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

Gennady Bocharov 1 Anas Bouchnita 2, 3, 4, 5 Jean Clairambault 6, 7 Vitaly Volpert 3, 8, 9, 4
2 Evaluation et modélisation des effets thérapeutiques
Département biostatistiques et modélisation pour la santé et l'environnement [LBBE]
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
ICJ - Institut Camille Jordan [Villeurbanne], Inria Grenoble - Rhône-Alpes, CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire
4 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
7 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris
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.
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Gennady Bocharov, Anas Bouchnita, Jean Clairambault, Vitaly Volpert. Mathematics of Pharmacokinetics and Pharmacodynamics: Diversity of Topics, Models and Methods. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2016. ⟨hal-01413795⟩

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