Skip to main content
SpringerLink
Log in

Pulsatile flow of blood through a 2D double-stenosed channel: effect of stenosis and pulsatility on wall shear stress

  • Published:
International Journal of Advances in Engineering Sciences and Applied Mathematics Aims and scope Submit manuscript

Abstract

Numerical simulations are performed for two-dimensional steady and pulsatile flow of blood through a channel with single as well as double stenosis (with varying gap) under aortic conditions (Re = 4000). A shear-thinning model based on experimental data is used for blood. The governing equations are developed in terms of vorticity and stream function and solved using a finite difference scheme with full-multigrid algorithm. Peak wall shear stress increases with both length of stenosis, and gap between stenosis; however, the effect of increasing length is much more compared to gap. Pulsatility plays a key role by shifting the location of peak wall shear stress from the primary to the secondary stenosis, and back again, during a cycle. This result is of importance when developing a model for plaque growth based purely on mechanical factors.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Anand, M., Rajagopal, K.R.: A shear-thinning viscoelastic fluid model for describing the flow of blood. Int J Cardiovasc Med Sci 4, 59–68 (2004)

    Google Scholar 

  2. Bodnar, T., Sequeira, A., Pirkl, L.: Numerical simulations of blood flow in a stenosed vessel under different flow rates using a generalized oldroyd-b model. Proceedings of AIP, Vol 1168, pp 645–648 (2009)

  3. Chakravarty, S., Dutta, A.: Dynamic response of arterial blood flow in the presence of multi-stenoses. Math Comput Model 13, 37–55 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chaturani, P., Ponnalagarsamy, R.: Pulsatile flow of Casson’s fluid through stenosed artery with applications to blood flow. Biorheology 23, 499–511 (1986)

    Google Scholar 

  5. Chien, S., Usami, S., Taylor, H.M., Lundberg, J.L., Gregersen, M.I.: Effects of hematocrit and plasma proteins on human blood rheology at low shear rates. J Appl Physiol 21(1), 81–7 (1966)

    Google Scholar 

  6. Deshpande, M.D., Giddens, D.P., Mabon, R.F.: Steady laminar flow through modeled vascular stenoses. J Biomech 9(4), 165–174 (1976)

    Article  Google Scholar 

  7. Tang, D., Yang, C., Kobayashi, S., Ku, D.N.: Generalized finite difference method for 3-D viscous flow in stenotic tubes with large wall deformation and collapse. Appl Numer Math 38, 49–68 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gould, K.L., Lipscomb, K.: Effects of coronary stenoses on coronary flow reserve and resistance. Am J Cardiol 34, 48–55 (1974)

    Article  Google Scholar 

  9. Ikbal, M.A.: Viscoelastic blood flow through arterial stenosis–effect of variable viscosity. Int J Non-Linear Mech 47, 888–894 (2012)

    Article  Google Scholar 

  10. David, NKu: Blood flow in arteries. Annu Rev Fluid Mech 29, 399–434 (1997)

    Article  MathSciNet  Google Scholar 

  11. Lee, T.S.: Numerical studies of fluid flow through tubes with double constrictions. Int J Numer Methods Fluids 11, 1113–1126 (1989)

    Article  MATH  Google Scholar 

  12. MacDonald, D.A.: On steady flow through modeled vascular stenosis. J Biomech 12(1), 13–20 (1979)

    Article  Google Scholar 

  13. Malek, A.M., Alper, L.S., Izumo, s: Hemodynamic shear stress and its role in atherosclerosis. J Am Med Assoc 282(21), 2035–2042 (1999)

    Article  Google Scholar 

  14. Mandal, D.K., Manna, N.K., Chakrabarti, C.: Numerical study of blood flow through different double bell- shaped stenosed coronary artery during the progression of the disease, atherosclerosis. Int J Numer methods Heat Fluid Flow 6, 670–699 (2010)

    Article  Google Scholar 

  15. Mandal, M.S., Mukhopadhyay, S., Layek, G.C.: Pulsatile flow of shear-dependent fluid in a stenosed artery. Theor Appl Mech 39, 209–231 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mandal, P.K., Chakravarty, S., Mandal, A.: Numerical study of the unsteady flow of non-Newtonian fluid through differently shaped arterial stenoses. Int J Comput Math 84, 1059–1077 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Marieb, E.N.: Human Anatomy and Physiology. Pearson Education, Inc, 6th edition, (2006)

