Pharmacokinetics (PK) is a field of clinical pharmacology that studies how a drug evolves in the body after administration. Thanks to mathematical modeling, clinical pharmacology is an interesting and promising field of application of control and system theory. We report on the population PK analysis of three case study drugs: hydroxychloroquine in COVID-19 patients, and temocillin and meropenem in patients with severe pneumonia. We developed data-driven models using a mixed-effects approach, meaning that parameters are characterized by a fixed and a random component. We also describe the results of internal and external validations that were performed. These systems are described by linear time-invariant state-space representations. They turn out to be nonnegative and stable, as expected. From these models, the aim is to provide methods for dosing rationale in patients (decision-making aid) based on relevant patient’s characteristics (covariates) and on other practical conditions (target exposure for efficacy and pharmacodynamic index, dosing interval, and duration of infusion). Our contributions in this field are the following. (1) A deterministic input-output (I/O) analysis of the system leads to an open-loop control law that enables the computation of an appropriate dosage for the average/nominal patient. This approach is then incorporated into the “worst-case” system based on the monotony of the state trajectories with respect to the clearance. (2) The I/O analysis is used to heuristically design a feedback dosing strategy based on the estimated state. (3) We finally describe an optimal control approach (minimum principle). This approach aims at improving the drug dosing by optimizing a criterion under input and state constraints.
Pharmacokinetic modeling and control design for drug dosing
THEMANS, P. (Author). 1 Jul 2021
Student thesis: Doc types › Doctor of Sciences