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Issue Math. Model. Nat. Phenom.
Volume 4, Number 3, 2009
Cancer modelling (Part. 2)
Page(s) 12 - 67
DOI 10.1051/mmnp/20094302
Published online 05 June 2009

Math. Model. Nat. Phenom. Vol. 4, No. 3, 2009, pp. 12-67
DOI: 10.1051/mmnp/20094302

Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments

J. Clairambault

INRIA Paris-Rocquencourt, BANG project-team, BP 105, F78153 Le Chesnay Cedex

jean.clairambault@inria.fr

Published online: 5 June 2009

Abstract
This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the focus will be set here. To this purpose, mathematical modelling should represent proliferating cell population dynamics with natural built-in control targets (which implies modelling the cell division cycle), together with the distribution of drugs in the organism and their molecular actions on different targets at the cell level on proliferation, i.e., molecular pharmacokinetics-pharmacodynamics of antiproliferative drugs. This should make possible optimal control of drug delivery with constraints to be determined according to the main pharmacological issues encountered in the clinic: unwanted toxic side-effects, occurrence of drug resistance. Mathematical modelling should also take into account physiological determinants of cell and tissue proliferation, such as intervention of the immune system, circadian control on cell cycle checkpoint proteins, and activity of intracellular drug processing enzymes together with individual variations in the activities of these proteins (genetic polymorphism). Taking these points into account will add to the rich scenery of normal or disrupted cell and tissue regulations, and their corrections by drugs, a natural environmental, whole body physiological, frame. It is necessary indeed to consider such a framework if one wants to eventually be actually helpful to clinicians who routinely treat by combinations of drugs living Humans with their complex whole body regulations, often dependent on genotypic variations, and not isolated cells or tissues.


Mathematics Subject Classification. 92-02, 92B05

Key words: cell proliferation -- population dynamics -- physiologically structured partial differential equations -- pharmacological control -- pharmacokinetics-pharmacodynamics -- physiological modelling -- cancer treatments -- therapeutic optimisation -- individualised medicine


© EDP Sciences 2009


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