Free Access
Math. Model. Nat. Phenom.
Volume 6, Number 7, 2011
Mathematical modeling in biomedical applications
Page(s) 82 - 99
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. [CrossRef] [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. [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. [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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.