Effect of body acceleration on pulsatile flow of Casson fluid through a mild stenosed artery

  • Nagarani, P. (Department of Mathematics & Computer Science, The University of the West Indies) ;
  • Sarojamma, G. (Department of Applied Mathematics, Sri Padmavati Women's University)
  • Published : 2008.12.31

Abstract

The pulsatile flow of blood through a stenosed artery under the influence of external periodic body acceleration is studied. The effect of non-Newtonian nature of blood in small blood vessels has been taken into account by modeling blood as a Casson fluid. The non-linear coupled equations governing the flow are solved using perturbation analysis assuming that the Womersley frequency parameter is small which is valid for physiological situations in small blood vessels. The effect of pulsatility, stenosis, body acceleration, yield stress of the fluid and pressure gradient on the yield plane locations, velocity distribution, flow rate, shear stress and frictional resistance are investigated. It is noticed that the effect of yield stress and stenosis is to reduce flow rate and increase flow resistance. The impact of body acceleration is to enhance the flow rate and reduces resistance to flow.

Keywords

References

  1. Arntzenius, A. C., J. D. Laird, A. Noordergraff, P. D. Verdouw and P. H. Huisman, 1972, Body acceleration synchronous with heart beat, Biophy. Cardiol. 29, 1-5
  2. Aroesty, J. and J. F. Gross, 1972a, The mathematics of pulsatile flow in small blood vessels, I. Casson theory, Micro Vascular Research 4, 1-12 https://doi.org/10.1016/0026-2862(72)90012-X
  3. Aroesty, J. and J. F. Gross, 1972b, Pulsatile flow in small blood vessels, I. Casson theory, Biorheology 9, 33- 42 https://doi.org/10.3233/BIR-1972-9104
  4. Belardinelli, E., M. Ursino and E. Lemmi, 1989, A preliminary theoretical study of arterial pressure perturbations under shock accelerations, ASME J. Biomech. Eng. 111, 233-240 https://doi.org/10.1115/1.3168372
  5. Burton, R. R., S. D. Leverett Jr and E. D. Michaelsow, 1974, Man at high sustained $+G_z$ acceleration: a review, Aerospace Med. 46, 1251-1253
  6. Caro, C. G., 1981, Recent advances in cardiovascular diseases- 2 (supplement), 6-11
  7. Charam, S. E. and G. S. Kurland, 1965, Viscometry of human blood for shear rates of 0-100,000 $sec^{−1}$, Nature 206, 617-618 https://doi.org/10.1038/206617a0
  8. Chaturani, P. and V. Palanisami, 1990a, Casson fluid model of pulsatile flow of blood flow under periodic body acceleration, Biorheol. 27, 619-630 https://doi.org/10.3233/BIR-1990-27501
  9. Chaturani, P. and V. Palanisami, 1990b, Pulsatile flow of powerlaw fluid model for blood flow under periodic body acceleration, Biorheol. 27, 747-758 https://doi.org/10.3233/BIR-1990-27510
  10. Cokelet, G. R., E. W. Merill, E. R. Gilliland, H. Shin, A. Britten and R. E. Wells, 1963, The rheology of human blood -measurement near and at zero shear rate, Trans. Soc. Rheol. 7, 303-317 https://doi.org/10.1122/1.548959
  11. Dintenfass, L., 1977, Viscosity factors in hypertensive and cardiovascular diseases, Cardiovascular Medicine 2, 337-353
  12. El-Shahed, M., 2003, Pulsatile flow of blood through a stenosed porous medium under periodic body acceleration, Applied Mathematics and Computation 138, 479-488 https://doi.org/10.1016/S0096-3003(02)00164-9
  13. Elshehawey, E. F., E. M. E. Elbarbary, M. E. Elsayed, N. A. S. Afifi and M. El-Shahed, 2000, Pulsatile flow of blood through a porous medium under periodic body acceleration, Int. Journal of theoretical Physics 39(1), 183-188 https://doi.org/10.1023/A:1003611604207
  14. Fry, D. I., 1968, Acute vascular endothelial changes associated with increased blood velocity gradients, Circulation Research 22, 165-197 https://doi.org/10.1161/01.RES.22.2.165
  15. Fung, Y. C., 1986, Biomechanics, Mechanical properties of living tissues, Springer-Verlag, New York, 68-81
  16. Hiatt, E. P., J. P. Meechan and Galambos, 1969, Reports on human acceleration, Washington, D.C, publication 901, NASNRC
  17. Mandal, P. K., S. Chakravarthy, A. Mandal and N. Amin, 2007, Effect of body acceleration on unsteady pulsatile flow of non- Newtonian fluid through a stenosed artery, Applied Mathematics and Computation 189, 766-779 https://doi.org/10.1016/j.amc.2006.11.139
  18. Majhi, S. N. and V. R. Nair, 1994, Pulsatile flow of third grade fluids under body acceleration - modelling blood flow, Int. J. Eng. Sci. 32, 839-846 https://doi.org/10.1016/0020-7225(94)90064-7
  19. Merrill, E. W., A. M. Benis, E. R. Gilliland, T. K. Sherwood and E. W. Salzman, 1965, Pressure flow relations of human blood in hollow fibre at low shear rates, Appl. Physiol. 20, 954-967 https://doi.org/10.1152/jappl.1965.20.5.954
  20. Merrill, E. W. and G. A. Pelletier, 1967, Viscosity of human blood: transition from Newtonian to non-Newtonian, J. Appl. Physiol. 23, 178-182 https://doi.org/10.1152/jappl.1967.23.2.178
  21. Misra, J. C. and B. K. Sahu, 1988, Flow through blood vessels under the action of a periodic acceleration field: a mathematical analysis, Comput. Math. Appl. 16, 993-1016 https://doi.org/10.1016/0898-1221(88)90256-8
  22. Sarojamma, G. and P. Nagarani, 2002, Pulsatile flow of Casson fluid in a homogeneous porous medium subject to external acceleration, Int. J. of Non-Linear Differential Equations Theory-Methods and Applications 7, 50-64
  23. Scott Blair, G. W., 1959, An equation for flow of blood serum through glass tubes, Nature 183, 613-614 https://doi.org/10.1038/183613a0
  24. Sud, V. K. and G. S. Sekhon, 1985, Arterial flow under periodic body acceleration, Bull. Math. Biol. 47, 35-52 https://doi.org/10.1007/BF02459645
  25. Usha, R. and K. Prema, 1999, Pulsatile flow of particle-fluid suspension model of blood under periodic body acceleration, ZAMP 50, 175-192 https://doi.org/10.1007/s000330050145
  26. Verdouw, P. D., A. Noordergraff, A. C. Arntzenius and P. H. Huisman, 1973, Relative movement between subject and support in body acceleration applied synchronously with the heartbeat (BASH), Biophy. Cardiol. 31, 57-62
  27. Young, D. F., 1968, Effect of a time-dependent stenosis on flow through a tube, J. Engng. Ind. Trans. ASME 90, 248-254 https://doi.org/10.1115/1.3604621