Modeling of Pharmacokinetic Systems Using Stochastic Deconvolution

In environments where complete mechanistic knowledge of the system dynamics is not available, a synergy of first-principle concepts, stochastic methods and statistical approaches can provide an efficient, accurate, and insightful strategy for model development. In this work, a system of ordinary differential equations describing system pharmacokinetics (PK) was coupled to a Wiener process for tracking the absorption rate coefficient, and was embedded in a nonlinear mixed effects population PK formalism. The procedure is referred to as “stochastic deconvolution” and it is proposed as a diagnostic tool to inform on a mapping function between the fraction of the drug absorbed and the fraction of the drug dissolved when applying one-stage methods to in vitro-in vivo correlation modeling. The goal of this work was to show that stochastic deconvolution can infer an a priori specified absorption profile given dense observational (simulated) data. The results demonstrate that the mathematical model is able to accurately reproduce the simulated data in scenarios where solution strategies for linear, time-invariant systems would assuredly fail. To this end, PK systems that are representative of Michaelis-Menten kinetics and enterohepatic circulation were investigated. Furthermore, the solution times are manageable using a modest computer hardware platform.