2( k2 p) Fractional Factorial Design viaFold Over: Application to Optimization of Novel Multicomponent Vesicular Systems Yannis L. Loukas† Centre for Drug Delivery Research, School of Pharmacy, University of London, 29–39 Brunswick Square, London, UK WC1N 1AX A computer-based technique based on a 2(k2p) fractional factorial design was applied for the optimization of recently described multicomponent protective liposomal formulations. These formulations contain riboflavin (vitamin B2) as a model, photosensitive drug, in addition to Oil Red O, deoxybenzone, oxybenzone and b-carotene as oil-soluble light absorbers and antioxidants incorporated into the lipid bilayer, and sulisobenzone as a water-soluble light absorber incorporated into the aqueous phase of liposomes. The presence or absence of these five different light absorbers in multilamellar liposomes containing the vitamin free or complexed with g-cyclodextrin comprised the six factors of the system, each one examined at two levels.The stabilization ratio of the vitamin and its percentage entrapment in liposomes were the two response variables of the system to be optimized. The entrapment values were calculated for all the materials, either spectrophotometrically, using second-order derivative spectrophotometry, or fluorimetrically. The response variables were predicted by multiple regression equations comprising combinations of the six formulation factors. Higher entrapment and higher protection for the drug should characterize the optimum formulation.Keywords: Experimental design; fractional factorial; fold over technique; optimization; vesicular systems Photosensitive drugs are known to degrade on exposure to light and lose their activity. Topical formulations of these drugs for medical or cosmetic reasons must be prepared in such a way as to achieve maximum stability. Known stabilizing systems in the literature include the use of certain antioxidants and light absorbers in the same preparation (solution or suspension) with the drug or the use of cyclodextrins as a complexing system which provides also moderate stability against the examined external factors (light and oxygen).We have recently proposed1 –3 a novel multicomponent stabilizing system based on liposomes, which provides high protection to sensitive drugs. This system is based generally on the liposome’s ability to accommodate both hydrophobic and hydrophilic substances into their lipid membranes and their aqueous phases, respectively. In brief, multilamellar liposomes consisting of phosphatidylcholine and cholesterol entrap the water-soluble sensitive drug, as such or in the form of a cyclodextrin complex, in the aqueous phase and one or more light absorbers either in the aqueous phase or in the lipid bilayers, depending on their characteristics (Scheme 1).In this study, riboflavin was chosen as a model photosensitive drug with rapid decomposition on exposure to light (t50% = 0.5 h).4 In order to increase the stability of the vitamin, it was entrapped as such or in the form of a g-cyclodextrin (cyclomaltooctaose) complex in dehydration–rehydration multicomponent liposomes containing one or more of the light absorbers Oil Red O, oxybenzone, deoxybenzone, sulisobenzone and the antioxidant b-carotene (Scheme 1).A liposomal formulation can be characterized as being efficient when it contains the vitamin at a high entrapment value with a higher stabilization ratio (the ratio k0/kL, where k0 and kL are the degradation rate constants of the vitamin in free form and in liposomal formulations, respectively). From the above-mentioned six factors (the presence or absence of the g-cyclodextrin cavity, Oil Red O, dioxybenzone, oxybenzone, sulisobenzone and b-carotene), each reporting a different behavior on the two responses of interest (stabilization ratio and percentage entrapment of the vitamin), it is not obvious how the optimum formulation can be achieved.In this present study, an experimental design5 can be used in order to derive valid and robust statistical significance tests for the factors examined with a minimum number of experiments. It is sufficient to consider the factors affecting the responses at two levels; for instance, the concentration of each light absorber may be set either to zero or to a constant molar ratio with the vitamin, and the vitamin may be in either free or complexed † Present address: Riga Ferreou 21, Ano Ilioupolis, 163 43 Athens, Greece.E-mail: ylloukas@compulink.gr Scheme 1 Schematic representation of the 16 runs. The scheme has been simplified by omitting the cholesterol molecules. Analyst, October 1997, Vol. 122 (1023–1027) 1023form (Table 1). The most intuitive approach to study these factors and how they affect the responses examined would be to vary the factors of interest in a 2k full factorial design (k factors at two levels), that is, to try all possible combinations.This would work well, except that the number of liposomal preparations necessary will increase exponentially. For example, the six factors examined in the present study require 26 = 64 preparations. Because each liposomal preparation is time consuming and requires costly materials, the use of a 2(k2p) fractional factorial design6 can reduce considerably the number of preparations (from 64 preparations to 8, in the present case of six factors at two levels each).In this study, the use of the original (fractional factorial) design only gave indications of significant factors rather than conclusive results and, as a consequence, the fold over design was used with all the results referring to this design. After adding the second fraction (the fold over part), the resolution of the design was increased from III to IV, isolating the factors’ main effects from any two-way interactions.Experimental Materials and Instrumentation Riboflavin (R) and g-cyclodextrin (gCD) were obtained from Aldrich Chemical (Gillingham, Dorset, UK), Oil Red O, oxybenzone, deoxybenzone, sulisobenzone, b-carotene and cholesterol from Sigma Chemical (Poole, Dorset, UK) and phosphatidylcholine (PC) from Lipid Products (Nuthill, Surrey, UK). All other reagents were of analytical-reagent grade. Doubly distilled water was used throughout.Photostability studies of R were carried out using a Blak-Ray long-wavelength (365 nm) UV lamp with 6 W rating and 460 mW cm22 dm21 intensity (Model UVGL-58, UVP, San Gabriel, CA, USA). Measurement of the degradation kinetics of R in various preparations was performed fluorimetrically (lex = 445 nm, lem 520 nm) and