  18. Moore, K.L.: Clinically oriented anatomy. Williams and Wilkins, Baltimore (1990)

    Google Scholar 

  19. Nadau, L., Sequeira, A.: Numerical simulations of shear dependent viscoelastic flows with a combined finite element-finite volume method. Comput Math Appl 53, 547–568 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Nichols, W.W., O’Rourke, M.F., Vlachopoulos, C., McDonald’s.: Blood Flow in Arteries: Theoretical, Experimental, and Clinical Principles, pages 48–53. CRC Press, Boca Raton, 6th edition, (2011)

  21. NandaKumar, N., Sahu, K.C., Anand, M.: Blood flow in stenosed artery: a computational study. Hyderabad TS, India., 2014. (poster presentation)IUTAM symposium

  22. NandaKumar, N., Kirti Chandra, Sahu, Anand, M.: Pulsatile flow of a shear-thinning fluid through a two-dimensional channel with a stenosis. Eur J Mech B-Fluid 49, 29–35 (2015)

    Article  Google Scholar 

  23. Owens, R.G.: A new microstructure-based constitutive model for human blood. J Non-Newton Fluid Mech 140, 57–70 (2006)

    Article  MATH  Google Scholar 

  24. Pincombe, B., Mazumdar, J.: The effects of post stenotic dilations on the flow of a blood analogue through stenosed coronary arteries. Math Comput Model 26(6), 57–70 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pontrelli, G.: Pulsatile blood flow in a pipe. Comput Fluids 27, 367–380 (1998)

    Article  MATH  Google Scholar 

  26. Pontrelli, G.: Blood flow through an axisymmetric stenosis. Proc Inst Mech Eng 215, 1–10 (2001)

    Article  Google Scholar 

  27. Sabbah, H.N., Stein, P.D.: Hemodynamics of multiple versus single 50 percent coronary arterial stenoses. Am J Cardiol 50, 276–280 (1982)

    Article  Google Scholar 

  28. Sahu, K.C.: Novel Stability problems in pipe flows. PhD thesis, JNCASR, Bangalore, Karnataka (2007)

  29. Sankar, D.S., Hemalatha, K.: Pulsatile flow of Herschel-Bulkley fluid through stenosed arteries–a mathematical model. Int J Non-Linear Mech 41, 979–990 (2006)

    Article  MATH  Google Scholar 

  30. Sarifuddin, Chakravarty, S., Mandal, P.K.: Effect of asymmetry and roughness of stenosis on non-Newtonian flow past an arterial segment. Int J Comput Methods 6, 361–388 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. Stroud, J.S., Berger, S.A., Saloner, D.: Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture. J Biomech 33(4), 443–455 (2000)

    Article  Google Scholar 

  32. Tannehill, J.C., Anderson, D.A., Pletcher, R.H.: Computational fluid mechanics and heat transfer, 2nd edn. Taylor & Francis, Washington (1997)

    MATH  Google Scholar 

  33. Thurston, G.B.: Viscoelasticity of human blood. J Biophys 12, 1205–1217 (1972)

    Article  Google Scholar 

  34. Tu, C., Deville, M., Dheur, L., Vanderschuren, L.: Finite-element simulation of pulsatile flow through arterial stenosis. J Biomech 25(10), 1141–1152 (1992)

    Article  Google Scholar 

  35. Wille, S.O., Wallloe, L.: Pulsatile pressure and flow in arterial stenosis simulated in a mathematical model. J Biomed Eng 3, 17–24 (1981)

    Article  Google Scholar 

  36. Yeleswarapu. K.K.: Evaluation of continuum models for characterizing the constitutive behavior of blood. PhD thesis, University of Pittsburgh, Pittsburgh, (1996)

  37. Yeleswarapu, K.K., Kameneva, M.V., Rajagopal, K.R., Antaki, J.F.: The flow of blood in tubes: theory and experiment. Mech Res Comm 25, 257–262 (1998)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

We thank Dr. Kirti Chandra Sahu for his valuable suggestions. NN was supported by the MHRD Fellowship for Research Scholars administered by IIT Hyderabad. We thank the Science and Engineering Research Board (SERB), of the Department of Science and Technology, for funding this work under the Fasttrack Scheme for Young Scientists Grant No. SR/FTP/ETA-16/2011.

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana, 502285, India

    N. Nandakumar & M. Anand

Authors
  1. N. Nandakumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Anand
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Anand.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nandakumar, N., Anand, M. Pulsatile flow of blood through a 2D double-stenosed channel: effect of stenosis and pulsatility on wall shear stress. Int J Adv Eng Sci Appl Math 8, 61–69 (2016). https://doi.org/10.1007/s12572-016-0165-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12572-016-0165-2

Keywords

Search

Navigation