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Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia

Mostafa Adimy 1, * Fabien Crauste 1, 2, * Abderrahim El Abdllaoui 3 
* Corresponding author
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We propose and analyze a mathematical model of hematopoietic stem cell dynamics, that takes two cell populations into account, an immature and a mature one. All cells are able to self-renew, and immature cells can be either in a proliferating or in a resting compartment. The resulting model is a system of age-structured partial di®erential equations, that reduces to a system of delay di®erential equations, with several distributed delays. We investigate the existence of positive and axial steady states for this system, and we obtain conditions for their stability. Numerically, we concentrate on the in°uence of variations in di®erentiation coe±cients on the behavior of the system. In particular, we focus on applications to acute myelogenous leukemia, a cancer of white cells characterized by a quick proliferation of immature cells that invade the circulating blood. We show that a blocking of di®erentiation at an early stage of immature cell development can result in the over-expression of very immature cells, with respect to the mature cell population.
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Submitted on : Friday, November 9, 2012 - 1:33:34 PM
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Mostafa Adimy, Fabien Crauste, Abderrahim El Abdllaoui. Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia. Journal of Biological Systems, World Scientific Publishing, 2008, 16 (3), pp.395-424. ⟨10.1142/S0218339008002599⟩. ⟨hal-00750276⟩



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