Reaction-diffusion model of atherosclerosis development

Journal of Mathematical Biology

Volumn 65, Issue 2, 2012, Pages 349-374

  El Khatib, N ^a   Genieys, S ^a   Kazmierczak, B ^b   Volpert, V ^a  

^a UNIVERSITÉ LYON 1   (France)

^b INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

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

Indexed keywords

CHOLESTEROL; LOW DENSITY LIPOPROTEIN;

ARTICLE; ATHEROSCLEROSIS; ATHEROSCLEROTIC PLAQUE; BIOLOGICAL MODEL; DIFFUSION; FOAM CELL; HUMAN; INFLAMMATION; INTIMA; MACROPHAGE; MATHEMATICAL COMPUTING; MONOCYTE; PATHOPHYSIOLOGY; PHYSIOLOGY; REACTION TIME;

ATHEROSCLEROSIS; CHOLESTEROL; DIFFUSION; FOAM CELLS; HUMANS; INFLAMMATION; LIPOPROTEINS, LDL; MACROPHAGES; MODELS, CARDIOVASCULAR; MONOCYTES; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PLAQUE, ATHEROSCLEROTIC; REACTION TIME; TUNICA INTIMA;

EID: 84864344134     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-011-0461-1     Document Type: Article

References (18)

1. Chow CC, Clermont G, Kumar R, Lagoa C, Tawadrous Z, Gallo D, Betten B, Bartels J, Constantine G, Fink MP, Billiar TR, Vodovotz Y (2005) The acute inflammatory response in diverse shock states. Shock 24(1): 74-84.
2. Edelstein-Keshet L, Spiros A (2002) Exploring the formation of Alzheimer's disease senile plaques in silico. J Theor Biol 216(3): 301-326.
3. El Khatib N, Genieys S, Volpert V (2007) Atherosclerosis initiation modeled as an inflammatory process. Math Model Nat Phenom 2(2): 126-141.
4. Fan J, Watanabe T (2003) Inflammatory reactions in the pathogenesis of atherosclerosis. J Atheroscler Thromb 10: 63-71.
5. Kazmierczak B (2009) Existence of global solutions to a model of chondrogenesis. Math Meth Appl Sci 32(3): 264-283.
6. Krasnoselskii MA, Zabreiko PP (1984) Geometrical methods of nonlinear analysis. Springer, New York.
7. Ladyzhenskaya OA, Solonnikov VA, Uraltseva NN (1967) Linear and quasi-linear equations of parabolic type. Moskva, Nauka.
8. LaRosa JC, He J, Vupputuri S (1999) Effect of statins on risk of coronary disease: a meta-analysis of randomized controlled trials. J Am Med Assoc 282: 2340-2346.
9. Leiderman KM, Miller LA, Fogelson AL (2008) The effects of spatial inhomogeneities on flow through the endothelial surface layer. J Theor Biol 252: 313-325.
10. Li Z-Y, Howarth SP, Tang T, Gillard JH (2006a) How critical is fibrous cap thickness to carotid plaque stability? A flow plaque interaction model. Stroke 37: 1195-1196.
11. Li Z-Y, Howarth SP, Trivedi RA, U-King-Im JM, Graves MJ, Brown A, Wang L, Gillard JH (2006b) Stress analysis of carotid plaque rupture based on in vivo high resolution MRI. J Biomech 39(14): 2611-2612.
12. Lieberman GM (1996) Second order parabolic differential equations. World Scientific, Singapore.
13. Østerud B, Bjørklid E (2003) Role of monocytes in atherogenesis. Physiol Rev 83: 1070-1086.
14. Poston RN, Poston DRM (2007) A typical atherosclerotic plaque morphology produced in silico by an atherogenesis model based on self-perpetuating propagating macrophage recruitment. Math Model Nat Phenom 2(2): 142-149.
15. Protter MH, Weinberger HF (1967) Maximum principles in differential equations. Springer, Berlin.
16. Ross R (1999) Atherosclerosis: an inflammatory disease. Mass Med Soc 340: 115-120.
17. Vincent PE, Sherwin SJ, Weinberg PD (2009) The effect of a spatially heterogeneous transmural water flux on concentration polarization of low density lipoprotein in arteries. Biophys J 96(8): 3102-3115.
18. Volpert AI, Volpert VA, Volpert VA (2000) Traveling wave solutions of parabolic systems. American Mathematical Society, Providence.