Skip to main content
SpringerLink
Log in

Two-fluid non-Newtonian models for blood flow in catheterized arteries — A comparative study

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

Steady flow of blood through catheterized arteries is studied by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is modeled as (i) Casson fluid and (ii) Herschel-Bulkley fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress and flow resistance, obtained by Sankar and Lee (2008a, 2008b) for the two-fluid Casson model and two-fluid Herschel-Bulkley model are used to get the data for comparison. It is noticed that the plug flow velocity, velocity distribution and flow rate for the two-fluid H-B model are considerably higher than that of the two-fluid Casson model for a given set of values of the parameters. Further, it is found that the resistance to flow is significantly lower for the two-fluid H-B model than that of the two-fluid Casson model. Thus, the two-fluid H-B model is more useful than the two-fluid Casson model to analyze the blood flow through catheterized arteries.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Daripa and R. K. Dash, A numerical study of pulsatile blood flow in an eccentric catheterized artery using a fast algorithm, Journal Engineering Mathematics 42 (2002) 1–22.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. K. Dash, G. Jayaraman and K. N. Metha, Flow in a catheterized curved artery with stenosis, Journal of Biomechanics 32 (1999) 49–61.

    Article  Google Scholar 

  3. L. H. Back, Estimated mean flow resistance increase during coronary artery catheterization, Journal of Biomechanics 27 (1994) 169–175.

    Article  Google Scholar 

  4. L. H. Back, E. Y. Kwack and M. R. Back, Flow rate-pressure drop relation in coronary angioplasty: Catheter obstruction effect, ASME Journal of Biomechanical Engineering 118 (1996) 83–89.

    Article  Google Scholar 

  5. G. Jayaraman and R. K. Dash, Numerical study of flow in a constricted curved annulus: An application to flow in a catheterized artery, Journal of Engineering Mathematics 40 (2001) 355–376.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Sarkar and G. Jayaraman, Correction to flow rate-pressure drop relation in coronary angioplasty: Steady streaming effect, Journal of Biomechanics 31 (1998) 781–791.

    Article  Google Scholar 

  7. D. A. MacDonald, Pulsatile flow in a catheterized artery, Journal of Biomechanics 19 (1986) 239–249.

    Article  Google Scholar 

  8. G. T. Karahalios, Some possible effects of a catheter on the arterial wall, Medical Physics 17 (1990) 922–925.

    Article  Google Scholar 

  9. G. Jayaraman, and K. Tiwari, Flow in a catheterized curved artery, Medical and Biological Engineering and Computing 33 (1995) 1–6.

    Article  Google Scholar 

  10. C. Tu and M. Deville, Pulsatile flow of non-Newtonian fluids through arterial stenosis, Journal of Biomechanics 29 (1996) 899–908.

    Article  Google Scholar 

  11. R. K. Dash, G. Jayaraman and K. N. Metha, Estimation of increased flow resistance in a narrow catheterized artery — A theoretical model, Journal of Biomechanics 29 (1996) 917–930.

    Article  Google Scholar 

  12. P. Chaturani and R. Ponnalagar Samy, A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases, Biorheology 22 (1985) 521–531.

    Google Scholar 

  13. P. Chaturani and R. Ponnalagar Samy, Pulsatile flow of a Casson fluid through stenosed arteries with application to blood flow, Biorheology 23 (1986) 499–511.

    Google Scholar 

  14. L. H. Back, Estimated mean flow resistance increase during coronary artery catheterization, Journal of Biomechanics 27 (1994) 169–175.

    Article  Google Scholar 

  15. S. Chakravarthy, S. Sarifuddin and P.K. Mandal, Unsteady flow of a two-layer blood stream past a tapered flexible artery under stenotic conditions, Computational Methods in Applied Mathematics 4 (2004) 391–409.

    MathSciNet  Google Scholar 

  16. J. C. Misra and S. K. Pandey, Peristaltic transport of blood in small vessels: Study of a mathematical model, Computers and Mathematics with Applications 43 (2002) 1183–1193.

