the root-mean-squared prediction errors (i.e., et or ec) must be large, therefore suggesting the occurrence of over-fitting during the learning procedure because the two prediction errors should be of comparable values.Experimental Materials In preparing the optode membrane, the following compounds were used as received: high relative molecular mass poly(vinyl chloride) (PVC) and bis(2-ethylhexyl) sebacate (BOS) from Aldrich (Milwaukee, WI, USA) and ETH 5294, ETH 2439, potassium tetrakis(4-chlorophenyl)borate (KTpClPB) from Fluka (Buchs, Switzerland).For the synthesis of the calixarene derivatives, calix[4]arene and calix[6]arene and ethyl bromoacetate were obtained from Aldrich. The hexaester and tetraester of calixarene were prepared according to literature procedures. 13,14 TRIS base for preparing buffer solutions was obtained from Sigma (St. Louis, MO, USA). Optode Membrane Preparation The Na+-selective optode membrane was prepared from a mixture of 50 mg of PVC, 100 mg of BOS, 1.02 mg of KTpClPB, 1.2 mg (0.0108 mmol) of ETH 5294 and 1.78 mg of tetraester of calix[4]arene.The K+-selective optode membrane was prepared from a mixture of 50 mg of PVC, 100 mg of BOS, 0.675 mg of KTpClPB, 1 mg (0.0108 mmol) of ETH 2439 and 1.25 mg of hexaester of calix[6]arene. The two mixtures were dissolved in 1.0 ml of tetrahydrofuran. By using a spin-on device, each membrane was cast on to a quartz plate. Two quartz plates with the two different ion-selective membranes were then mounted on the measurement cell as shown in Fig. 1. The optode device was placed in an OLIS Cary 15 UV/VIS spectrophotometer (On-line Instrument Systems Inc., Bogart, GA, USA) and the absorption spectrum (i.e., the optode spectrum) was measured. In order to cover the common range of concentrations of potassium and sodium ions in human blood, the experimental design for the training set and the control set of mixtures of the two ions is shown in Table 1. The corresponding optode spectra of these mixture samples are shown in Fig. 4. All solutions were prepared with distilled water. All inorganic chemicals were of analytical-reagent grade and were used as received. TRIS–HCl buffer solutions (0.1 mol l21) of suitable pH were used in obtaining the response curves for the optode membrane. Results and Discussion Different detection ranges of analyte concentration may be defined by adjusting the pH of the solution.3,4 However, with regard to the chromo-ionophores, ETH 5294 works better in an alkaline medium whereas ETH 2439 performs well in a slightly Table 1 Experimental design for mixtures of potassium and sodium ions Na+/mmol l21 K+/mmol l21 Samples of training set— 52.80 1.90 69.60 2.53 86.40 3.16 103.20 3.79 120.00 4.42 136.80 5.05 153.60 5.68 170.40 6.31 187.20 6.94 204.00 7.57 Samples of control set— 94.80 3.48 111.60 4.11 128.40 4.74 Analyst, July 1997, Vol. 122 659acidic medium. For the simultaneous determination of sodium and potassium, pH 7 was selected as a reasonable compromise for the sensitive use of both chromo-ionophores.As shown in Fig. 5, at pH 7, the working dynamic range for both potassium and sodium ions covers at least three orders of magnitude, which is superior to that at other pH values studied. Hence the optode spectral measurements were made at pH 7. Unlike multivariate calibration in conventional absorption spectrophotometry, in optode spectral measurements there is no simple linear relationship between the absorbance and the concentration of the analyte as described by the Lambert–Beer law.3 The relationship between the concentrations of the components and the optode spectra, f, is essentially a non-linear one.The results obtained by PCR, a linear multivariate calibration technique, confirmed this conclusion. The PCR calibration results are given in Table 2. In principle, two principal components should be sufficient for this twocomponent system. However, it is apparent from Table 2 that the results cannot be analysed by PCR using only two principal components. Slight improvements were obtained when four and five principal components were included, but the resultant errors were >10%, which is unacceptable in any quantitative chemical analysis.A non-linear multivariate calibration technique is therefore necessary. The results from BP-ANN with five principal components as inputs and seven hidden nodes are given in Table 3. From this table, we can see that the best model approximation (curve A in Fig. 6), obtained with just over 900 Fig. 4. Measured optode spectra for 13 samples with different concentrations of Na+ and K+ as listed in Table 1. Fig. 5. Response curves for the two optode membranes at pH 7. Curve a is the response curve of the K+-selective optode membrane and curve b is the response curve for the Na+-selective optode membrane. Table 2 Results from PCR with different numbers of principal components.N denotes the number of principal components included in regression. Relative error (%) N = 2 N = 4 N = 5 Set Na+ K+ Na+ K+ Na+ K+ Training set 224.24 225.20 214.90 215.47 23.86 24.00 0.07 0.04 2.34 2.38 22.01 22.10 3.04 3.12 0.20 0.20 26.11 26.24 3.60 3.67 23.70 3.78 23.45 23.53 11.74 11.95 11.45 11.65 11.18 11.38 11.30 11.47 13.17 13.37 12.38 12.55 3.63 3.68 1.44 1.46 1.77 1.80 1.25 1.27 0.65 0.66 2.42 2.44 26.81 26.88 28.73 28.82 27.42 27.50 28.97 29.06 24.44 4.49 25.45 25.51 Test set 3.13 3.20 2.00 2.05 21.72 21.75 20.49 20.50 26.22 26.34 26.66 26.79 12.76 12.97 10.84 11.01 12.48 12.67 Table 3 Relative prediction errors (%) from BP-ANN with five input and seven hidden nodes Results for best model approximation (965 iterations) Results with 3000 iterations in learning procedure Set Na+ K+ Na+ K+ Training set 2.32 3.51 0.01 0.05 23.44 23.86 20.07 20.09 2.67 2.27 0.04 20.01 21.37 21.30 0.00 0.04 21.76 21.61 20.09 20.12 2.48 2.05 0.10 0.13 0.61 1.07 0.07 0.06 20.60 20.63 20.10 20.10 21.66 21.45 20.03 20.04 0.28 20.18 0.02 20.01 Test set 23.74 23.94 25.59 25.66 0.84 0.39 21.17 21.11 1.29 1.44 3.51 3.51 Fig. 6. Mean relative prediction errors for the training set and the control set and model approximation in BP-ANN learning procedure. A, Model approximation defined in eqn. (5); B, mean relative prediction errors for the control set; and C, mean relative prediction errors for the training set. 660 Analyst, July 1997, Vol. 122iterations in the learning procedure, was satisfactory.With an increasing number of iterations in the learning procedure, the over-fitting problem emerges. The results from BP-ANN with 3000 iterations in the learning procedure illustrate this point (see Table 3). The relative prediction errors are very low ( < 0.1%), for the training set, but fairly high for the control set, with a maximum of 5.7% obtained. This is characteristic of over-fitting in BP-ANN, as illustrated previously in Fig. 3. Another problem in BP-ANN is the proper choice of the numbers of input and hidden nodes in the neural network. In order to reduce the number of input nodes, PCA was used to preprocess our data.15 In this procedure, sample scores representing the spectral data were used instead of the actual sample spectra themselves. By using a combination of these two techniques, the number of input data (i.e., input nodes) can be reduced to a small number of principal components without losing any information in the original spectral data.Consequently, the training time is dramatically reduced. Table 4 gives the prediction errors of BP-ANN modelling with different numbers of input and hidden nodes in the neural network. In this study, the best result was obtained with five input and seven hidden nodes in the network. Conclusion An optode device that contains two optical ion-selective membranes was constructed for the simultaneous determination of mixtures of sodium and potassium ions. The BP-ANN model, recently developed in chemometrics, proved to be a useful tool for handling the non-linear optode spectral data obtained using this device. An index for addressing the model over-fitting problem in BP-ANN was also defined and proved effective in controlling over-fitting in the BP-ANN learning procedure. Financial support from the Hong Kong Research Grant Council (grant number HKBC 143/95P) is gratefully acknowledged. References 1 Seiler, K., Wang, K., Bakker, E., Morf, W. E., Rusterholz, B., Sprichiger, U. E., and Simon, W., Clin. Chem. (Winston-Salem, N. C.), 1991, 37, 1350. 2 Wang, K, Seiler, K., Morf, W. E., Sprichiger, U. E., Simon, W., Lindner, E., and Pungor, E., Anal. Sci., 1990, 6, 715. 3 Chan, W. H., Lee, A. W. M., Lee, C. M., Yau, K. W., and Wang, K., Analyst, 1995, 120, 1963. 4 Chan, W. H., Lee, A. W. M., Kwong, D. W. J., Tam, W. L., and Wang, K. M., Analyst, 1996, 121, 531. 5 Simits, J. R. M., Melssen, W. J., Buydens, L. M. C., and Kateman, G., Chemom. Intell. Lab. Syst., 1994, 22, 165. 6 Simits, J. R. M., Melssen, W. J., Buydens, L. M. C., and Kateman, G., Chemom. Intell. Lab. Syst., 1994, 23, 267. 7 Liu, P., Liang, Y., Wang, S., Seng, X., and Yu, R., Chem. J. Chin. Univ., 1995, 16, 456. 8 Frank, I. E., Chemom. Intell. Lab. Syst., 1995, 27, 1. 9 Zupan, J., and Gasteiger, J., Neural Networks for Chemists: an Introduction, VCH, Weinheim, 1993. 10 Burns, J. A., and Whitesides, G. M., Chem. Rev., 1993, 93, 2583. 11 Withoff, B. J., Chemom. Intell. Lab. Syst., 1993, 18, 115. 12 Wold, S., Technometrics, 1978, 20, 397. 13 McKervey, M. A., Seward, E. M., Ferguson, G., Ruhl, B., and Harris, S. J., J. Chem. Soc., Chem. Commun., 1985, 8. 14 Iwamoto, K., Araki, K., and Shinkai, S., J. Org. Chem., 1993, 56, 4955. 15 Gemperline, P. J., Long, J. R., and Gregoriou, V. G., Anal. Chem., 1991, 63, 2313. Paper 6/08541E Received December 23, 1996 Accepted March 20, 1997 Table 4 Mean relative prediction errors (%) for BP-ANN with different numbers of input and hidden nodes (input : hidden) in network 3:5 4:5 4:8 4:9 5:7 6:8 6:9 7:8 7:9 6.61 2.65 2.76 2.60 1.78 1.93 1.81 4.36 4.09 Analyst, July 1997, Vol. 122 661

