Geodesic
Mathematical modelling of the atherosclerotic plaque formation
Vincent Calvez1 ; Abderrhaman Ebde2 ; Nicolas Meunier3 ; 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; ;
ESAIM. Proceedings, Tome 28 (2009), pp. 1-12.

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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. 

DOI : 10.1051/proc/2009036

Vincent Calvez 1 ; Abderrhaman Ebde 2 ; Nicolas Meunier 3 ; Annie Raoult 3

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; ; 
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     author = {Vincent Calvez and Abderrhaman Ebde and Nicolas Meunier and Annie Raoult},
     title = {Mathematical modelling of the atherosclerotic plaque formation},
     journal = {ESAIM. Proceedings},
     pages = {1--12},
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     doi = {10.1051/proc/2009036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009036/}
}
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Vincent Calvez; Abderrhaman Ebde; Nicolas Meunier; Annie Raoult. Mathematical modelling of the atherosclerotic plaque formation. ESAIM. Proceedings, Tome 28 (2009), pp. 1-12. doi : 10.1051/proc/2009036. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009036/

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