A Stochastic Analysis of the One Compartment Pharmacokinetic Model Considering Optimal Controls

Abstract

First-order 1-compartment pharmacokinetic model for extravascular administered drugs can be used to derive many useful quantities by comparing the predicted values with actual data. However, less research has been done in actually formulating them as optimal control problems. Moreover, real pharmacological processes are always exposed to influences that are not completely understood or not feasible to model explicitly. Ignoring these phenomena in the modeling may affect the estimation of PK/PD models' (pharmacokinetic/pharmacodynamic models') parameters and the derived conclusions.Therefore there is an increasing need to extend the deterministic models to models including a stochastic component. In our study, we modify the 1-compartment pharmacokinetic model to a stochastic differential equation model based on an optimal control problem. A schedule of optimal dosing and timing has been given from our proposed model.

Keywords

• Stochastic differential equation
• optimal control
• pharmacokinetics
• stability
• E-M method