Suspension model for blood flow through a catheterized arterial stenosis with peripheral layer of plasma free from cells

Regular Article


The present article describes the blood flow in a catheterized artery with radially symmetric and axially asymmetric stenosis. To understand the effects of red cell concentration, plasma layer thickness and catheter size simultaneously, blood is considered by a two-layered model comprising a core region of suspension of all the erythrocytes (particles) supposed to be a particle-fluid mixture and a peripheral zone of cell-free plasma. The analytical expressions for flow features, such as fluid phase and particle phase velocities, flow rate, wall shear stress and resistive force are obtained. It is witnessed that the presence of the catheter causes a substantial increase in the frictional forces on the walls of arterial stenosis and catheter, shear stress and flow resistance, in addition to that, have occurred due to the presence of red cells concentration (volume fraction density of the particles) and the absence of peripheral plasma layer near the wall of the stenosed artery. The introduction of an axially asymmetric nature of stenosis and plasma layer thickness causes significant reduction in flow resistance. One can notice that the two-phase fluid (suspension model) is more profound to the thickness of peripheral plasma layer and catheter than the single-phase fluid.


  1. 1.
    D.F. Young, J. Eng. Ind. Trans. AMSE 90, 248 (1968)CrossRefGoogle Scholar
  2. 2.
    R. Ponalagusamy, Blood Flow Through Stenosed Tube, PhD Thesis, IIT, Bombay, India (1986)Google Scholar
  3. 3.
    P. Chaturani, R. Ponnalagarsamy, Biorheology 23, 499 (1986)Google Scholar
  4. 4.
    D.F. Young, J. Biomech. Eng. Trans. ASME 101, 157 (1979)CrossRefGoogle Scholar
  5. 5.
    C.G. Caro, Recent Adv. Cardiovasc. Dis. 2, 6 (1981)Google Scholar
  6. 6.
    L. Distenfass, Cardiovasc. Med. 2, 337 (1971)Google Scholar
  7. 7.
    D.L. Fry, Circ. Res. 22, 165 (1968)CrossRefGoogle Scholar
  8. 8.
    R. Ponalagusamy, J. Franklin Inst. 349, 2861 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    M.D. Deshpamde, D.P. Giddens, R.F. Mabon, J. Biomech. 9, 65 (1979)Google Scholar
  10. 10.
    J.H. Forrester, D.F. Young, J. Biomech. 3, 297 (1970)CrossRefGoogle Scholar
  11. 11.
    D.A. Macdonald, J. Biomech. 12, 13 (1979)CrossRefGoogle Scholar
  12. 12.
    P. Chaturani, R. Ponnalagarsamy, Blood flow through stenosed arteries, in Proceedings of The First International Conference on Physiological Fluid Dynamics (1983) pp. 63--67Google Scholar
  13. 13.
    J.B. Shukla, R.S. Parihar, S.P. Gupta, Bull. Math. Biol. 42, 797 (1980)CrossRefGoogle Scholar
  14. 14.
    G.R. Cokelet, The Rheology of Human Blood, in Biomechanics (Prentice-Hall, Englewood Cliffs, N.J., 1972)Google Scholar
  15. 15.
    R.H. Haynes, Am. J. Physiol. 198, 1193 (1960)Google Scholar
  16. 16.
    R. Skalak, Mechanics of Microcirculation, in Biomechanics, Its Foundation and Objectives, edited by Y.C. Furg (Prentice Hall Publ. Co., Englewood Cliffs, 1972)Google Scholar
  17. 17.
    L.M. Srivastava, V.P. Srivastava, Biorheology 20, 761 (1983)Google Scholar
  18. 18.
    L.M. Srivastava, Int. J. Bio-Med. Comput. 38, 141 (1995)CrossRefGoogle Scholar
  19. 19.
    Kh.S. Mekheimer, M.A. Kot, El, Chem. Eng. Comm. 197, 1195 (2010)CrossRefGoogle Scholar
  20. 20.
    G. Bugliarello, J. Sevilla, Biorheology l7, 85 (1970)Google Scholar
  21. 21.
    G. Bugliarello, J.W. Hayden, Trans. Soc. Rheol. 7, 209 (1963)CrossRefGoogle Scholar
  22. 22.
    J.B. Shukla, R.S. Parihar, S.P. Gupta, Biorheology 17, 403 (1980)Google Scholar
  23. 23.
    P. Chaturani, P.N. Kaloni, Biorheology 13, 243 (1976)Google Scholar
  24. 24.
    P. Chaturani, R. Ponalagusamy, A two-layered model for blood flow through stenosed arteries, in Proceedings of the 11th National Conference on Fluid Mechanics and Fluid Power, B.H.E.L (R & D) (Hydrabad, India, 1982) pp. 16--22Google Scholar
  25. 25.
    R. Ponalagusamy, J. Appl. Sci. 7, 1071 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    V.P. Srivastava, R. Rastogi, R. Vishnoi, Comp. Math. Appl. 60, 432 (2010)CrossRefGoogle Scholar
  27. 27.
    R. Ponalagusamy, R. Tamil Selvi, J. Franklin Ins. 348, 2308 (2011)CrossRefGoogle Scholar
  28. 28.
    R. Ponalagusamy, R. Tamil Selvi, Meccanica 48, 2427 (2013)MathSciNetCrossRefGoogle Scholar
  29. 29.
    R. Ponalagusamy, R. Tamil Selvi, Meccanica 50, 927 (2015)MathSciNetCrossRefGoogle Scholar
  30. 30.
    H. Kanai, M. Lizuka, K. Sakamotos, Med. Biol. Eng. 28, 483 (1970)CrossRefGoogle Scholar
  31. 31.
    P. Gunj, R. Abben, P.L. Friedman, J.D. Granic, W.H. Barry, D.C. Levin, Am. J. Cardiol. 55, 910 (1985)CrossRefGoogle Scholar
  32. 32.
    H.V. Anderson, G.S. Roubin, P.P. Leimgruber, W.R. Cox, J.S. Douglas Jr., S.B. King III, A.R. Gruentzig, Circulation 73, 1223 (1986)CrossRefGoogle Scholar
  33. 33.
    L.H. Back, E.Y. Kwack, M.R. Back, J. Biomed. Eng. 118, 83 (1996)Google Scholar
  34. 34.
    A. Sarkar, G. Jayaraman, J. Biomech. 31, 781 (1998)CrossRefGoogle Scholar
  35. 35.
    D.A. Drew, Arch. Ration. Mech. Anal. 62, 149 (1976)CrossRefGoogle Scholar
  36. 36.
    S.E. Charm, G.S. Kurland, Blood Flow and Microcirculation (John Wiley, New York, 1974)Google Scholar
  37. 37.
    C.K.W. Tam, J. Fluid Mech. 38, 537 (1969)ADSCrossRefGoogle Scholar
  38. 38.
    D.A. Drew, Phys. Fluids 19, 2081 (1979)ADSCrossRefGoogle Scholar
  39. 39.
    V.P. Srivastava, M. Sexena, Math. Biosci. 139, 79 (1997)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of TechnologyTamilnaduIndia

Personalised recommendations