Reaction-Diffusion Model of Atherosclerosis Development.

Vitaly Volpert 1 N. El Khatib Stéphane Génieys 2, * Bogdan Kazmierczak 3
* Corresponding author
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGMC - Centre de génétique moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne], UCBL - Université Claude Bernard Lyon 1 : EA
Abstract : Atherosclerosis begins as an inflammation in blood vessel walls (intima). The inflammatory response of the organism leads to the recruitment of monocytes. Trapped in the intima, they differentiate into macrophages and foam cells leading to the production of inflammatory cytokines and further recruitment of white blood cells. This self-accelerating process, strongly influenced by low-density lipoproteins (cholesterol), results in a dramatic increase of the width of blood vessel walls, formation of an atherosclerotic plaque and, possibly, of its rupture. We suggest a 2D mathematical model of the initiation and development of atherosclerosis which takes into account the concentration of blood cells inside the intima and of pro- and anti-inflammatory cytokines. The model represents a reaction-diffusion system in a strip with nonlinear boundary conditions which describe the recruitment of monocytes as a function of the concentration of inflammatory cytokines. We prove the existence of travelling waves described by this system and confirm our previous results which suggest that atherosclerosis develops as a reaction-diffusion wave. The theoretical results are confirmed by the results of numerical simulations.
Document type :
Journal articles
Journal of Mathematical Biology, Springer Verlag (Germany), 2012, 65 (2), pp.349-374. <10.1007/s00285-011-0461-1>
Contributor : Vitaly Volpert <>
Submitted on : Saturday, November 17, 2012 - 11:22:26 AM
Last modification on : Friday, December 18, 2015 - 1:12:53 AM




Vitaly Volpert, N. El Khatib, Stéphane Génieys, Bogdan Kazmierczak. Reaction-Diffusion Model of Atherosclerosis Development.. Journal of Mathematical Biology, Springer Verlag (Germany), 2012, 65 (2), pp.349-374. <10.1007/s00285-011-0461-1>. <hal-00753096>




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