ISSN:0003-2654    

DOI:10.1039/a608541e

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Determination of Trimethylamine in Fish by Pervaporation and Photometric Detection J. A. Garc�ýa-Garrido and M. D. Luque de Castro* Department of Analytical Chemistry, Faculty of Sciences, University of C�ordoba, C�ordoba, E-14004, Spain. E-mail: qa1lucam@uco.es A method for the determination of trimethylamine (TMA) in liquid and solid samples is proposed. The method is based on pervaporation of the analyte and monitoring of the change in colour of a pH indicator (Bromothymol Blue) caused by the basic character of the amine.When applied to liquid samples the method is developed in a continuous manifold into which the sample is injected, transported to the separation module and detected after crossing the hydrophobic membrane and leading to the detector. The linear portion of the calibrations curve thus obtained ranges between 2 and 30 mg l21 of TMA, with an RSD of 4.7% and a sample throughput of 8 s h21. Integration of leaching and pervaporation occurs when the method is applied to solid samples as the solid is directly weighed in the pervaporator where the reagents for removal of the target analyte are injected.The linear range in this case is 0.1–10 mg g21, with a similar precision and a sampling rate of 2 h21. The method was applied to both filtrate extracts of fish muscle and to the direct analysis of fish muscle without pre-treatment and showed excellent agreement with the standard method. Keywords: Fish; solid samples; trimethylamine; photometry; pervaporation Traditionally, the evaluation of fish quality has been based on subjective criteria such as organoleptic tests.The rapidity of fish deterioration calls for reliable methods which allow an objective determination of fish freshness. A remarkable feature of the post-mortem chemical changes which take place in fish muscle is the increase in the level of volatile amine compounds, strongly influenced by conditions and duration of storage.Trimethylamine oxide is a product of the metabolic route for nitrogen removal. This compound is bacteriologically (Shewanella putrefaciens) or enzymically (phosphatase, oxidases, etc.) reduced to trimethylamine (TMA), responsible for the characteristic smell of fish.1 In addition to TMA, the aminic fraction contains small amounts of dimethylamine (DMA), methylamine (MA), ammonia and some other amines from the decarboxylation of amino acids. The concentration of TMA is an objective parameter for fish quality evaluation,2 which correlates well with organoleptic estimation.3 Several methods have been proposed for the determination of TMA, the most common of which is based on leaching with perchloric or trichloroacetic acid and subsequent reaction of the target analyte with picric acid in toluene, which gives rise to a coloured compound.4 This is a complex method subject to multiple errors, which involves several time-consuming steps.Other methods are based on distillation,5 Conway microdiffusion, 6 gas chromatography after headspace pre-treatment, 729 liquid chromatography10 and the use of a TMAselective electrode.11 Enzymic methods12 and the use of bacterial sensors13 have also been reported.Recently, Hayashi et al.14 proposed a chemiluminescence method for the rapid measurement of the fish freshness index based on the use of alkaline phosphatase, xanthine oxidase and peroxidase. The principle behind the method is the decomposition of inosine 5A- monophosphate to uric acid and hydrogen peroxide, the latter being used as indicator.Methods based on flow injection (FI), which involve continuous separation of the volatile analyte using membrane-based separation techniques, have also been reported.15217 These methods show serious shortcomings such as pumping of organic solvents and complex hydrodynamic manifolds, in addition to clogging and deterioration of the membrane due to direct contact with the sample.The method proposed here is based on a simple, continuous manifold which incorporates a pervaporation module18,19 for removal of the volatile analyte either from the solid sample or from an extract of it. Pervaporation emphasizes in its name the fact that the analyte or its volatile reaction product undergoes a phase change from liquid to vapour before permeating through a membrane (usually hydrophobic). This technique has long been used in industry in competition with other separation techniques such as distillation, extraction and adsorption.On a laboratory scale, pervaporation involves the integration of two principles of analytical separations: evaporation and gas diffusion, thus endowing the process with simplicity and miniaturisation and improving the quality of the analytical determination. Pervaporation is not only endowed with the advantages characteristic of membrane-based separation techniques, but also with others arising from the absence of sample– membrane contact (no clogging or deterioration of the membrane) and sometimes with those from the integration of separation and detection.20 A continuous manifold has been designed and used for the introduction of liquid samples into the pervaporator.Solid samples are weighed in the module where the leaching reagents are injected, thus integrating the leaching and separation steps. Experimental Reagent and Solutions All chemicals were of analytical-reagent grade and ultrapure water from a Milli-Q Plus system (Millipore, Bedford, MA, USA) was used.An indicator stock standard solution was prepared from 0.0624 g of Bromothymol Blue (BTB) dissolved in 40 ml of ethanol (96%; Panreac, Barcelona, Spain) and diluted to 100 ml with ultrapure water.21 This solution is stable for at least 1 month. The acceptor solution contained 1 3 1024 m BTB and was prepared daily from 25 ml of the indicator stock standard solution diluted to 250 ml with ultrapure water.The pH of this solution was adjusted to 6.00 ± 0.02 with dilute NaOH solution. The donor was 1 m NaOH (Merck, Darmstadt, Germany) solution. A stock standard solution of TMA containing 1000 mg l21 of the analyte was prepared from TMA chlorohydrate, dried at 100 °C for 1 h and dissolved in 0.5 m trichloroacetic acid (TCA). From this, working standard solutions were prepared by dilution with 0.5 m TCA. A 6.5 m aqueous formaldehyde solution was also prepared.Hydrophobic membranes were supplied by Millipore and Trace (Braunschweig, Germany). Analyst, July 1997, Vol. 122 (663–666) 663Instruments and Apparatus The hydrodynamic manifold was built from two Gilson (Wortlington, OH, USA) Minipuls-3 peristaltic pumps, a Rheodyne (Cotati, CA, USA) rotary injection valve and PTFE tubing of 0.5 mm id. The change in colour of the indicator solution was monitored with a Pye Unicam (Cambridge, UK) Model 8625 spectrophotometer equipped with a Hellma (Jamaica, NY, USA) 178.12QS flow cell (inner volume 18 ml and optical path 10 mm) and connected to a Merck–Hitachi (Darmstadt, Germany) D-2500 integrator for peak area collection. The pervaporation module was designed by the authors and made of methacrylate, except for the membrane support, which was made of Teflon as described elsewhere.18220 This module consists of a donor, sample chamber and an acceptor, upper chamber (both provided with inlet and outlet orifices in order to be coupled in-line with the hydrodynamic manifold) and a membrane support.The volume of both chambers can be changed by locating spacers of the appropriate thickness between the corresponding chamber and the membrane support. Metallic rods, screws and two aluminium supports permit close contact between the pervaporator parts. A Selecta (Barcelona, Spain) 382-S water-bath was used for heating the donor chamber as required. Procedure Liquid samples The continuous manifold used for liquid samples is shown in Fig. 1. Prior to filling the loop of the injection valve IV1, the sample merges with a formaldehyde stream which acts as a masking agent of other volatile amines. The sample is then injected into NaOH solution and also merges with a secondary stream of NaOH, which makes the pH along the injected plug homogeneous, thus also making the formation of the volatile form of the target analyte homogeneous. The homation is improved along reactor RC2, which also allows an increase in the temperature of the injected plug, which is thus closer to the working temperature of the lower chamber of the pervaporator.The injection valve IV2 is in its filling position during the pervaporation step, thus allowing the contents of the loop to remain static. Meanwhile, the acceptor stream is led to the detector in order to establish the baseline. After a pre-set interval for sufficient enrichment of the acceptor solution with the analyte (change in colour of the pH indicator in the acceptor solution), valve IV2 is switched to the inject position and the acceptor stream leads the coloured portion to the detector.Solid samples The experimental set-up for solid samples is shown in Fig. 2. This is a hybrid discontinuous–continuous approach in which the continuous subsystem (upper part of the overall system) is as that designed for liquid samples. The sample (approximately 0.1 g) is weighed in the donor chamber, which is then tightly joined to a 2 mm spacer, the membrane support and upper chamber.The inlet and outlet orifices of the donor chamber are closed with septa and through them the reagents (1 ml of trichloroacetic acid for leaching the analyte, 1 ml of formaldehyde for masking other amines and 1 ml of NaOH for formation of the volatile form of TMA) are injected by means of a syringe helped by a hypodermic needle. The separation module is then placed in a thermostated bath provided with a magnetic stirrer and leaching of the analyte, masking of the interferences, formation of the volatile product, evaporation and diffusion through the membrane take place simultaneously.After a preset interval, the subsequent step takes place in the upper subsystem as described for liquid samples. Conventional Procedure The sample is weighed (100 ± 0.5 g) and placed in a macerator with 300 ml of 5% TCA. The macerator is run for approximately 30 min until a homogeneous suspension is obtained, which is centrifuged for 15 min in order to obtain a clear extract.A portion of not more than 4 ml of extract is taken and water is added to a total volume of 4 ml. Volumes of 1 ml of 20% formaldehyde, 10 ml of toluene and 3 ml of sodium hydroxide solution are added, then the mixture is shaken vigorously for 10 min and 8–9 ml of the toluene layer are transferred into a testtube containing 0.3 g of anhydrous sodium sulfate.The tube is shaken gently (5 min) to dry the toluene and allowed to settle. A 5 ml volume of the toluene layer is transferred into a test-tube containing 5 ml of picric acid solution and mixed by swirling gently (5 min). The absorbance is then monitored at 410 nm. Sample Pre-treatment The recommendations of the Commission of Analytical Methods for Analysis of Fish and Derivatives22 were followed. For direct analysis of solid samples the pre-treatment consisted of removing the skin and homogenising the muscle with a domestic meat cutter for 10 min.An additional extraction step with TCA and subsequent filtration by gravity are required for liquid samples. Results and Discussion Optimisation of Variables The optimisation study of variables concerning the performance of the acceptor subsystem was common for both solid and liquid Fig. 1. Manifold for the determination of trimethylamine in liquid samples. After merging with the masking solution of formaldehyde, the sample is injected and the basic pH along the plug is homogenised by merging with an additional stream of NaOH before reaching the pervaporation module (PM).The flow through the acceptor chamber is halted by switching valve IV2 to the filling position for a pre-set time, after which the flow is restarted by changing IV2 to injection. The waste is aspirated in order to avoid pulses. P, peristaltic pump; S, sample; RC, reaction coil; D, detector; W, waste; and BTB, Bromothymol Blue.Fig. 2 Manifold for the determination of trimethylamine in solid samples. After weighing the sample in the donor chamber, the reagents are injected through the septa (Se). Valve IV allows the flow in the upper chamber to be halted in order to preconcentrate the analyte. Other abbreviations as in Fig. 1. 664 Analyst, July 1997, Vol. 122samples. This study can be divided into three parts: (a) variables of the upper subsystem and those of the (b) donor dynamic and (c) donor static subsystems.Optimisation of the upper subsystem The composition, concentration and pH of the acceptor solution affect the features of the determination step. The analytical signal (both area and height of the peak) increases about 65% when the concentration of BTB changes from 1 3 1026 to 1 3 1024 m. Above the latter concentration the percentage of ethanol necessary for solubilisation of the indicator causes deterioration of the hydrophobic membrane.The pH of this solution has a contradictory effect on the sensitivity and linearity range of the method. Hence a pH of 6.00 was adopted as a compromise. The stability of the baseline decreases when the pH increases. The presence of a buffer system such as acetic acid–sodium acetate, to adjust the pH, decreases the sensitivity and does not improve the reproducibility of the method. Variables affecting the donor dynamic subsystem The composition, concentration and pH of the donor solution condition the conversion of the protonated analyte into the neutral, volatile form. A 2 m NaOH solution is sufficient to guarantee the total conversion into non-protonated TMA.This solution is used both as a carrier and as a merging stream in order to ensure a constant pH along the injected plug of sample. No salting-out effect was observed when NaCl in the range 1–5 m was added to the donor solution, probably owing to both the low boiling-point of the target analyte (3 °C) and the concentration of the NaOH solution.The flow rate in both subsystems is a key variable in order to obtain optimum performance. A low flow rate of the acceptor solution (between 0.2 and 0.6 ml min21 causes significant dispersion, thus giving rise to both flat and wide signals and long determination times. On the other hand, flow rates ! 0.8 ml min21 produce an overpressure on the hydrophobic membrane. A flow rate of 1.0 ml min21 was adopted as a compromise. A low flow rate of the donor solution increases the level in the donor chamber owing to overpressure caused by the presence of glass beads which pack this chamber in order to increase reproducibility.18,19 An increase in the level in this chamber results in both undesirable dilution and irreproducibility. A flow rate of 1.0 ml min21 avoids this shortcoming and provides both an acceptable sample frequency and residence time of the sample in the corresponding chamber.The best results in terms of reproducibility and absence of overpressure are obtained when the flow rates in both chambers are identical.An injected sample volume of 500 ml is the best in order to obtain good sensitivity, precision, linearity range and sampling frequency. An increase in temperature of the donor chamber increases the efficiency of the separation, but also accelerates membrane deterioration. Owing to the volatility of the analyte, a temperature of 60 °C was sufficient for obtaining good mass transfer through the membrane.Other variables influencing the pervaporation step are the stop time of the acceptor solution, membrane type and thickness and the presence of spacers. The adoption of 3 min as a halt time was a compromise between sensitivity and sample throughput. PTEF gas-diffusion membranes give more reproducible results than ultrafiltration membranes of the same material.18,19 Both the durability of the membrane and the sensitivity of the method depend on the membrane thickness, so a 1 mm thick membrane was used as a compromise.The location of spacers between the donor chamber and the membrane support decreases the sensitivity, but they can be used in order to fit the absorbance obtained to the linear range for concentrated samples. Variables affecting the donor, static subsystem The variables of the donor chamber for optimum discontinuous performance were studied using diatomaceous earth spiked with TMA and consisted of the concentration and volume of the reagents injected for leaching and formation of the volatile species.The concentration of leacher (TCA) between 4.0 and 8.0 m gives a constant value of the signal for this step, which decreases to 12% for a concentration of 10 m. A 1 ml volume of this agent with stirring for 5 min is sufficient when 0.1 g samples are used (larger samples provide signals above the linear range in most cases). Concentrations of NaOH of ! 4 m provide a constant formation of volatile product which is 9.2% higher than that provided by a 2 m solution.Injected volumes above 1 ml decrease the analytical signal, probably owing to dilution of the analyte. Table 1 gives the values of the optimised variables. Features of the Method Calibration curves were obtained using both the manifold in Fig. 1 (injection of standard solutions of TMA) and that in Fig. 2 (diatomaceous earth spiked with standard solutions of TMA). The precision of the method for solid samples was significantly improved when the transient signal was evaluated in terms of peak area (RSD 3.47%) instead of peak height (RSD 7.89%).The equations, linear ranges, correlation coefficients and RSDs are given in Table 2. The sampling frequency was 8 and 2 h21 for liquid and solid samples, respectively. The detection limits, calculated as proposed by Miller and Miller,23 were 0.08 mg g21 and 1.6 mg l21 for solid and liquid samples, respectively.Study of Interferences Table 3 shows the disturbance of the analytical signal caused by the main nitrogen-containing bases which usually are found in fish together with the analyte. Different concentrations of formaldehyde were examined as masking agents and a 20% Table 1 Optimisation of variables Range Optimum Parameter studied value Liquid samples— [BTB]/m 1 3 1024–1 3 1026 1 3 1024 Acceptor solution pH 5–7.5 6.0 [NaOH]/m 1 2 Acceptor flow rate/ml min21 0.2–1.2 1.0 Donor flow rate/ml min21 0.5–2.0 1.0 Volume injected/ml 100–1000 500 Temperature/°C 40–80 60 Stop-time of acceptor solution/min 0–5 3 Solid samples— [TCA]/m 5–10 6.5 Sample amount/g 0.1–1 0.1 [NaOH]/m 2–6 6 Leaching time/min 1–10 5 Table 2 Features of the proposed method Linear range/mg TMA per 100 g RSD (%) Sample Equation* sample (n = 11) r Solid y = 6.914x + 28.06 0.1–10 3.47 0.998 Liquid y = 5.726x + 328 2.0–30 4.27 0.999 * Solid samples: y = peak area, x = mg TMA g21 sample.Liquid samples: y = peak height, x = mg l21 of TMA. Analyst, July 1997, Vol. 122 665aqueous solution proved to be appropriate in order to obtain acceptable tolerance levels, taking into account that the working pH is not the optimum for the masking reaction.24 The study was performed with both the manifold in Fig. 2 (injection of the masking solution) and that in Fig. 1 (inclusion of an additional channel which merges with the sample channel). After addition of this reagent to the overall system, the concentration of NaOH solution which provided the best results was 6 m.Application of the Method to Fish Samples Samples of both fresh and frozen fish of different types were analysed using both procedures and the results were compared with those provided by the recommended method4 in all instances. The comparison (t-test, adopting as null hypothesis the absence of significant differences) showed non-significant differences between the two methods for a confidence level P = 0.05.Table 4 gives the concentrations found by both the proposed and the conventional methods and the RSD for n = 3. Conclusions Simple continuous and hybrid manifolds coupled to a pervaporation module have proved to be an excellent system for the determination of fish freshness through the formation of trimethylamine. Compared with the recommended method, similar results are obtained in a shorter time (8 and 28 min for liquid and solid samples, respectively, versus 65 min for the conventional method).The continuous manifold for liquid samples requires a prior sample treatment, but in turn the determination can be easily automated. Filtration of the pre-treated sample can be avoided if tubing of sufficient diameter is used. The discontinuous–continuous approach allows the development of the overall analytical process with little human participation (only for sample weighing, closing of the separation module and injection of reagents).In both instances the usefulness of pervaporation for the development of an automated or semi-automated method for the determination of TMA in fish has been demonstrated. The capability of this separation technique for the integration of different steps provides the possibility of miniaturisation. The Comisi�on Interministerial de Ciencia y Tecnolog�ýa is thanked for financial support (Project No. PB 93-0827). References 1 Ringo, E., Stenberg, E., and Stroem, A.R., Appl. Environ. Microbiol., 1984, 47, 1084. 2 Belitz, H. D., and Grosch, W., Food Chemistry, Springer, Berlin, 1987. 3 Hoogland, P. L., J. Fish. Res. Bd. Can., 1958, 15, 15. 4 Association of Official Analytical Chemists, Official Method of Analysis of the Association of Official Analytical Chemists, AOAC, Arlington, VA, 15th edn., 1990, vol. 1, p. 869. 5 Shewan, J. M., Gibson, D. M., and Murray, C. K., Fish Insp. Qual. Control, 1971, 71, 183. 6 Conway, W. J., Microdiffusion Analysis and Volumetric Error, Crosby Lockwood, London, 1962, p. 98. 7 Fiddler, W., Doerr, R. C., and Gates, R. A., J. Assoc. Off. Anal. Chem., 1992, 74, 400. 8 Dacosta, K. A., Vrbanac, J. J., and Zeisel, S. H., Anal. Biochem., 1990, 187, 234. 9 Lundstrom, R. C., and Racicot, L. D., J. Assoc. Off. Anal. Chem., 1983, 66, 1168. 10 Gill, T. A., and Thomson, J., J. Food Sci., 1984, 49, 603. 11 Chang, G. W., Chang, W. L., and Lew, K. B. K., J. Food Sci., 1976, 41, 723. 12 Wong, K., and Gill, T.A., J. Food Sci., 1987, 52, 1. 13 Gamati, S., Luong, J. H. T., and Mulchandani, A., Biosens. Bioelectron.,1991, 6, 125. 14 Hayashi, T., Imato, T. and Asano, Y., Anal. Chim. Acta, 1996, 317, 284. 15 Le�on, A., Chica, A., Garc�ýa-Raurich, J., and Centrich, F., Quim. Anal., 1994, 13, 78. 16 Zhi, Z.-L., R�ýos, A., and Valc�arcel M., Anal. Chem., 1995, 34, 247. 17 Sadok, S., Uglow, R. F., and Haswell, S. J., Anal. Chim. Acta, 1996, 321, 69. 18 Mattos, I. L., Luque de Castro, M.D., and Valc�arcel, M., Talanta, 1995, 42, 755. 19 Mattos, I. L., and Luque de Castro, M. D., Anal. Chim. Acta, 1994, 298, 159. 20 Papafstathiou, I., and Luque de Castro, M. D., Anal. Chem., 1995, 67, 3916. 21 Bishop, E., Indicators, Pergamon Press, Oxford, 1972, p. 109. 22 Analytical Methods Committee, The Analyst, 1979, 104, 434. 23 Miller, J. C., and Miller, J. N., Statistics for Analytical Chemistry, Ellis Horwood, Chichester, 2nd edn., 1988, p. 120. 