assays of the components entrapped into liposomes were carried out with a Compuspec UV/VIS spectrophotometer (Wallac, Turku, Finland) connected to a personal computer which can also process the spectra into their derivatives. Preparation of R : gCD Complex and Multilamellar Liposomes The inclusion complex of R with gCD was prepared according to the freeze-drying method.7 Multilamellar liposomes were prepared according to the dehydration–rehydration method with some modifications: briefly, small unilamellar vesicles (SUV) prepared from equimolar PC and cholesterol were mixed with R (free or complexed) dissolved in de-ionized water, diluted to 10 ml with water and freeze-dried overnight.The dry powder was subjected to controlled rehydration and then centrifuged at 27 300g for 20 min to separate the entrapped and non-entrapped R. The liposomal pellet containing multilamellar dehydration– rehydration vesicles (DRV) was washed three times by centrifugation in 0.1 m sodium phosphate buffer containing 0.9% NaCl (pH 7.4) (PBS) and resuspended in 4 ml of PBS before use. DRV liposomes incorporating the vitamin and the lipid-soluble components in their lipid bilayers were prepared as above with the absorbers and the lipids dissolved in chloroform, prior to the generation of the SUV precursor vesicles. When the water-soluble light absorber sulisobenzone was also entrapped into DRV liposomes, this was dissolved together with free or complexed R in the aqueous solution to be subsequently mixed with the SUV.Determination of Liposome-entrapped Materials Entrapment values for R and light absorbers were determined by measuring the concentrations of the materials in both the DRV liposomal pellets obtained and the separated pooled supernatants fluorimetrically for R and by derivative UV spectrophotometry for the rest of the components.8 The use of the second-order derivative (D2) of the spectra was found to provide both good resolution and high signal-to-noise ratios (S/N).Photostability Studies The photostabilization of R in the different DRV formulations exposed to UV radiation was calculated fluorimetrically.The assay procedure is briefly as follows: the liposomal suspension of R (3 ml) was transferred into an open quartz cuvette and was placed in front of the UV lamp. The liposomal suspension was stirred continuously in order to make it homogeneous during the study and in order for the whole suspension to be equally irradiated. At time intervals, 100 ml of the liposomal suspension was dialyzed with 200 ml of propan-2-ol and the resultant clear solution was diluted to 3 ml with water and was measured at lex = 445 nm and lem = 520 nm. 2(k2p) Fractional Factorial Design via Fold Over The six factors were examined at two levels (Table 1), calculating also how they affect the two different responses (the stabilization ratio and the percentage entrapment value). The first fraction of the experiment (eight runs) is described as a 2(623) design of resolution III.9 This means that overall k = 6 factors (the first number in parentheses) were studied; however, p = 3 of those factors (the second number in parentheses) were generated from the interactions of a full 2[(623) = 3] factorial design.As a result, the design does not give full resolution; that is, there are certain interaction effects that are confounded with (identical with) other effects. In this study, R is equal to III and therefore, no L = 1 level interactions (i.e., main effects) are confounded with any other interaction of order less than R 2 L = 3 2 1 = 2.Hence, the main effects in this design are aliased (or confounded) with the two-way interactions. For instance, in the present study, the factor 4 main effect is confounded with the interaction of factors 1 and 2. Similarly, factor 5 is confounded with the interaction of factors 1 and 3 and factor 6 with the interaction of factors 2 and 3. To clarify the main effect of factors 4, 5 and 6 from the two-factor interactions, another fraction of eight runs is added— the fold over—and the design can then be turned to a resolution of IV.The fold over fraction copies the entire design (the first eight runs) and appends it to the end, reversing all signs. In the resulting design of resolution IV, no main effects of the examined factors are confounded with any other interaction of order less than R = 4 2 1 = 3. In this design, then, the main Table 1 Low and high settings (levels) for the six factors examined Factor setting Factor name Type* Low High (1) Free–Complex Q Free† Complex† (2) Oil Red O C Out In (0.2 mmol) (3) Oxybenzone C Out In (0.2 mmol) (4) b-Carotene C Out In (0.2 mmol) (5) Sulisobenzone C Out In (0.2 mmol) (6) Deoxybenzone C Out In (0.2 mmol) * Q and C denote a qualitative factor (cannot be varied continuously) and a continuous factor (can be varied continuously), respectively.† In all the liposomal preparations, egg PC and cholesterol were kept at 1 mmol and R (free or complexed) at 0.1 mmol. 1024 Analyst, October 1997, Vol. 122effects are not confounded with two-way interactions, but only with three-way interactions. Also, no two-way interactions are confounded with any other interaction of order less than R = 4 2 2 = 2. Hence, the two-way interactions in this design are confounded with each other. In this study, the calculation of the variability of measurements (pure error), through all partial replications, was omitted in order to simplify the study.10 A statistical software package11 with experimental design capabilities was used to perform the calculations and to illustrate all the interactive graphics.The 16 formulations listed in Table 1 were evaluated in random order to nullify the effect of extraneous or nuisance variables. After the two responses (Table 2) had been collected, the system was ready for analysis. Results and Discussion Calculation of Entrapped Materials The interest for the entrapment values is concentrated not only on R but also on the light absorbers since their entrapment values affect the stability and probably the entrapment value of R.In this study, the pellets were first disrupted with propan-2-ol and the resulting solutions were calculated fluorimetrically for R and by derivative UV spectrophotometry for the light absorbers. Second, the pooled supernatants were measured for the unentrapped materials by disruption of possible small unilamellar vesicles (SUV) and solubilization of the unentrapped light absorbers with propan-2-ol.The three combined supernatants were also measured fluorimetrically