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On a Model of Leukemia Development with a Spatial Cell Distribution

By A. Ducrot and V. Volpert

Abstract

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

Topics: leukemia, bone marrow, space cell distribution, reaction-diffusion system, porous medium
Publisher: EDP Sciences
Year: 2008
DOI identifier: 10.1051/mmnp:2007005
OAI identifier: oai:edpsciences.org:dkey/10.1051/mmnp:2007005
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