Physiologically structured cell population dynamic models with applications to combined drug delivery optimisation in oncology

Jean Clairambault (1, 2) , Olivier Fercoq (3)

1 MAMBA - Modelling and Analysis for Medical and Biological Applications
2 LJLL - Laboratoire Jacques-Louis Lions
3 LTCI - Laboratoire Traitement et Communication de l'Information

In this paper, we introduce a model for drug delivery optimisation in a chronotherapeu-tics framework. We present a pharmacokinetics and pharmacodynamics model for oxaliplatin and 5-Fluorouracil, a classic therapeutic association in the treatment of colorectal cancer. We derive the phar-macokinetics model using law of mass action and enzyme kinetics. We design an age-structured cell cycle PDE model with drug damage and repair phases to account for the effect of the drugs on proliferating cell populations, with different parameters for healthy and cancerous cells. Our goal is to minimise the growth rate of cancerous cells while maintaining the growth rate of healthy cells above a given toxicity threshold. We numerically optimise the drug delivery schedules under our model and obtain theoretically efficient infusion schemes in a chronotherapeutics framework.

Mots clés: Cell population dynamics; Age-structured models; Cell division cycle; Pharmacological models; Drug delivery optimisation

Domaines: Equations aux dérivées partielles [math.AP]

Jean Clairambault, Olivier Fercoq. Physiologically structured cell population dynamic models with applications to combined drug delivery optimisation in oncology. 2016. ⟨hal-01321536⟩