Model-based Strategies of Drug Dosing for Pharmacokinetic Systems

The aim of this paper is to report analytical and individual-based methods for antibiotic dose selection, that are based on tools from system and control theory. A brief system analysis of standard population pharmacokinetic models proves that such models are nonnegative and stable. Then, an input-output analysis leads to an open-loop control law which yields a dosing for the “average” patient, based on the equilibrium trajectory of the system. This approach is then incorporated into a “worst-case” analysis based on the monotony of the state trajectories with respect to the clearance (model parameter). Finally, an heuristic method of an estimated state feedback is presented. Thanks to numerical simulations, these methods were successively illustrated on a model describing the pharmacokinetic of meropenem, an intravenous antibiotic for treatment of severe sepsis.