Physiologically Structured Cell Population Dynamic Models with Applications to Combined Drug Delivery Optimisation in Oncology

In this paper, we introduce a model for drug delivery optimisation in a chronotherapeutics 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 pharmacokinetics 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 cancer cell populations focused on their different synchronisation responses to circadian clock triggering. 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, with as well as without circadian clock involvement in the molecular pharmacological model.