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Articles

Generalized Navier–Stokes equations with non-standard conditions for blood flow in atherosclerotic artery

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Pages 1645-1670 | Received 19 Dec 2014, Accepted 29 Jun 2015, Published online: 22 Jul 2015

References

  • Delfino A, Stergiopulos N Jr, Moore JE, Meister JJ. Residual strain effects on the field in a thick wall finite element model of the human carotid bifurcation. J. Biomech. 1997;30:777–786.
  • Biros G, Kaoui B, Misbah C. Why do red blood cells have asymmetric shapes even in a symmetric flow? Phys. Rev. Lett. 2009;103:188101.
  • Leray J. Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’hydrodynamique [A study of diverse non-linear integral equations and some problems issued from hydrodynamic]. J. Math. Pures Appl. 1933;12:1–82.
  • Leray J. Essai sur les mouvements plans d’un liquide visqueux que limitent des parois [Trial on planar motions of a viscous liquid limited by walls]. J. Math. Pures Appl. 1934;13:331–418.
  • Leray J. Sur le mouvement d’un liquide visqueux remplissant l’espace [On the motion of a viscous liquid filling the space]. Acta Math. 1934;63:193–248.
  • Ladyzhenskaya OA. The mathematical theory of viscous incompressible flow. New York (NY): Gordon and Breach; 1965.
  • Lions JL. Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires [Some solving methods for non-linear boundary problems]. Paris: Dunod; 1969.
  • Temam R. Navier--Stokes equations: theory and numerical analysis. Amsterdam: North Holland; 1977.
  • Verfürth R. Finite element approximation of steady Navier--Stokes equations with mixed boundary conditions. RIRO Modél. Math. Anal. Numér. 1985;19:461–475.
  • Verfürth R. Finite element approximation of incompressible Navier--Stokes equations with slip boundary condition. Numér. Math. 1987;50:697–721.
  • Conca C, Murat F, Pironneau O. The Stokes and Navier--Stokes equations with boundary conditions involving the pressure. Japan. J. Math. 1994;20:279–318.
  • Boujena S. Étude d’une classe de fluides non-Newtoniens, les fluides Newtoniens généralisés [A study of a class of non-Newtonian fluids, the generalized Newtonian fluids]. Thèse de troisième cycle [PhD. thesis]. Paris 6: Univ. Pierre et Marie-Curie; 1986.
  • Hundertmark A, Lukacova-Medvidova M, Necasova S. On the weak solution of the fluid-structure interaction problem for shear-dependent fluids. In: Amann H, Giga Y, Kozono H, Okamoto H, Yamazaki M,editors. Recent developments of mathematical fluid mechanics. Series of advanced in mathematical fluid mechanics. Prague: Birkhauser Verlag; 2014.
  • Muha B, Canic S. Existence of a solution to a fluid-multi-layered-structure interaction problem. J. Differ. Equ. 2014;256:658–706.
  • Janela J, Moura A, Sequeira A. A 3D non-Newtonian fluid-structure interaction model for blood flow in arteries. J. Comput. Appl. Math. 2010;234:2783–2791.
  • Crosetto P, Raymond P, Deparis S, Kontaxakis D, Stergiopulos N, Quarteroni A. Fluid-structure interaction simulations of physiological blood flow in the aorta. Computers and fluids. 2011;43:46–57. ISSN: 0045–7930.
  • Li ZY, Howarth PSS, Tang T, Gillard JH. How critical is fibrous cap thickness to carotid plaque stability? A flow-plaque interaction model. Stroke. 2006;37:1195–1196.
  • El Khatib N. Modélisation mathématique de l’athérosclérose [Mathematical modeling of atherosclerosis] [PhD thesis]. Lyon: Université Claude Bernard -- Lyon 1; 2009.
  • Boujena S, Kafi O, El Khatib N. A 2D mathematical model of blood flow and its interactions in an atherosclerotic artery. Math. Model. Nat. Phenom. 2014;6:32–54.
  • Thiriet M, Martin-Borret G, Hecht F. Ecoulement rhéofluidifiant dans un coude et une bifurcation plane symétrique [Laminar flow in a planar symmetric bifurcation]. Application l’écoulement sanguin dans la grande circulation. J. Phys. III France [Application to blood flow in large circulation]. 1996;6:529–542.
  • Thurston GB, Jeng M, Henderson NM. Viscoelastic properties of blood on analogues. In: How TV,editor. Advances in hemodynamics and hemorheology. Jai Press, Inc.; 2004.
  • Aboulaich R, Boujena S, EL Guarmah E. A non linear diffusion model with non homogeneous boundary conditions in image restoration. Esc10 Milan. 2009;10:22–26.
  • Raviart PA, Thomas JM. Introduction à l’analyse numérique des équations aux dérivées partielles [Introduction to the numerical analysis of partial differential equations]. Paris: Masson; 1993.
  • Ciarlet PG. Mathematical elasticity. Vol. 1, Three dimensional elasticity. Elsevier; 2004.
  • Ait Moudid L. Couplage fluide-structure pour la simulation numérique des écoulements fluides dans une conduite à parois rigides ou élastiques, en présence d’obstacles ou non [Fluid-structure coupling for the numerical simulation of fluid flows in a pipe with rigid or compliant walls with and without obstacles] [PhD thesis]. Compiègne: Université d’Artois; 2007.
  • Gambaruto AM, Janela J, Moura A, Sequeira A. Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology. Math. Biosci. Eng. 2011;8:409–423.
  • Li ZY, Howarth S, Rikin A, et al. Stress analysis of carotid plaque rupture based on in vivo high resolution MRI. J. Biomech. 2006;39:2611–2612.
  • Tang D, Yang C, Zheng J, et al. 3D MRI-based multicomponent FSI models for atherosclerotic plaques. Ann. Biomed. Eng. 2004;32:947–960.
  • Liu B, Tang D. Influence of non-Newtonian properties of blood on the wall shear stress in human atherosclerotic right coronary arteries. Mol. Cell. Biomech. 2011;8:73–90.
  • El Khatib N, Génieys S, Zine AM, Volpert V. Non-Newtonian effects in a fluid-structure interaction model for atherosclerosis. J. Tech. Phys. 2009;50:55–64.
  • Bayliss LE. Deformation and flow in biological systems. Amsterdam: Frey-Wyssling editor; 1952.
  • Gijsen FJ, Allanic E, van de Vosse FN, Janssen JD. The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in 90° curved tube. J. Biomech. 1999;32:705–713.

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