Designing proliferating cell population models with functional targets for control by anti-cancer drugs

Frédérique Billy; Jean Clairambault

doi:10.3934/dcdsb.2013.18.865

Article Contents

2013, Volume 18, Issue 4: 865-889. Doi: 10.3934/dcdsb.2013.18.865 open access

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Designing proliferating cell population models with functional targets for control by anti-cancer drugs

Frédérique Billy^1, and
Jean Clairambault^1,

1.
INRIA Paris-Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, F-78153 Le Chesnay Cedex

Received: June 30, 2012

Revised: August 31, 2012

Published: May 2013

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Abstract

We review the main types of mathematical models that have been designed to represent and predict the evolution of a cell population under the action of anti-cancer drugs that are in use in the clinic, with effects on healthy and cancer tissue growth, which from a cell functional point of view are classically divided between ``proliferation, death and differentiation''. We focus here on the choices of the drug targets in these models, aiming at showing that they must be linked in each case to a given therapeutic application. We recall some analytical results that have been obtained in using models of proliferation in cell populations with control in recent years. We present some simulations performed when no theoretical result is available and we state some open problems. In view of clinical applications, we propose possible ways to design optimal therapeutic strategies by using combinations of drugs, cytotoxic, cytostatic, or redifferentiating agents, depending on the type of cancer considered, acting on different targets at the level of cell populations.

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Mathematics Subject Classification: Primary: 92-02; Secondary: 92D25, 92C50, 35Q92.

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