24 Morrison, R., and Boyd, R., Organic Chemistry, Allyn and Bacon, Boston, 4th edn., 1983. Paper 7/00547D Received January 23, 1997 Accepted April 23, 1997 Table 3 Interference study (%)* Analyte-to-foreign species ratio† Foreign species 2 : 1 1 : 1 1 : 2 1 : 5 1 : 10 1 : 15 1 : 20 Methylamine – – – 13.9 58.1 88.2 Dimethylamine – – – 16.9 49.5 90.3 Ammonia – – – – – 8.9 26.8 * Percentage increase of the analytical signal (absorbance) caused by the inferent. † mg TMA: mg foreign species; 4.5 mg TMA per 100 g sample.Table 4 Application of the method and comparison with official method.4 Concentrations in mg l21 and mg g21 for liquid and solid samples, respectively Sample Proposed method Official method Solid samples— Frozen turbot 2.9 ± 0.27 2.74 ± 0.08 Frozen turbot (1 month) 3.7 ± 0.19 3.3 ± 0.11 Frozen hake 9.7 ± 0.26 10.1 ± 0.06 Frozen hake (2 months) 11.9 ± 0.31 13.6 ± 0.08 Fresh hake 6.9 ± 0.46 6.3 ± 0.10 Liquid samples— Frozen turbot 2.3 ± 0.39 2.6 ± 0.06 Frozen lemon fish 2.9 ± 0.42 2.04 ± 0.09 Frozen hake I 4.62 ± 0.29 4.9 ± 0.06 Frozen hake II 11.9 ± 0.30 12.6 ± 0.05 Elaborated sole 2.7 &p04 ± 0.07 Frozen turbot (3 months) 4.78 ± 0.29 4.34 ± 0.08 Mackerel (tinned) 23.7 ± 0.26 22.6 ± 0.1 Fresh sardine 14.1 ± 0.47 13.13 ± 0.07 Fresh salmon 1.9 ± 0.17 2.1 ± 0.05 666 Analyst, July 1997, Vol. 122 Determination of Trimethylamine in Fish by Pervaporation and Photometric Detection J. A. Garc�ýa-Garrido and M. D.Luque de Castro* Department of Analytical Chemistry, Faculty of Sciences, University of C�ordoba, C�ordoba, E-14004, Spain. E-mail: qa1lucam@uco.es A method for the determination of trimethylamine (TMA) in liquid and solid samples is proposed. The method is based on pervaporation of the analyte and monitoring of the change in colour of a pH indicator (Bromothymol Blue) caused by the basic character of the amine. When applied to liquid samples the method is developed in a continuous manifold into which the sample is injected, transported to the separation module and detected after crossing the hydrophobic membrane and leading to the detector. The linear portion of the calibrations curve thus obtained ranges between 2 and 30 mg l21 of TMA, with an RSD of 4.7% and a sample throughput of 8 s h21. Integration of leaching and pervaporation occurs when the method is applied to solid samples as the solid is directly weighed in the pervaporator where the reagents for removal of the target analyte are injected.The linear range in this case is 0.1–10 mg g21, with a similar precision and a sampling rate of 2 h21. The method was applied to both filtrate extracts of fish muscle and to the direct analysis of fish muscle without pre-treatment and showed excellent agreement with the standard method. Keywords: Fish; solid samples; trimethylamine; photometry; pervaporation Traditionally, the evaluation of fish quality has been based on subjective criteria such as organoleptic tests.The rapidity of fish deterioration calls for reliable methods which allow an objective determination of fish freshness. A remarkable feature of the post-mortem chemical changes which take place in fish muscle is the increase in the level of volatile amine compounds, strongly influenced by conditions and duration of storage. Trimethylamine oxide is a product of the metabolic route for nitrogen removal. This compound is bacteriologically (Shewanella putrefaciens) or enzymically (phosphatase, oxidases, etc.) reduced to trimethylamine (TMA), responsible for the characteristic smell of fish.1 In addition to TMA, the aminic fraction contains small amounts of dimethylamine (DMA), methylamine (MA), ammonia and some other amines from the decarboxylation of amino acids.The concentration of TMA is an objective parameter for fish quality evaluation,2 which correlates well with organoleptic estimation.3 Several methods have been proposed for the determination of TMA, the most common of which is based on leaching with perchloric or trichloroacetic acid and subsequent reaction of the target analyte with picric acid in toluene, which gives rise to a coloured compound.4 This is a complex method subject to multiple errors, which involves several time-consuming steps.Other methods are based on distillation,5 Conway microdiffusion, 6 gas chromatography after headspace pre-treatment, 729 liquid chromatography10 and the use of a TMAselective electrode.11 Enzymic methods12 and the use of bacterial sensors13 have also been reported.Recently, Hayashi et al.14 proposed a chemiluminescence method for the rapid measurement of the fish freshness index based on the use of alkaline phosphatase, xanthine oxidase and peroxidase. The principle behind the method is the decomposition of inosine 5A- monophosphate to uric acid and hydrogen peroxide, the latter being used as indicator.Methods based on flow injection (FI), which involve continuous separation of the volatile analyte using membrane-based separation techniques, have also been reported.15217 These methods show serious shortcomings such as pumping of organic solvents and complex hydrodynamic manifolds, in addition to clogging and deterioration of the membrane due to direct contact with the sample. The method proposed here is based on a simple, continuous manifold which incorporates a pervaporation module18,19 for removal of the volatile analyte either from the solid sample or from an extract of it.Pervaporation emphasizes in its name the fact that the analyte or its volatile reaction product undergoes a phase change from liquid to vapour before permeating through a membrane (usually hydrophobic). This technique has long been used in industry in competition with other separation techniques such as distillation, extraction and adsorption. On a laboratory scale, pervaporation involves the integration of two principles of analytical separations: evaporation and gas diffusion, thus endowing the process with simplicity and miniaturisation and improving the quality of the analytical determination.Pervaporation is not only endowed with the advantages characteristic of membrane-based separation techniques, but also with others arising from the absence of sample– membrane contact (no clogging or deterioration of the membrane) and sometimes with those from the integration of separation and detection.20 A continuous manifold has been designed and used for the introduction of liquid samples into the pervaporator.Solid samples are weighed in the module where the leaching reagents are injected, thus integrating the leaching and separation steps. Experimental Reagent and Solutions All chemicals were of analytical-reagent grade and ultrapure water from a Milli-Q Plus system (Millipore, Bedford, MA, USA) was used.An indicator stock standard solution was prepared from 0.0624 g of Bromothymol Blue (BTB) dissolved in 40 ml of ethanol (96%; Panreac, Barcelona, Spain) and diluted to 100 ml with ultrapure water.21 This solution is stable for at least 1 month. The acceptor solution contained 1 3 1024 m BTB and was prepared daily from 25 ml of the indicator stock standard solution diluted to 250 ml with ultrapure water. The pH of this solution was adjusted to 6.00 ± 0.02 with dilute NaOH solution.The donor was 1 m NaOH (Merck, Darmstadt, Germany) solution. A stock standard solution of TMA containing 1000 mg l21 of the analyte was prepared from TMA chlorohydrate, dried at 100 °C for 1 h and dissolved in 0.5 m trichloroacetic acid (TCA). From this, working standard solutions were prepared by dilution with 0.5 m TCA. A 6.5 m aqueous formaldehyde solution was also prepared. Hydrophobic membranes were supplied by Millipore and Trace (Braunschweig, Germany). Analyst, July 1997, Vol. 122 (663–666) 663Instruments and Apparatus The hydrodynamic manifold was built from two Gilson (Wortlington, OH, USA) Minipuls-3 peristaltic pumps, a Rheodyne (Cotati, CA, USA) rotary injection valve and PTFE tubing of 0.5 mm id.The change in colour of the indicator solution was monitored with a Pye Unicam (Cambridge, UK) Model 8625 spectrophotometer equipped with a Hellma (Jamaica, NY, USA) 178.12QS flow cell (inner volume 18 ml and optical path 10 mm) and connected to a Merck–Hitachi (Darmstadt, Germany) D-2500 integrator for peak area collection.The pervaporation module was designed by the authors and made of methacrylate, except for the membrane support, which was made of Teflon as described elsewhere.18220 This module consists of a donor, sample chamber and an acceptor, upper chamber (both provided with inlet and outlet orifices in order to be coupled in-line with the hydrodynamic manifold) and a membrane support. The volume of both chambers can be changed by locating spacers of the appropriate thickness between the corresponding chamber and the membrane support. Metallic rods, screws and two aluminium supports permit close contact between the pervaporator parts.A Selecta (Barcelona, Spain) 382-S water-bath was used for heating the donor chamber as required. Procedure Liquid samples The continuous manifold used for liquid samples is shown in Fig. 1. Prior to filling the loop of the injection valve IV1, the sample merges with a formaldehyde stream which acts as a masking agenther volatile amines.The sample is then injected into NaOH solution and also merges with a secondary stream of NaOH, which makes the pH along the injected plug homogeneous, thus also making the formation of the volatile form of the target analyte homogeneous. The homogenisation is improved along reactor RC2, which also allows an increase in the temperature of the injected plug, which is thus closer to the working temperature of the lower chamber of the pervaporator.The injection valve IV2 is in its filling position during the pervaporation step, thus allowing the contents of the loop to remain static. Meanwhile, the acceptor stream is led to the detector in order to establish the baseline. After a pre-set interval for sufficient enrichment of the acceptor solution with the analyte (change in colour of the pH indicator in the acceptor solution), valve IV2 is switched to the inject position and the acceptor stream leads the coloured portion to the detector.Solid samples The experimental set-up for solid samples is shown in Fig. 2. This is a hybrid discontinuous–continuous approach in which the continuous subsystem (upper part of the overall system) is as that designed for liquid samples. The sample (approximately 0.1 g) is weighed in the donor chamber, which is then tightly joined to a 2 mm spacer, the membrane support and upper chamber.The inlet and outlet orifices of the donor chamber are closed with septa and through them the reagents (1 ml of trichloroacetic acid for leaching the analyte, 1 ml of formaldehyde for masking other amines and 1 ml of NaOH for formation of the volatile form of TMA) are injected by means of a syringe helped by a hypodermic needle. The separation module is then placed in a thermostated bath provided with a magnetic stirrer and leaching of the analyte, masking of the interferences, formation of the volatile product, evaporation and diffusion through the membrane take place simultaneously.After a preset interval, the subsequent step takes place in the upper subsystem as described for liquid samples. Conventional Procedure The sample is weighed (100 ± 0.5 g) and placed in a macerator with 300 ml of 5% TCA. The macerator is run for approximately 30 min until a homogeneous suspension is obtained, which is centrifuged for 15 min in order to obtain a clear extract.A portion of not more than 4 ml of extract is taken and water is added to a total volume of 4 ml. Volumes of 1 ml of 20% formaldehyde, 10 ml of toluene and 3 ml of sodium hydroxide solution are added, then the mixture is shaken vigorously for 10 min and 8–9 ml of the toluene layer are transferred into a testtube containing 0.3 g of anhydrous sodium sulfate. The tube is shaken gently (5 min) to dry the toluene and allowed to settle. A 5 ml volume of the toluene layer is transferred into a test-tube containing 5 ml of picric acid solution and mixed by swirling gently (5 min).The absorbance is then monitored at 410 nm. Sample Pre-treatment The recommendations of the Commission of Analytical Methods for Analysis of Fish and Derivatives22 were followed. For direct analysis of solid samples the pre-treatment consisted of removing the skin and homogenising the muscle with a domestic meat cutter for 10 min. An additional extraction step with TCA and subsequent filtration by gravity are required for liquid samples.Results and Discussion Optimisation of Variables The optimisation study of variables concerning the performance of the acceptor subsystem was common for both solid and liquid Fig. 1. Manifold for the determination of trimethylamine in liquid samples. After merging with the masking solution of formaldehyde, the sample is injected and the basic pH along the plug is homogenised by merging with an additional stream of NaOH before reaching the pervaporation module (PM).The flow through the acceptor chamber is halted by switching valve IV2 to the filling position for a pre-set time, after which the flow is restarted by changing IV2 to injection. The waste is aspirated in order to avoid pulses. P, peristaltic pump; S, sample; RC, reaction coil; D, detector; W, waste; and BTB, Bromothymol Blue. Fig. 2 Manifold for the determination of trimethylamine in solid samples. After weighing the sample in the donor chamber, the reagents are injected through the septa (Se).Valve IV allows the flow in the upper chamber to be halted in order to preconcentrate the analyte. Other abbreviations as in Fig. 1. 664 Analyst, July 1997, Vol. 122samples. This study can be divided into three parts: (a) variables of the upper subsystem and those of the (b) donor dynamic and (c) donor static subsystems. Optimisation of the upper subsystem The composition, concentration and pH of the acceptor solution affect the features of the determination step. The analytical signal (both area and height of the peak) increases about 65% when the concentration of BTB changes from 1 3 1026 to 1 3 1024 m.Above the latter concentration the percentage of ethanol necessary for solubilisation of the indicator causes deterioration of the hydrophobic membrane. The pH of this solution has a contradictory effect on the sensitivity and linearity range of the method.Hence a pH of 6.00 was adopted as a compromise. The stability of the baseline decreases when the pH increases. The presence of a buffer system such as acetic acid–sodium acetate, to adjust the pH, decreases the sensitivity and does not improve the reproducibility of the method. Variables affecting the donor dynamic subsystem The composition, concentration and pH of the donor solution condition the conversion of the protonated analyte into the neutral, volatile form. A 2 m NaOH solution is sufficient to guarantee the total conversion into non-protonated TMA.This solution is used both as a carrier and as a merging stream in order to ensure a constant pH along the injected plug of sample. No salting-out effect was observed when NaCl in the range 1–5 m was added to the donor solution, probably owing to both the low boiling-point of the target analyte (3 °C) and the concentration of the NaOH solution. The flow rate in both subsystems is a key variable in order to obtain optimum performance. A low flow rate of the acceptor solution (between 0.2 and 0.6 ml min21 causes significant dispersion, thus giving rise to both flat and wide signals and long determination times.On the other hand, flow rates ! 0.8 ml min21 produce an overpressure on the hydrophobic membrane. A flow rate of 1.0 ml min21 was adopted as a compromise. A low flow rate of the donor solution increases the level in the donor chamber owing to overpressure caused by the presence of glass beads which pack this chamber in order to increase reproducibility.18,19 An increase in the level in this chamber results in both undesirable dilution and irreproducibility.A flow rate of 1.0 ml min21 avoids this shortcoming and provides both an acceptable sample frequency and residence time of the sample in the corresponding chamber. The best results in terms of reproducibility and absence of overpressure are obtained when the flow rates in both chambers are identical.An injected sample volume of 500 ml is the best in order to obtain good sensitivity, precision, linearity range and sampling frequency. An increase in temperature of the donor chamber increases the efficiency of the separation, but also accelerates membrane deterioration. Owing to the volatility of the analyte, a temperature of 60 °C was sufficient for obtaining good mass transfer through the membrane. Other variables influencing the pervaporation step are the stop time of the acceptor solution, membrane type and thickness and the presence of spacers.The adoption of 3 min as a halt time was a compromise between sensitivity and sample throughput. PTEF gas-diffusion membranes give more reproducible results than ultrafiltration membranes of the same material.18,19 Both the durability of the membrane and the sensitivity of the method depend on the membrane thickness, so a 1 mm thick membrane was used as a compromise. The location of spacers between the donor chamber and the membrane support decreases the sensitivity, but they can be used in order to fit the absorbance obtained to the linear range for concentrated samples.Variables affecting the donor, static subsystem The variables of the donor chamber for optimum discontinuous performance were studied using diatomaceous earth spiked with TMA and consisted of the concentration and volume of the reagents injected for leaching and formation of the volatile species.The concentration of leacher (TCA) between 4.0 and 8.0 m gives a constant value of the signal for this step, which decreases to 12% for a concentration of 10 m. A 1 ml volume of this agent with stirring for 5 min is sufficient when 0.1 g samples are used (larger samples provide signals above the linear range in most cases). Concentrations of NaOH of ! 4 m provide a constant formation of volatile product which is 9.2% higher than that provided by a 2 m solution.Injected volumes above 1 ml decrease the analytical signal, probably owing to dilution of the analyte. Table 1 gives the values of the optimised variables. Features of the Method Calibration curves were obtained using both the manifold in Fig. 1 (injection of standard solutions of TMA) and that in Fig. 2 (diatomaceous earth spiked with standard solutions of TMA). The precision of the method for solid samples was significantly improved when the transient signal was evaluated in terms of peak area (RSD 3.47%) instead of peak height (RSD 7.89%).The equations, linear ranges, correlation coefficients and RSDs are given in Table 2. The sampling frequency was 8 and 2 h21 for liquid and solid samples, respectively. The detection limits, calculated as proposed by Miller and Miller,23 were 0.08 mg g21 and 1.6 mg l21 for solid and liquid samples, respectively. Study of Interferences Table 3 shows the disturbance of the analytical signal caused by the main nitrogen-containing bases which usually are found in fish together with the analyte.Different concentrations of formaldehyde were examined as masking agents and a 20% Table 1 Optimisation of variables Range Optimum Parameter studied value Liquid samples— [BTB]/m 1 3 1024–1 3 1026 1 3 1024 Acceptor solution pH 5–7.5 6.0 [NaOH]/m 1 2 Acceptor flow rate/ml min21 0.2–1.2 1.0 Donor flow rate/ml min21 0.5–2.0 1.0 Volume injected/ml 100–1000 500 Temperature/°C 40–80 60 Stop-time of acceptor solution/min 0–5 3 Solid samples— [TCA]/m 5–10 6.5 Sample amount/g 0.1–1 0.1 [NaOH]/m 2–6 6 Leaching time/min 1–10 5 Table 2 Features of the proposed method Linear range/mg TMA per 100 g RSD (%) Sample Equation* sample (n = 11) r Solid y = 6.914x + 28.06 0.1–10 3.47 0.998 Liquid y = 5.726x + 328 2.0–30 4.27 0.999 * Solid samples: y = peak area, x = mg TMA g21 sample.Liquid samples: y = peak height, x = mg l21 of TMA. Analyst, July 1997, Vol. 122 665aqueous solution proved to be appropriate in order to obtain acceptable tolerance levels, taking into account that the working pH is not the optimum for the masking reaction.24 The study was performed with both the manifold in Fig. 2 (injection of the masking solution) and that in Fig. 1 (inclusion of an additional channel which merges with the sample channel). After addition of this reagent to the overall system, the concentration of NaOH solution which provided the best results was 6 m.Application of the Method to Fish Samples Samples of both fresh and frozen fish of different types were analysed using both procedures and the results were compared with those provided by the recommended method4 in all instances. The comparison (t-test, adopting as null hypothesis the absence of significant differences) showed non-significant differences between the two methods for a confidence level P = 0.05. Table 4 gives the concentrations found by both the proposed and the conventional methods and the RSD for n = 3.Conclusions Simple continuous and hybrid manifolds coupled to a pervaporation module have proved to be an excellent system for the determination of fish freshness through the formation of trimethylamine. Compared with the recommended method, similar results are obtained in a shorter time (8 and 28 min for liquid and solid samples, respectively, versus 65 min for the conventional method). The continuous manifold for liquid samples requires a prior sample treatment, but in turn the determination can be easily automated.Filtration of the pre-treated sample can be avoided if tubing of sufficient diameter is used. The discontinuous–continuous approach allows the development of the overall analytical process with little human participation (only for sample weighing, closing of the separation module and injection of reagents). In both instances the usefulness of pervaporation for the development of an automated or semi-automated method for the determination of TMA in fish has been demonstrated.The capability of this separation technique for the integration of different steps provides the possibility of miniaturisation. The Comisi�on Interministerial de Ciencia y Tecnolog�ýa is thanked for financial support (Project No. PB 93-0827). References 1 Ringo, E., Stenberg, E., and Stroem, A. R., Appl. Environ. Microbiol., 1984, 47, 1084. 2 Belitz, H. D., and Grosch, W., Food Chemistry, Springer, Berlin, 1987. 3 Hoogland, P. L., J. Fish. Res. Bd. Can., 1958, 15, 15. 4 Association of Official Analytical Chemists, Official Method of Analysis of the Association of Official Analytical Chemists, AOAC, Arlington, VA, 15th edn., 1990, vol. 1, p. 869. 5 Shewan, J. M., Gibson, D. M., and Murray, C. K., Fish Insp. Qual. Control, 1971, 71, 183. 6 Conway, W. J., Microdiffusion Analysis and Volumetric Error, Crosby Lockwood, London, 1962, p. 98. 7 Fiddler, W., Doerr, R. C., and Gates, R.A., J. Assoc. Off. Anal. Chem., 1992, 74, 400. 8 Dacosta, K. A., Vrbanac, J. J., and Zeisel, S. H., Anal. Biochem., 1990, 187, 234. 9 Lundstrom, R. C., and Racicot, L. D., J. Assoc. Off. Anal. Chem., 1983, 66, 1168. 10 Gill, T. A., and Thomson, J., J. Food Sci., 1984, 49, 603. 11 Chang, G. W., Chang, W. L., and Lew, K. B. K., J. Food Sci., 1976, 41, 723. 12 Wong, K., and Gill, T. A., J. Food Sci., 1987, 52, 1. 13 Gamati, S., Luong, J. H. T., and Mulchandani, A., Biosens. Bioelectron.,1991, 6, 125. 14 Hayashi, T., Imato, T. and Asano, Y., Anal. Chim. Acta, 1996, 317, 284. 15 Le�on, A., Chica, A., Garc�ýa-Raurich, J., and Centrich, F., Quim. Anal., 1994, 13, 78. 16 Zhi, Z.-L., R�ýos, A., and Valc�arcel M., Anal. Chem., 1995, 34, 247. 17 Sadok, S., Uglow, R. F., and Haswell, S. J., Anal. Chim. Acta, 1996, 321, 69. 18 Mattos, I. L., Luque de Castro, M. D., and Valc�arcel, M., Talanta, 1995, 42, 755. 19 Mattos, I. L., and Luque de Castro, M. D., Anal. Chim. Acta, 1994, 298, 159. 20 Papafstathiou, I., and Luque de Castro, M. D., Anal. Chem., 1995, 67, 3916. 21 Bishop, E., Indicators, Pergamon Press, Oxford, 1972, p. 109. 22 Analytical Methods Committee, The Analyst, 1979, 104, 434. 23 Miller, J. C., and Miller, J. N., Statistics for Analytical Chemistry, Ellis Horwood, Chichester, 2nd edn., 1988, p. 120. 24 Morrison, R., and Boyd, R., Organic Chemistry, Allyn and Bacon, Boston, 4th edn., 1983. Paper 7/00547D Received January 23, 1997 Accepted April 23, 1997 Table 3 Interference study (%)* Analyte-to-foreign species ratio† Foreign species 2 : 1 1 : 1 1 : 2 1 : 5 1 : 10 1 : 15 1 : 20 Methylamine – – – 13.9 58.1 88.2 Dimethylamine – – – 16.9 49.5 90.3 Ammonia – – – – – 8.9 26.8 * Percentage increase of the analytical signal (absorbance) caused by the inferent. † mg TMA: mg foreign species; 4.5 mg TMA per 100 g sample. Table 4 Application of the method and comparison with official method.4 Concentrations in mg l21 and mg g21 for liquid and solid samples, respectively Sample Proposed method Official method Solid samples— Frozen turbot 2.9 ± 0.27 2.74 ± 0.08 Frozen turbot (1 month) 3.7 ± 0.19 3.3 ± 0.11 Frozen hake 9.7 ± 0.26 10.1 ± 0.06 Frozen hake (2 months) 11.9 ± 0.31 13.6 ± 0.08 Fresh hake 6.9 ± 0n; 0.10 Liquid samples— Frozen turbot 2.3 ± 0.39 2.6 ± 0.06 Frozen lemon fish 2.9 ± 0.42 2.04 ± 0.09 Frozen hake I 4.62 ± 0.29 4.9 ± 0.06 Frozen hake II 11.9 ± 0.30 12.6 ± 0.05 Elaborated sole 2.7 ± 0.43 2.04 ± 0.07 Frozen turbot (3 months) 4.78 ± 0.29 4.34 ± 0.08 Mackerel (tinned) 23.7 ± 0.26 22.6 ± 0.1 Fresh sardine 14.1 ± 0.47 13.13 ± 0.07 Fresh salmon 1.9 ± 0.17 2.1 ± 0.05 666 Analyst, July 1997, Vol. 122

