Mathematical Modelling of Natural Phenomena

Table of Contents - 2009 - Volume 4, Issue 03 (Cancer modelling (Part 2))  

Research Article

Dynamics of Erythroid Progenitors and Erythroleukemia

N. Bessonova1a2, F. Craustea2, I. Demina2 and V. Volperta2

a1 Institute of Problems of Mechanical Engineering, St. Petersburg, 199178 Russia

a2 Université de Lyon, Université Lyon 1, CNRS, UMR 5208, Institut Camille Jordan, Bâtiment 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 chemotherapy 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.

(Online publication June 5 2009)

Key Words:

  • erythropoiesis;
  • leukemia;
  • reaction-diffusion systems;
  • cellular modelling

Mathematics Subject Classification:

  • 35K57;
  • 92C37

Correspondence:

c1 crauste@math.univ-lyon1.fr

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