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.
