A Mathematical modeling of a two layered blood flow through constricted vessels


Department of Mathematics, Urmia University of technology, Urmia, Iran


A mathematical model of pulsatile and two-layered blood flow through constriction vessels is simulated in this paper. The blood vessel has been assumed to be elastic and the blood flow is treated as a two-layered fluid, such that the core region is a micropolar fluid and the peripheral layer is a Newtonian plasma fluid. By applying suitable coordinate transformation, the governing equations have been solved numerically using the finite difference method, and the velocity profile of the two-layered blood flow has been achieved. The flow characteristics including the volumetric flow rate and the resistive impedance were obtained, and the effects of the stenosis size on these characteristic have been discussed.


Main Subjects

Download Fulltext

[1] Naghavi M., Libby P., Falk E., Casscells S. W., Litovsky S., Rumberger J., Badimon J. J., Stefanadis C., Moreno P. and Pasterkamp G. (2003), From vulnerable plaque to vulnerable patient a call for new definitions and risk assessment strategies:
part I, Circulation, 108(14), 1664-1672. [2] Tu C. and Deville M. (1996), Pulsatile flow of non-Newtonian fluids through arterial stenoses, J. biomechanics, 29(7), 899-908. [3] Chakravarty S. and Mandal P. K. (2004), Unsteady flow of a two-layer blood
stream past a tapered flexible artery under stenotic conditions, Comput. Methods Appl. Math., 4(4), 391-409. [4] Sankar D. (2011), Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries, International Journal of Non-Linear Mechanics, 46(1), 296-305. [5] Sankar D. and Lee U. (2011), FDM analysis for MHD flow of a nonNewtonian fluid for blood flow in stenosed arteries, j. mech. sci. technol, 25(10), 2573-2581. [6] Haghighi A. R. (2012), Mathematical model of the impact of pressure drop on human body, Selcuk J. Appl. Math 13(1), 35-40. [7] Long Q., Xu X., Ramnarine K. and Hoskins P. (2001), Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis, J. biomechanics, 34(10), 1229-1242. [8] Belardinelli E. and Cavalcanti S. (1991), A new nonlinear twodimensional model of blood motion in tapered and elastic
vessels, Comput. Biol. Med, 21(1), 1-13. [9] Chakravarty S. and Mandal P. K. (2000), Two-dimensional blood flow through tapered arteries under stenotic conditions ,Internat. J. NonLinear Mech, 35(5), 779-793. [10] Mandal P. K. (2005), An unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis, Internat. J. Non-Linear Mech, 40(1), 151-164.
[11] Ikbal M. A., Chakravarty S., Wong K. K ,.Mazumdar J. and Mandal P. K. (2009), Unsteady response of non-Newtonian blood flow through a stenosed artery in magnetic field, Comput. Appl. Math, 230(1), 243-259. [12] Ismail Z., Abdullah I., Mustapha N. and Amin N. (2008), A power-law model of blood flow through a tapered overlapping stenosed artery, Appl. Math. Comput, 195(2), 669-680