and by derivative UV spectrophotometry. The entrapment values for each compound were calculated according to the equation entrapment (%) = P P S A A A + �100 where AP is the absorbance of the materials in the pellets and AS is the absorbance of non-entrapped materials in the pooled supernatants, after a dilution correction to achieve identical dilutions for both AP and AS.Specifically, in the liposomal formulation No. 1 in Table 2, where all the compounds are present, the entrapment values for all the compounds were calculated indirectly according to the equation entrapment (%) = A A A 0 0 100 - � where A0 is the absorbance of the initial concentration of materials and A denotes the absorbance of non-entrapped materials in the organic and aqueous phases (obtained on extraction of the combined supernatants with chloroform) after a dilution correction to achieve identical dilutions for both A0 and A.For the quantification, the second-order derivative was used following the ‘zero crossing method’ for the simultaneous determination of the four lipid-soluble sunscreens (the procedure is described in detail elsewhere).3,12 Determination of the Six Factors on the Two Responses Check of main effects and ANOVA results Table 2 and Scheme 1 present the 16 runs (liposomal formulations) and the calculated responses.After the calculations, the system is ready for analysis, beginning with the calculation of the main effects of the factors (the design is of resolution IV after the addition of the fold over fraction; hence the two-way interactions confound each other and they cannot be estimated from this design). In Table 3, the first numeric column for each response contains the factor’s main effect estimates, which can be interpreted as deviations of the mean of the negative settings from the mean of the positive settings for the respective factors.For example, if the vitamin is entrapped in complexed form, an improvement in stabilization ratio by 86.125 and a decrease in entrapment value by 18.75 can be expected (Table 3; negative values for the effects denote a decrease in the response value). Furthermore, the presence of the Oil Red O increases the stabilization ratio by 126.125 and does not change significantly the entrapment value of the vitamin (Table 3).The second numeric column for each response in Table 3 contains the factor’s main effect regression coefficients. These are the coefficients that could be used for the prediction of each response for new factor settings, via the linear equation ypred. = b0 + b1x1 + . . . + b6x6 where ypred. is the predicted response (stabilization ratio or percentage entrapment), x1– x6 are the settings (1–6), b1–b6 are the respective coefficients and b0 is intercept or mean.For this design, the main effect estimates do not show the standard errors, because this is a saturated design,13 where all degrees of freedom (i.e., information) are used to estimate the factors’ main effects and no independent assessment of the error variance is available. After the estimation of the factors’ main effects, the determination of the significant factors afing the dependent variables of interest (responses) is carried out by performing an ANOVA for each response separately (Tables 4 and 5).In these tables the sum of squares (SS) is the information that was used Table 2 Sixteen liposomal formulations and the estimated responses (1) Free– (2) Oil (3) Oxy- (4) (5) Suliso- (6) Deoxy- Stability Entrapment Case complex Red O benzone b-Carotene benzone benzone ratio (%) 1 Complex In In In In In 265.00 10.00 2 Complex In Out In Out Out 225.00 20.00 3 Complex Out In Out In Out 40.00 9.00 4 Complex Out Out Out Out In 30.00 21.00 5 Free In In Out Out In 85.00 48.00 6 Free In Out Out In Out 75.00 20.00 7 Free Out In In Out Out 25.00 47.00 8 Free Out Out In In In 35.00 19.00 9 Free Out Out Out Out Out 4.00 49.00 10 Free Out In Out In In 27.00 22.00 11 Free In Out In Out In 73.00 47.00 12 Free In In In In Out 83.00 19.00 13 Complex Out Out In In Out 41.00 10.00 14 Complex Out In In Out In 45.00 22.00 15 Complex In Out Out In In 235.00 9.00 16 Complex In In Out Out Out 215.00 20.00 Analyst, October 1997, Vol. 122 1025to estimate the factors’ main effects and the F-ratios (F) are the ratios of the respective mean square effect and the mean square error. Furthermore, because the factors in this study have two levels, each ANOVA main effect has one degree of freedom (df). Finally, the p values indicate when the main effect of each factor is statistically significant (p < 0.05) or marginally significant (p < 0.10). Therefore, the ANOVA data for the first response (Table 4) support the conclusion that, indeed, factors 1 and 2 significantly affect the stabilization ratio of the vitamin since they show the largest parameter estimates (Table 3); hence the settings of these two factors were most important for the resultant stabilization ratio.This means that the vitamin expresses the highest stability when in complexed form (R : gCD) is entrapped in the aqueous phase of liposomes containing at least Oil Red O in their bilayers. Similarly, from the ANOVA in Table 5 it appears that mainly factors 1 and 6 affect the percentage entrapment values of the vitamin, meaning that the liposomal formulation provides the highest entrapment values when the vitamin is in free form and the hydrophilic sulisobenzone is absent. From the above observations, the formulator can easily conclude that the presence of at least one hydrophobic light absorber in a liposomal formulation, containing the vitamin in free form, provides both better stability and a higher entrapment value.Also, the presence of the hydrophilic sulisobenzone adds little to the overall stability, decreasing at the same time the entrapment value considerably. Finally, if the Table 3 Estimated factors’ main effects and the coefficients for the predictive mathematical models (Response 1) (Response 2) Stabilization ratio Entrapped R (%) Factor Effect Coefficient Effect Coefficient Mean/intercept 93.9375 93.93750 24.5000 24.50000 (1) Free–complex 86.1250 43.06250 218.7500 29.37500 (2) Oil Red O 126.1250 63.06250 20.7500 20.37500 (3) Oxybenzone 8.3750 4.18750 0.2500 0.12500 (4) b-Carotene 10.1250 5.06250 20.5000 20.25000 (5) Sulisobenzone 12.3750 6.18750 219.5000 29.75000 (6) Deoxybenzone 10.8750 5.43750 0.5000 0.25000 Table 4 ANOVA for the stabilization ratio (r2 = 0.84) Factor SS df MS F p (1) Free–complex 29670.1 1 29670.06 13.41555 0.005213 (2) Oil Red O 63630.1 1 63630.06 28.77082 0.000454 (3) Oxybenzone 280.6 1 280.56 0.12686 0.729918 (4) b-Carotene 410.1 1 410.06 0.18541 0.676890 (5) Sulisobenzone 612.6 1 612.56 0.27697 0.611412 (6) Deoxybenzone 473.1 1 473.06 0.21390 0.654706 Error 19904.6 9 2211.62 Total SS 114980.9 15 Table 5 ANOVA for the percentage entrapment value (r2 = 0.92) Factor SS df MS F p (1) Free–complex 1406.250 1 1406.250 45.16057 0.000087 (2) Oil Red O 2.250 1 2.250 0.07226 0.794139 (3) Oxybenzone 0.250 1 0.250 0.00803 0.930566 (4) b-Carotene 1.000 1 1.000 0.03211 0.861747 (5) Sulisobenzone 1521.000 1 1521.000 48.84567 0.000064 (6) Deoxybenzone 1.000 1 1.000 0.03211 0.861747 Error 280.250 9 31.139 Total SS 3212.000 15 Fig. 1 Normal probability plots of residual values for the stabilization ratio and the percentage entrapment. Fig. 2 Pareto charts for the factors’ main effects on stabilization ratio and on percentage entrapment. 