Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 7, 2011
Mathematical modeling in biomedical applications
Page(s) 82 - 99
DOI https://doi.org/10.1051/mmnp:20116707
Published online 15 June 2011
  1. G. Cheng, H. Loree, R. Kamm, M. Fishbein, R. Lee. Distribution of circumferential stress in ruptured and stable atherosclerotic lesions: a structural analysis with histopathological correlation. Circulation, 87 (1993), 1179–1187. [PubMed] [Google Scholar]
  2. L. Formaggia, A. Quarteroni, A. Veneziani. Cardiovascular mathematics, Vol. 1. Heidelberg, Springer, 2009. [Google Scholar]
  3. A. Green, J. Adkins. Large Elastic Deformation. Clarendon Press, Oxford, 1970. [Google Scholar]
  4. G. Holzapfel, R. Ogden (Eds.). Mechanics of Biological Tissue, Vol. XII. 2006. [Google Scholar]
  5. G. Holzapfel, R. Ogden. Constitutive modelling of arteries. Proc. R. Soc. A, 466 (2010), No. 2118, 1551–1597. [CrossRef] [Google Scholar]
  6. J. Humphrey. Continuum biomechanics of soft biological tissues. Proc. R. Soc. Lond. A 459, (2003), 3–46. [CrossRef] [Google Scholar]
  7. V. Koshelev, S. Mukhin, T. Sokolova, N. Sosnin, A. Favorski. Mathematical modelling of cardio-vascular hemodynamics with account of neuroregulation. Matem. Mod., 19 (2007), No. 3, 15–28 (in Russian). [Google Scholar]
  8. R. Lee, A. Grodzinsky, E. Frank, R. Kamm, F. Schoen. Structuredependent dynamic mechanical behavior of fibrous caps from human atherosclerotic plaques. Circulation, 83 (1991), 1764–1770. [PubMed] [Google Scholar]
  9. J. Ohayon et al. Influence of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: Potential impact for evaluating the risk of plaque rupture. Am. J. Physiol. Heart Circ. Physiol. 293 (2007), 1987–1996. [CrossRef] [Google Scholar]
  10. T.J. Pedley, X.Y. Luo. Modelling flow and oscillations in collapsible tubes. Theor. Comp. Fluid Dyn., 10 (1998), No. 1–4, f–294. [Google Scholar]
  11. A. Quarteroni, L. Formaggia. Mathematical modelling and numerical simulation of the cardiovascular system. In: Handbook of numerical analysis, Vol.XII, Amsterdam, Elsevier, 2004, 3–127. [Google Scholar]
  12. W. Riley, R. Barnes, et al. Ultrasonic measurement of the elastic modulus of the common carotid. The Atherosclerosis Risk in Communities (ARIC) Study. Stroke, 23 (1992), 952–956. [CrossRef] [PubMed] [Google Scholar]
  13. M. Rosar, C. Peskin. Fluid flow in collapsible elastic tubes: a three-dimensional numerical model. New York J. Math., 7 (2001), 281–302. [MathSciNet] [Google Scholar]
  14. S.S. Simakov, A.S. Kholodov. Computational study of oxygen concentration in human blood under low frequency disturbances. Mat. Mod. Comp. Sim., 1 (2009), 283–295. [CrossRef] [MathSciNet] [Google Scholar]
  15. C. Tu, C. Peskin. Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods. SIAM J. Sci. Stat. Comp., 6 (1992), No. 13, 1361–1376. [Google Scholar]
  16. Y.V. Vassilevski, S.S. Simakov, S.A. Kapranov. A multi-model approach to intravenous filter optimization. Int. J. Num. Meth. Biomed. Engrg., 26 (2010), No. 7, 915–925. [Google Scholar]
  17. Y. Vassilevski, S. Simakov, V. Salamatova, Y. Ivanov, T. Dobroserdova. Blood flow simulation in atherosclerotic vascular network using fiber-spring representation of diseased wall. Math. Model. Nat. Phen. (in press), 2011. [Google Scholar]
  18. R. Vito, S. Dixon. Blood vessel constitutive models, 1995-2002. Annu. Rev. Biomed. Engrg., 5 (2003), 413–439. [CrossRef] [Google Scholar]
  19. R. Wulandana. A nonlinear and inelastic constitutive equation for human cerebral arterial and aneurysm walls. Dissertation, University of Pittsburgh, Pittsburgh, 2003. [Google Scholar]

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