ISSN:0003-2654    

DOI:10.1039/a700547d

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Determination of Thallium in River Sediment by Flow Injection On-line Sorption Preconcentration in a Knotted Reactor Coupled With Electrothermal Atomic Absorption Spectrometry Elissaveta Ivanova†, Xiu-Ping Yan, Willy van Mol and Freddy Adams* Department of Chemistry, University of Antwerp (UIA), B-2610, Antwerp (Wilrijk), Belgium A flow injection on-line sorption preconcentration electrothermal atomic absorption spectrometric (ETAAS) method was developed for the determination of thallium.The Tl3+–tetramethylenedithiocarbamate (pyrrolidinedithiocarbamate) complex formed in strongly acidic medium (0–3 mol l21 HNO3, 0–3 mol l21 H2SO4, 0–2.5 mol l 21 HClO4 or 0–2 mol l21 HCl) is sorbed on the inner walls of a PTFE knotted reactor (100 cm 3 0.5 mm id) and quantitatively eluted with 45 ml of ethanol. The ETAAS determination is performed in parallel with the preconcentration of the next sample. Using a preconcentration time of 30 s and a sample loading rate of 4.8 ml min21, an enhancement factor of 27 is obtained in comparison with direct injection of 45 ml of aqueous solution. The adsorption efficiency is 51%.The detection limit (3s) is 0.015 mg l21 and the precision (RSD) is 2.9% for 0.4 mg l21 Tl (n = 11). The accuracy of the method is demonstrated by the analysis of a Community Bureau of Reference certified reference material 320 river sediment (indicative value for thallium concentration). Keywords: Flow injection; on-line preconcentration; knotted reactor; thallium; electrothermal atomic absorption spectrometry; river sediment The determination of thallium in environmental samples is of interest because of the high toxicity of its compounds.The main sources of thallium pollution at present are cement production and fossil fuel combustion. Owing to its increasing use in the semiconductor and electrical engineering industries, leading to increasing emissions into the environment, thallium has acquired growing importance as a pollutant.Both Tl+ and Tl3+ are biologically active.1 Natural environmental levels of thallium are comparatively low, e.g., the mean concentration in soils is 0.25 mg g21.2 The Community Bureau of Reference (BCR) certified reference material (CRM) river sediment was found to contain 0.537 mg l21.3 Owing to their high sensitivity and selectivity, atomic absorption spectrometric and particularly electrothermal atomic absorption spectrometric (ETAAS) methods are widely used for thallium determination in environmental samples.4,5 The determination of thallium in a graphite furnace suffers, however, from severe interferences in the presence of halides,4–7 carbides4 and iron,8 so that the ETAAS determination of thallium in samples of complex matrix composition should be preceded by separation and preconcentration by, e.g., solvent extraction,8–12 ion exchange13–15 or sorption.16,17 The batch performance of such procedures is, however, time consuming and labour intensive and suffers risks of analyte loss and contamination.Coupling of flow injection (FI) on-line separation and preconcentration with AAS is a way to overcome the above-mentioned drawbacks.18 For thallium determination, an FI on-line ion exchange preconcentration flame AAS system with a controlled pore glass–quinolin-8-ol column has been developed.19 A novel FI on-line preconcentration technique is based on the sorption of metal chelate complexes on the inner walls of a PTFE knotted reactor (KR).Coupled with AAS, it has been successfully applied to the determination of cadmium, copper, antimony, cobalt and lead in environmental and biological samples.20–25 In this work, the technique was extended to the determination of thallium by ETAAS. The separation and preconcentration of thallium is achieved by the selective formation of the Tl3+ chelate with ammonium tetramethylenedithiocarbamate [ammonium pyrrolidinedithiocarbamate (APDC)] over a wide range of sample acidities, its adsorption on the inner walls of the KR, elution with ethanol and detection with ETAAS.The accuracy of the method is demonstrated by the analysis of the BCR CRM 320 river sediment (indicative value for thallium concentration). Experimental Apparatus All AAS measurements were carried out using a Perkin-Elmer (Norwalk, CT, USA) Model 3030 atomic absorption spectrometer equipped with a deuterium arc background corrector and a Model HGA-500 graphite furnace.A thallium hollow-cathode lamp (Z-tek, Amsterdam, The Netherlands) was used as the radiation source at a current of 10 mA and a wavelength of 276.8 nm with a 0.7 nm spectral bandpass. Pyrolytic graphitecoated standard tubes (Z-tek) were employed. The graphite tubes were pre-treated with iridium modifier as follows:26 a 50 ml aliquot of a 1000 mg l21 iridium solution was injected into the graphite tube, which was then heated using the furnace programme given in Table 1.The procedure was repeated three times. The pre-treatment was found to be effective for at least 300 repetitive determinations of thallium using the furnace programme shown in Table 2. Peak height (absorbance), peak area (integrated absorbance) and statistical data were printed out using a Perkin-Elmer Model PR-100 printer. The integrated absorbance (Aint) values were used for the evaluation owing to their good day-to-day and tube-to-tube precision.The FI on-line separation and preconcentration were performed using a Perkin-Elmer Model FIAS-200 FI accessory. † On leave from the Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria. Table 1 Graphite furnace temperature programme for graphite tube pretreatment with iridium Step Temperature/°C Ramp time/s Hold time/s Argon flow rate/ ml min21 1 110 1 40 300 2 130 20 50 300 3 1200 20 30 300 4 2000 1 5 300 Analyst, July 1997, Vol. 122 (667–671) 667The standard valve of the FIAS-200 was replaced with a prototype eight-channel, 16-port multifunctional injector valve (Tecator, H�ogan�as, Sweden). A KR, laboratory made from PTFE tubing (100 cm 3 0.5 mm id),22 was used for the collection of the analyte chelate. Ismaprene pump tubes (Ismatec, Wertheim, Germany) were employed for propelling the sample, reagent, eluent and air. Small-bore (0.35 mm id) PTFE tubing was used for all connections, which were kept as short as possible in order to minimize the dead volumes.The FI manifold and the operating sequences for the separation and preconcentration procedure are shown in Fig. 1 and Table 3. The preconcentration was performed in parallel with the ETAAS determination of the previous preconcentrated sample. A detailed description of the manifold and operation sequences can be found in a previous paper.23 A complete preconcentration cycle lasted 138 s, which was about the same as the furnace temperature programme (including the cooling sequence) and permitted their operation in parallel. Thallium determination in the river sediment was performed using aqueous standards for calibration.The least-squares linear regression method was used to fit the data obtained from standard solutions in the range 0.05–1.5 mg l21 for establishing the calibration function. Reagents All reagents were of the highest available purity and of at least analytical-reagent grade.Doubly de-ionized water (18 MW cm21) obtained from a Milli-Q water system (Millipore, Bedford, MA, USA) was used throughout. Table 2 Graphite furnace temperature programme for thallium determination Step Temperature/°C Ramp time/s Hold time/s Argon flow rate/ ml min21 Drying 100 5 30 300 Pyrolysis 600 5 20 300 Atomization 1300 0 3 0 Cleaning 2000 1 3 300 Fig. 1 FI manifold for on-line sorption preconcentration ETAAS. P1, P2, peristaltic pumps; S, sample; CR, chelating reagent (APDC); E, eluent (ethanol); WL, wash liquid (0.1% v/v H2SO4); KR, knotted reactor (100 cm 3 0.5 mm id PTFE tubing, 30 knots); W, waste; EL, eluent loop; EC, eluent container; V, injector valve; DT, delivery tube; and ETA, electrothermal atomizer.Valve positions: (a) inject; and (b) fill. Fig. 2 Influence of sample acidity on the preconcentration of 0.4 mg l21 of thallium, (5) without a wasep; and (-) with a wash step. Sample acidified with: (a) HNO3; (b) H2SO4; (c) HCl; and (d) HClO4. 668 Analyst, July 1997, Vol. 122A solution of the chelating agent was prepared daily by dissolving APDC (Merck–Schuchardt, Darmstadt, Germany) in de-ionized water. A stock standard solution of thallium (1000 mg l21) was prepared by dissolving thallium nitrate (Merck) in de-ionized water. Working standard solutions were obtained by stepwise dilution of the stock standard solution just before use. Suprapur concentrated acids (30% m/m HCl, 40% m/m HF, 70% m/m HClO4, 65% m/m HNO3 and 95–97% m/m H2SO4) (Merck) were used for sample digestion and adjustment of sample acidity.A saturated solution of bromine (Fluka, Buchs, Switzerland) was prepared in de-ionized water. Sample Preparation A 0.1 g amount of the river sediment weighed into a 10-ml PTFE beaker was gently heated on a hot-plate with 2 ml of HNO3 (65%) and 3 ml of HF (40%) until fuming. After cooling, 1 ml of HClO4 (70%) was added and the solution was heated again until a clear, colourless solution was obtained. The latter was transferred with de-ionized water into a 250 ml calibrated flask, 200 ml of saturated aqueous bromine were added and the acidity was adjusted to 2 mol l21 HNO3 .Method Development A univariate approach was used for optimization, the integrated absorbance (peak area) being taken as the main figure of merit with simultaneous consideration of precision ( < 3% RSD) and efficiency. Measures that had proved to be effective in earlier developments23–25 were adopted in this work.These included the use of ethanol as eluent and an eluent loop for eluent delivery, washing of the KR and removal of residual liquid from the KR and connecting tubing before elution. The parameters studied include sample acidity, concentrations of chelating agent and bromine, sample loading flow rate and time, composition of wash liquid, flow rate and time, eluent volume and flow rate and pyrolysis and atomization temperatures.Results and Discussion Optimization of Chemical and FI Variables Sample preconcentration In this work Tl3+ was used as it is the chelate-forming species in acidic media.27 The FI on-line KR sorption preconcentration of Tl3+ was studied over a wide range of concentrations of HNO3, H2SO4, HClO4 and HCl, because, singly or in combination, these acids are widely used for the digestion of inorganic and organic samples. The influence of sample acidity on the preconcentration of Tl3+ as a PDC complex is shown in Fig. 2(a–d) for HNO3, H2SO4, HClO4 and HCl media, with and without a wash step. Provided that a wash step is included, there is a broad optimum acidity range of thallium preconcentration, particularly in HNO3 or H2SO4 medium. Tl+ is more stable than Tl3+ in aqueous solutions, the latter rapidly reverting to Tl+ on standing. Moreover, APDC has been found to reduce Tl3+ to Tl+.28 To avoid this, an oxidant should be present in the sample solution during the complexation reaction.Aqueous bromine has been found to be efficient for this purpose.12 As Fig. 3 shows, the low integrated absorbance signal in the absence of bromine sharply increases on addition of a small amount of the latter and remains constant with further increases. It can therefore be assumed that in the absence of the oxidant APDC partially reduces Tl3+ to Tl+, which cannot be preconcentrated in acidic medium, while the addition of bromine interferes with this process.The effect of bromine is observed over the whole acidity range examined. Up to 0.3% v/v of aqueous bromine present in the sample solution does not affect the integrated absorbance of thallium. In most of the previous methods based on FI on-line KR sorption preconcentration for AAS, a dithiocarbamate reagent was used to form the chelate complexes. APDC was chosen in this work due to its stability in acid solutions.29 The Tl3+–PDC chelate is the species collected on the walls of the KR, since in absence of APDC no thallium is recovered.The optimum range of APDC concentrations is 0.001–0.25 % m/v at sample acidities below 1 mol l21, while at higher acidities the lower limit is shifted to 0.01% m/v, probably owing to decomposition of APDC . In further work an APDC concentration of 0.05% m/v was used. The effect of sample loading flow rate on the collection of the Tl3+–PDC chelate was studied with a preconcentration time of 30 s.The integrated absorbance increases almost linearly up to a loading flow rate of 4.8 ml min21, levelling off with further increases. With a sample loading flow rate of 4.8 ml min21, the integrated absorbance increases almost linearly up to a loading time of 30 s, after which the slope gradually decreases. Variation of the reagent flow rate within the range 1.0–2.5 Table 3 Operating sequences of the FI on-line sorption preconcentration system for ETAAS determination of thallium Sequence Fig.Valve position Pump active Pumped medium Flow rate/ ml min21 Time/s Function 1 1(a) Inject 1 Sample 4.8 20 Prefill APDC 1.3 2 1(b) Fill 1 Sample 4.8 30 Load sample APDC 1.3 3 1(a) Inject 1 Wash liquid 3.5 25 Wash KR 4 1(a) Inject 2 Air 4.1 25 Remove residual solution 5 1(b) Fill 2 Ethanol 1.1 7 Fill EL 6 — Inject — — — 5 Insert DT into ETA 7 1(a) Inject 2 Air 2.9 45 Elute and introduce eluate to ETA 8 — Fill — — — 1 Withdraw DT Fig. 3 Effect of bromine on the integrated absorbance of 0.4 mg l21 of thallium.Analyst, July 1997, Vol. 122 669ml min21 at a sample flow rate of 4.8 ml min21, has no effect on the integrated absorbance of thallium. Values for the sample flow rate and loading time at the upper limit of the corresponding linear ranges were chosen for the present study (see Table 3). Washing of the KR As Fig. 2 shows, omitting of the wash step in Tl3+ preconcentration from strongly acidic solutions leads to a decrease in the integrated absorbance signal, the effect being more pronounced in HCl and HClO4 media.427 Evidently, residual acid adhering to the KR and connecting tubing is entrained into the graphite tube with the eluate and causes the interference.At the high concentrations of HNO3 and H2SO4 in the sample solutions, rinsing with water is sufficient to restore the maximum integrated absorbance signal. For HClO4 and HCl media, rinsing with 1% H2SO4 is more efficient. The flow rate of wash liquid has no effect on the integrated absorbance of thallium in the range 3.0–4.8 ml min21.A steady signal is maintained after a 30 s wash time, which may be considered as evidence for the high stability of the Tl3+–PDC complex. Analyte elution As in previous work,23–25 a KR tube length of 100 cm is used as a compromise between sensitivity and eluent volume. As Fig. 4 shows, 45 ml of ethanol is the minimum eluent volume required for the quantitative elution of the retained analyte chelate from the 100 cm KR.Variation of the elution flow rate in the range 2.0–4.0 ml min21 has no effect on the elution efficiency. Optimization of ETAAS Parameters The 45 ml ethanolic eluate is accommodated in the graphite tube without a pre-heating step. The optimum pyrolysis temperature is 600 °C and the optimum atomization temperature is 1300 °C. Coating of the graphite tube with iridium, as proposed by Yan et al.,26 serves as a long-term modifier for thallium and improves the precision of the determinations.Interference Studies Potential interferences from various species were evaluated. No interference was found from alkali or alkaline earth metal ions and aluminium, normally present at high concentrations in sediments and related samples since these ions do not react with APDC. However, several heavy metal ions, e.g., Cu2+, Mo6+, Pb2+ and Fe3+, which form dithiocarbamate complexes of similar or higher stability to that of Tl3+30 would compete with the latter for the complexing agent, and subsequently, for the active sites of the KR.Table 4 presents the results of thallium preconcentration in the presence of co-existing metal ions from HNO3 medium. Similar results were obtained in H2SO4 and HClO4 media. As can be seen, higher heavy metal interferentto- thallium ratios are achieved at higher sample acidities, thus allowing the separation of thallium from heavy metal ions at the Fig. 4 Effect of eluent volume on the integrated absorbance of 0.4 mg l21 of thallium (100 cm 3 0.5 mm id KR).Table 4 Effect of co-existing heavy metal ions on the determination of 0.2 mg l21 of Tl3+ HNO3/mol l21 Interferent Concentration/mg l21 Interferent-tothallium ratio Thallium recovery (%) 0.2 Mn2+ 10 000 5 3104 100.5 0.2 Pb2+ 10 50 100.0 0.2 Cu2+ 4 20 84.0 1.0 20 1 3 102 96.5 0.2 Mo6+ 10 50 84.0 1.0 10 50 101.5 0.2 Fe3+ 1 000 5 3 103 51.0 1.0 20 000 1 3 105 101.0 2.0 50 000 2.5 3 105 100.0 2.0 Fe3+ 20 000 2 3 105 101.5 + Cu2+ 20 1 3 102 + Pb2+ 20 1 3 102 Table 5 Characteristic performance data for the FI on-line sorption preconcentration system for ETAAS determination of Tl3+ (30 s preconcentration with a 100 cm 3 0.5 mm id PTFE KR) Sample loading rate/ml min21 4.8 Sample throughput/h21 26 Sample consumption/ml 4.4 Reagent consumption/ml Ethanol 0.045 0.05% APDC 1.2 0.1% v/v H2SO4 3.2 RSD (%) (n = 11) 2.9 (0.4 mg l21) Detection limit (3s)/ng l21 15 Calibration function (five standards, 0.05–1.5 mg l21, n = 3, CTl in mg l21) Aint = 0.0002 + 0.3736CTl Correlation coefficient 0.9999 Enhancement factor* 27 Adsorption efficiency (%)† 51 * Compared with direct injection of 45 ml of aqueous solution.† Compared with total analyte mass loaded on to the KR. 670 Analyst, July 1997, Vol. 122concentration levels usually encountered in sediments and soils. Performance of the FI On-line KR Sorption System Characteristic performance data for the FI on-line KR sorption preconcentration ETAAS system are presented in Table 5.The enhancement factor was determined as the ratio between the analyte concentrations before and after preconcentration; the adsorption efficiency was determined from the integrated absorbance values compared with the total loaded analyte mass.18 A higher enhancement factor achieved with a longer loading time or a higher sample flow rate and some sacrifice in sample throughput can be employed if thallium concentrations below the range defined in Table 5 are to be determined.As no suitable standard reference materials with certified values for thallium are currently available in this laboratory, the accuracy of the method was checked by the analysis of BCR CRM 320 river sediment with an indicative value for the thallium content. The value obtained by the present method, 543 ± 19 ng g21 (mean ± s, n = 3) is in good agreement with the indicative value of 537 ± 6 ng g21, indicating that the proposed method permits interference-free thallium determination in this sample.E. Ivanova is grateful to DWTC (Belgium) and UIA for financing her postdoctoral research. References 1 Tsalev, D. L., and Zaprianov, Z. K., Atomic Absorption Spectrometry in Occupational and Environmental Health Practice, Vol.1, Analytical Aspects and Health Significance, CRC Press , Boca Raton, FL, 1983, pp. 196–199. 2 Ure, A. M., and Berrow, M. L., in Environmental Chemistry, ed.Bowen, H. J., Royal Society of Chemistry, London, 1982, vol. 2, pp. 155–195. 3 Weidmann, E., Stoeppler, M., and Heininger, P., Analyst, 1992, 117, 295. 4 Leloux, M. S., Lich, N. P., and Claude, J.-R., At. Spectrosc., 1987, 8, 72. 5 Manning, D. C., and Slavin, W., Spectrochim. Acta, Part B, 1988, 43, 1157. 6 Shan, X.-Q., Ni, Z.-M., and Zhang, L., Talanta, 1984, 31, 150. 7 Fuller, C. W., Anal. Chim. Acta, 1976, 81, 199. 8 Schmidt, W., and Dietl, F., Fresenius’ Z. Anal.Chem., 1983, 315, 687. 9 De Ruck, A., Vandecasteele, C., and Dams, R., Anal. Lett., 1989, 22, 469. 10 Sighinolfi, G. P., At. Absorpt. Newsl., 1973, 12, 36. 11 Ikramuddin, M., At. Spectrosc., 1983, 4, 101. 12 Ivanova, E., Stoimenova, M., and Gentscheva, G., Fresenius’ J. Anal. Chem., 1994, 348, 317. 13 Tsakovski, S., Ivanova, E., and Havezov, I., Talanta, 1994, 41, 721. 14 Calderoni, G., and Ferri, T., Talanta, 1982, 29, 371. 15 Riley, J. P., and Siddiqui, S. A., Anal.Chim. Acta, 1986, 181, 117. 16 Berndt, H., Messerschmidt, J., Alt, F., and Sommer, D., Fresenius’ Z. Anal. Chem., 1981, 306, 385. 17 Berndt, H., Harms, U., and Sonneborn, M., Fresenius’ Z. Anal. Chem., 1985, 322, 329. 18 Fang, Z., Flow Injection Atomic Absorption Spectrometry, Wiley, Chichester, 1995. 19 Mohammad, B., Ure, A. M., and Littlejohn, D., Mikrochim. Acta, 1994, 113, 325. 20 Chen, H., Xu, S., and Fang, Z., Anal. Chim. Acta, 1994, 298, 167. 21 Fang, Z., Xu, S., Dong, L., and Li, W., Talanta, 1994, 41, 2165. 22 Sperling, M., Yan, X.-P., and Welz, B., Spectrochim. Acta, Part B, 1996, 51, 1891. 23 Yan, X.-P., Van Mol, W., and Adams, F., Analyst, 1996, 121, 1061. 24 Yan, X.-P., Van Mol, W., and Adams, F., Lab. Robot. Autom., in the press. 25 Yan, X.-P., Van Mol, W., and Adams, F., J. Anal. At. Spectrom., in the press. 26 Yan, X.-P., Sperling, M., and Welz, B., to be published. 27 Stary, J., Solvent Extraction of Metal Chelates, Pergamon Press, Oxford, 1964. 28 Evans, W. H., Brooke, P.J., and Lucas, B. E., Anal. Chim. Acta, 1983, 148, 203. 29 Subramanian, K. S., and Meranger, J. C., Anal. Chim. Acta, 1981, 124, 131. 