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On a Model of Leukemia Development with a SpatialCell Distribution

Published online by Cambridge University Press:  15 June 2008

A. Ducrot  and
V. Volpert
A. Ducrot
Affiliation:
UMR CNRS 5466, MAB & INRIA Futurs, Université Victor Segalen Bordeaux 2, 33076 Bordeaux, France
V. Volpert*
Affiliation:
UMR CNRS 5208, Université Lyon 1, 69622 Villeurbanne, France
*
ducrot@sm.u-bordeaux2.fr
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Abstract

In this paper we propose a mathematical model to describe the evolution of leukemiain the bone marrow. The model is based on a reaction-diffusion system of equations in a porousmedium. We show the existence of two stationary solutions, one of them corresponds to the normalcase and another one to the pathological case. The leukemic state appears as a result of a bifurcationwhen the normal state loses its stability. The critical conditions of leukemia developmentare determined by the proliferation rate of leukemic cells and by their capacity to diffuse. Theanalytical results are confirmed and illustrated by numerical simulations.

Keywords

leukemiabone marrowspace cell distributionreaction-diffusion systemporousmedium
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 2 , Issue 3: Cancer modelling , 2007 , pp. 101 - 120
Copyright
© EDP Sciences, 2007

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