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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 465835, 26 pages
http://dx.doi.org/10.1155/2010/465835
Research Article

Pulsatile Flow of a Two-Fluid Model for Blood Flow through Arterial Stenosis

School of Mathematical Sciences, University Science Malaysia, 11800 Penang, Malaysia

Received 25 January 2010; Accepted 4 April 2010

Academic Editor: Saad A. Ragab

Copyright © 2010 D. S. Sankar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Liepsch, M. Singh, and M. Lee, “Experimental analysis of the influence of stenotic geometry on steady flow,” Biorheology, vol. 29, no. 4, pp. 419–431, 1992. View at Google Scholar · View at Scopus
  2. D. S. Sankar and K. Hemalatha, “Pulsatile flow of Herschel-Bulkley fluid through stenosed arteries-A mathematical model,” International Journal of Non-Linear Mechanics, vol. 41, no. 8, pp. 979–990, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. M. S. Moayeri and G. R. Zendehbudi, “Effects of elastic property of the wall on flow characteristics through arterial stenoses,” Journal of Biomechanics, vol. 36, no. 4, pp. 525–535, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. P. K. Mandal, “An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis,” International Journal of Non-Linear Mechanics, vol. 40, no. 1, pp. 151–164, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. I. Marshall, S. Zhao, P. Papathanasopoulou, P. Hoskins, and X. Y. Xu, “MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models,” Journal of Biomechanics, vol. 37, no. 5, pp. 679–687, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Chakravarty and P. K. Mandal, “Two-dimensional blood flow through tapered arteries under stenotic conditions,” International Journal of Non-Linear Mechanics, vol. 35, no. 5, pp. 779–793, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. G.-T. Liu, X.-J. Wang, B.-Q. Ai, and L.-G. Liu, “Numerical study of pulsating flow through a tapered artery with stenosis,” Chinese Journal of Physics, vol. 42, no. 4, pp. 401–409, 2004. View at Google Scholar · View at Scopus
  8. Q. Long, X. Y. Xu, K. V. Ramnarine, and P. Hoskins, “Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis,” Journal of Biomechanics, vol. 34, no. 10, pp. 1229–1242, 2001. View at Publisher · View at Google Scholar · View at Scopus
  9. C. Tu and M. Deville, “Pulsatile flow of Non-Newtonian fluids through arterial stenoses,” Journal of Biomechanics, vol. 29, no. 7, pp. 899–908, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Chaturani and R. P. Samy, “Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow,” Biorheology, vol. 23, no. 5, pp. 499–511, 1986. View at Google Scholar · View at Scopus
  11. M. Texon, “A hemodynamic concept of atherosclerosis with particular reference to coronary occlusion,” Archives of Internal Medicine, vol. 99, pp. 418–430, 1957. View at Google Scholar
  12. M. Texon, “The hemodynamic concept of atherosclerosis,” Bulletin of the New York Academy of Medicine, vol. 36, pp. 263–273, 1960. View at Google Scholar
  13. D. F. Young and F. Y. Tsai, “Flow characteristics in models of arterial stenoses: I. Steady flow,” Journal of Biomechanics, vol. 6, no. 4, pp. 395–410, 1973. View at Google Scholar · View at Scopus
  14. B. E. Morgan and D. F. Young, “An integral method for the analysis of flow in arterial stenoses,” Bulletin of Mathematical Biology, vol. 36, no. 1, pp. 39–53, 1974. View at Google Scholar · View at Scopus
  15. D. A. MacDonald, “On steady flow through modeled vascular stenosis,” Journal of Biomechanics, vol. 12, pp. 13–20, 1979. View at Google Scholar
  16. D. F. Young, “Fluid mechanics of arterial stenosis,” Journal of Biomechanical Engineering, vol. 101, no. 3, pp. 157–175, 1979. View at Google Scholar · View at Scopus
  17. A. Sarkar and G. Jayaraman, “Correction to flow rate—pressure drop relation in coronary angioplasty: steady streaming effect,” Journal of Biomechanics, vol. 31, no. 9, pp. 781–791, 1998. View at Publisher · View at Google Scholar · View at Scopus
