The so-calledmatrix modelis a general thermodynamic framework for microrheological modeling. This model has already been proven to be applicable for a wide class of systems, in particular to models formulated at the configuration tensor level of description. For models formulated at the configuration space level of description a matrix formulation is readily obtained, but for the subsequent analysis one still needs an explicit solution of the configuration space distribution functions. In the present paper we describe an approach in which this problem is solved by combining the matrix model with a Lagrangian simulation method in configuration space developed recently by Szeri and Leal. The result is a consistent and unified formulation of stress tensor expressions, including the stress averaging, and the evolution equations. This formulation is also suited for numerical simulations. In this way, the range of applicability of the matrix model is extended substantially. In order to clarify the principles of the method and some aspects of its implementation, a simple example is discussed in some detail.