Mathematics of Pharmacokinetics and Pharmacodynamics: Diversity of Topics, Models and Methods

¹ Institute of Numerical Mathematics of the Russian Academy of Sciences, Gubkina Street 8, Moscow, Russia
² LBBE, UMR 5558 CNRS, University Lyon 1, 69622 Villeurbanne, France
³ LERMA, Mohammadia School of Engineering, University Mohamed V, Rabat, Morocco
⁴ INRIA Team Mamba, INRIA Paris, 2 rue Simone Iff, CS 42112, 75589 Paris, France
⁵ Sorbonne Universit′es, UPMC, Lab. J.-L. Lions UMR 7598 CNRS, 4, pl. Jussieu, b. c. 187, 75252 Paris, France
⁶ Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
⁷ INRIA Team Dracula, INRIA Antenne Lyon la Doua, Villeurbanne, Lyon, France
⁸ Laboratoire Poncelet, UMI 2615 CNRS, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia

Abstract

A short review on pharmacokinetics-pharmacodynamics (PK-PD) presented below aims to show the evolution of some concepts and ideas in this field. Some of them are developed in more detail in the papers of this issue. The key question for a practical application of PK-PD models is the ability to estimate the model parameters using patients data. In [1] a novel approach to an accurate quantification of the uncertainty in parameter estimates attributed to inter-individual variability is proposed. The analyzed PK-PD model is formulated as a compartmental ODE system. The methodology of recognizing and capturing the uncertainty in predicted quantities of interest due to inter-individual variability when the individual is not available for repeated measurements may prove to be invaluable in the risk assessment of future experiments and drug applications. Anticancer molecular PK-PD in a cell population dynamics model with drug delivery optimisation is discussed in [2]. The works [3] and [4] deal with various aspects of hemostasis modelling, and [5] with metabolic aspects in a whole-body setting. These studies represent the diversity of aspects of PK-PD modelling nowadays: theoretical about parameter estimation in general versus applied to medical questions in particular, localised cell population versus whole-body settings, cell population and whole-body versus patient population settings.