Skip to main content

Computational Study of Blood Flow Through Elastic Arteries with Porous Effects

  • Conference paper
  • First Online:
Proceedings of the Third International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 258))

Abstract

In this paper, two different non-Newtonian models for blood flow, first a sample power law model displaying shear thinning viscosity, and second a generalized Maxwell model displaying both shear thinning viscosity and oscillating flow viscous-elasticity have been considered. The investigation depicts that the model considered here is capable of taking into account the rheological properties affecting the blood flow and hemodynamical features, which may be important for medical doctors to predict diseases for individuals on the basis of the pattern of flow for an elastic artery in porous effects. The governing equations have been solved by Crank-Nichlson technique. The results are interpreted in the context of blood in the elastic arteries keeping the porous effects view.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Berger, S.A., Jou, L.D.: Flows in Stenotic vessels. Annu. Rev. Fluid Mech. 32, 347–384 (2000)

    Article  MathSciNet  Google Scholar 

  2. Datta, A., Tarball, J.M.: Influence of non-Newtonian behavior of blood on flow in an elastic artery model. ASME, J. Biomech. Eng 118, 111–119 (1996)

    Article  Google Scholar 

  3. Greenfield, J.C., Patel, D.J.: Relation between pressure and diameter in the ascending Aorta of man. Circ. Res. 10, 778 (1962)

    Article  Google Scholar 

  4. Katiyar, V.K., Mbah, G.C.: Effect of time dependant stenosis on the pulsetile flow through an elastic tube. In: International Conference on Mathematical and its Application in Engineering and Industries, pp. 439–447. Narosa Publishing House (1997)

    Google Scholar 

  5. Karner, G., Perktold, K.: Effect of endothelial and increased blood process on albumin accumulation in the arterial wall: a numerical study. J. Biomech. 33, 709–715 (2000)

    Article  Google Scholar 

  6. Korenga, R., Ando, J., Kamiya, A.: The effect of laminar flow on the gene expression of the adhesion molecule in endothelial cells. Jpn. J. Med. Electron. Bio. Eng. 36, 266–272 (1998)

    Google Scholar 

  7. Lee, R., Libby, P.: The unstable atheroma, atherosclerosis thrombosis vascular Biology. 17, 1859–1867 (1997)

    Google Scholar 

  8. Liepsch, D., Moravec, S.: Pulsatile flow of non-Newtonian fluid in distensible models of human arteries. Biorheology 21, 571–583 (1984)

    Google Scholar 

  9. Milnor, W.R.: Hemodynamics, 2nd edn. Williams and Wilkins, Baltmore (1989)

    Google Scholar 

  10. Nazemi, M., Kleinstreuer, C., Archie, J.P.: Pulsatile two-dimensional flow and plaque formation in a carotid artery bifurcation. J. Biomech. 23(10), 1031–1037 (1990)

    Article  Google Scholar 

  11. Patel, D.J., Janicki, J.S., Vaishnav, R.N., Young, J.T.: Dynamic anisotropic visco-elastic properties of the aorta in living dogs. Circ. Res. 32, 93 (1973)

    Article  Google Scholar 

  12. Perktold, K., Thurner, E., Kenner, T.: Flow and stress characteristics in rigid walled compliant carotid artery bifurcation models. Med. Biol. Eng. Compu. 32, 19–26 (1994)

    Article  Google Scholar 

  13. Rees, J.M., Thompson, D.S.: Shear stress in arterial stenoses: a momentum integral model. J. Biomech. 31, 1051–1057 (1999)

    Article  Google Scholar 

  14. Rodkiewicz, C.M., Sinha, P., Kennedy, J.S.: On the application of constitutive equation for whole human blood. J. Biomech. Eng. 112, 198–206 (1990)

    Article  Google Scholar 

  15. Sharma, G.C., Kapoor, J.: Finite element computation of two-dimensional arterial flow in the presence of a transverse magnetic field. Int. J. numerical methods in fluid dynamics 20, 1153–1161 (1995)

    Article  MATH  Google Scholar 

  16. Sharma, G.C., Jain, M., Kumar, A.: Finite element Galerkin’s approach for a computational study of arterial flow. Appl. Math. Mech, China 22(9), 1012–1018 (2001)