    Article  MATH  MathSciNet  Google Scholar 

  17. 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 27 (1994) 921–928.

    Article  Google Scholar 

  18. J. B. Shukla, R. S. Parihar and S. P. Gupta, Biorheological aspects of blood flow through artery with mild stenosis: Effects of peripheral layer, Biorheology 17 (1980) 403–410.

    Google Scholar 

  19. M. Sharan and A.S. Popel, A two-phase model for flow of blood in narrow tunes with increased effective viscosity near the wall, Biorheology 28 (2001) 415.

    Google Scholar 

  20. D. S. Sankar and U. Lee, Two-fluid Herschel-Bulkley model for blood flow in catheterized arteries, Journal of Mechanical Science and Technology 22 (2008a) 1008–1018.

    Article  Google Scholar 

  21. D. S. Sankar and U. Lee, Two-fluid non-linear model for flow in catheterized blood vessels, Int. J. Non-Linear Mechanics 43 (2008b) 622–631.

    Article  Google Scholar 

  22. G. W. Scott Blair and D. C. Spanner, An introduction to Biorheology, Elsevier Scient. Publ. Co., Amsterdam, Oxford and New York (1974).

    Google Scholar 

  23. N. Iida, Influence of plasma layer on steady blood flow in microvessels, Japanese Journal of Applied Physics 17 (1978) 203–214.

    Article  Google Scholar 

  24. D. S. Sankar, and K. Hemalatha, A Non-Newtonian fluid flow model for blood flow through a catheterized artery — Steady flow, Applied Mathematical Modeling 31 (2007) 1847–1864.

    Article  MATH  Google Scholar 

  25. R. F. Wilson, M. R. Johnson, M. L. Marcus, P. E.G. Alyward, D. J. Skorton, S. Collings and C. W. White, The effect of coronary angioplasty on coronary flow reserv, Circulation 77 (1988) 873–885.

    Google Scholar 

  26. E. L. Johnson, P. G. Yock, V. K. Hargrave, J. P. Srebro, S. M. Manubens, W. Seitz and T. A. Ports, Assessment of severity of coronary stenosis using a Doppler catheter. Validation of a method based on the continuity equation, Circulation 80 (1989) 625–635.

    Google Scholar 

  27. P. Ganz, D. P. Harrington, J. Gaspar and W. H. Barry, Phasic pressure gradients across coronary and renal artery stenosis in humans, Am. Heart J. 106 (1983) 399–1406.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    D. S. Sankar

  2. Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon, 402-751, Republic of Korea

    Usik Lee

Authors
  1. D. S. Sankar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Usik Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Usik Lee.

Additional information

This paper was recommended for publication in revised form by Associate Editor Haecheon Choi

Dr. D. S. Sankar received his B. Sc degree in Mathematics from the University of Madras, India, in 1989. He then received his M.Sc, M. Phil and Ph.D. degrees from Anna University, India in 1991, 1992 and 2004, respectively. Dr. D. S. Sankar is currently working at the School of Mathematical Sciences, University Science Malaysia, Malaysia. He serves as a referee for several reputed international journals. Dr. D. S. Sankar’s research interests include Fluid Dynamics, Hemodynamics, Differential Equations and Numerical Analysis.

Dr. Usik Lee received his B.S. degree in Mechanical Engineering from Yonsei University, Korea in 1979. He then received his M.S. and Ph.D. degrees in Mechanical Engineering from Stanford University, USA in 1982 and 1985, respectively. Dr. Lee is currently a Professor at the Department of Mechanical Engineering at Inha University in Incheon, Korea. He serves as a referee for many reputed international journals. Dr. Lee’s research interests include structural dynamics, biomechanics, and computational mechanics.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sankar, D.S., Lee, U. Two-fluid non-Newtonian models for blood flow in catheterized arteries — A comparative study. J Mech Sci Technol 23, 2444–2455 (2009). https://doi.org/10.1007/s12206-009-0708-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-009-0708-6

Keywords

Search

Navigation