| Issue |
Math. Model. Nat. Phenom.
Volume 2, Number 3, 2007
Cancer modelling
|
|
|---|---|---|
| Page(s) | 101 - 120 | |
| DOI | https://doi.org/10.1051/mmnp:2007005 | |
| Published online | 15 June 2008 | |
On a Model of Leukemia Development with a Spatial Cell Distribution
1
UMR CNRS 5466, MAB & INRIA Futurs, Université Victor Segalen Bordeaux 2, 33076 Bordeaux, France
2
UMR CNRS 5208, Université Lyon 1, 69622 Villeurbanne, France
Corresponding author: ducrot@sm.u-bordeaux2.fr
In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by the proliferation rate of leukemic cells and by their capacity to diffuse. The analytical results are confirmed and illustrated by numerical simulations.
Mathematics Subject Classification: 92C45 / 35K57 / 76V05
Key words: leukemia / bone marrow / space cell distribution / reaction-diffusion system / porous medium
© EDP Sciences, 2007
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