1026 Analyst, October 1997, Vol. 122main aim is the highest stability, then the vitamin can be used in complexed form ‘sacrificing’ the highest entrapment value.Diagnostic plots of residuals and Pareto charts of effects From the ANOVA tables, specific ‘models’ that include a particular number of effects for each of the two responses could be concluded (see above). Furthermore, the distribution of the residual values,10 which is the difference between the predicted values (as predicted by the current models) and the observed values, could also be examined. Fig. 1 presents the normal probability plot of residuals for each response separately, by assessing how closely the set of observed values follow a theoretical distribution.Since all values fall around a straight line, it can be concluded that they follow the normal distribution. Another useful plot for identifying the factors that are important is the Pareto chart of effects (Fig. 2). This graph will show the ANOVA effect estimates plotted against the horizontal axis. This plot will also include a vertical line to indicate the p = 0.05 threshold for statistical significance (an effect that exceeds the vertical line may be considered significant).After completing the first eight runs, the Pareto chart for the percentage entrapment showed that the main effects of sulisobenzone and free–complex were marginally significant (not shown). The addition of the fold over fraction highlighted the significance of these two factors, as shown in Fig. 2. Normal probability plot of effects Another useful, albeit more technical, summary graph is the normal probability plot of effects10 which is constructed as follows (Fig. 3). First, the effect estimates are rank ordered. From these ranks, z values (i.e., standard values of the normal distribution) can be computed based on the assumption that the estimates come from a normal distribution with a common mean. These z values are plotted on the left y-axis in the plot and the corresponding normal probabilities are shown on the right yaxis.If the actual estimates (plotted on the x-axis) are normally distributed, then all values should fall on a straight line. This plot is very useful for separating random noise from ‘real’ effects. The estimates for effects that are actually zero in the population will assume a normal distribution around a common mean of zero; effects that truly exist will be shown as outliers. In Fig. 3, the points for Oil Red O and free–complex (for the stabilization ratio) and the points for free–complex and sulisobenzone (for the percentage entrapment), the main effects appear different from the other effects.In conclusion, such multicomponent vesicular formulations may include more factors during the preparation (e.g., the lipid : cholesterol molar ratio, the presence of a second lipid and its molar ratio to the first lipid, different combinations of light absorbers, different cyclodextrins for the complexation of the drug, the binding constant value of the complexes formed, different preparation methods for the liposomes), making the interpretation of the system extremely complicated.In order for all the factors to be used at their optimum levels and for the best responses to be achieved, many experiments must be performed, including all the possible combinations between the different factors. The use of fractional factorial design, as described here, can decrease considerably the number of experiments necessary, give useful conclusions for the main effects and interactions between the factors examined and clarify complicated interactions through graphical representations.In this study, the 2(k2p) fractional design was introduced. This design identified quickly and efficiently the factors which are active and also provided some information on two-factor interactions. Sequential assembly of these designs via fold over was found to be very effective to gain additional information about the factors’ main effects that an initial experiment may identify as possibly important. References 1 Gregoriadis, G., and Loukas, Y.L., PCT Int. Pat. Appl., GB95/01258, 1995. 2 Loukas, Y. L., Jayasekera, P., and Gregoriadis, G., J. Phys. Chem., 1995, 99, 11035. 3 Loukas, Y. L., Jayasekera, P., and Gregoriadis, G., Int. J. Pharm., 1995, 117, 85. 4 Ho, A., Puri, K., and Sugden, J., Int. J. Pharm., 1994, 107, 199. 5 Montgomery, D., Design and Analysis of Experiments, Wiley, Chichester, 1991. 6 Box, G. E. P., Hunter, W. G., and Hunter, S. J., Statistics for Experimenters: an Introduction to Design, Data Analysis, and Model Building, Wiley, New York, 1978. 7 Loukas, Y. L., J. Phys. Chem. B, 1997, 101, 4863. 8 Loukas, Y. L., Analyst, 1996, 121, 279. 9 Box, G. E. P., and Draper, N. R., Empirical Model-Building and Response Surfaces, Wiley, New York, 1987. 10 Deming, S. N., and Morgan, S. L., Experimental Design: a Chemometric Approach, Elsevier, Amsterdam, 2nd edn., 1993. 11 Statistics for Windows Version 5, StatSoft, Biggleswade UK, 1995. 12 Loukas, Y. L., Vraka, V., and Gregoriadis, G., Pharm. Sci., 1996, 2, 523. 