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Optimisation of time-scheduled regimen for anti-cancer drug infusion

Published online by Cambridge University Press:  15 November 2005

Claude Basdevant ,
Jean Clairambault  and
Francis Lévi
Claude Basdevant
Affiliation:
Université Paris-Nord, Villetaneuse and École Normale Supérieure, 75005 Paris, France. [email protected]
Jean Clairambault
Affiliation:
INRIA, projet BANG, 78153 Rocquencourt, France. [email protected] (corresponding author)
Francis Lévi
Affiliation:
INSERM E 0354, Hôpital Paul-Brousse, 94800 Villejuif, France. [email protected]
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Abstract

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique to search for the best drug infusion laws. The mathematical model is a set of six coupled differential equations governing the time evolution of both the tumour cell population (cells of Glasgow osteosarcoma, a mouse tumour) and the mature jejunal enterocyte population, to be shielded from unwanted side effects during a treatment by oxaliplatin. Starting from known tumour and villi populations, and a time dependent free platinum Pt (the active drug) infusion law being given, the mathematical model allows to compute the time evolution of both tumour and villi populations. The tumour population growth is based on Gompertz law and the Pt anti-tumour efficacy takes into account the circadian rhythm. Similarly the enterocyte population is subject to a circadian toxicity rhythm. The model has been derived using, as far as possible, experimental data. We examine two different optimisation problems. The eradication problem consists in finding the drug infusion law able to minimise the number of tumour cells while preserving a minimal level for the villi population. On the other hand, the containment problem searches for a quasi periodic treatment able to maintain the tumour population at the lowest possible level, while preserving the villi cells. The originality of these approaches is that the objective and constraint functions we use are L∞ criteria. We are able to derive their gradients with respect to the infusion rate and then to implement efficient optimisation algorithms.

Keywords

Dynamical systemsoptimisationcircadian rhythmsdrugstherapeuticscancer.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 6 , November 2005 , pp. 1069 - 1086
Copyright
© EDP Sciences, SMAI, 2005

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