Computational Study of Blood Flow Through Elastic Arteries with Porous Effects

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


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.


Elastic artery model Crank-Niclson technique Porosity Wall shear stress 



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.


  1. 1.
    Berger, S.A., Jou, L.D.: Flows in Stenotic vessels. Annu. Rev. Fluid Mech. 32, 347–384 (2000)CrossRefMathSciNetGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 3.
    Greenfield, J.C., Patel, D.J.: Relation between pressure and diameter in the ascending Aorta of man. Circ. Res. 10, 778 (1962)CrossRefGoogle Scholar
  4. 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. 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)CrossRefGoogle Scholar
  6. 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. 7.
    Lee, R., Libby, P.: The unstable atheroma, atherosclerosis thrombosis vascular Biology. 17, 1859–1867 (1997)Google Scholar
  8. 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. 9.
    Milnor, W.R.: Hemodynamics, 2nd edn. Williams and Wilkins, Baltmore (1989)Google Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 13.
    Rees, J.M., Thompson, D.S.: Shear stress in arterial stenoses: a momentum integral model. J. Biomech. 31, 1051–1057 (1999)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)CrossRefMATHGoogle Scholar
  16. 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)MATHGoogle Scholar
  17. 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. 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. 19.
    Srivastava, V.P.: Arterial blood flow through a non-symmetrical stenosis with applications. Jpn. J. Appl. Phy 34, 6539–6545 (1995)CrossRefGoogle Scholar
  20. 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. 21.
    Thurston, G.B.: Rheological parameter for the viscosity, visco-elasticity and Thrixotropy of blood. Biorheology 16, 149–155 (1979)Google Scholar
  22. 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)CrossRefMATHGoogle Scholar
  23. 23.
    Walburn, F.J., Schneck, D.J.: A constitutive equation for whole human blood. Biorheology 18, 201 (1976)Google Scholar
  24. 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. 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, 2010Google Scholar
  26. 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. 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. 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. 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. 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. 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)CrossRefGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Applied MathematicsWorld Institute of TechnologyGurgaonIndia
  2. 2.Civil EngineeringWorld Institute of TechnologyGurgaonIndia

Personalised recommendations