Paper Details

A MATHEMATICAL STUDY OF BLOOD FLOW THROUGH STENOSED ARTERY

Vol. 1, Jan-Dec 2015 | Page: 26-37

Sapna Ratan Shah
Department of Mathematics, Harcourt Butler Technological Institute, Kanpur - 208002, (India)

Received: 05-01-2015, Accepted: 10-02-2015, Published Online: 18-02-2015


. Download Full Paper

Abstract

This paper deals with the rheological character of blood flow through stenosed artery by assuming blood as Bingham Plastic and Herschel-Bulkley fluid model. The irregularity of artery geometry is a frequent effect of vascular disease. Such constrictions disturb normal blood flow through the vessel. The results show that blood pressure increases very significantly in the upstream zone of the stenotic artery as the degree of the stenosis area severity increases. It is also shown that the non-Newtonian behaviour of blood has significant effects on the velocity profile of the blood flow and the magnitude of the wall shear stresses. It has been concluded in this paper that the Herschel-Bulkley fluid model is more realistic in comparison to Bingham Plastic fluid model. Present model is able to predict the main characteristics of the physiological flow of blood

References

  1. Texon, M., A homodynamic concept of atherosclerosis with particular refere nce to coronary occlusion. 99. 418: (1957).
  2. May, A. G., Deweese, J. A. and Rob, C. B., Hemodynamic effects of arterial stenosis. Surgery, 53: 513-524. (1963).
  3. Hershey, D., Cho, S. J., Blood flow in ridig tubes: Thickness and slip veloc ity of plasma film at the wall. J. Appli. Physiolo.21:27. ( 1966).
  4. Young, D. F., Effects of a time-dependent stenosis on flow through a tube. J. Eng. India. Trans. ASME. 90: 248-254. (1968).
  5. Forrester, J. H. and Young, D. F., Flow through a converging diverging tube and its implications in occlusive vascular disease. J. Biomech. 3: 297-316. (1970).
  6. Caro, C. G., Fitz-Gerald J. M., and Schroter R. C., Atheroma and arterial wall shear observation, Correlation and proposal of a shear dependent mass transfer mechanism for Atherogenesis. Proc. R. Soc. 177: 109-159. (1971).
  7. Fry, D. L., Localizing factor in arteriosclerosis, In atherosclerosis and coronary heart disease, NewYork: Grune Stratton. 85, (1972)
  8. Young, D. F. and Tsai, F. Y., Flow characteristics in models of arterial stenosis–II, unsteady flow. J. Biomech. 6: 547-558. (1973).
  9. Lee, J. S., On the coupling and detection of motion between an artery with a localized lesion and its surrounding tissue. J. Biomech. 7: 403. (1974).
  10. Richard, L. K., Young, D. F. and Chalvin, N. R., Wall vibrations induced by flow through simulated stenosis in models and arteries. J. Biomech. 10: 431. (1977).
  11. Charm, S. E., and Kurland G. S., Viscometry of human blood for shear rate of 100,000sec-1 . Nature London. 206: 617-618. (1965).
  12. Hershey, D., Byrnes, R. E., Deddens, R. L. and Roa. A. M., Blood rheology: Temperature dependence of the power law model. Paper presented at A.I.Ch.E. Boston (1964).
  13. Whitmore R. L., Rheology of the circulation, Perg NewYork (1968).
  14. Cokelet, G. R., The rheology of human blood. In Biomechanics, Ed. By Y. C. Fung et al., 63, Englewood Cliffs: Prentice-Hall, (1972).
  15. Lih, M.M, Transport Phenomena in Medicine and Biology. Wiley, New York, (1975).
  16. Shukla, J. B., Parihar, R. S., Gupta, S. P.,Biorheological aspects of blood flow through artery with mild stenosis:Effects of peripheral layer.Biorhe.17:403-410. (1990)
  17. Casson, N. A flow equation for pigment oil suspensions of the printing ink type. In Rheology of disperse systems, Ed. Mill., C.C., London. 84-102. (1959).
  18. Reiner, M. and Scott Baldair G.W., The flow of the blood through narrow tube. Nature, London, 184: 354-359, (1959).
  19. Labarbera, M., Principles of design of fluid transport systems in zoology. Science. 249: 992- 1000. (1997)
  20. K. Haldar, Effects of the shape of stenosis on the resistance to blood flow through an artery. Bull. Mathe. Bio. 47: 545-550. (1985).
  21. Pontrelli, G., “Blood flow through an axisymmetric stenosis”, Proc. Inst Mech. Eng, Part H, Eng Med., 215: 1-10. (2013).
  22. Tandon, P. N., Nirmala, P., Tewari, M. and Rana, U. S., Analysis of nutritional transport through a capillary: Normal and stenosed. Compu. Math. Appli. 22. 12: 3-13, (1991).
  23. Jung, H., Choil, J. W. and Park, C. G., (2011) “Asymmetric flows of non-Newtonian fluids in symmetric stenosis artey” Vol. 16, 2 june pp. 101-108.