13 Ryan, T. P., Statistical Methods for Quality Improvement, Wiley, New York, 1989. Paper 7/02701J Received April 21, 1997 Accepted June 12, 1977 Fig. 3 Normal probability plot of the facotrs’ main effects on the stabilization ratio and on percentage entrapment. (The right y-axis denotes the percentage cumulative frequency, which is equal to the cumulative frequency divided by n + 1, where the cumulative frequency for a measurement denotes the measurements less than or equal to that measurement and n is the total number of measurements).Analyst, October 1997, Vol. 122 1027 2( k2 p) Fractional Factorial Design viaFold Over: Application to Optimization of Novel Multicomponent Vesicular Systems Yannis L. Loukas† Centre for Drug Delivery Research, School of Pharmacy, University of London, 29–39 Brunswick Square, London, UK WC1N 1AX A computer-based technique based on a 2(k2p) fractional factorial design was applied for the optimization of recently described multicomponent protective liposomal formulations.These formulations contain riboflavin (vitamin B2) as a model, photosensitive drug, in addition to Oil Red O, deoxybenzone, oxybenzone and b-carotene as oil-soluble light absorbers and antioxidants incorporated into the lipid bilayer, and sulisobenzone as a water-soluble light absorber incorporated into the aqueous phase of liposomes.The presence or absence of these five different light absorbers in multilamellar liposomes containing the vitamin free or complexed with g-cyclodextrin comprised the six factors of the system, each one examined at two levels. The stabilization ratio of the vitamin and its percentage entrapment in liposomes were the two response variables of the system to be optimized. The entrapment values were calculated for all the materials, either spectrophotometrically, using second-order derivative spectrophotometry, or fluorimetrically.The response variables were predicted by multiple regression equations comprising combinations of the six formulation factors. Higher entrapment and higher protection for the drug should characterize the optimum formulation. Keywords: Experimental design; fractional factorial; fold over technique; optimization; vesicular systems Photosensitive drugs are known to degrade on exposure to light and lose their activity.Topical formulations of these drugs for medical or cosmetic reasons must be prepared in such a way as to achieve maximum stability. Known stabilizing systems in the literature include the use of certain antioxidants and light absorbers in the same preparation (solution or suspension) with the drug or the use of cyclodextrins as a complexing system which provides also moderate stability against the examined external factors (light and oxygen).We have recently proposed1 –3 a novel multicomponent stabilizing system based on liposomes, which provides high protection to sensitive drugs. This system is based generally on the liposome’s ability to accommodate both hydrophobic and hydrophilic substances into their lipid membranes and their aqueous phases, respectively. In brief, multilamellar liposomes consisting of phosphatidylcholine and cholesterol entrap the water-soluble sensitive drug, as such or in the form of a cyclodextrin complex, in the aqueous phase and one or more light absorbers either in the aqueous phase or in the lipid bilayers, depending on their characteristics (Scheme 1).In this study, riboflavin was chosen as a model photosensitive drug with rapid decomposition on exposure to light (t50% = 0.5 h).4 In order to increase the stability of the vitamin, it was entrapped as such or in the form of a g-cyclodextrin (cyclomaltooctaose) complex in dehydration–rehydration multicomponent liposomes containing one or more of the light absorbers Oil Red O, oxybenzone, deoxybenzone, sulisobenzone and the antioxidant b-carotene (Scheme 1).A liposomal formulation can be characterized as being efficient when it contains the vitamin at a high entrapment value with a higher stabilization ratio (the ratio k0/kL, where k0 and kL are the degradation rate constants of the vitamin in free form and in liposomal formulations, respectively). From the above-mentioned six factors (the presence or absence of the g-cyclodextrin cavity, Oil Red O, dioxybenzone, oxybenzone, sulisobenzone and b-carotene), each reporting a different behavior on the two responses of interest (stabilization ratio and percentage entrapment of the vitamin), it is not obvious how the optimum formulation can be achieved.In this present study, an experimental design5 can be used in order to derive valid and robust statistical significance tests for the factors examined with a minimum number of experiments.It is sufficient to consider the factors affecting the responses at two levels; for instance, the concentration of each light absorber may be set either to zero or to a constant molar ratio with the vitamin, and the vitamin may be in either free or complexed † Present address: Riga Ferreou 21, Ano Ilioupolis, 163 43 Athens, Greece. E-mail: ylloukas@compulink.gr Scheme 1 Schematic representation of the 16 runs. The scheme has been simplified by omitting the cholesterol molecules.Analyst, October 1997, Vol. 122 (1023–1027) 1023form (Table 1). The most intuitive approach to study these factors and how they affect the responses examined would be to vary the factors of interest in a 2k full factorial design (k factors at two levels), that is, to try all possible combinations. This would work well, except that the number of liposomal preparations necessary will increase exponentially. For example, the six factors examined in the present study require 26 = 64 preparations.Because each liposomal preparation is time consuming and requires costly materials, the use of a 2(k2p) fractional factorial design6 can reduce considerably the number of preparations (from 64 preparations to 8, in the present case of six factors at two levels each). In this study, the use of the original (fractional factorial) design only gave indications of significant factors rather than conclusive results and, as a consequence, the fold over design was used with all the results referring to this design.After adding the second fraction (the fold over part), the resolution of the design was increased from III to IV, isolating the factors’ main effects from any two-way interactions. Experimental Materials and Instrumentation Riboflavin (R) and g-cyclodextrin (gCD) were obtained from Aldrich Chemical (Gillingham, Dorset, UK), Oil Red O, oxybenzone, deoxybenzone, sulisobenzone, b-carotene and cholesterol from Sigma Chemical (Poole, Dorset, UK) and phosphatidylcholine (PC) from Lipid Products (Nuthill, Surrey, UK).All other reagents were of analytical-reagent grade. Doubly distilled water was used throughout. Photostability studies of R were carried out using a Blak-Ray long-wavelength (365 nm) UV lamp with 6 W rating and 460 mW cm22 dm21 intensity (Model UVGL-58, UVP, San Gabriel, CA, USA). Measurement of the degradation kinetics of R in various preparations was performed fluorimetrically (lex = 445 nm, lem 520 nm) and