EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Free access article

Issue Math. Model. Nat. Phenom.
Volume 2, Number 3, 2007
Cancer modelling
Page(s) 101 - 120
DOI 10.1051/mmnp:2007005

Math. Model. Nat. Phenom. Vol. 2, No. 3, 2007, pp. 101-120
DOI: 10.1051/mmnp:2007005

On a Model of Leukemia Development with a Spatial Cell Distribution

A. Ducrot1 and V. Volpert2

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

ducrot@sm.u-bordeaux2.fr

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.


Mathematics Subject Classification. 92C45, 35K57, 76V05

Key words: leukemia -- bone marrow -- space cell distribution -- reaction-diffusion system -- porous medium




What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.