  18. R. K. Dash, G. Jayaraman, and K. N. Mehta, “Flow in a catheterized curved artery with stenosis,” Journal of Biomechanics, vol. 32, no. 1, pp. 49–61, 1999. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Chakravarty, A. Datta, and P. K. Mandal, “Analysis of nonlinear blood flow in a stenosed flexible artery,” International Journal of Engineering Science, vol. 33, no. 12, pp. 1821–1837, 1995. View at Google Scholar · View at Scopus
  20. S. Charm and G. Kurland, “Viscometry of human blood for shear rates of 0-100,000 sec−1,” Nature, vol. 206, no. 4984, pp. 617–618, 1965. View at Publisher · View at Google Scholar · View at Scopus
  21. C. D. Han and B. Barnett, Measurement of Rheological Properties of Biological Fluids, edited by H. L. Gabelnick, M. Litt, Charles C. Thomas, Springfield, Ill, USA, 1973.
  22. C. E. Huckabe and A. W. Hahn, “A generalized approach to the modeling of arterial blood flow,” The Bulletin of Mathematical Biophysics, vol. 30, no. 4, pp. 645–662, 1968. View at Publisher · View at Google Scholar · View at Scopus
  23. E. W. Merrill, “Rheology of human blood and some speculations on its role in vascular homeostasis,” in Biomechanical Mechanisms in Vascular Homeostasis and Intravascular Thrombus, P. N. Sawyer, Ed., Appleton Century Crafts, New York, NY, USA, 1965. View at Google Scholar
  24. R. L. Whitemore, Rheology of the Circulation, Pergamon Press, New York, NY, USA, 1968.
  25. V. P. Srivastava and M. Saxena, “Two-layered model of casson fluid flow through stenotic blood vessels: applications to the cardiovascular system,” Journal of Biomechanics, vol. 27, no. 7, pp. 921–928, 1994. View at Publisher · View at Google Scholar · View at Scopus
  26. J. B. Shukla, R. S. Parihar, and S. P. Gupta, “Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis,” Bulletin of Mathematical Biology, vol. 42, no. 6, pp. 797–805, 1980. View at Google Scholar · View at Scopus
  27. J. B. Shukla, R. S. Parihar, and B. R. P. Rao, “Effects of stenosis on non-Newtonian flow of the blood in an artery,” Bulletin of Mathematical Biology, vol. 42, no. 3, pp. 283–294, 1980. View at Google Scholar · View at Scopus
  28. P. Chaturani and V. R. Ponnalagar Samy, “A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases,” Biorheology, vol. 22, no. 6, pp. 521–531, 1985. View at Google Scholar · View at Scopus
  29. G. Bugliarello and J. Sevilla, “Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes,” Biorheology, vol. 7, no. 2, pp. 85–107, 1970. View at Google Scholar · View at Scopus
  30. G. R. Cokelet, “The rheology of human blood,” in Biomechanics, Y. C. Fung, Ed., pp. 63–103, Prentice-Hall, Englewood Cliffs, NJ, USA, 1972. View at Google Scholar
  31. V. P. Srivastava, “Arterial blood flow through a nonsymmetrical stenosis with applications,” Japanese Journal of Applied Physics, vol. 34, no. 12, pp. 6539–6545, 1995. View at Google Scholar · View at Scopus
  32. V. P. Srivastava, “Two-phase model of blood flow through stenosed tubes in the presence of a peripheral layer: applications,” Journal of Biomechanics, vol. 29, no. 10, pp. 1377–1382, 1996. View at Publisher · View at Google Scholar · View at Scopus
  33. R. N. Pralhad and D. H. Schultz, “Two-layered blood flow in stenosed tubes for different diseases,” Biorheology, vol. 25, no. 5, pp. 715–726, 1988. View at Google Scholar · View at Scopus
  34. N. Iida, “Influence of plasma layer on steady blood flow in micro vessels,” Japanese Journal of Applied Physics, vol. 17, pp. 203–214, 1978. View at Google Scholar
  35. E. W. Errill, “Rheology of blood,” Physiological Reviews, vol. 49, no. 4, pp. 863–888, 1969. View at Google Scholar · View at Scopus
  36. J.-J. Chiu, D. L. Wang, S. Chien, R. Skalak, and S. Usami, “Effects of disturbed flow on endothelial cells,” Journal of Biomechanical Engineering, vol. 120, no. 1, pp. 2–8, 1998. View at Google Scholar · View at Scopus
  37. G. G. Galbraith, R. Skalak, and S. Chien, “Shear stress induces spatial reorganization of the endothelial cell cytoskeleton,” Cell Motility and the Cytoskeleton, vol. 40, no. 4, pp. 317–330, 1998. View at Publisher · View at Google Scholar · View at Scopus
  38. T. Karino and H. L. Goldsmith, “Flow behaviour of blood cells and rigid spheres in an annular vortex,” Philosophical Transactions of the Royal Society of London B, vol. 279, no. 967, pp. 413–445, 1977. View at Google Scholar · View at Scopus