Skip to main content
SpringerLink
Log in

Two -fluid nonlinear mathematical model for pulsatile blood flow through catheterized arteries

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

Abstract

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The resulting system of the nonlinear implicit system of partial differential equations is solved by perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. The velocity and flow rate are observed to decrease, and the wall shear stress and resistance to flow increase when the yield stress increases. The plug flow velocity and flow rate decrease, and the longitudinal impedance increases when the catheter radius ratio increases. The velocity and flow rate increase while the wall shear stress and longitudinal impedance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the longitudinal impedance are significantly lower for the present two-fluid model than those of the single-fluid model.

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 algorithms, Journal of Engineering Mathematics, 42 (2002) 1–22.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  3. D. S. Sankar and K. Hemalatha, Pulsatile flow of Herschel-Bulkley fluid for blood flow through a catheterized artery — A mathematical model, Applied Mathematical Modeling, 31 (2007) 1497–1517.

    Article  MATH  Google Scholar 

  4. 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. 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 

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

    Article  Google Scholar 

  12. 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 

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

    Article  Google Scholar 

  14. D. S. Sankar and K. Hemalatha, Pulsatile flow of Herschel-Bulkley fluid through stenosed arteries — A mathematical model,” International Journal of Non-Linear Mechanics, 41 (2006) 979–990.

    Article  MATH  Google Scholar 

  15. G. Bugliarello and J. Sevilla, Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology, 7 (1970) 85–107.

    Google Scholar 

  16. G. R. Cokelet, The rheology of human blood, In: Biomech. (Edited by Y.C. Fung), Prentice-Hall, N. J., U. S. A, 1972.

    Google Scholar 

  17. 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 

  18. V. P. Srivastava and M. Saxena, Two-layered model of Casson fluid flow through stenotic blood vessels: Applications to the cardiovascular system,” Journal Biomechanics, 27 (1994) 921–928.

    Article  Google Scholar 

  19. D. S. Sankar and U. Lee, Two-phase non-linear model for the flow through stenosed blood vessels, Journal of Mechanical Science and Technology, 21 (2007) 678–689.

    Article  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 (2008) 1008–1018.

    Article  Google Scholar 

  21. E. W. Merrill, Rheology of blood, Physiological Reviews, 49 (1969) 863–888.

    Google Scholar 

Download references

Author information

Author notes

  1. D. S. Sankar & Usik Lee

    Present address: School of Mathematical Sciences, University Science Malaysia, 11800, Penang, Malaysia

Authors and Affiliations

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

    D. S. Sankar & 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 Gihun Son

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 nonlinear mathematical model for pulsatile blood flow through catheterized arteries. J Mech Sci Technol 23, 1650–1669 (2009). https://doi.org/10.1007/s12206-009-0355-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-009-0355-y

Keywords

Search

Navigation