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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 865 - 889, Volume 18, Issue 4, June 2013      doi:10.3934/dcdsb.2013.18.865

 
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Frédérique Billy - INRIA Paris-Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, F-78153 Le Chesnay Cedex, France (email)
Jean Clairambault - INRIA Paris-Rocquencourt, Domaine de Voluceau, Rocquencourt, B.P. 105, F-78153 Le Chesnay Cedex, France (email)

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.

Keywords:  Cell population dynamics, proliferation, cell division cycle, adaptive dynamics, cancer drugs, control targets.
Mathematics Subject Classification:  Primary: 92-02; Secondary: 92D25, 92C50, 35Q92.

Received: July 2012;      Revised: September 2012;      Available Online: February 2013.

 References