Pauline Thémans (UNamur)

Title: Pharmacokinetic modeling and strategies for drug dosing recommendation: application to meropenem

Abstract: Pharmacokinetics (PK) studies the link between the dose and the drug exposure in patients. Thanks to mathematical modeling, clinical pharmacology is an interesting and promising field of application of control and system theory. We focus on time-dependent antibiotic given by constant intravenous (IV) infusion at regular dosing interval. Meropenem is used as a particular case for which numerical results are reported.

We report on the study of two kinds of models: a population pharmacokinetic (popPK) model (empirical approach, mixed effects modeling) and a physiologically-based pharmacokinetic (PBPK) model (mechanistic approach, human physiology and drug’s properties considerations). We will describe the results of internal and external validations that were performed. Both models are described by linear time-invariant state-space models. They are shown to be nonnegative and stable, as expected.

From these models, the aim is to provide guidelines (decision-making aid) for drug dosing in patients based on relevant patient’s characteristics (covariates) and on other practical conditions (target exposure for efficacy, dosing interval, time of infusion, etc.). The studied approaches are based on open-loop methods. (1) A standard input-output analysis yields the analytical expression of the output trajectories and the asymptotic response. A formula is then derived to compute the dose needed to maintain the (steady) concentration trajectory above a given lower bound. (2) We also describe an optimal control approach on the discrete-time model (minimum principle).