A new stochastic approach to multi-compartment pharmacokinetic models: probability of traveling route and distribution of residence time in linear and nonlinear systems.

Drug kinetics in human has been studied from both deterministic and stochastic perspectives. However, little research has been done to systematically determine the probability for a drug molecule to follow a specific traveling route. Recently a method was developed to estimate this probability and the probability density function of residence time in linear systems. In this paper, we provide a rigorous proof of the main results of the previous paper and extend the method to nonlinear multi-compartment systems. A novel concept of compartment expansion is introduced to facilitate the development of our method. This formulation resolves computational difficulties associated with nonlinear systems, allowing for direct estimation of the probability intensity coefficients, and subsequently the transition probability and probability density function of the residence time. With such expansion of the methodology, it becomes both practical and feasible to apply it in the real-world drug development where drug disposition patterns are often nonlinear. The method can be used to estimate drug exposure at any site of interest, thus may help us to gain better understanding about the impact of drug exposure on efficacy and safety.