assays of the components entrapped into liposomes were carried out with a Compuspec UV/VIS spectrophotometer (Wallac, Turku, Finland) connected to a personal computer which can also process the spectra into their derivatives. Preparation of R : gCD Complex and Multilamellar Liposomes The inclusion complex of R with gCD was prepared according to the freeze-drying method.7 Multilamellar liposomes were prepared according to the dehydration–rehydration method with some modifications: briefly, small unilamellar vesicles (SUV) prepared from equimolar PC and cholesterol were mixed with R (free or complexed) dissolved in de-ionized water, diluted to 10 ml with water and freeze-dried overnight. The dry powder was subjected to controlled rehydration and then centrifuged at 27 300g for 20 min to separate the entrapped and non-entrapped R.The liposomal pellet containing multilamellar dehydration– rehydration vesicles (DRV) was washed three times by centrifugation in 0.1 m sodium phosphate buffer containing 0.9% NaCl (pH 7.4) (PBS) and resuspended in 4 ml of PBS before use.DRV liposomes incorporating the vitamin and the lipid-soluble components in their lipid bilayers were prepared as above with the absorbers and the lipids dissolved in chloroform, prior to the generation of the SUV precursor vesicles. When the water-soluble light absorber sulisobenzone was also entrapped into DRV liposomes, this was dissolved together with free or complexed R in the aqueous solution to be subsequently mixed with the SUV.Determination of Liposome-entrapped Materials Entrapment values for R and light absorbers were determined by measuring the concentrations of the materials in both the DRV liposomal pellets obtained and the separated pooled supernatants fluorimetrically for R and by derivative UV spectrophotometry for the rest of the components.8 The use of the second-order derivative (D2) of the spectra was found to provide both good resolution and high signal-to-noise ratios (S/N).Photostability Studies The photostabilization of R in the different DRV formulations exposed to UV radiation was calculated fluorimetrically. The assay procedure is briefly as follows: the liposomal suspension of R (3 ml) was transferred into an open quartz cuvette and was placed in front of the UV lamp. The liposomal suspension was stirred continuously in order to make it homogeneous during the study and in order for the whole suspension to be equally irradiated.At time intervals, 100 ml of the liposomal suspension was dialyzed with 200 ml of propan-2-ol and the resultant clear solution was diluted to 3 ml with water and was measured at lex = 445 nm and lem = 520 nm. 2(k2p) Fractional Factorial Design via Fold Over The six factors were examined at two levels (Table 1), calculating also how they affect the two different responses (the stabilization ratio and the percentage entrapment value).The first fraction of the experiment (eight runs) is described as a 2(623) design of resolution III.9 This means that overall k = 6 factors (the first number in parentheses) were studied; however, p = 3 of those factors (the second number in parentheses) were generated from the interactions of a full 2[(623) = 3] factorial design. As a result, the design does not give full resolution; that is, there are certain interaction effects that are confounded with (identical with) other effects.In this study, R is equal to III and therefore, no L = 1 level interactions (i.e., main effects) are confounded with any other interaction of order less than R 2 L = 3 2 1 = 2. Hence, the main effects in this design are aliased (or confounded) with the two-way interactions. For instance, in the present study, the factor 4 main effect is confounded with the interaction of factors 1 and 2.Similarly, factor 5 is confounded with the interaction of factors 1 and 3 and factor 6 with the interaction of factors 2 and 3. To clarify the main effect of factors 4, 5 and 6 from the two-factor interactions, another fraction of eight runs is added— the fold over—and the design can then be turned to a resolution of IV. The fold over fraction copies the entire design (the first eight runs) and appends it to the end, reversing all signs. In the resulting design of resolution IV, no main effects of the examined factors are confounded with any other interaction of order less than R = 4 2 1 = 3.In this design, then, the main Table 1 Low and high settings (levels) for the six factors examined Factor setting Factor name Type* Low High (1) Free–Complex Q Free† Complex† (2) Oil Red O C Out In (0.2 mmol) (3) Oxybenzone C Out In (0.2 mmol) (4) b-Carotene C Out In (0.2 mmol) (5) Sulisobenzone C Out In (0.2 mmol) (6) Deoxybenzone C Out In (0.2 mmol) * Q and C denote a qualitative factor (cannot be varied continuously) and a continuous factor (can be varied continuously), respectively.† In all the liposomal preparations, egg PC and cholesterol were kept at 1 mmol and R (free or complexed) at 0.1 mmol. 1024 Analyst, October 1997, Vol. 122effects are not confounded with two-way interactions, but only with three-way interactions. Also, no two-way interactions are confounded with any other interaction of order less than R = 4 2 2 = 2.Hence, the two-way interactions in this design are confounded with each other. In this study, the calculation of the variability of measurements (pure error), through all partial replications, was omitted in order to simplify the study.10 A statistical software package11 with experimental design capabilities was used to perform the calculations and to illustrate all the interactive graphics. The 16 formulations listed in Table 1 were evaluated in random order to nullify the effect of extraneous or nuisance variables.After the two responses (Table 2) had been collected, the system was ready for analysis. Results and Discussion Calculation of Entrapped Materials The interest for the entrapment values is concentrated not only on R but also on the light absorbers since their entrapment values affect the stability and probably the entrapment value of R. In this study, the pellets were first disrupted with propan-2-ol and the resulting solutions were calculated fluorimetrically for R and by derivative UV spectrophotometry for the light absorbers.Second, the pooled supernatants were measured for the unentrapped materials by disruption of possible small unilamellar vesicles (SUV) and solubilization of the unentrapped light absorbers with propan-2-ol. The three combined supernatants were also measured fluorimetrically