Reaction-Diffusion Model of Atherosclerosis Development

Nader El Khatib (1) , Stéphane Génieys (1) , Bogdan Kazmierczak (2) , Vitaly Volpert (1)

1 ICJ - Institut Camille Jordan
2 IPPT - Institute of Fundamental Technological Research

Atherosclerosis begins as an inflammation in blood vessel walls (intima). Anti-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, in 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 show that atherosclerosis develops as a reaction-diffusion wave. The theoretical results are confirmed by the results of numerical simulations.

Mots clés: atherosclerosis; reaction-diffusion waves; nonlinear boundary conditions; existence; numerical simulations

Domaines: Equations aux dérivées partielles [math.AP]; Adaptation et Systèmes auto-organisés [nlin.AO]

Nader El Khatib, Stéphane Génieys, Bogdan Kazmierczak, Vitaly Volpert. Reaction-Diffusion Model of Atherosclerosis Development. 2009. ⟨hal-00353029⟩