Solutions of the inverse problem of pharmacokinetics for the three-compartment model

Abstract

This article discusses the incorrectness of the inverse pharmacokinetics problem for a three-chamber linear model. The formulation of the pharmacokinetics problem for a three-chamber linear model is described. The direct problem is the Cauchy problem for a system of ordinary differential equations. Solving a direct problem analytically, the concentration for the first camera is determined. Using the Laplace transform to solve the inverse problem for given experimental ones, the existence of four solutions is proved. As a result, the non-uniqueness of the inverse problem is shown.