Math Model Nat Phenom Vol No pp DOI: mmnp


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Math. Model. Nat. Phenom. Vol. 4, No. 3, 2009, pp. 210-232 DOI: 10.1051/mmnp/20094309 Dynamics of Erythroid Progenitors and Erythroleukemia N. Bessonova,b, F. Crausteb1, I. Deminb, V. Volpertb a Institute of Problems of Mechanical Engineering, St. Petersburg, 199178 Russia b Universite de Lyon, Universite Lyon 1, CNRS, UMR 5208, Institut Camille Jordan, Batiment du Doyen Jean Braconnier, 43, blvd du 11 novembre 1918, F - 69222 Villeurbanne Cedex, France Abstract. The paper is devoted to mathematical modelling of erythropoiesis, production of red blood cells in the bone marrow. We discuss intra-cellular regulatory networks which determine self-renewal and differentiation of erythroid progenitors. In the case of excessive self-renewal, immature cells can fill the bone marrow resulting in the development of leukemia. We introduce a parameter characterizing the strength of mutation. Depending on its value, leukemia will or will not develop. The simplest model of treatment of acute myeloid leukemia with chemother- apy allows us to determine the conditions of successful treatment or of its failure. We show that insufficient treatment can worsen the situation. In some cases curing may not be possible even without resistance to treatment. Modelling presented in this work is based on ordinary differential equations, reaction-diffusion systems and individual based approach.

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