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Issue ESAIM: Proc.
Volume 28, 2009
CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids
Page(s) 1 - 12
DOI http://dx.doi.org/10.1051/proc/2009036
Published online 23 November 2009

ESAIM: Proc., 2009, Vol. 28, pp. 1-12
DOI: 10.1051/proc/2009036

Mathematical modelling of the atherosclerotic plaque formation

Vincent Calvez1, Abderrhaman Ebde2, Nicolas Meunier3 and Annie Raoult3

1  Unité de mathématiques pures et appliquées ENS Lyon, CNRS UMR 5669;
2  Département de mathématiques et applications DMA Ecole Normale Supérieure 45, rue d'Ulm Paris 75230 Cedex 05 France;
3  MAP5, Université Paris Descartes 45 rue des Saints Pères 75270 Paris Cedex 06. France; ;

vincent.calvez@umpa.ens-lyon.fr
Abderrahman.Ebde@ens.fr
nicolas.meunier@math-info.univ-paris5.fr
Annie.Raoult@parisdescartes.fr

Published online: 23 November 2009

Abstract
This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. Following the work of El Khatib, Genieys and Volpert [1], we model atherosclerosis as an inflammatory disease. We consider that the inflammatory process starts with the penetration of Low Density Lipoproteins cholesterol in the intima. This phenomenon is related to the local blood flow dynamics. Using a system of reaction-diffusion equations, we first provide a one-dimensional model of lesion growth. Then we perform numerical simulations on a two-dimensional geometry mimicking the carotid artery. We couple the previous mathematical model with blood flow and we provide a model in which the lesion appears in the area of lower shear stress. 



Résumé
Cet article est consacré à la construction d'un modèle mathématique décrivant la formation de lésions précoces dans l'athérosclérose. Suite au travail de El Khatib, Genieys and Volpert [1], nous modélisons l'athérosclérose comme une maladie inflammatoire. Nous considérons que le procesus inflammatoire débute avec la pénétration de "Low Density Lipoproteins cholesterol" dans l'intima. Ce phénomène est relié à la dynamique locale de l'écoulement du sang. En utilisant un système d'équations de réaction-diffusion, nous donnons tout d'abord un modèle monodimensionel de croissance de lésion. Puis, dans le cas d'une bifurcation bidimensionnelle, nous couplons le modèle mathématique précédent avec l'écoulement du sang et nous fournissons un modèle dans lequel la lésion apparaît dans la zone de plus faible cisaillement.



© EDP Sciences, ESAIM 2009


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