A PSE approach to patient-individualized physiologically-based pharmacokinetic modeling

In this work an optimization framework is presented to support the model builder in postulating compartmental models that plausibly describe data that is obtained during experimentation. In the proposed approach, one specifies a priori the maximum number of compartments and the type of flows (e.g., zero order, first order, second order rate flows) to contemplate. With this input, the mathematical model follows a “flexible” approach, which inherently considers all feasible flows between any pair of compartments. The model activates those flows/compartments that provide the optimal fit for a given set of experimental data. A regularized log-likelihood function is formulated as performance metric in order to handle parameter over-fitting. To deal with the resulting set of differential equations orthogonal collocation on finite elements is employed. A case study related to the pharmacokinetics of an oncological agent is reported to demonstrate the advantages and limitations of the proposed approach. Numerical results show that the proposed approach can provide 33 % smaller mean prediction errors in comparison with a compartmental model previously suggested in the literature that employs a larger number of parameters.