30 Ruzicka, J., and Arndal, A., Anal. Chim. Acta, 1989, 216, 243. Paper 6/08539C Received December 23, 1996 Accepted April 18, 1997 Analyst, July 1997, Vol. 122 671 Determination of Thallium in River Sediment by Flow Injection On-line Sorption Preconcentration in a Knotted Reactor Coupled With Electrothermal Atomic Absorption Spectrometry Elissaveta Ivanova†, Xiu-Ping Yan, Willy van Mol and Freddy Adams* Department of Chemistry, University of Antwerp (UIA), B-2610, Antwerp (Wilrijk), Belgium A flow injection on-line sorption preconcentration electrothermal atomic absorption spectrometric (ETAAS) method was developed for the determination of thallium.The Tl3+–tetramethylenedithiocarbamate (pyrrolidinedithiocarbamate) complex formed in strongly acidic medium (0–3 mol l21 HNO3, 0–3 mol l21 H2SO4, 0–2.5 mol l 21 HClO4 or 0–2 mol l21 HCl) is sorbed on the inner walls of a PTFE knotted reactor (100 cm 3 0.5 mm id) and quantitatively eluted with 45 ml of ethanol.The ETAAS determination is performed in parallel with the preconcentration of the next sample. Using a preconcentration time of 30 s and a sample loading rate of 4.8 ml min21, an enhancement factor of 27 is obtained in comparison with direct injection of 45 ml of aqueous solution. The adsorption efficiency is 51%.The detection limit (3s) is 0.015 mg l21 and the precision (RSD) is 2.9% for 0.4 mg l21 Tl (n = 11). The accuracy of the method is demonstrated by the analysis of a Community Bureau of Reference certified reference material 320 river sediment (indicative value for thallium concentration). Keywords: Flow injection; on-line preconcentration; knotted reactor; thallium; electrothermal atomic absorption spectrometry; river sediment The determination of thallium in environmental samples is of interest because of the high toxicity of its compounds.The main sources of thallium pollution at present are cement production and fossil fuel combustion. Owing to its increasing use in the semiconductor and electrical engineering industries, leading to increasing emissions into the environment, thallium has acquired growing importance as a pollutant. Both Tl+ and Tl3+ are biologically active.1 Natural environmental levels of thallium are comparatively low, e.g., the mean concentration in soils is 0.25 mg g21.2 The Community Bureau of Reference (BCR) certified reference material (CRM) river sediment was found to contain 0.537 mg l21.3 Owing to their high sensitivity and selectivity, atomic absorption spectrometric and particularly electrothermal atomic absorption spectrometric (ETAAS) methods are widely used for thallium determination in environmental samples.4,5 The determination of thallium in a graphite furnace suffers, however, from severe interferences in the presence of halides,4–7 carbides4 and iron,8 so that the ETAAS determination of thallium in samples of complex matrix composition should be preceded by separation and preconcentration by, e.g., solvent extraction,8–12 ion exchange13–15 or sorption.16,17 The batch performance of such procedures is, however, time consuming and labour intensive and suffers risks of analyte loss and contamination.Coupling of flow injection (FI) on-line separation and preconcentration with AAS is a way to overcome the above-mentioned drawbacks.18 For thallium determination, an FI on-line ion exchange preconcentration flame AAS system with a controlled pore glass–quinolin-8-ol column has been developed.19 A novel FI on-line preconcentration technique is based on the sorption of metal chelate complexes on the inner walls of a PTFE knotted reactor (KR).Coupled with AAS, it has been successfully applied to the determination of cadmium, copper, antimony, cobalt and lead in environmental and biological samples.20–25 In this work, the technique was extended to the determination of thallium by ETAAS.The separation and preconcentration of thallium is achieved by the selective formation of the Tl3+ chelate with ammonium tetramethylenedithiocarbamate [ammonium pyrrolidinedithiocarbamate (APDC)] over a wide range of sample acidities, its adsorption on the inner walls of the KR, elution with ethanol and detection with ETAAS.The accuracy of the method is demonstrated by the analysis of the BCR CRM 320 river sediment (indicative value for thallium concentration). Experimental Apparatus All AAS measurements were carried out using a Perkin-Elmer (Norwalk, CT, USA) Model 3030 atomic absorption spectrometer equipped with a deuterium arc background corrector and a Model HGA-500 graphite furnace. A thallium hollow-cathode lamp (Z-tek, Amsterdam, The Netherlands) was used as the radiation source at a current of 10 mA and a wavelength of 276.8 nm with a 0.7 nm spectral bandpass.Pyrolytic graphitecoated standard tubes (Z-tek) were employed. The graphite tubes were pre-treated with iridium modifier as follows:26 a 50 ml aliquot of a 1000 mg l21 iridium solution was injected into the graphite tube, which was then heated using the furnace programme given in Table 1. The procedure was repeated three times. The pre-treatment was found to be effective for at least 300 repetitive determinations of thallium using the furnace programme shown in Table 2.Peak height (absorbance), peak area (integrated absorbance) and statistical data were printed out using a Perkin-Elmer Model PR-100 printer. The integrated absorbance (Aint) values were used for the evaluation owing to their good day-to-day and tube-to-tube precision. The FI on-line separation and preconcentration were performed using a Perkin-Elmer Model FIAS-200 FI accessory. † On leave from the Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria. Table 1 Graphite furnace temperature programme for graphite tube pretreatment with iridium Step Temperature/°C Ramp time/s Hold time/s Argon flow rate/ ml min21 1 110 1 40 300 2 130 20 50 300 3 1200 20 30 300 4 2000 1 5 300 Analyst, July 1997, Vol. 122 (667–671) 667The standard valve of the FIAS-200 was replaced with a prototype eight-channel, 16-port multifunctional injector valve (Tecator, H�ogan�as, Sweden).A KR, laboratory made from PTFE tubing (100 cm 3 0.5 mm id),22 was used for the collection of the analyte chelate. Ismaprene pump tubes (Ismatec, Wertheim, Germany) were employed for propelling the sample, reagent, eluent and air. Small-bore (0.35 mm id) PTFE tubing was used for all connections, which were kept as short as possible in order to minimize the dead volumes. The FI manifold and the operating sequences for the separation and preconcentration procedure are shown in Fig. 1 and Table 3. The preconcentration was performed in parallel with the ETAAS determination of the previous preconcentrated sample. A detailed description of the manifold and operation sequences can be found in a previous paper.23 A complete preconcentration cycle lasted 138 s, which was about the same as the furnace temperature programme (including the cooling sequence) and permitted their operation in parallel. Thallium determination in the river sediment was performed using aqueous standards for calibration.The least-squares linear regression method was used to fit the data obtained from standard solutions in the range 0.05–1.5 mg l21 for establishing the calibration function. Reagents All reagents were of the highest available purity and of at least analytical-reagent grade. Doubly de-ionized water (18 MW cm21) obtained from a Milli-Q water system (Millipore, Bedford, MA, USA) was used throughout. Table 2 Graphite furnace temperature programme for thallium determination Step Temperature/°C Ramp time/s Hold time/s Argon flow rate/ ml min21 Drying 100 5 30 300 Pyrolysis 600 5 20 300 Atomization 1300 0 3 0 Cleaning 2000 1 3 300 Fig. 1 FI manifold for on-line sorption preconcentration ETAAS. P1, P2, peristaltic pumps; S, sample; CR, chelating reagent (APDC); E, eluent (ethanol); WL, wash liquid (0.1% v/v H2SO4); KR, knotted reactor (100 cm 3 0.5 mm id PTFE tubing, 30 knots); W, waste; EL, eluent loop; EC, eluent container; V, injector valve; DT, delivery tube; and ETA, electrothermal atomizer.Valve positions: (a) inject; and (b) fill. Fig. 2 Influence of sample acidity on the preconcentration of 0.4 mg l21 of thallium, (5) without a wash step; and (-) with a wash step. Sample acidified with: (a) HNO3; (b) H2SO4; (c) HCl; and (d) HClO4. 668 Analyst, July 1997, Vol. 122A solution of the chelating agent was prepared daily by dissolving APDC (Merck–Schuchardt, Darmstadt, Germany) in de-ionized water.A stock standard solution of thallium (1000 mg l21) was prepared by dissolving thallium nitrate (Merck) in de-ionized water. Working standard solutions were obtained by stepwise dilution of the stock standard solution just before use. Suprapur concentrated acids (30% m/m HCl, 40% m/m HF, 70% m/m HClO4, 65% m/m HNO3 and 95–97% m/m H2SO4) (Merck) were used for sample digestion and adjustment of sample acidity. A saturated solution of bromine (Fluka, Buchs, Switzerland) was prepared in de-ionized water. Sample Preparation A 0.1 g amount of the river sediment weighed into a 10-ml PTFE beaker was gently heated on a hot-plate with 2 ml of HNO3 (65%) and 3 ml of HF (40%) until fuming.After cooling, 1 ml of HClO4 (70%) was added and the solution was heated again until a clear, colourless solution was obtained. The latter was transferred with de-ionized water into a 250 ml calibrated flask, 200 ml of saturated aqueous bromine were added and the acidity was adjusted to 2 mol l21 HNO3 .Method Development A univariate approach was used for optimization, the integrated absorbance (peak area) being taken as the main figure of merit with simultaneous consideration of precision ( < 3% RSD) and efficiency. Measures that had proved to be effective in earlier developments23–25 were adopted in this work. These included the use of ethanol as eluent and an eluent loop for eluent delivery, washing of the KR and removal of residual liquid from the KR and connecting tubing before elution.The parameters studied include sample acidity, concentrations of chelating agent and bromine, sample loading flow rate and time, composition of wash liquid, flow rate and time, eluent volume and flow rate and pyrolysis and atomization temperatures. Results and Discussion Optimization of Chemical and FI Variables Sample preconcentration In this work Tl3+ was used as it is the chelate-forming species in acidic media.27 The FI on-line KR sorption preconcentration of Tl3+ was studied over a wide range of concentrations of HNO3, H2SO4, HClO4 and HCl, because, singly or in combination, these acids are widely used for the digestion of inorganic and organic samples.The influence of sample acidity on the preconcentration of Tl3+ as a PDC complex is shown in Fig. 2(a–d) for HNO3, H2SO4, HClO4 and HCl media, with and without a wash step. Provided that a wash step is included, there is a broad optimum acidity range of thallium preconcentration, particularly in HNO3 or H2SO4 medium.Tl+ is more stable than Tl3+ in aqueous solutions, the lr rapidly reverting to Tl+ on standing. Moreover, APDC has been found to reduce Tl3+ to Tl+.28 To avoid this, an oxidant should be present in the sample solution during the complexation reaction. Aqueous bromine has been found to be efficient for this purpose.12 As Fig. 3 shows, the low integrated absorbance signal in the absence of bromine sharply increases on addition of a small amount of the latter and remains constant with further increases.It can therefore be assumed that in the absence of the oxidant APDC partially reduces Tl3+ to Tl+, which cannot be preconcentrated in acidic medium, while the addition of bromine interferes with this process. The effect of bromine is observed over the whole acidity range examined. Up to 0.3% v/v of aqueous bromine present in the sample solution does not affect the integrated absorbance of thallium. In most of the previous methods based on FI on-line KR sorption preconcentration for AAS, a dithiocarbamate reagent was used to form the chelate complexes. APDC was chosen in this work due to its stability in acid solutions.29 The Tl3+–PDC chelate is the species collected on the walls of the KR, since in absence of APDC no thallium is recovered.The optimum range of APDC concentrations is 0.001–0.25 % m/v at sample acidities below 1 mol l21, while at higher acidities the lower limit is shifted to 0.01% m/v, probably owing to decomposition of APDC .In further work an APDC concentration of 0.05% m/v was used. The effect of sample loading flow rate on the collection of the Tl3+–PDC chelate was studied with a preconcentration time of 30 s. The integrated absorbance increases almost linearly up to a loading flow rate of 4.8 ml min21, levelling off with further increases. With a sample loading flow rate of 4.8 ml min21, the integrated absorbance increases almost linearly up to a loading time of 30 s, after which the slope gradually decreases.Variation of the reagent flow rate within the range 1.0–2.5 Table 3 Operating sequences of the FI on-line sorption preconcentration system for ETAAS determination of thallium Sequence Fig. Valve position Pump active Pumped medium Flow rate/ ml min21 Time/s Function 1 1(a) Inject 1 Sample 4.8 20 Prefill APDC 1.3 2 1(b) Fill 1 Sample 4.8 30 Load sample APDC 1.3 3 1(a) Inject 1 Wash liquid 3.5 25 Wash KR 4 1(a) Inject 2 Air 4.1 25 Remove residual solution 5 1(b) Fill 2 Ethanol 1.1 7 Fill EL 6 — Inject — — — 5 Insert DT into ETA 7 1(a) Inject 2 Air 2.9 45 Elute and introduce eluate to ETA 8 — Fill — — — 1 Withdraw DT Fig. 3 Effect of bromine on the integrated absorbance of 0.4 mg l21 of thallium. Analyst, July 1997, Vol. 122 669ml min21 at a sample flow rate of 4.8 ml min21, has no effect on the integrated absorbance of thallium.Values for the sample flow rate and loading time at the upper limit of the corresponding linear ranges were chosen for the present study (see Table 3). Washing of the KR As Fig. 2 shows, omitting of the wash step in Tl3+ preconcentration from strongly acidic solutions leads to a decrease in the integrated absorbance signal, the effect being more pronounced in HCl and HClO4 media.427 Evidently, residual acid adhering to the KR and connecting tubing is entrained into the graphite tube with the eluate and causes the interference.At the high concentrations of HNO3 and H2SO4 in the sample solutions, rinsing with water is sufficient to restore the maximum integrated absorbance signal. For HClO4 and HCl media, rinsing with 1% H2SO4 is more efficient. The flow rate of wash liquid has no effect on the integrated absorbance of thallium in the range 3.0–4.8 ml min21. A steady signal is maintained after a 30 s wash time, which may be considered as evidence for the high stability of the Tl3+–PDC complex.Analyte elution As in previous work,23–25 a KR tube length of 100 cm is used as a compromise between sensitivity and eluent volume. As Fig. 4 shows, 45 ml of ethanol is the minimum eluent volume required for the quantitative elution of the retained analyte chelate from the 100 cm KR. Variation of the elution flow rate in the range 2.0–4.0 ml min21 has no effect on the elution efficiency.Optimization of ETAAS Parameters The 45 ml ethanolic eluate is accommodated in the graphite tube without a pre-heating step. The optimum pyrolysis temperature is 600 °C and the optimum atomization temperature is 1300 °C. Coating of the graphite tube with iridium, as proposed by Yan et al.,26 serves as a long-term modifier for thallium and improves the precision of the determinations. Interference Studies Potential interferences from various species were evaluated. No interference was found from alkali or alkaline earth metal ions and aluminium, normally present at high concentrations in sediments and related samples since these ions do not react with APDC.However, several heavy metal ions, e.g., Cu2+, Mo6+, Pb2+ and Fe3+, which form dithiocarbamate complexes of similar or higher stability to that of Tl3+30 would compete with the latter for the complexing agent, and subsequently, for the active sites of the KR. Table 4 presents the results of thallium preconcentration in the presence of co-existing metal ions from HNO3 medium.Similar results were obtained in H2SO4 and HClO4 media. As can be seen, higher heavy metal interferentto- thallium ratios are achieved at higher sample acidities, thus allowing the separation of thallium from heavy metal ions at the Fig. 4 Effect of eluent volume on the integrated absorbance of 0.4 mg l21 of thallium (100 cm 3 0.5 mm id KR). Table 4 Effect of co-existing heavy metal ions on the determination of 0.2 mg l21 of Tl3+ HNO3/mol l21 Interferent Concentration/mg l21 Interferent-tothallium ratio Thallium recovery (%) 0.2 Mn2+ 10 000 5 3104 100.5 0.2 Pb2+ 10 50 100.0 0.2 Cu2+ 4 20 84.0 1.0 20 1 3 102 96.5 0.2 Mo6+ 10 50 84.0 1.0 10 50 101.5 0.2 Fe3+ 1 000 5 3 103 51.0 1.0 20 000 1 3 105 101.0 2.0 50 000 2.5 3 105 100.0 2.0 Fe3+ 20 000 2 3 105 101.5 + Cu2+ 20 1 3 102 + Pb2+ 20 1 3 102 Table 5 Characteristic performance data for the FI on-line sorption preconcentration system for ETAAS determination of Tl3+ (30 s preconcentration with a 100 cm 3 0.5 mm id PTFE KR) Sample loading rate/ml min21 4.8 Sample throughput/h21 26 Sample consumption/ml 4.4 Reagent consumption/ml Ethanol 0.045 0.05% APDC 1.2 0.1% v/v H2SO4 3.2 RSD (%) (n = 11) 2.9 (0.4 mg l21) Detection limit (3s)/ng l21 15 Calibration function (five standards, 0.05–1.5 mg l21, n = 3, CTl in mg l21) Aint = 0.0002 + 0.3736CTl Correlation coefficient 0.9999 Enhancement factor* 27 Adsorption efficiency (%)† 51 * Compared with direct injection of 45 ml of aqueous solution.† Compared with total analyte mass loaded on to the KR. 670 Analyst, July 1997, Vol. 122concentration levels usually encountered in sediments and soils. Performance of the FI On-line KR Sorption System Characteristic performance data for the FI on-line KR sorption preconcentration ETAAS system are presented in Table 5. The enhancement factor was determined as the ratio between the analyte concentrations before and after preconcentration; the adsorption efficiency was determined from the integrated absorbance values compared with the total loaded analyte mass.18 A higher enhancement factor achieved with a longer loading time or a higher sample flow rate and some sacrifice in sample throughput can be employed if thallium concentrations below the range defined in Table 5 are to be determined.As no suitable standard reference materials with certified values for thallium are currently available in this laboratory, the accuracy of the method was checked by the analysis of BCR CRM 320 river sediment with an indicative value for the thallium content.The value obtained by the present method, 543 ± 19 ng g21 (mean ± s, n = 3) is in good agreement with the indicative value of 537 ± 6 ng g21, indicating that the proposed method permits interference-free thallium determination in this sample. E. Ivanova is grateful to DWTC (Belgium) and UIA for financing her postdoctoral research.References 1 Tsalev, D. L., and Zaprianov, Z. K., Atomic Absorption Spectrometry in Occupational and Environmental Health Practice, Vol.1, Analytical Aspects and Health Significance, CRC Press , Boca Raton, FL, 1983, pp. 196–199. 2 Ure, A. M., and Berrow, M. L., in Environmental Chemistry, ed. Bowen, H. J., Royal Society of Chemistry, London, 1982, vol. 2, pp. 155–195. 3 Weidmann, E., Stoeppler, M., and Heininger, P., Analyst, 1992, 117, 295. 4 Leloux, M. S., Lich, N. P., and Claude, J.-R., At. Spectrosc., 1987, 8, 72. 5 Manning, D. C., and Slavin, W., Spectrochim. Acta, Part B, 1988, 43, 1157. 6 Shan, X.-Q., Ni, Z.-M., and Zhang, L., Talanta, 1984, 31, 150. 7 Fuller, C. W., Anal. Chim. Acta, 1976, 81, 199. 8 Schmidt, W., and Dietl, F., Fresenius’ Z. Anal. Chem., 1983, 315, 687. 9 De Ruck, A., Vandecasteele, C., and Dams, R., Anal. Lett., 1989, 22, 469. 10 Sighinolfi, G. P., At. Absorpt. Newsl., 1973, 12, 36. 11 Ikramuddin, M., At. Spectrosc., 1983, 4, 101. 12 Ivanova, E., Stoimenova, M., and Gentscheva, G., Fresenius’ J. Anal. Chem., 1994, 348, 317. 13 Tsakovski, S., Ivanova, E., and Havezov, I., Talanta, 1994, 41, 721. 14 Calderoni, G., and Ferri, T., Talanta, 1982, 29, 371. 15 Riley, J. P., and Siddiqui, S. A., Anal. Chim. Acta, 1986, 181, 117. 16 Berndt, H., Messerschmidt, J., Alt, F., and Sommer, D., Fresenius’ Z. Anal. Chem., 1981, 306, 385. 17 Berndt, H., Harms, U., and Sonneborn, M., Fresenius’ Z. Anal. Chem., 1985, 322, 329. 18 Fang, Z., Flow Injection Atomic Absorption Spectrometry, Wiley, Chichester, 1995. 19 Mohammad, B., Ure, A. M., and Littlejohn, D., Mikrochim. Acta, 1994, 113, 325. 20 Chen, H., Xu, S., and Fang, Z., Anal. Chim. Acta, 1994, 298, 167. 21 Fang, Z., Xu, S., Dong, L., and Li, W., Talanta, 1994, 41, 2165. 22 Sperling, M., Yan, X.-P., and Welz, B., Spectrochim. Acta, Part B, 1996, 51, 1891. 23 Yan, X.-P., Van Mol, W., and Adams, F., Analyst, 1996, 121, 1061. 24 Yan, X.-P., Van Mol, W., and Adams, F., Lab. Robot. Autom., in the press. 25 Yan, X.-P., Van Mol, W., and Adams, F., J. Anal. At. Spectrom., in the press. 26 Yan, X.-P., Sperling, M., and Welz, B., to be published. 27 Stary, J., Solvent Extraction of Metal Chelates, Pergamon Press, Oxford, 1964. 28 Evans, W. H., Brooke, P.J., and Lucas, B. E., Anal. Chim. Acta, 1983, 148, 203. 29 Subramanian, K. S., and Meranger, J. C., Anal. Chim. Acta, 1981, 124, 131. 30 Ruzicka, J., and Arndal, A., Anal. Chim. Acta, 1989, 216, 243. Paper 6/08539C Received December 23, 1996 Accepted April 18, 1997 Analyst, July 1997, Vol. 122 671

