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Oscillatory Viscoelastic Model of Blood Flow in Stenotic Artery

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Abstract

An analytic solution for the two-layered model of pulsatile blood flow in stenotic arteries is discussed. The blood flow in narrow arteries is assumed to obey the two-fluid model: non-Newtonian viscoelastic as Jeffrey fluid in core region, and Newtonian as plasma fluid in peripheral region. The present study is aimed to develop an oscillatory viscoelastic model of blood flow and obtain the analytic expressions for velocity of pulsatile blood flow in a stenotic artery. The velocity of pulsatile blood flow is used to discuss the wall shear stress and volume flow rate through stenotic artery and to relate relaxation time, retardation time, height of the stenosis with the velocity, volume flow rate and wall shear stress. The solution of the model boundary value problem is obtained by the method of special functions under the assumption of steady oscillations. It is found that the velocity is directly proportional to relaxation time and on the other hand retardation time is inversely proportional. For non-zero time period, the wall shear stress increases as relaxation time increases and decreases as retardation time increases. It reveals a significant influence of relaxation and retardation time on oscillatory blood flow in stenotic artery under the pathological state of cardiovascular disease.

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REFERENCES

  1. Lambossy, P., Helv. Phys. Acta, 1952, vol. 25, p. 371.

    CAS  Google Scholar 

  2. Peterson, L.H., Circ. Res., 1954, vol. 2, p. 127.

    Article  CAS  Google Scholar 

  3. Womersley, J.R., J. Physiol., 1955, vol. 127, p. 553.

    Article  CAS  Google Scholar 

  4. Hale, J.F., McDonald, D.A., and Womersley, J.R., J. Physiol., 1955, vol. 128, p. 629.

    Article  CAS  Google Scholar 

  5. McDonald, D.A., J. Physiol., 1955, vol. 127, p. 533.

    Article  CAS  Google Scholar 

  6. Womersley, J.R., Phys. Med. Biol., 1957, vol. 2, p. 178.

    Article  CAS  Google Scholar 

  7. Martin, A.T., Nicholas, D.S., and Teoman, A., J. Rhe-ol. (NY), 1973, vol. 17, p. 1.

    Google Scholar 

  8. Gopalan, N.P., B. Math. Biol., 1981, vol. 43, p. 563.

    Article  CAS  Google Scholar 

  9. Fåhraeus, R., Physiol. Rev., 1929, vol. 9, p. 241.

  10. Fåhraeus, R. and Lindqvist, T., Am. J. Physiol.-Legacy Content, 1931, vol. 96, p. 562.

  11. Bugliarello, G. and Sevilla, J., Biorheology, 1970, vol. 70, p. 85.

    Article  Google Scholar 

  12. Chakravarty, S. and Datta, A., Math. Comput. Model., 1992, vol. 16, p. 35.

    Article  Google Scholar 

  13. Sankar, D.S. and Ismail, A.I.M., Bound. Value Probl., 2009, Article no. 568657.

  14. Sankar, D.S. and Lee, U., J. Mech. Sci. Technol., 2007, vol. 21, p. 678.

    Article  Google Scholar 

  15. Srivastava, V.P. and Saxena, M., J. Biomech., 1994, vol. 27, p. 921.

    Article  CAS  Google Scholar 

  16. Tiwari, A. and Chauhan, S.S., Cardiovasc. Eng. Tech., 2019, vol. 10, p. 155.

    Article  Google Scholar 

  17. Sharma, B.D., Yadav, P.K., and Filippov, A.N., Colloid J., 2017, vol. 79, p. 849.

    Article  CAS  Google Scholar 

  18. Sharma, B.D. and Yadav, P.K., Transport Por. Media, 2017, vol. 120, no. 1, p. 239.

    Article  Google Scholar 

  19. Misra, J.C., Patra, M.K., and Sahu, B.K., Comput. Math. Appl., 1992, vol. 24, p. 19.

    Article  Google Scholar 

  20. Pontrelli, G., Comput. Fluids, 1998, vol. 27, p. 367.

    Article  Google Scholar 

  21. Khadrawi, A.F., Al-Nimr, M.A., and Othman, A., Chem. Eng. Sci., 2005, vol. 60, p. 7131.

    Article  CAS  Google Scholar 

  22. Sankar, D.S. and Lee, U., Commun. Nonlin. Sci., 2010, vol. 15, p. 2086.

    Article  Google Scholar 

  23. Young, D.F., J. Eng. Ind., 1968, vol. 90, p. 248.

    Article  Google Scholar 

  24. Rao, R.A., Acta Mech., 1983, vol. 46, p. 155.

    Article  Google Scholar 

  25. Bugliarello, G., J. Rheol. (NY), 1963, vol. 7, p. 209.

    Google Scholar 

  26. Haynes, R.H., Am. J. Physiol., 1960, vol. 198, p. 1193.

    Article  CAS  Google Scholar 

  27. Blair, G.W., Rheol. Acta, 1972, vol. 11, p. 237.

    Article  Google Scholar 

  28. Charm, S. and Kurland, G.S., Am. J. Physiol., 1962, vol. 203, p. 417.

    Article  CAS  Google Scholar 

  29. Ponalagusamy, R. and Tamil Selvi, R., Meccanica, 2013, vol. 48, p. 2427.

    Article  Google Scholar 

  30. Katritsis, D., Kaiktsis, L., Chaniotis, A., Pantos, J., Efstathopoulos, E.P., and Marmarelis, V., Prog. Cardiovasc. Dis., 2007, vol. 49, p. 307.

    Article  Google Scholar 

  31. Nallapu, S. and Radhakrishnamacharya, G., Int. J. Sci. Eng. Res., 2013, vol. 4, p. 468.

    Google Scholar 

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Funding

First author is thankful to SERB, New Delhi for supporting this research work under the research grant SR/FTP/MS-47/2012.

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, India

    Pramod Kumar Yadav

  2. Department of Mathematics, VIT-AP University Amaravati, Andhra Pradesh, 522237, Amaravati, India

    Bhupesh Dutt Sharma

  3. Department of Higher Mathematics, National University of Oil and Gas “Gubkin University”, 119991, Moscow, Russia

    A. N. Filippov

Authors
  1. Pramod Kumar Yadav
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  2. Bhupesh Dutt Sharma
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  3. A. N. Filippov
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Correspondence to A. N. Filippov.

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Yadav, P.K., Sharma, B.D. & Filippov, A.N. Oscillatory Viscoelastic Model of Blood Flow in Stenotic Artery. Colloid J 82, 617–625 (2020). https://doi.org/10.1134/S1061933X20050178

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  • DOI: https://doi.org/10.1134/S1061933X20050178

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