Non-Newtonian effects in a fluid-structure interaction model for atherosclerosis

• Autorzy: El Khatib N. , Genieys S. , Zine A. M. , Volpert V.
• Języki publikacji: EN

Abstrakty

EN

The inflammatory process of atherosclerosis leads to the formation of an atheroma plaque in the blood vessel. The interaction between the blood and the plaque may have dangerous consequences such as the rupture of the plaque. This rupture exposes tissue factors to the blood flow, leading to the formation of a clot that might result in a heart attack or an ischemic stroke. The blood-plaque interaction may also produce recirculations downstream of the plaque, and these recirculations enhance the risk of clot formation. In this paper we study the blood-plaque interaction using a fluid-structure interaction model. The atheroma plaque is composed of a lipid pool and a fibrous cap and both are modeled as hyperelastic materials. The blood is supposed to be a non-Newtonian fluid with a variable viscosity modeled by the Carreau law. The parameters used in our simulations are taken from experimental data. We investigate the non-Newtonian effects on the recirculations downstream of the atheroma plaque and on the stress over the plaque. The simulations show that the Newtonian model significantly overestimates the recirculations in comparison with the non-Newtonian model. They also show that the Newtonian model slightly underestimates the stress over the plaque for usual shear rates, but that this underestimation can become significant for low shear rates.

Słowa kluczowe

EN

atherosclerosis; blood flow; non-Newtonian fluid; fluid-structure interaction

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 2009
• Tom: Vol. 50, no 1
• Strony: 55--64
• Opis fizyczny: Bibliogr. 24 poz., wykr.

Twórcy

autor

El Khatib N.

autor

Genieys S.

autor

Zine A. M.

autor

Volpert V.

• Universite de Lyon, Universite Lyon 1, INSA de Lyon, F-69621 Ecole Centrale de Lyon CNRS, UMR5208, Institut Camille Jordan 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France,

Bibliografia

• 1. J. FAN and T. WATANABE, Inflammatory Reactions in the Pathogenesis of Atherosclerosis, Journal of Atherosclerosis and Thrombosis, 10, 63-71, 2003.
• 2. N. EL KHATIB, S. GENIEYS and V. VOLPERT, Atherosclerosis initiation modeled as an inflammatory process, or Mathematical model of the inflammatory part of atherosclerosis, Mathematical Modelling of Natural Phenomena, 2, 126-141, 2007.
• 3. F. MOBILE, Numerical Approximation of Fluid-Structure Interaction Problems with Aplication to Haemodynamics, PhD thesis, 2001.
• 4. T.J.R. HUGHES, W.K. LIU and T.K. ZIMMERMANN, Arbitrary Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Computer Methods in Applied Mechanics and Engineering, 29, 329-349, 1981.
• 5. L. ACHAB, S. BENHADID, Application d’étude loi constitutive dans l’etude numérique de l’écoulement sanguin ŕ travers une artčre sténosée, Rhéologie, 7, 28-34, 2005.
• 6. R. Ross, Atherosclerosis - An inflammatory disease, Massachussets Medical Society, 340, 115-120, 1999.
• 7. B. OSTERUD and E. BJORKLID, Role of Monocytes in Atherogenesis, Physiol. Rev., 83, 1070-1086, 2003.
• 8. Z.Y. LI, S. HOWARTH, T. TANG, J.H. GILLARD, How Critical Is Fibrous Cap Thickness to Carotid Plaque Stability? A Flow Plaque Interaction Model, Stroke, 37, 1195-1196, 2006.
• 9. Z.Y. LI, S. HOWARTH, R.A. TRIVEDI, J.M. U-KING-IM, M.J. GRAVES, A. BROWN, L. WANG and J.H. GILLARD, Stress analysis of carotid plaque rupture based on in vivo high resolution MRI, Journal of Biomechanics, 39, 2611-2622, 2006.
• 10. D. TANG, C. YANG, J. ZHENG, P.K. WOODARD, G.A. SICARD, J.E. SAFPITZ and CHUN YUAN, 3D MRI-Based Multicomponent FSI Models for Atherosclerotic Plaques, Annals of Biomedical Engineering, 32, 947-960, 2004.
• 11. S.A. KOCK, J.V. NYGAARD, N. ELDRUP, E.T. FRUND, A. KLÆRKE, W.P. PAASKE, E. FALK and W.Y. KIM, Mechanical stresses in carotid plaques using MRI-based fluid-structure interaction models, Journal of Biomechanics, 41, 1651-1658, 2008.
• 12. T. ISHIKAWA, L.F.R. GUIMARAES, S. OSHIMA and R. YAMANE, Effect of non-Newtonian property of blood on flow through a stenosed tube, Fluid dynamics research, 22, 251-264, 1998.
• 13. M. THIRIET, G. MARTIN-BORRET, F. HECHT, Ecoulement rhofluidifiant dans un coude et une bifurcation plane symetrique. Application l’coulement sanguin dans la grande circulation, Journal de Physique III, 6, 529-542, 1996.
• 14. K.T. NGUYEN, C.D. CLARK, T.J. CHANCELLOR, D.V. PAPAVASSILIOU, Carotid geometry effects on blood flow and on risk for vascular disease, Journal of Biomechanics, 41, 11-19, 2008.
• 15. A.K. POLITIS, G.P. STAVROPOULOS, M.N. CHRISTOLIS, P.G. PANAGOPOULOS, N.S. VLACHOS and N.C. MARKATOS, Numerical modelling of simulated blood flow in idealized composite arterial coronary grafts: Transient flow, Journal of Biomechanics, 41, 25-39, 2008.
• 16. R.N. POSTON and D.R.M. POSTON, A Typical Atherosclerotic Plaque Morphology Produced in Silica by an Atherogenesis Model Based on Self-Perpetuating Propagating Macrophage Recruitment, Mathematical Modelling of Natural Phenomena, 3, 1-3, 2008.
• 17. T.E. TEZDUYAR, M. BEHR and J. LIOU, A new strategy for finite element computations involving moving boundaries and interfaces - the deforming-spatial-domain/space-time procedure: I. The concept and preliminary numerical tests, Computer methods in applied mechanics and engineering, 94, 339-351, 1992.
• 18. T.E. TEZDUYAR, M. BEHR, S. MITTAL and J. LIOU, A new strategy for finite element computations involving moving boundaries and interfaces - the deforming-spatial domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows and flows with drifting cylinders, Computer Methods in Applied Mechanics and Engineering, 94, 339-351, 1992.
• 19. S. MITTAL and T.E. TEZDUYAR, Parallel finite element simulation of 3D incompressible flows: fluid-structure interactions, International Journal for Numerical Methods in Fluids, 21, 933-953, 1995.
• 20. Y.C. CHANG, T.Y. HOU, B. MERRIMAN and S. OSHER, A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, Journal of Computational Physics, 124, 449-464, 1996.
• 21. C.S. PESKIN, Numerical Analysis of Blood Flow in the Heart, Journal of Computational Physics, 25, 220-252, 1977.
• 22. C.S. PESKIN and D.M. McQUEEN, A Three-Dimensional Computational Method for Blood Flow in the Heart - I Immersed Elastic Fibers in a Viscous Incompressible Fluid, Journal of Computational Physics, 81, 372-405, 1989.
• 23. R. GLOWINSKI, T.W. PAN and J. PERIAUX, A fictitious domain method for dirichlet problem and applications, Computer Methods in Applied Mechanics and Engineering, 111, 283-303, 1994.
• 24. R. GLOWINSKI, T.W. PAN and J. PERIAUX, A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 112, 133-148, 1994.