Journal of Mathematical Biology

, Volume 65, Issue 2, pp 349–374 | Cite as

Reaction–diffusion model of atherosclerosis development

  • N. El Khatib
  • S. Genieys
  • B. Kazmierczak
  • V. Volpert
Open Access
Article

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.

Keywords

Atherosclerosis Reaction–diffusion equations Nonlinear boundary conditions Existence of travelling waves Numerical simulations 

Mathematics Subject Classification (2000)

35K57 92C50 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • N. El Khatib
    • 1
  • S. Genieys
    • 1
  • B. Kazmierczak
    • 2
  • V. Volpert
    • 1
  1. 1.Institute of MathematicsUniversité Lyon 1, UMR 5208 CNRSVilleurbanneFrance
  2. 2.Institute of Fundamental Technological Research of PASWarsawPoland

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