Analysis of ill-posedness and numerical methods of solving a nonlinear inverse problem in pharmacokinetics for the two-compartmental model with extravascular drug administration

A nonlinear inverse problem of pharmacokinetics for the dual-compartment model with extravascular route of the drug administration is considered. The problem is significantly ill-posed: its solution is not unique and is unstable. We discuss nonuniqueness of the inverse problem and the degree of ill-posedness. The initial problem is reduced to a linear operator equation by linearization. It is demonstrated that the resolving ability of the inverse problem can be improved by varying of the location of measurement data points. Results of numerical experiments are presented. The question of choosing the initial approximations is considered.