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Reaction-Diffusion Model of Atherosclerosis Development.
Volpert V., El Khatib N., Génieys S., Kazmierczak B.
Journal of Mathematical Biology 65, 2 (2012) 349-374 - http://hal.archives-ouvertes.fr/hal-00753096
Mathématiques/Equations aux dérivées partielles
Reaction-Diffusion Model of Atherosclerosis Development.
Vitaly Volpert (, http://math.univ-lyon1.fr/~volpert)1, N. El Khatib2, Stéphane Génieys ()3, Bogdan Kazmierczak4
1 :  INRIA Grenoble Rhône-Alpes / Institut Camille Jordan - DRACULA
INRIA – CNRS : UMR5534 – Université Claude Bernard - Lyon I : EA – Institut Camille Jordan
Institut Camille Jordan Université Claude Bernard Lyon 1 43 boulevard du 11 novembre 1918 69622 Villeurbanne cedex France
2 :  IPNL - Institut de Physique Nucléaire de Lyon
CNRS : UMR5822 – IN2P3 – Université Claude Bernard - Lyon I
3 :  ICJ - Institut Camille Jordan
CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées [INSA] - Lyon
Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX
4 :  IPPT - Institute of Fundamental Technological Research
Polish Academy of Sciences
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.

Journal of Mathematical Biology (J Math Biol)
Publisher Springer Verlag (Germany)
ISSN 0303-6812 (eISSN : 1432-1416)
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