Hematocrit effects of the axisymmetric blood flow through an artery with stenosis arteries

Sanjeev Kumar; Chandrashekhar Diwakar

doi:https://doi.org/10.14445/22315373/IJMTT-V4I6P2

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 4 | Issue 6 | Year 2013 | Article Id. IJMTT-V4I6P2 | DOI : https://doi.org/10.14445/22315373/IJMTT-V4I6P2

Hematocrit effects of the axisymmetric blood flow through an artery with stenosis arteries

Sanjeev Kumar , Chandrashekhar Diwakar

Citation :

Sanjeev Kumar , Chandrashekhar Diwakar, "Hematocrit effects of the axisymmetric blood flow through an artery with stenosis arteries," International Journal of Mathematics Trends and Technology (IJMTT), vol. 4, no. 6, pp. 91-96, 2013. Crossref, https://doi.org/10.14445/22315373/IJMTT-V4I6P2

Abstract

When the nature of blood flow changes from its usual state to a disturbed flow condition due to the presence of a stenosis in an artery. Then it has been suggested that the deposits of cholesterol on the arterial wall and proliferation of connective tissue may be responsible for the abnormal growth in the lumen of an artery. Therefore a study about the blood flow in an arterial segment having a stenosis is important because of its unusual state disturbe the flow behaviour. An axisymmetric flow of blood through a circular tube with an axially symmetric stenosis is considered. The unsteady nonlinear Navier-Stokes equations in cylindrical coordinate system governing flow assuming axial symmetry under laminar flow condition is then solved numerically so that the problem effectively becomes two-dimensional. In this investigation, we observe the effects of red cell concentration (hematocrit) on blood flow characteristics in the presence of stenosis, and it is found that the flow resistance and the wall shear stress increases with hematocrits.

Keywords

Stenosis, blood flow, hematocrit

References

[1] Hayens, R.H. (1960): “Physical basis of the dependence of blood viscosity on tube radius”, American Journal of Physiology, vol. 198, pp. 1193-1205.
[2] Young, D.F. (1968): “Effect of time dependent stenosis of flow through a tube”, J. Engg. Ind., vol.90, pp. 248-254.
[3] Cokelet, G.R. (1972): “The rheology of human blood”, Biomechanics (Edited by Fung, Y.C),. Prentice-Hall, Englewood Cliffs, NJ, pp.63-103.
[4] Padley, T.J.,(1980), “The Fluid Mechanics of Large Blood Vessels”, Cambridge University Press Cambridge.
[5] Shukla, J.B., Parihar, R.S. and Gupta, S.P. (1980): “Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis”, Bulletin of Mathematical Biology, vol.42, pp. 797-805.
[6] Srivastava, L.M. and Srivastava, V.P. (1983): “Two phase model of pulsatile blood flow with entrance effects”, Biorheology, vol.20, pp. 761-777.
[7] Srivastava, L.M. (1985): “Flow of a couple-stress fluid through stenotic blood vessels”, J. Biomechanics, vol.8 (9), pp. 695-701.
[8] Chaturani, P. and Samy, R.P. (1986): “Pulsatile flow of casson fluid through stenosed arteries with application to blood flow”, Biorheology, vol.23, pp. 499-511.
[9] Chakravarty, S. and Choudhary, G. (1988): “Response of blood flow through an artery under stenotic conditions”, Rhelogical Acta, vol.27, pp. 418- 427.
[10] Mann, D.E. and Tarbell, J.M. (1990): “Flow of non-Newtonian blood analog fluids in rigid curved and straight artery models”, Biorheology, vol. 27, pp. 711-733.
[11] Sud, V.K. (1990): “Simulation of steady cardiovascular flow in the presence of stenosis using a finite element method”, Phy. Med. Biol., vol. 35, pp. 947-959.
[12] Taylor, C.A., Hughes, T.J.R. and Zarins, C.K. (1998): “Finite element modeling of three-dimensional pulsatile flow in the abdominal aorta: Relevance to atherosclerosis”, Ann. Biomedical Engg., vol. 26, pp. 975-987.
[13] Waters, S.L. and Pedley, T.J. (1999): “Oscillatory flow in a tube of time dependent curvature part-1. Perturbation to flow in a stationary curved tube”, J. Fluid Mech., vol. 383, pp. 327-352.
[14] Zhang, J.B. and Kuang, Z.B. (2000): “Study on blood constitutive parameters in different blood constitutive equations”, J. Biomech., vol. 3, pp. 355- 360.
[15] Secomb, T.W., Hsu, R. and Pries, A.R. (2002): “Blood flow and red blood cell deformation in non uniform capillaries effects of the endothelial surface layer”, Microcirculation, vol. 9, pp. 189-196.
[16] Steinman, D. A. and Taylor, C.A. (2005): “Flow imaging and computing: large artery hemodynamics”, Ann. Biomed. Engg., vol.33, pp. 1704-1709.
[17] Kumar, S. and Kumar, S. (2006): “Numerical study of the axisymmetric blood flow in a constricted rigid tube”, International Review of Pure and Applied Mathematics, vol.2 (2), pp. 99-109.
[18] Bali, R. and Awasthi, U. (2007): “Effect of a magnetic field on the resistance of blood flow through stenotic artery", Applied Mathematics and Computation, vol.188 (2), pp. 1635-1641.
[19] Layek, G.C., Mukhopadhaya, S. and Gorla, R.S.R., (2009): “Unsteady viscous flow with variable viscosity in a vascular tube with a double constriction", Int. J. Eng. Sci., 47 649-659.
[20] Verma, N. and Parihar,R.S., (2010). “Mathematical model of blood flow through a tapered artery with mild stenosis and hematocrit ", J. Applied Math. Comput., 1: 30-46.
[21] Misra, J.C., Sinha, A. and Shit, G.C., (2011): “A numerical model for the magnetohydrodynamic flow of blood in a porous channel", J. Mech. Med. Biol., 11 , 547-562.
[22] Eldesoky, I. M. (2012): “Influence of slip condition on peristaltic transport of a compressible Maxwell fluid through porous medium in a tube,” International Journal of Applied Mathematics and Mechanics, vol. 8, no. 2, pp. 99-117.
[23] Kumar, S. and Diwakar, C.S. (2012), A biomagentic fluid dynamic model for the MHD Couette flow between two infinite horizontal parallel porous plates, Int. J. of Phy. Sci. Vol. 24(3)B, 483-488.
[24] Kumar, S. and Diwakar, C.S. (2012), A mathematical model for Newtonian blood flow in the presence of applied magnetic field, Aryabhatta J. of Math & Infomatics, Vol. 4, 265-278.