ISSN:0003-2654    

DOI:10.1039/a608539c

出版商:RSC    

年代:1997

数据来源: RSC

摘要:

Derivatization of Amphetamine and Methamphetamine With 1,2-Naphthoquinone 4-Sulfonic Acid Into Solid-phase Extraction Cartridges. Determination of Amphetamine in Pharmaceutical and Urine Samples Pilar Camp�ýns Falc�o*, Carmen Molins Legua, Adela Sevillano Cabeza and Rosa Porras Serrano Departamento de Qu�ýmica Anal�ýtica, Facultad de Qu�ýmica, Universidad de Valencia, Doctor Moliner, 50, 46100-Burjassot, Valencia, Spain The derivatization of amphetamine and methamphetamine with 1,2-naphthoquinone-4-sulfonate (NQS) into solid-phase extraction cartridges (C18) is described.Optimum conditions were the use of carbonate–hydrogencarbonate buffer of pH 10, a 10 min reaction time at 25 °C and an NQS concentration of 9.6 3 1023 m. The accuracy and the precision of the method were tested. The results obtained with the proposed liquid–solid procedure were compared with those obtained with a traditional liquid–liquid extraction with hexane–ethyl acetate. The procedure was used to measure amphetamine in pharmaceutical and urine samples Keywords: Amphetamines; derivatization; solid-phase extraction; pharmaceuticals; urine Derivatization has long been accepted as an effective modification technique that can improve the overall specificity and sensitivity of trace analyses.The usual methodology involves a solution-based derivatization procedure. Over the past decade, immobilized solid-phase reagents on a polymeric solid support have become increasingly popular for easy conversion of analytes into more detectable species.The derivatization step plays a significant role in determining amphetamine and amphetamine-related compounds.1 Reagents such as o-phthalaldehyde,2 1,2-naphthoquinone-4-sulfonate (NQS)3 and dansyl chloride4 have been proposed. Solid-phase reagents have also been investigated. Gao et al.5 studied a polymeric reagent containing an activated ester linkage to a 9-fluorenyl group. Zhou et al.6 described the preparation of a covalently bound, fluorescencesensitive tag, 9-fluoreneacetyl, on a pore size-controlled, rigid polystyrene–divinylbenzene resin.A solid-phase reagent containing the 3,5-dinitrophenyl tag for the improved derivatization of chiral and achiral amines, amino alcohols and amino acids has also been proposed.7 All these reagents have been employed as pre-column derivatization reagents in liquid chromatography. Suzuki et al.8 developed a screening method for methamphetamine in urine by a color reaction using a Sep-Pak C18 cartridge.In this procedure, methamphetamine, retained selectively on the resin, is colored with Simon’s reagent. NQS is a solution-based derivatization reagent and provides the sensitivity required for the quantitative analysis of urine and plasma samples containing amphetamines;9 it is also recommended in Clarke’s Isolation and Identification of Drugs.10 In previous papers, we described liquid–liquid extraction combined with spectrophotometric procedures for the individual determination of amphetamine11 and methamphetamine12 in urine samples using NQS as derivatizing agent.The kinetics of the reaction have also been studied.13 The determination of amphetamine and methamphetamine in urine by the Hpoint standard additions method has been proposed.14 We also examined the determination of both drugs in urine by normalphase high-performance liquid chromatography with NQS and solid-phase extraction for sample clean-up.15 In another study we optimized the derivatization procedure with NQS into C18 solid-phase extraction (SPE) cartridges for the determination of amphetamine and methamphetamine in urine samples using a reversed-phase HPLC method with UV/VIS detection.16 Recently, we demonstrated the possibility of performing on-line derivatization into pre-columns for the determination of drugs by liquid chromatography and column switching.17 This paper describes a simple and rapid spectrophotometric procedure for both clean-up and derivatization with NQS of amphetamine or methamphetamine on solid-phase extraction cartridges.A commercial C18 packing material was used instead of polymeric reagents specially prepared for solid-phase derivatization. The method was compared with solution-based method and applied to the analysis of pharmaceutical and urine samples using a UV/VIS spectrophotometer. Experimental Apparatus All spectrophotometric measurements were made on a Hewlett- Packard (Avondale, PA, USA) HP 8452 A diode-array spectrophotometer furnished with quartz cuvettes with a 1 cm pathlength.Reagents Solutions were prepared with distilled water and all reagents were of analytical-reagent grade, unless stated otherwise. Hydrogencarbonate solution (8% m/v) was prepared by dissolving sodium hydrogencarbonate (Probus, Badalona, Spain) (8 g) in 100 ml of water. The pH was adjusted to different values by adding the minimum amount of sodium hydroxide solution (10 m) or hydrochloride acid (1 m).Buffers of pH 10 were prepared by dissolving sodium hydrogencarbonate and sodium carbonate (1% and 8% m/v and 5 m) in water. This solution was then diluted further to yield appropriate working standard solutions, which were prepared daily. A 1,2-naphthoquinone-4-sulfonic acid stock standard solution was prepared by dissolving the sodium salt (Sigma, St. Louis, MO, USA) in distilled water. This solution was prepared freshly for each experiment and was stored in the dark.Methamphetamine hydrochloride and amphetamine sulfate (Sigma) stock standard solutions were prepared by dissolving 100 mg in distilled water and diluting to 100 ml. Working standard solutions were prepared daily by appropriate dilution of the stock standard solutions. Chloroform, diethyl ether, propan-2-ol, methanol and acetonitrile were of HPLC grade from Scharlau (Barcelona, Spain); hydrochloric Analyst, July 1997, Vol. 122 (673–677) 673acid (Probus) and sodium hydroxide (Panreac, Barcelona, Spain) were also used. C18 (200 mg ml21), C8 and C2 (100 mg ml21) Bond Elut columns were obtained from Varian (Harbor City, CA, USA). Pharmaceutical Sample Centramine tablets, labelled to contain 10 mg of amphetamine sulfate per tablet, lactose and other excipients were obtained from Laboratorio Miquel (Barcelona, Spain). Derivatization Into Solid-phase Extraction Columns C18 extraction columns were previously conditioned by drawing through 1 ml of methanol, followed by 1 ml of 1% m/v hydrogencarbonate–carbonate solution at pH 10.Subsequently, 2 ml volumes of sample solution containing different amine concentrations were transferred to the column and washed with 2.50 ml of distilled water. When the amines were retained in the column, 0.5 ml of NQS reagent (1% m/ v) and 0.5 ml of 8% m/v hydrogencarbonate–carbonate solution at pH 10, previously mixed, were added.After 10 min for amphetamine or 15 min for methamphetamine at 25 °C, the columns were washed with water. The reaction products (amine–NQS) were eluted from the columns with 2 ml of acetonitrile–water (1+1). The absorbance between 190 and 820 nm was recorded. Absorbance was measured against the reagent blank at 25 °C. Three or more replicates were processed in all cases. The analytical signal was measured at 450 nm for amphetamine and 480 nm for methamphetamine.Centramine Tablets With Amphetamine Sulfate Three tablets were weighed and powdered. The required amount was suspended in distilled water and filtered. The filtrate was diluted with distilled water. Different volumes of this sample solution were taken, following the procedure for the standard samples. Urine Samples Two different sample treatments were applied. (1) Aliquots of urine samples (14 ml) were spiked at different amphetamine concentration levels and 0.3 ml of carbonate– hydrogencarbonate buffer (5 m) at pH 10 was added.The samples were centrifuged for 10 min at 1500 rpm and filtered before derivatization into the column. Subsequently, 10 ml of these urine samples were processed according to the procedure described above except that the columns were washed with 5 ml of acetonitrile–water (1+4). (2) A 100 ml volume of urineas made alkaline by adding 2 ml of carbonate–hydrogencarbonate buffer (5 m) at pH 10 and the mixture was centrifuged and filtered.Aliquots of these samples were spiked at different concentration levels with amphetamine stock solution. Subsequently 10 ml of these samples were processed according to the procedure described above except that the columns were washed with 5 ml of acetonitrile–water (1+4). Youden and Standard Addition Methods The Youden method20 was applied to pharmaceutical samples. Different volumes of pharmaceutical sample solution between 0.2 and 1 ml were taken and processed according to the procedure described above.For the standard addition method, volumes of 0.4 ml of pharmaceutical solution were employed, to which various volumes of amphetamine sulfate stock solution and water were added up to 2 ml. For urine samples, the standard addition method was applied. To 14 ml of urine sample, 0.7 ml of 51.4 mg ml21 amphetamine sulfate solution and 0.3 ml of hydrogencarbonate–carbonate saturated buffer solution (5 m) of pH 10 were added.The mixture was centrifuged for 10 min and filtered. Aliquots of this sample were spiked at different concentrations with 275 mg ml21 amphetamine sulfate solution. The samples were then processed as described above. Results and Discussion Optimization of the Working Conditions The reaction is carried out at basic pH, and the influence of this parameter was studied in the range 7.5–10.5 (with derivatization at 25 °C for 10 min). The results are expressed graphically in Fig. 1. The analytical signal was found not to be dependent on pH over the range 10.0–10.5 for methamphetamine, whereas it decreased outside this range. However, for amphetamine the highest analytical signal was obtained at pH 10. At pH < 10, the derivatization time for amphetamines was longer. To provide the appropiate pH, NaHCO3–NaOH (pH 10) solution was used. After studying the concentration effect of this solution in the range 0.1–1.0 m, a hydrogencarbonate solution of 0.5 m was selected.In most reported procedures dealing with the amine–NQS reaction, the derivatization is carried out at high temperatures (70 °C3,9 or 60 °C4) and the mixture samples are heated for a long time (between 20 and 40 min). We observed that this reaction occurs at lower temperatures and in a shorter time when the pH is high.12 We therefore selected pH 10.0 in order to increase the reaction rate and perform the derivatization procedure at room temperature (25 °C). The signal corresponding to the NQS–amphetamine was approximately constant after 10 min (Fig. 2). However, methamphetamine seems to react more slowly and more time is required to reach the plateau. Fig. 1 Graph of absorbance versus pH for NQS reagent recorded against acetonitrile blank, l = 450 nm, at 10 min (1), NQS–amphetamine, l = 450 nm, at 10 min (2) and NQS–methamphetamine, l = 480 nm, at 15 min (3), recorded against a reagent blank. Conditions: NQS, 9.6 3 1023 m; amines, 20.0 mg ml21; temperature 25 °C and eluent acetonitrile.Fig. 2 Absorbance at 450 or 480 nm corresponding for the reaction product, amphetamine-NQS or methamphetamine–NQS, recorded against a reagent blank at different reaction times. Conditions: NQS, 9.6 3 1023 m; amphetamine, 20.0 mg ml21; methamphetamine, 25.0 mg ml21; pH, 10; temperature, 25 °C; and eluent, acetonitrile–water (1 + 1) 674 Analyst, July 1997, Vol. 122Times of 10 and 15 min were selected for the derivatization of amphetamine and methamphetamine, respectively.The effect of the NQS concentration was evaluated in the range 9.6 3 1024–5.8 3 1022 m, the amphetamine and methamphetamine concentrations being 5.4 3 1025 and 1.3 3 1024 m, respectively. Fig. 3 shows the absorbance as a function of the NQS to amine concentration ratio. The analytical signal of these systems increased linearly up to 9.6 3 1023 m, and for both amines remained constant above this limit. The signal of the blank reagent increased with increase in concentration.In order to have low blank interferences, the reagent concentration chosen was 9.6 31023 m. Different water volumes were passed thought the column to eliminate the excess of reagent and a water volume between 2.5 and 5 ml was selected as optimum. Chloroform, diethyl ether, methanol, propan-2-ol and acetonitrile were tested as eluents. For the analytes studied, similar analytical signals were obtained using methanol, acetonitrile and propan-2-ol .However, the sensitivity decreased when chloroform or diethyl ether was used. Analogous results were obtained for the NQS reagent [Fig. 4 (a) and (b)]. Acetonitrile was selected as providing the greatest sensitivity and the lowest analytical signal for the NQS reagent . Although 1 ml of solvent was sufficient to elute all the reaction product formed, we eluted with 2 ml of acetonitrile–water (1+1) to provide a sufficient volume to measure the analytical signal.In this solvent the derivatives remain stables for at least 1 week if they are stored at 4 °C. The columns were cleaned up for further derivatization with 3 ml of methanol acidified with HCl (pH 2). Different Bond-Elut columns (C18, C8 and C2) were tested. The highest analytical signal of the reaction product was considered to be 100%. The recoveries obtained using carbonate –hydrogencarbonate buffer (pH 10) at 25 °C for 10 min, with an amphetamine concentration of 20 mg ml21, an NQS concentration of 9.6 3 1023 m and acetonitrile–water (1+1) as eluent for NQS–amphetamine products were 96 ± 3, 74 ± 2 and 67 ± 3%, using C18, C2 and C8, respectively. The differences between the results obtained were not very large, but the amount of reaction product formed was highest with C18, probably because the retention of the analytes was largest in this column.These results are in agreement with previous results.15 For methamphetamine the results obtained using Bond-Elut were adequate.For both analytes the packing selected was C18. The C18 columns were usable for a long time (3 months, equivalent to about 200 runs) and the results were reproducible. Table 1 shows the regression equation, calculated from the calibration graph of absorbance versus amphetamine or methamphetamine concentration, dynamic ranges of concentration and the detection limits using standard solutions under the optimized conditions. The lower limit of the dynamic range of concentration was the quantification limit, calculated as 10sB/ b,18 where sB = 0.004 is the standard deviation of the NQS blank and b is the slope of the calibration graph.The upper limit is the last point fitted by the linear least-squares method. The limits of detection were 1.0 and 0.7 mg ml21 for amphetamine and methamphetamine, respectively, calculated as 3sB/b.19 The results obtained by this procedure were compared with those obtained with the conventional liquid–liquid procedure. 11,12,14 To compare the two procedures, the highest analytical signal (regardless of the procedure) was considered to represent 100% recovery. Table 1 gives the different conditions and the recoveries obtained for each procedure. The differences between the two procedures were not large; the conventional procedure seems to be better for methamphetamine. However, the procedure involving derivatization on to the SPE columns has some advantages, such as a decrease in the analysis time and the amounts of solvent and reagent required (very important for environmental protection), and the fact that there is no need to heat the sample.Pharmaceutical Sample The content of dl-amphetamine sulfate in tablets was determined. The standard addition method (MOSA) and the Youden method20 were applied. The total Youden blank (TYB) was 0.0285 for tablets containing amphetamine. The fact that this TYB value coincided with the analytical signal of the reagent blank (0.029 ± 0.006, n = 10), showed that there was no constant error for the sample. The slope obtained by applying MOSA (b = 0.01118 ± 0.00064, number of calibrates n = 3 ) was similar to that obtained using the calibration graph with Fig. 3 Analytical signal of NQS–amine derivative versus NQS/amine molar concentration ratio. The absorbance was recorded against a reagent blank. NQS–amphetamine derivative at 450 nm and 10 min (4) and NQS– methamphetamine derivative at 480 nm and 15 min (D).Conditions: amphetamine, 20.0 mg ml21; methamphetamine, 25.0 mg ml21; pH, 10; temperature, 25 °C; and eluent, acetonitrile–water (1 + 1 ) Fig. 4 Spectra in the range 190–820 nm for different extraction solvents: a, chloroform; b, diethyl ether; c, methanol, d, acetonitrile; and e, propan- 2-ol. (a) NQS reagent recorded against solvent blank, (b) NQS–amphetamine recorded against reagent blank. Conditions: NQS, 9.6 3 1023 m; amphetamine, 20 mg ml21; pH, 10; and temperature, 25 °C for 10 min.Analyst, July 1997, Vol. 122 675standards (b = 0.0132 ± 0.0015, n = 3). Therefore, no proportional bias error had been introduced by the sample. By subtracting the reagent blank value from the analytical signal, the concentration of amphetamine in the sample was determined and Table 2 gives the results obtained. No differences were obtained by applying the calibration graph with standards or MOSA. The concentration of amphetamine sulfate found in this sample was 9.9 ± 0.6 mg (n = 8), which corresponded to the labelled concentration of 10 mg per tablet.Urine Samples The washing step after derivatization was studied using water and different acetonitrile–water mixtures (1 + 4, 1 + 3 and 0 + 1). When water was used as the washing solvent, the interferences from the urine sample were not eliminated. However, a significant improvement was observed on including acetonitrile in the washing mixture. Fig. 5 shows the analytical signals corresponding to the different collected fractions of 1 ml (from 1 up to 7 ml) of the flushed eluent [acetonitrile–water (1 + 3)] for solutions of reagent, amphetamine standard, urine and urine spiked with amphetamine standard.As can be seen, the endogenous compounds of urine are eliminated in the first 3 ml of eluent. The absorbance value obtained on adding the Table 1 Analytical characteristics for derivatization of amphetamine and methamphetamine on SPE columns (C18), and conventional liquid–liquid procedure using NQS reagent Conventional derivatization SPE derivatization (C18) (hexane–ethyl acetate) Conditions Amphetamine Methamphetamine Amphetamine11 Methamphetamine12 pH (buffer) 10 (carbonate) 10 (carbonate) 7.5 (phosphate) 10 (carbonate) NQS concentration/m 9.6 3 1023 9.6 3 1023 6.4 3 1023 6.4 3 1023 Reaction time/min 10 15 30 5 Reaction temperature/°C Room Room 70 45 Dynamic range of concentration/mg ml21 3.4–70.0 2.2–70.0 1.4–50.0 0.9–35.0 Calibration graphs A = 7.08 3 1023 + 0.0116C A= 0.03355 + 0.0184C A= 28.86 3 1023 + 0.01460C A= 0.0049 + 0.0212C (l = 450 nm) (l = 480 nm) (l = 450 nm) (l = 450 nm) Recovery (%) 102 83 100 100 Detection limit in urine sample (10 ml) mg ml21 0.3 – 0.4 0.9 Table 2 Found concentration of dl-amphetamine in tablets by applying conventional calibration graph with standards and MOSA method at 450 nm.Conditions: NQS, 9.6 3 1023 m; pH, 10; 10 min; temperature, 25 °C; and extraction solvent, acetonitrile Standard addition Conventional method (MOSA) calibration graph Labelled AMP content/ Found/ Error Found/ Error (mg/ml21 AMP added/mg ml21 (mg ml21 (%) mg ml21 (%) 17.8 – 18.4 +3.4 16.9 25.1 10 9.2 28 15 14.9 20.7 30 29 23.3 18.2 – 17.7 22.7 16.8 27.7 10 9.3 27 20 18.5 27.5 30 30.2 +0.7 17.8 – 16.8 25.6 17.3 22.7 15 15.6 +3.8 20 21.8 +9.3 17.8 – 17.8 0 26.7 – 24.8 27.1 35.6 – 32.5 28.7 Fig. 5 Analytical signals corresponding to the different fractions of eluent acetonitrile–water (1 + 3) for solutions of NQS, amphetamine standard, urine and urine spiked with amphetamine standard.Conditions: NQS 9.6 3 1023 m, amphetamine, 25 mg ml21; pH, 10, and temperature 25 °C for 10 min. Table 3 Recoveries of 25 mg ml21 amphetamine in a urine sample using 5 ml of acetonitrile–water (1 + 4) and 3 ml of acetonitrile–water (1 + 3). Conditions: NQS, 9.6 3 1023 m; pH, 10; 10 min; and temperature, 25 °C Recovery (%) MeCN–H2O (1 + 4) MeCN–H2O (1 + 3) Buffer H2O Buffer H2O Sample conditioned conditioned conditioned conditioned Standard 100 92 81 58 Urine 89 89 62 82 676 Analyst, July 1997, Vol. 122analytical signals of urine and amphetamine standard and subtracting the analytical signal of the reagent, was similar to the absorbance value for the urine sample spiked with the standard. The amphetamine was similarly recovered from the standard or urine. Better results were obtained using 5 ml of acetonitrile–water (1 + 4) than using 3 ml of acetonitrile–water (1 + 3), as can be seen from the recoveries given in Table 3.In order to establish whether the amphetamine present in the sample can be affected by the sample treatment, two different procedures were studied (see Experimental). In procedure 1 the amphetamine was added to the urine before any treatment and in procedure 2 it was added after it. The similarity between the calibration graphs for urine sample obtained using the two procedures (procedure 1, A = 215 3 1023 + 0.01273C, syx = 9.4 3 1023; procedure 2, A = 29 3 1023 + 0.01280C, syx = 3.1 3 1022) shows that the amphetamine recovery was not influenced by the sample treatment.When MOSA was applied to fortified urine samples, the slope obtained (b = 0.0128) was similar to that obtained for standard samples. This indicates that matrix effects are not present and means that the calibration obtained for pure amine can be used to obtain the analyte concentration.In addition, different urine samples without amphetamine were processed according to these procedures and all the samples gave similar values at the working wavelength (for n = 14, A = 0.18 ± 0.02). This permitted the use, as a blank, of a urine sample from a drug-free subject. The concentrations of amphetamine found in the sample by applying procedures 1 and 2 are given in Table 4. As can be seen, similar results were obtained with both procedures and the relative error is acceptable in all instances.The precision and accuracy for the samples are generally good, and therefore it seems that the determination does not depend on the urine matrix in any of the cases tested. Since the matrix of the samples does not affect the determinations, an estimate of the inter-day precision can be obtained from these data. Table 1 shows the detection limit in a urine sample using SPE and the conventional liquid–liquid procedure.11 No interference is produced by the presence in urine of ephedrine or norephedrine.Conclusions This study has shown the possibility of determining spectrophotometrically primary and secondary amines, previously retained in C18 columns, by using NQS as the derivatization reagent. The procedure used optimizes the reaction conditions in the C18 cartridges and has been applied to the determination of amphetamine in pharmaceutical and urine samples. The recovery of derivatives was similar to that obtained for the derivatization reaction in aqueous solutions.This is a simple procedure which allows amines to be measured rapidly. It avoids heating the mixture sample and allows the use of more polar solvents such as acetonitrile or methanol than those employed in liquid–liquid extraction for the recovery of the reaction products. The volume of solvent employed is smaller than that required for derivatization in aqueous solution. The authors are grateful to the CICYT for financial support (Project No.SAF95-0586). References 1 Camp�ýns Falc�o, P., Sevillano Cabeza, A., and Molins Legua, C., J. Liq. Chromatogr., 1994, 17, 731. 2 Kinberger, B., J. Chromatogr., 1981, 213, 166. 3 Endo, M., Imamichi, H., Moriyasu, M., and Hasmimoto, Y., J. Chromatogr., 1980, 196, 334. 4 Hayakawa, K., Hasegawa, K., Imaizumi, K., Wong, O. S., and Miyazaki, M., J. Chromatogr., 1989, 464 343. 5 Gao, C. X., Chou, T. Y., and Krull, I. S., Anal. Chem., 1989, 61, 1538. 6 ZhF. X., Krull, I. S., and Feibush, B., J. Chromatogr., 1992, 609, 103. 7 Bourque A. J., and Krull, I. R., J. Chromatogr., 1991, 537, 123. 8 Suzuki, S., Inoue, T., and Niwaguchi, T., J. Chromatogr., 1983, 267, 381. 9 Farrell, B. M., and Jefferies, T. M., J. Chromatogr., 1983, 272, 111. 10 Pharmaceutical Society of Britian, Clarke’s Isolation and Identification of Drugs, Pharmceutical Press, London, 1986, pp. 349 and 763. 11 Molins Legua, C., Camp�ýns Falc�o, P., and Sevillano Cabeza, A., Anal.Chim. Acta, 1993, 283, 635. 12 Molins Legua, C., Camp�ýns Falc�o P., and Sevillano Cabeza, A., Fresenius’ J. Anal. Chem., 1994, 349, 311. 13 Sevillano Cabeza, A., Camp�ýns Falc�o, P., and Molins Legua, C., Anal. Letters, 1994, 27, 1095. 14 Camp�ýns Falc�o, P., Bosch Reig, F., Sevillano Cabeza, A., and Molins Legua, C., Anal. Chim. Acta., 1994, 287, 41. 15 Camp�ýns Falc�o, P., Molins Legua, C., Herraez Hern�andez, R., and Sevillano Cabeza, A., J. Chromatogr.B, 1995, 663, 235. 16 Camp�ýns Falc�o, P., Sevillano Cabeza, A., Molins Legua, C., and Kohlmann, M., J. Chromatogr. B, 1996, 687, 239. 17 Herr�aez Hern�andez, R., Camp�ýns Falc�o, P., and Sevillano Cabeza, A., Anal. Chem., 1996, 68, 734. 18 ACS Committee on Environmental Improvement, Anal. Chem., 1980, 52, 2242. 19 IUPAC, ‘Compendium of Analytical Nomenclature’, Pergamon Press, Oxford, 1978. 20 Youden, W. J., Anal. Chem., 1947, 19, 946. Paper 7/01134B Received February 18, 1997 Accepted April 24, 1997 Table 4 Found concentration of amphetamine in urine samples by applying conventional calibration graph.Conditions: NQS, 9.6 3 1023 m; pH 10; 10 min; and temperature, 25°C Concentration found by conventional calibration/mg ml21 Concentration added mg ml21 Procedure 1 Procedure 2 Mean 2.5 2.5 ± 0.4 (n = 6) 2.6 ± 0.5 (n = 4) 2.5 ± 0.4 (n = 10) 4.9 4.4 ± 0.6 (n = 4) 4.5 ± 0.1 (n = 3) 4.4 ± 0.4 (n = 7) 7.3 7.9 ± 0.5 (n = 8) 7.4 ± 0.7 (n = 5) 7.6 ± 0.6 (n = 13) 9.7 9.5 ± 1 (n = 3) 9.0 ± 0.7 (n = 3) 9.3 ± 0.9 (n = 6) 11.8 12.3 ± 0.5 (n = 4) 11.3 ± 0.9 (n = 3) 11.9 ± 0.8 (n = 7) Analyst, July 1997, Vol. 122 677 Derivatization of Amphetamine and Methamphetamine With 1,2-Naphthoquinone 4-Sulfonic Acid Into Solid-phase Extraction Cartridges. Determination of Amphetamine in Pharmaceutical and Urine Samples Pilar Camp�ýns Falc�o*, Carmen Molins Legua, Adela Sevillano Cabeza and Rosa Porras Serrano Departamento de Qu�ýmica Anal�ýtica, Facultad de Qu�ýmica, Universidad de Valencia, Doctor Moliner, 50, 46100-Burjassot, Valencia, Spain The derivatization of amphetamine and methamphetamine with 1,2-naphthoquinone-4-sulfonate (NQS) into solid-phase extraction cartridges (C18) is described.Optimum conditions were the use of carbonate–hydrogencarbonate buffer of pH 10, a 10 min reaction time at 25 °C and an NQS concentration of 9.6 3 1023 m. The accuracy and the precision of the method were tested. The results obtained with the proposed liquid–solid procedure were compared with those obtained with a traditional liquid–liquid extraction with hexane–ethyl acetate. The procedure was used to measure amphetamine in pharmaceutical and urine samples Keywords: Amphetamines; derivatization; solid-phase extraction; pharmaceuticals; urine Derivatization has long been accepted as an effective modification technique that can improve the overall specificity and sensitivity of trace analyses.The usual methodology involves a solution-based derivatization procedure.Over the past decade, immobilized solid-phase reagents on a polymeric solid support have become increasingly popular for easy conversion of analytes into more detectable species. The derivatization step plays a significant role in determining amphetamine and amphetamine-related compounds.1 Reagents such as o-phthalaldehyde,2 1,2-naphthoquinone-4-sulfonate (NQS)3 and dansyl chloride4 have been proposed.Solid-phase reagents have also been investigated. Gao et al.5 studied a polymeric reagent containing an activated ester linkage to a 9-fluorenyl group. Zhou et al.6 described the preparation of a covalently bound, fluorescencesensitive tag, 9-fluoreneacetyl, on a pore size-controlled, rigid polystyrene–divinylbenzene resin. A solid-phase reagent containing the 3,5-dinitrophenyl tag for the improved derivatization of chiral and achiral amines, amino alcohols and amino acids has also been proposed.7 All these reagents have been employed as pre-column derivatization reagents in liquid chromatography. Suzuki et al.8 developed a screening method for methamphetamine in urine by a color reaction using a Sep-Pak C18 cartridge.In this procedure, methamphetamine, retained selectively on the resin, is colored with Simon’s reagent. NQS is a solution-based derivatization reagent and provides the sensitivity required for the quantitative analysis of urine and plasma samples containing amphetamines;9 it is also recommended in Clarke’s Isolation and Identification of Drugs.10 In previous papers, we described liquid–liquid extraction combined with spectrophotometric procedures for the individual determination of amphetamine11 and methamphetamine12 in urine samples using NQS as derivatizing agent. The kinetics of the reaction have also been studied.13 The determination of amphetamine and methamphetamine in urine by the Hpoint standard additions method has been proposed.14 We also examined the determination of both drugs in urine by normalphase high-performance liquid chromatography with NQS and solid-phase extraction for sample clean-up.15 In another study we optimized the derivatization procedure with NQS into C18 solid-phase extraction (SPE) cartridges for the determination of amphetamine and methamphetamine in urine samples using a reversed-phase HPLC method with UV/VIS detection.16 Recently, we demonstrated the possibility of performing on-line derivatization into pre-columns for the determination of drugs by liquid chromatography and column switching.17 This paper describes a simple and rapid spectrophotometric procedure for both clean-up and derivatization with NQS of amphetamine or methamphetamine on solid-phase extraction cartridges.A commercial C18 packing material was used instead of polymeric reagents specially prepared for solid-phase derivatization. The method was compared with solution-based method and applied to the analysis of pharmaceutical and urine samples using a UV/VIS spectrophotometer.Experimental Apparatus All spectrophotometric measurements were made on a Hewlett- Packard (Avondale, PA, USA) HP 8452 A diode-array spectrophotometer furnished with quartz cuvettes with a 1 cm pathlength. Reagents Solutions were prepared with distilled water and all reagents were of analytical-reagent grade, unless stated otherwise. Hydrogencarbonate solution (8% m/v) was prepared by dissolving sodium hydrogencarbonate (Probus, Badalona, Spain) (8 g) in 100 ml of water. The pH was adjusted to different values by adding the minimum amount of sodium hydroxide solution (10 m) or hydrochloride acid (1 m).Buffers of pH 10 were prepared by dissolving sodium hydrogencarbonate and sodium carbonate (1% and 8% m/v and 5 m) in water. This solution was then diluted further to yield appropriate working standard solutions, which were prepared daily.A 1,2-naphthoquinone-4-sulfonic acid stock standard solution was prepared by dissolving the sodium salt (Sigma, St. Louis, MO, USA) in distilled water. This solution was prepared freshly for each experiment and was stored in the dark. Methamphetamine hydrochloride and amphetamine sulfate (Sigma) stock standard solutions were prepared by dissolving 100 mg in distilled water and diluting to 100 ml. Working standard solutions were prepared daily by appropriate dilution of the stock standard solutions.Chloroform, diethyl ether, propan-2-ol, methanol and acetonitrile were of HPLC grade from Scharlau (Barcelona, Spain); hydrochloric Analyst, July 1997, Vol. 122 (673oxide (Panreac, Barcelona, Spain) were also used. C18 (200 mg ml21), C8 and C2 (100 mg ml21) Bond Elut columns were obtained from Varian (Harbor City, CA, USA). Pharmaceutical Sample Centramine tablets, labelled to contain 10 mg of amphetamine sulfate per tablet, lactose and other excipients were obtained from Laboratorio Miquel (Barcelona, Spain).Derivatization Into Solid-phase Extraction Columns C18 extraction columns were previously conditioned by drawing through 1 ml of methanol, followed by 1 ml of 1% m/v hydrogencarbonate–carbonate solution at pH 10. Subsequently, 2 ml volumes of sample solution containing different amine concentrations were transferred to the column and washed with 2.50 ml of distilled water.When the amines were retained in the column, 0.5 ml of NQS reagent (1% m/ v) and 0.5 ml of 8% m/v hydrogencarbonate–carbonate solution at pH 10, previously mixed, were added. After 10 min for amphetamine or 15 min for methamphetamine at 25 °C, the columns were washed with water. The reaction products (amine–NQS) were eluted from the columns with 2 ml of acetonitrile–water (1+1). The absorbance between 190 and 820 nm was recorded. Absorbance was measured against the reagent blank at 25 °C.Three or more replicates were processed in all cases. The analytical signal was measured at 450 nm for amphetamine and 480 nm for methamphetamine. Centramine Tablets With Amphetamine Sulfate Three tablets were weighed and powdered. The required amount was suspended in distilled water and filtered. The filtrate was diluted with distilled water. Different volumes of this sample solution were taken, following the procedure for the standard samples.Urine Samples Two different sample treatments were applied. (1) Aliquots of urine samples (14 ml) were spiked at different amphetamine concentration levels and 0.3 ml of carbonate– hydrogencarbonate buffer (5 m) at pH 10 was added. The samples were centrifuged for 10 min at 1500 rpm and filtered before derivatization into the column. Subsequently, 10 ml of these urine samples were processed according to the procedure described above except that the columns were washed with 5 ml of acetonitrile–water (1+4).