and by derivative UV spectrophotometry. The entrapment values for each compound were calculated according to the equation entrapment (%) = P P S A A A + �100 where AP is the absorbance of the materials in the pellets and AS is the absorbance of non-entrapped materials in the pooled supernatants, after a dilution correction to achieve identical dilutions for both AP and AS.Specifically, in the liposomal formulation No. 1 in Table 2, where all the compounds are present, the entrapment values for all the compounds were calculated indirectly according to the equation entrapment (%) = A A A 0 0 100 - � where A0 is the absorbance of the initial concentration of materials and A denotes the absorbance of non-entrapped materials in the organic and aqueous phases (obtained on extraction of the combined supernatants with chloroform) after a dilution correction to achieve identical dilutions for both A0 and A.For the quantification, the second-order derivative was used following the ‘zero crossing method’ for the simultaneous determination of the four lipid-soluble sunscreens (the procedure is described in detail elsewhere).3,12 Determination of the Six Factors on the Two Responses Check of main effects and ANOVA results Table 2 and Scheme 1 present the 16 runs (liposoformulations) and the calculated responses.After the calculations, the system is ready for analysis, beginning with the calculation of the main effects of the factors (the design is of resolution IV after the addition of the fold over fraction; hence the two-way interactions confound each other and they cannot be estimated from this design).In Table 3, the first numeric column for each response contains the factor’s main effect estimates, which can be interpreted as deviations of the mean of the negative settings from the mean of the positive settings for the respective factors. For example, if the vitamin is entrapped in complexed form, an improvement in stabilization ratio by 86.125 and a decrease in entrapment value by 18.75 can be expected (Table 3; negative values for the effects denote a decrease in the response value).Furthermore, the presence of the Oil Red O increases the stabilization ratio by 126.125 and does not change significantly the entrapment value of the vitamin (Table 3). The second numeric column for each response in Table 3 contains the factor’s main effect regression coefficients. These are the coefficients that could be used for the prediction of each response for new factor settings, via the linear equation ypred. = b0 + b1x1 + .. . + b6x6 where ypred. is the predicted response (stabilization ratio or percentage entrapment), x1– x6 are the settings (1–6), b1–b6 are the respective coefficients and b0 is intercept or mean. For this design, the main effect estimates do not show the standard errors, because this is a saturated design,13 where all degrees of freedom (i.e., information) are used to estimate the factors’ main effects and no independent assessment of the error variance is available.After the estimation of the factors’ main effects, the determination of the significant factors affecting the dependent variables of interest (responses) is carried out by performing an ANOVA for each response separately (Tables 4 and 5). In these tables the sum of squares (SS) is the information that was used Table 2 Sixteen liposomal formulations and the estimated responses (1) Free– (2) Oil (3) Oxy- (4) (5) Suliso- (6) Deoxy- Stability Entrapment Case complex Red O benzone b-Carotene benzone benzone ratio (%) 1 Complex In In In In In 265.00 10.00 2 Complex In Out In Out Out 225.00 20.00 3 Complex Out In Out In Out 40.00 9.00 4 Complex Out Out Out Out In 30.00 21.00 5 Free In In Out Out In 85.00 48.00 6 Free In Out Out In Out 75.00 20.00 7 Free Out In In Out Out 25.00 47.00 8 Free Out Out In In In 35.00 19.00 9 Free Out Out Out Out Out 4.00 49.00 10 Free Out In Out In In 27.00 22.00 11 Free In Out In Out In 73.00 47.00 12 Free In In In In Out 83.00 19.00 13 Complex Out Out In In Out 41.00 10.00 14 Complex Out In In Out In 45.00 22.00 15 Complex In Out Out In In 235.00 9.00 16 Complex In In Out Out Out 215.00 20.00 Analyst, October 1997, Vol. 122 1025to estimate the factors’ main effects and the F-ratios (F) are the ratios of the respective mean square effect and the mean square error. Furthermore, because the factors in this study have two levels, each ANOVA main effect has one degree of freedom (df).Finally, the p values indicate when the main effect of each factor is statistically significant (p < 0.05) or marginally significant (p < 0.10). Therefore, the ANOVA data for the first response (Table 4) support the conclusion that, indeed, factors 1 and 2 significantly affect the stabilization ratio of the vitamin since they show the largest parameter estimates (Table 3); hence the settings of these two factors were most important for the resultant stabilization ratio.This means that the vitamin expresses the highest stability when in complexed form (R : gCD) is entrapped in the aqueous phase of liposomes containing at least Oil Red O in their bilayers. Similarly, from the ANOVA in Table 5 it appears that mainly factors 1 and 6 affect the percentage entrapment values of the vitamin, meaning that the liposomal formulation provides the highest entrapment values when the vitamin is in free form and the hydrophilic sulisobenzone is absent.From the above observations, the formulator can easily conclude that the presence of at least one hydrophobic light absorber in a liposomal formulation, containing the vitamin in free form, provides both better stability and a higher entrapment value. Also, the presence of the hydrophilic sulisobenzone adds little to the overall stability, decreasing at the same time the entrapment value considerably. Finally, if the Table 3 Estimated factors’ main effects and the coefficients for the predictive mathematical models (Response 1) (Response 2) Stabilization ratio Entrapped R (%) Factor Effect Coefficient Effect Coefficient Mean/intercept 93.9375 93.93750 24.5000 24.50000 (1) Free–complex 86.1250 43.06250 218.7500 29.37500 (2) Oil Red O 126.1250 63.06250 20.7500 20.37500 (3) Oxybenzone 8.3750 4.18750 0.2500 0.12500 (4) b-Carotene 10.1250 5.06250 20.5000 20.25000 (5) Sulisobenzone 12.3750 6.18750 219.5000 29.75000 (6) Deoxybenzone 10.8750 5.43750 0.5000 0.25000 Table 4 ANOVA for the stabilization ratio (r2 = 0.84) Factor SS df MS F p (1) Free–complex 29670.1 1 29670.06 13.41555 0.005213 (2) Oil Red O 63630.1 1 63630.06 28.77082 0.000454 (3) Oxybenzone 280.6 1 280.56 0.12686 0.729918 (4) b-Carotene 410.1 1 410.06 0.18541 0.676890 (5) Sulisobenzone 612.6 1 612.56 0.27697 0.611412 (6) Deoxybenzone 473.1 1 473.06 0.21390 0.654706 Error 19904.6 9 2211.62 Total SS 114980.9 15 Table 5 ANOVA for the percentage entrapment value (r2 = 0.92) Factor SS df MS F p (1) Free–complex 1406.250 1 1406.250 45.16057 0.000087 (2) Oil Red O 2.250 1 2.250 0.07226 0.794139 (3) Oxybenzone 0.250 1 0.250 0.00803 0.930566 (4) b-Carotene 1.000 1 1.000 0.03211 0.861747 (5) Sulisobenzone 1521.000 1 1521.000 48.84567 0.000064 (6) Deoxybenzone 1.000 1 1.000 0.03211 0.861747 Error 280.250 9 31.139 Total SS 3212.000 15 Fig. 1 Normal probability plots of residual values for the stabilization ratio and the percentage entrapment.Fig. 2 Pareto charts for the factors’ main effects on stabilization ratio and on percentage entrapment. 