Uncertain pharmacokinetic model based on uncertain differential equation

Abstract

Pharmacokinetics is the study of the time course of drug concentrations in body compartments. The majority of drugs are eliminated at first order kinetics with a nonconstant elimination rate due to spontaneous erratic variations in the metabolic processes and individual difference. Noting the paradox of stochastic pharmacokinetic models, this paper proposes an uncertain pharmacokinetic model for mono-compartmental drugs administered with intravenous administration based on uncertain differential equations. Uncertainty distributions, expected values and confidence intervals of the half-life and the area under the curve are provided. For this method to achieve its full potential, this paper derives moment estimations for unknown parameters in this uncertain pharmacokinetic model. Finally a numerical example and a real data analysis illustrate our methods.