Individualization of a pharmacokinetic model by fractional and nonlinear fit improvement

Abstract

This study presents application of a new linear and nonlinear fractional derivative two compartmental model to the evaluation of individual pharmacokinetics. In the model, the integer order derivatives are replaced by derivatives of real order. A specific nonlinear function is used for the fit improvement of a fractional derivative two compartmental model with the mass balance conservation. The agreement of the values predicted by the proposed model with the values obtained through experiments with bumetanide tablets in human volunteers is shown to be good. Thus, pharmacokinetics of bumetanide can be described well by a linear or a nonlinear two compartmental model with fractional derivatives of the same order proposed here. Parameters in the model are determined by the least squares method and the particle swarm optimization numerical procedure is used. The results show that the linear fractional order two compartmental model for bumetanide is useful improvement of the classical (integer order) two compartmental model and that the nonlinear fractional order model is useful improvement of the linear model in a great number of volunteers. © 2012 Springer-Verlag France.