1026 Analyst, October 1997, Vol. 122main aim is the highest stability, then the vitamin can be used in complexed form ‘sacrificing’ the highest entrapment value. Diagnostic plots of residuals and Pareto charts of effects From the ANOVA tables, specific ‘models’ that include a particular number of effects for each of the two responses could be concluded (see above).Furthermore, the distribution of the residual values,10 which is the difference between the predicted values (as predicted by the current models) and the observed values, could also be examined. Fig. 1 presents the normal probability plot of residuals for each response separately, by assessing how closely the set of observed values follow a theoretical distribution. Since all values fall around a straight line, it can be concluded that they follow the normal distribution.Another useful plot for identifying the factors that are important is the Pareto chart of effects (Fig. 2). This graph will show the ANOVA effect estimates plotted against the horizontal axis. This plot will also include a vertical line to indicate the p = 0.05 threshold for statistical significance (an effect that exceeds the vertical line may be considered significant). After completing the first eight runs, the Pareto chart for the percentage entrapment showed that the main effects of sulisobenzone and free–complex were marginally significant (not shown). The addition of the fold over fraction highlighted the significance of these two factors, as shown in Fig. 2. Normal probability plot of effects Another useful, albeit more technical, summary graph is the normal probability plot of effects10 which is constructed as follows (Fig. 3). First, the effect estimates are rank ordered. From these ranks, z values (i.e., standard values of the normal distribution) can be computed based on the assumption that the estimates come from a normal distribution with a common mean.These z values are plotted on the left y-axis in the plot and the corresponding normal probabilities are shown on the right yaxis. If the actual estimates (plotted on the x-axis) are normally distributed, then all values should fall on a straight line. This plot is very useful for separating random noise from ‘real’ effects. The estimates for effects that are actually zero in the population will assume a normal distribution around a common mean of zero; effects that truly exist will be shown as outliers.In Fig. 3, the points for Oil Red O and free–complex (for the stabilization ratio) and the points for free–complex and sulisobenzone (for the percentage entrapment), the main effects appear different from the other effects. In conclusion, such multicomponent vesicular formulations may include more factors during the preparation (e.g., the lipid : cholesterol molar ratio, the presence of a second lipid and its molar ratio to the first lipid, different combinations of light absorbers, different cyclodextrins for the complexation of the drug, the binding constant value of the complexes formed, different preparation methods for the liposomes), making the interpretation of the system extremely complicated.In order for all the factors to be used at their optimum levels and for the best responses to be achieved, many experiments must be performed, including all the possible combinations between the different factors. The use of fractional factorial design, as described here, can decrease considerably the number of experiments necessary, give useful conclusions for the main effects and interactions between the factors examined and clarify complicated interactions through graphical representations. In this study, the 2(k2p) fractional design was introduced. This design identified quickly and efficiently the factors which are active and also provided some information on two-factor interactions. Sequential assembly of these designs via fold over was found to be very effective to gain additional information about the factors’ main effects that an initial experiment may identify as possibly important. References 1 Gregoriadis, G., and Loukas, Y. L., PCT Int. Pat. Appl., GB95/01258, 1995. 2 Loukas, Y. L., Jayasekera, P., and Gregoriadis, G., J. Phys. Chem., 1995, 99, 11035. 3 Loukas, Y. L., Jayasekera, P., and Gregoriadis, G., Int. J. Pharm., 1995, 117, 85. 4 Ho, A., Puri, K., and Sugden, J., Int. J. Pharm., 1994, 107, 199. 5 Montgomery, D., Design and Analysis of Experiments, Wiley, Chichester, 1991. 6 Box, G. E. P., Hunter, W. G., and Hunter, S. J., Statistics for Experimenters: an Introduction to Design, Data Analysis, and Model Building, Wiley, New York, 1978. 7 Loukas, Y. L., J. Phys. Chem. B, 1997, 101, 4863. 8 Loukas, Y. L., Analyst, 1996, 121, 279. 9 Box, G. E. P., and Draper, N. R., Empirical Model-Building and Response Surfaces, Wiley, New York, 1987. 10 Deming, S. N., and Morgan, S. L., Experimental Design: a Chemometric Approach, Elsevier, Amsterdam, 2nd edn., 1993. 11 Statistics for Windows Version 5, StatSoft, Biggleswade UK, 1995. 12 Loukas, Y. L., Vraka, V., and Gregoriadis, G., Pharm. Sci., 1996, 2, 523. 13 Ryan, T. P., Statistical Methods for Quality Improvement, Wiley, New York, 1989. Paper 7/02701J Received April 21, 1997 Accepted June 12, 1977 Fig. 3 Normal probability plot of the facotrs’ main effects on the stabilization ratio and on percentage entrapment. (The right y-axis denotes the percentage cumulative frequency, which is equal to the cumulative frequency divided by n + 1, where the cumulative frequency for a measurement denotes the measurements less than or equal to that measurement and n is the total number of measurements). Analyst, October 1997, Vol. 122 1027