Simultaneous modelling of a nonlinear multiresponse pharmacokinetic system

Abstract

Concentration-time curves of an anticancer drug and two of its metabolites were analyzed simultaneously by using a pharmacokinetic mathematical model. The nonlinearities observed in the collected data of the first metabolite could be explained by enzymatic pathways; therefore the model proposed in this paper is an enzymatic nonlinear model. The simultaneous modelling of the three concentration- time curves introduces, at a given time, the concept of a multivariate measurement error, with a zero mean multinormal distribution and a fixed structure of the variance model. The maximum likelihood principle used as an estimation criterion allows the separation of pharmacokinetic model and error variance model parameters. For model validation we a posteriori verify by residual analysis the hypotheses postulated on the error at the beginning. This methodology introduces intrakinetic and interkinetic variabilities, which provide an automatic weighting between successive measurements and between entire concentration-time curves, respectively.