    MATH  Google Scholar 

  17. Anil Kumar, C.L., Varshney, G. C., Sharma.:Computational technique for flow in blood vessels with porous effects. Int. J. Appl. Math. Mech. (Engl. Ed) 26(1) 63–72 (2005)

    Google Scholar 

  18. Anil Kumar, C.L., Varshney, G.C., Sharma.: Performance modeling and analysis of blood flow in elastic arteries, Int. J. Appl. Math. Mech (Engl. Ed) 26(3) 345–354 (2005)

    Google Scholar 

  19. Srivastava, V.P.: Arterial blood flow through a non-symmetrical stenosis with applications. Jpn. J. Appl. Phy 34, 6539–6545 (1995)

    Article  Google Scholar 

  20. 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, pp. 443–455 (2000)

    Google Scholar 

  21. Thurston, G.B.: Rheological parameter for the viscosity, visco-elasticity and Thrixotropy of blood. Biorheology 16, 149–155 (1979)

    Google Scholar 

  22. Tang, D., Yang, C., Huang, Y., Ku, D.N.: Wall stress and strain analysis using a three-dimensional thick wall model with fluid-structure interactions for blood flow in carotid arteries with stenoses. Comput. Struct 72, 341–377 (1999)

    Article  MATH  Google Scholar 

  23. Walburn, F.J., Schneck, D.J.: A constitutive equation for whole human blood. Biorheology 18, 201 (1976)

    Google Scholar 

  24. White, K.C.: Hemo-dynamics and wall shear rate measurements in the abdominal aorta of dogs. Ph.D. thesis, The Pennsylvania State University (1979)

    Google Scholar 

  25. Anil Kumar: Mathematical model of Blood flow in Arteries with Porous Effects, International Federation for Medical and Biological Engineering (IFMBE). Conference 6th World Congress on Biomechanics (WCB 2010). In: Edited by C.T. Lim and J.C.H. Goh (Eds.): WCB 2010, International Federation for Medical and Biological Engineering (IFMBE) Proceedings 31 Springer Publishing, DOI: 10.1007/978-3-642-14515-5_5 pp. 18–21, 2010

    Google Scholar 

  26. Shigeru, T., Tarbell, J.M.: Interstitial flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells. Am J. Physiol—Heart and Circulatory Physiol, Vol. 278 pp. H1589-H1597 (2000)

    Google Scholar 

  27. Mishra, J.C., Sinha , A.: Effects of hall current and heat radiation on flow of a fluid through a porous medium subject to an external magnetic field. Spl. Topics Rev. Porous Media—An Int. J., DOI: 10.1615/SpecialTopicsRevPorousMedia.v4.i2.40 pp. 147–158 (2013)

  28. Tiwari ,A., Satya Deo.:pulsatile flow in a cylindrical tube with porous walls: applications to blood flow, DOI: 10.1615/JPorMedia.v16.i4.50 J. Porous Media, pp. 335–340 (2013)

  29. Tang1, A.Y-S., Chan1, H-N., Tsang2, A.C-O., GK-K Leung2, Leung3, K-M., Yu4, A.C-H., Chow1.K-W.: The effects of stent porosity on the endovascular treatment of intracranial aneurysms located near a bifurcation, J. Biomed Sci Eng. 6, pp. 812–822 (2013)

    Google Scholar 

  30. Li, W.G., Hill, N.A., Going, J., Luo, X.Y.: Breaking analysis of artificial elastic tubes and human artery. J. Appl. Mech. ISSN 0021–8936, 55–67 (2013)

    Google Scholar 

  31. Mekheimer, KhS, Haroun, M.H., Elkot, M.A.: Induced magnetic field influences on blood flow through an anisotropically tapered elastic arteries with overlapping stenosis in an annulus. Can. J. Phys. 89, 201–212 (2011)

    Article  Google Scholar 

Download references

Acknowledgment

Authors are grateful to World Institute Technology Sohna Gurgaon affiliated to MD University, Rohtak India, for providing facilities and encouragement to complete this work. Also the corresponding authors are thankful to the learned referees for their fruitful suggestions for improving the presentation of this work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anil Kumar .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer India

About this paper

Cite this paper

Kumar, A., Agrawal, S.P. (2014). Computational Study of Blood Flow Through Elastic Arteries with Porous Effects. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 258. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1771-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-1771-8_1

  • Published:

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1770-1

  • Online ISBN: 978-81-322-1771-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics