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Numerical integration of an erythropoiesis model with explicit growth factor dynamics

Oscar Angulo 1 Fabien Crauste 2, 3 Juan Carlos López-Marcos 1 
3 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 : Erythropoiesis, the red blood cell production process, involves interactions between cell populations with different differentiation states, mainly immature progenitor cells and mature erythrocytes, and growth factors such as erythropoietin and glucocorticoids, known to respectively inhibit cell apoptosis, stimulate proliferation and differentiation, and stimulate self-renewal. The feedback regulation of this process allows a very fast and efficient recovery in the case of a severe anemia. We consider an age-structured model of red blood cell production accounting for these feedback regulations and the dynamics of growth factors. We theoretically show the existence of a unique positive steady state for the model and we propose a numerical method to obtain an approximation to its solution. Experiments are reported to show numerically, on one hand, the optimal convergence order of the numerical scheme and, on the other hand, a fine approximation to real experimental data, with a suitable selection of the parameters involved.
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Submitted on : Friday, December 1, 2017 - 1:43:14 PM
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Oscar Angulo, Fabien Crauste, Juan Carlos López-Marcos. Numerical integration of an erythropoiesis model with explicit growth factor dynamics. Journal of Computational and Applied Mathematics, 2018, 330, pp.770 - 782. ⟨10.1016/j.cam.2017.01.033⟩. ⟨hal-01646786⟩

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