Unsteady Two-Dimensional Blood Flow in Porous Artery with Multi-Irregular Stenoses

The flow characteristics of an unsteady axisymmetric two-dimensional (2D) blood flow in a diseased porous arterial segment with flexible walls are investigated. The arterial walls mimic the irregular constrictions whereas the lumen containing the thrombus, cholesterol, and fatty plaques represents the porous medium. The governing equations with appropriate initial and boundary conditions are solved numerically using MAC method. The discretization is done on staggered grid with non-uniform grid size and pressure-poisson equation is solved following SOR method. The pressure and velocity corrections are made cyclically until the steady state is achieved. It is observed that for decreasing permeability, flow is highly decelerated while pressure drop and wall shear stress increases. The separation zones and re-circulation regions are found for severe stenoses. Flow separation and re-circulation diminishes for decreasing permeability of the porous medium. Comparisons are provided with published experimental and numerical results.

[1]  D W Crawford,et al.  Measurement and prediction of flow through a replica segment of a mildly atherosclerotic coronary artery of man. , 1986, Journal of biomechanics.

[2]  V. P. Srivastava,et al.  A two-layered suspension blood flow through an overlapping stenosis , 2010, Comput. Math. Appl..

[3]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[4]  D Kilpatrick,et al.  Mathematical modelling of flow through an irregular arterial stenosis. , 1991, Journal of biomechanics.

[5]  D. A. Mcdonald.  Blood flow in arteries , 1974 .

[6]  R N Vaishnav,et al.  Compressibility of the Arterial Wall , 1968, Circulation research.

[7]  W. Milnor,et al.  Pulsatile blood flow. , 1972, The New England journal of medicine.

[8]  V. P. Srivastava,et al.  Suspension model for blood flow through stenotic arteries with a cell-free plasma layer. , 1997, Mathematical biosciences.

[9]  A. Fyles,et al.  The relationship between elevated interstitial fluid pressure and blood flow in tumors: a bioengineering analysis. , 1999, International journal of radiation oncology, biology, physics.

[10]  Prashanta Kumar Mandal,et al.  A numerical simulation of unsteady blood flow through multi-irregular arterial stenoses , 2010 .

[11]  R M Nerem,et al.  An in vivo study of aortic flow disturbances. , 1972, Cardiovascular research.

[12]  D. Liepsch.  An introduction to biofluid mechanics--basic models and applications. , 2002, Journal of biomechanics.

[13]  H. Andersson,et al.  Effects of surface irregularities on flow resistance in differently shaped arterial stenoses. , 2000, Journal of biomechanics.

[14]  A. A. Amsden,et al.  The SMAC method: A numerical technique for calculating incompressible fluid flow , 1970 .

[15]  Moustafa El-Shahed,et al.  Pulsatile flow of blood through a stenosed porous medium under periodic body acceleration , 2003, Appl. Math. Comput..

[16]  D W Crawford,et al.  Effect of mild atherosclerosis on flow resistance in a coronary artery casting of man. , 1984, Journal of biomechanical engineering.

[17]  R. Banerjee,et al.  Estimated flow resistance increase in a spiral human coronary artery segment. , 2000, Journal of biomechanical engineering.

[18]  Ranjan K. Dash,et al.  Casson fluid flow in a pipe filled with a homogeneous porous medium , 1996 .

[19]  V. G. Ferreira,et al.  The MAC method , 2008 .

[20]  D. F. Young.  Effect of a Time-Dependent Stenosis on Flow Through a Tube , 1968 .

[21]  K. Vafai,et al.  Critical assessment of arterial transport models , 2008 .

[22]  Kambiz Vafai,et al.  Modeling of low-density lipoprotein (LDL) transport in the artery—effects of hypertension , 2006 .

[23]  G. C. Layek,et al.  Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions , 2003 .

[24]  Lei Xiaoxiao,et al.  Mass transport in solid tumors (I)—Fluid dynamics , 1998 .

[25]  L. Grinberg,et al.  Modeling rough stenoses by an immersed-boundary method. , 2005, Journal of biomechanics.

[26]  G. Sekhon,et al.  Flow through a stenosed artery subject to periodic body acceleration , 1987, Medical and Biological Engineering and Computing.

[27]  Kambiz Vafai,et al.  Effects of gender-related geometrical characteristics of aorta–iliac bifurcation on hemodynamics and macromolecule concentration distribution , 2008 .

[28]  Kambiz Vafai,et al.  The role of porous media in modeling flow and heat transfer in biological tissues , 2003 .

[29]  Kh. S. Mekheimer,et al.  Influence of magnetic field and Hall currents on blood flow through a stenotic artery , 2008 .

[30]  J. Kennedy,et al.  BLOOD FLOW IN ARTERIES (2nd ed) , 1975 .

[31]  H S Borovetz,et al.  A model of pulsatile flow in a uniform deformable vessel. , 1992, Journal of biomechanics.

[32]  R. Jain,et al.  Transmural coupling of fluid flow in microcirculatory network and interstitium in tumors. , 1997, Microvascular research.

[33]  Kambiz Vafai,et al.  Low-density lipoprotein (LDL) transport in an artery – A simplified analytical solution , 2008 .

[34]  K. Rhee,et al.  Effects of surface geometry and non-newtonian viscosity on the flow field in arterial stenoses , 2009 .

[35]  Kambiz Vafai,et al.  A coupling model for macromolecule transport in a stenosed arterial wall , 2006 .