(2) A 100 ml volume of urine samples was made alkaline by adding 2 ml of carbonate–hydrogencarbonate buffer (5 m) at pH 10 and the mixture was centrifuged and filtered. Aliquots of these samples were spiked at different concentration levels with amphetamine stock solution. Subsequently 10 ml of these samples were processed according to the procedure described above except that the columns were washed with 5 ml of acetonitrile–water (1+4).Youden and Standard Addition Methods The Youden method20 was applied to pharmaceutical samples. Different volumes of pharmaceutical sample solution between 0.2 and 1 ml were taken and processed according to the procedure described above. For the standard addition method, volumes of 0.4 ml of pharmaceutical solution were employed, to which various volumes of amphetamine sulfate stock solution and water were added up to 2 ml. For urine samples, the standard addition method was applied.To 14 ml of urine sample, 0.7 ml of 51.4 mg ml21 amphetamine sulfate solution and 0.3 ml of hydrogencarbonate–carbonate saturated buffer solution (5 m) of pH 10 were added. The mixture was centrifuged for 10 min and filtered. Aliquots of this sample were spiked at different concentrations with 275 mg ml21 amphetamine sulfate solution. The samples were then processed as described above. Results and Discussion Optimization of the Working Conditions The reaction is carried out at basic pH, and the influence of this parameter was studied in the range 7.5–10.5 (with derivatization at 25 °C for 10 min).The results are expressed graphically in Fig. 1. The analytical signal was found not to be dependent on pH over the range 10.0–10.5 for methamphetamine, whereas it decreased outside this range. However, for amphetamine the highest analytical signal was obtained at pH 10. At pH < 10, the derivatization time for amphetamines was longer. To provide the appropiate pH, NaHCO3–NaOH (pH 10) solution was used.After studying the concentration effect of this solution in the range 0.1–1.0 m, a hydrogencarbonate solution of 0.5 m was selected. In most reported procedures dealing with the amine–NQS reaction, the derivatization is carried out at high temperatures (70 °C3,9 or 60 °C4) and the mixture samples are heated for a long time (between 20 and 40 min). We observed that this reaction occurs at lower temperatures and in a shorter time when the pH is high.12 We therefore selected pH 10.0 in order to increase the reaction rate and perform the derivatization procedure at room temperature (25 °C).The signal corresponding to the NQS–amphetamine was approximately constant after 10 min (Fig. 2). However, methamphetamine seems to react more slowly and more time is required to reach the plateau. Fig. 1 Graph of absorbance versus pH for NQS reagent recorded against acetonitrile blank, l = 450 nm, at 10 min (1), NQS–amphetamine, l = 450 nm, at 10 min (2) and NQS–methamphetamine, l = 480 nm, at 15 min (3), recorded against a reagent blank.Conditions: NQS, 9.6 3 1023 m; amines, 20.0 mg ml21; temperature 25 °C and eluent acetonitrile. Fig. 2 Absorbance at 450 or 480 nm corresponding for the reaction product, amphetamine-NQS or methamphetamine–NQS, recorded against a reagent blank at different reaction times. Conditions: NQS, 9.6 3 1023 m; amphetamine, 20.0 mg ml21; methamphetamine, 25.0 mg ml21; pH, 10; temperature, 25 °C; and eluent, acetonitrile–water (1 + 1) 674 Analyst, July 1997, Vol. 122Times of 10 and 15 min were selected for the derivatization of amphetamine and methamphetamine, respectively.The effect of the NQS concentration was evaluated in the range 9.6 3 1024–5.8 3 1022 m, the amphetamine and methamphetamine concentrations being 5.4 3 1025 and 1.3 3 1024 m, respectively. Fig. 3 shows the absorbance as a function of the NQS to amine concentration ratio. The analytical signal of these systems increased linearly up to 9.6 3 1023 m, and for both amines remained constant above this limit.The signal of the blank reagent increased with increase in concentration. In order to have low blank interferences, the reagent concentration chosen was 9.6 31023 m. Different water volumes were passed thought the column to eliminate the excess of reagent and a water volume between 2.5 and 5 ml was selected as optimum.Chloroform, diethyl ether, methanol, propan-2-ol and acetonitrile were tested as eluents. For the analytes studied, similar analytical signals were obtained using methanol, acetonitrile and propan-2-ol . However, the sensitivity decreased when chloroform or diethyl ether was used. Analogous results were obtained for the NQS reagent [Fig. 4 (a) and (b)]. Acetonitrile was selected as providing the greatest sensitivity and the lowest analytical signal for the NQS reagent . Although 1 ml of solvent was sufficient to elute all the reaction product formed, we eluted with 2 ml of acetonitrile–water (1+1) to provide a sufficient volume to measure the analytical signal.In this solvent the derivatives remain stables for at least 1 week if they are stored at 4 °C. The columns were cleaned up for further derivatization with 3 ml of methanol acidified with HCl (pH 2). Different Bond-Elut columns (C18, C8 and C2) were tested. The highest analytical signal of the reaction product was considered to be 100%.The recoveries obtained using carbonate –hydrogencarbonate buffer (pH 10) at 25 °C for 10 min, with an amphetamine concentration of 20 mg ml21, an NQS concentration of 9.6 3 1023 m and acetonitrile–water (1+1) as eluent for NQS–amphetamine products were 96 ± 3, 74 ± 2 and 67 ± 3%, using C18, C2 and C8, respectively. The differences between the results obtained were not very large, but the amount of reaction product formed was highest with C18, probably because the retention of the analytes was largest in this column.These results are in agreement with previous results.15 For methamphetamine the results obtained using Bond-Elut were adequate. For both analytes the packing selected was C18. The C18 columns were usable for a long time (3 months, equivalent to about 200 runs) and the results were reproducible. Table 1 shows the regression equation, calculated from the calibration graph of absorbance versus amphetamine or methamphetamine concentration, dynamic ranges of concentration and the detection limits using standard solutions under the optimized conditions.The lower limit of the dynamic range of concentration was the quantification limit, calculated as 10sB/ b,18 where sB = 0.004 is the standard deviation of the NQS blank and b is the slope of the calibration graph. The upper limit is the last point fitted by the linear least-squares method. The limits of detection were 1.0 and 0.7 mg ml21 for amphetamine and methamphetamine, respectively, calculated as 3sB/b.19 The results obtained by this procedure were compared with those obtained with the conventional liquid–liquid procedure. 11,12,14 To compare the two procedures, the highest analytical signal (regardless of the procedure) was considered to represent 100% recovery. Table 1 gives the different conditions and the recoveries obtained for each procedure. The differences between the two procedures were not large; the conventional procedure seems to be better for methamphetamine. However, the procedure involving derivatization on to the SPE columns has some advantages, such as a decrease in the analysis time and the amounts of solvent and reagent required (very important for environmental protection), and the fact that there is no need to heat the sample.Pharmaceutical Sample The content of dl-amphetamine sulfate in tablets was determined. The standard addition method (MOSA) and the Youden method20 were applied.The total Youden blank (TYB) was 0.0285 for tablets containing amphetamine. The fact that this TYB value coincided with the analytical signal of the reagent blank (0.029 ± 0.006, n = 10), showed that there was no constant error for the sample. The slope obtained by applying MOSA (b = 0.01118 ± 0.00064, number of calibrates n = 3 ) was similar to that obtained using the calibration graph with Fig. 3 Analytical signal of NQS–amine derivative versus NQS/amine molar concentration ratio.The absorbance was recorded against a reagent blank. NQS–amphetamine derivative at 450 nm and 10 min (4) and NQS– methamphetamine derivative at 480 nm and 15 min (D). Conditions: amphetamine, 20.0 mg ml21; methamphetamine, 25.0 mg ml21; pH, 10; temperature, 25 °C; and eluent, acetonitrile–water (1 + 1 ) Fig. 4 Spectra in the range 190–820 nm for different extraction solvents: a, chloroform; b, diethyl ether; c, methanol, d, acetonitrile; and e, propan- 2-ol.(a) NQS reagent recorded against solvent blank, (b) NQS–amphetamine recorded against reagent blank. Conditions: NQS, 9.6 3 1023 m; amphetamine, 20 mg ml21; pH, 10; and temperature, 25 °C for 10 min. Analyst, July 1997, Vol. 122 675standards (b = 0.0132 ± 0.0015, n = 3). Therefore, no proportional bias error had been introduced by the sample. By subtracting the reagent blank value from the analytical signal, the concentration of amphetamine in the sample was determined and Table 2 gives the results obtained.No differences were obtained by applying the calibration graph with standards or MOSA. The concentration of amphetamine sulfate found in this sample was 9.9 ± 0.6 mg (n = 8), which corresponded to the labelled concentration of 10 mg per tablet. Urine Samples The washing step after derivatization was studied using water and different acetonitrile–water mixtures (1 + 4, 1 + 3 and 0 + 1). When water was used as the washing solvent, the interferences from the urine sample were not eliminated.However, a significant improvement was observed on including acetonitrile in the washing mixture. Fig. 5 shows the analytical signals corresponding to the different collected fractions of 1 ml (from 1 up to 7 ml) of the flushed eluent [acetonitrile–water (1 + 3)] for solutions of reagent, amphetamine standard, urine and urine spiked with amphetamine standard. As can be seen, the endogenous compounds of urine are eliminated in the first 3 ml of eluent.The absorbance value obtained on adding the Table 1 Analytical characteristics for derivatization of amphetamine and methamphetamine on SPE columns (C18), and conventional liquid–liquid procedure using NQS reagent Conventional derivatization SPE derivatization (C18) (hexane–ethyl acetate) Conditions Amphetamine Methamphetamine Amphetamine11 Methamphetamine12 pH (buffer) 10 (carbonate) 10 (carbonate) 7.5 (phosphate) 10 (carbonate) NQS concentration/m 9.6 3 1023 9.6 3 1023 6.4 3 1023 6.4 3 1023 Reaction time/min 10 15 30 5 Reaction temperature/°C Room Room 70 45 Dynamic range of concentration/mg ml21 3.4–70.0 2.2–70.0 1.4–50.0 0.9–35.0 Calibration graphs A = 7.08 3 1023 + 0.0116C A= 0.03355 + 0.0184C A= 28.86 3 1023 + 0.01460C A= 0.0049 + 0.0212C (l = 450 nm) (l = 480 nm) (l = 450 nm) (l = 450 nm) Recovery (%) 102 83 100 100 Detection limit in urine sample (10 ml) mg ml21 0.3 – 0.4 0.9 Table 2 Found concentration of dl-amphetamine in tablets by applying conventional calibration graph with standards and MOSA method at 450 nm. Conditions: NQS, 9.6 3 1023 m; pH, 10; 10 min; temperature, 25 °C; and extraction solvent, acetonitrile Standard addition Conventional method (MOSA) calibration graph Labelled AMP content/ Found/ Error Found/ Error (mg/ml21 AMP added/mg ml21 (mg ml21 (%) mg ml21 (%) 17.8 – 18.4 +3.4 16.9 25.1 10 9.2 28 15 14.9 20.7 30 29 23.3 18.2 – 17.7 22.7 16.8 27.7 10 9.3 27 20 18.5 27.5 30 30.2 +0.7 17.8 – 16.8 25.6 17.3 22.7 15 15.6 +3.8 20 21.8 +9.3 17.8 – 17.8 0 26.7 – 24.8 27.1 35.6 – 32.5 28.7 Fig. 5 Analytical signals corresponding to the different fractions of eluent acetonitrile–water (1 + 3) for solutions of NQS, amphetamine standard, urine and urine spiked with amphetamine standard. Conditions: NQS 9.6 3 1023 m, amphetamine, 25 mg ml21; pH, 10, and temperature 25 °C for 10 min. Table 3 Recoveries of 25 mg ml21 amphetamine in a urine sample using 5 ml of acetonitrile–water (1 + 4) and 3 ml of acetonitrile–water (1 + 3).Conditions: NQS, 9.6 3 1023 m; pH, 10; 10 min; and temperature, 25 °C Recovery (%) MeCN–H2O (1 + 4) MeCN–H2O (1 + 3) Buffer H2O Buffer H2O Sample conditioned conditioned conditioned conditioned Standard 100 92 81 58 Urine 89 89 62 82 676 Analyst, July 1997, Vol. 122analytical signals of urine and amphetamine standard and subtracting the analytical signal of the reagent, was similar to the absorbance value for the urine sample spiked with the standard.The amphetamine was similarly recovered from the standard or urine. Better results were obtained using 5 ml of acetonitrile–water (1 + 4) than using 3 ml of acetonitrile–water (1 + 3), as can be seen from the recoveries given in Table 3. In order to establish whether the amphetamine present in the sample can be affected by the sample treatment, two different procedures were studied (see Experimental). In procedure 1 the amphetamine was added to the urine before any treatment and in procedure 2 it was added after it.The similarity between the calibration graphs for urine sample obtained using the two procedures (procedure 1, A = 215 3 1023 + 0.01273C, syx = 9.4 3 1023; procedure 2, A = 29 3 1023 + 0.01280C, syx = 3.1 3 1022) shows that the amphetamine recovery was not influenced by the sample treatment. When MOSA was applied to fortified urine samples, the slope obtained (b = 0.0128) was similar to that obtained for standard samples. This indicates that matrix effects are not present and means that the calibration obtained for pure amine can be used to obtain the analyte concentration. In addition, different urine samples without amphetamine were processed according to these procedures and all the samples gave similar values at the working wavelength (for n = 14, A = 0.18 ± 0.02).This permitted the use, as a blank, of a urine sample from a drug-free subject.The concentrations of amphetamine found in the sample by applying procedures 1 and 2 are given in Table 4. As can be seen, similar results were obtained with both procedures and the relative error is acceptable in all instances. The precision and accuracy for the samples are generally good, and therefore it seems that the determination does not depend on the urine matrix in any of the cases tested. Since the matrix of the samples does not affect the determinations, an estimate of the inter-day precision can be obtained from these data.Table 1 shows the detection limit in a urine sample using SPE and the conventional liquid–liquid procedure.11 No interference is produced by the presence in urine of ephedrine or norephedrine. Conclusions This study has shown the possibility of determining spectrophotometrically primary and secondary amines, previously retained in C18 columns, by using NQS as the derivatization reagent. The procedure used optimizes the reaction conditions in the C18 cartridges and has been applied to the determination of amphetamine in pharmaceutical and urine samples.The recovery of derivatives was similar to that obtained for the derivatization reaction in aqueous solutions. This is a simple procedure which allows amines to be measured rapidly. It avoids heating the mixture sample and allows the use of more polar solvents such as acetonitrile or methanol than those employed in liquid–liquid extraction for the recovery of the reaction products.The volume of solvent employed is smaller than that required for derivatization in aqueous solution. The authors are grateful to the CICYT for financial support (Project No. SAF95-0586). References 1 Camp�ýns Falc�o, P., Sevillano Cabeza, A., and Molins Legua, C., J. Liq. Chromatogr., 1994, 17, 731. 2 Kinberger, B., J. Chromatogr., 1981, 213, 166. 3 Endo, M., Imamichi, H., Moriyasu, M., and Hasmimoto, Y., J. Chromatogr., 1980, 196, 334. 4 Hayakawa, K., Hasegawa, K., Imaizumi, K., Wong, O. S., and Miyazaki, M., J. Chromatogr., 1989, 464 343. 5 Gao, C. X., Chou, T. Y., and Krull, I. S., Anal. Chem., 1989, 61, 1538. 6 Zhou, F. X., Krull, I. S., and Feibush, B., J. Chromatogr., 1992, 609, 103. 7 Bourque A. J., and Krull, I. R., J. Chromatogr., 1991, 537, 123. 8 Suzuki, S., Inoue, T., and Niwaguchi, T., J. Chromatogr., 1983, 267, 381. 9 Farrell, B. M., and Jefferies, T. M., J. Chromatogr., 1983, 272, 111. 10 Pharmaceutical Society of Britian, Clarke’s Isolation and Identification of Drugs, Pharmceutical Press, London, 1986, pp. 349 and 763. 11 Molins Legua, C., Camp�ýns Falc�o, P., and Sevillano Cabeza, A., Anal. Chim. Acta, 1993, 283, 635. 12 Molins Legua, C., Camp�ýns Falc�o P., and Sevillano Cabeza, A., Fresenius’ J. Anal. Chem., 1994, 349, 311. 13 Sevillano Cabeza, A., Camp�ýns Falc�o, P., and Molins Legua, C., Anal. Letters, 1994, 27, 1095. 14 Camp�ýns Falc�o, P., Bosch Reig, F., Sevillano Cabeza, A., and Molins Legua, C., Anal. Chim. Acta., 1994, 287, 41. 15 Camp�ýns Falc�o, P., Molins Legua, C., Herraez Hern�andez, R., and Sevillano Cabeza, A., J. Chromatogr. B, 1995, 663, 235. 16 Camp�ýns Falc�o, P., Sevillano Cabeza, A., Molins Legua, C., and Kohlmann, M., J. Chromatogr. B, 1996, 687, 239. 17 Herr�aez Hern�andez, R., Camp�ýns Falc�o, P., and Sevillano Cabeza, A., Anal. Chem., 1996, 68, 734. 18 ACS Committee on Environmental Improvement, Anal. Chem., 1980, 52, 2242. 19 IUPAC, ‘Compendium of Analytical Nomenclature’, Pergamon Press, Oxford, 1978. 20 Youden, W. J., Anal. Chem., 1947, 19, 946. Paper 7/01134B Received February 18, 1997 Accepted April 24, 1997 Table 4 Found concentration of amphetamine in urine samples by applying conventional calibration graph. Conditions: NQS, 9.6 3 1023 m; pH 10; 10 min; and temperature, 25°C Concentration found by conventional calibration/mg ml21 Concentration added mg ml21 Procedure 1 Procedure 2 Mean 2.5 2.5 ± 0.4 (n = 6) 2.6 ± 0.5 (n = 4) 2.5 ± 0.4 (n = 10) 4.9 4.4 ± 0.6 (n = 4) 4.5 ± 0.1 (n = 3) 4.4 ± 0.4 (n = 7) 7.3 7.9 ± 0.5 (n = 8) 7.4 ± 0.7 (n = 5) 7.6 ± 0.6 (n = 13) 9.7 9.5 ± 1 (n = 3) 9.0 ± 0.7 (n = 3) 9.3 ± 0.9 (n = 6) 11.8 12.3 ± 0.5 (n = 4) 11.3 ± 0.9 (n = 3) 11.9 ± 0.8 (n

ISSN:0003-2654    

DOI:10.1039/a701134b

出版商:RSC    

年代:1997

数据来源: RSC