D. K. Mandal, S. Chakrabarti / J. Biomedical Science and Engineering 6 (2013) 1109-1116

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tery under stenotic conditions. In their work, they have

studied the effects of constricted flow characteristics and

the wall motion on the wall shear stress, the concentra-

tion profile and the mass transfer. The influences of WSS

on LDL transport by modeling the blood flow and solute

transport in the lumen and arterial wall are investigated

by Nanfeng Sun et al. [4]. The unsteady non-Newtonian

blood flow and mass transfer in symmetric and non-

symmetric stenotic arteries are numerically simulated by

Valencia and Villanueva [5], where they have considered

the fluid-structure interaction in their simulation. Valeria

et al. [6] have made a simple model for the plaque

growth rate based on the accumulation of oxidized LDL

in the artery wall, including a dependence of the endo-

thelial permeability on the shear stresses, and on the

LDL blood concentration. Sun et al. [7] have studied the

influence of pulsatile flow on LDL transport and exam-

ine the validity of steady flow assumption. Yang and

Vafai [8,9] have developed a robust multi-layer porous

model for the description of the mass transport in the

arterial wall coupled with the mass transport in the arte-

rial lumen. From their study, they have concluded that

the LDL transport in the arterial wall is one-dimensional

when a straight circular geometry is considered. Olgac et

al. [10] have studied the effects of the local arterial wall

shear stress distribution on the endothelial cell layer in

order to accurately calculate LDL transport. They have

chosen a realistic 3-D coronary artery segment with a

single-layer porous arterial wall. Khakpour and Vafai [11]

have critically assessed the different arterial transport

models as far as the recent research activities on this is-

sue are concerned with the help of the relevant governing

equations in the study of fluid flow and mass transfer

within the arteries by giving emphasis on the role of po-

rous media.

From the available literature, it is noted that very little

work has been done on the issue of quantifying the mass

deposition of the plaque in the arterial wall. Therefore, in

the present study, an attempt has been made to study

initially the effect of fluid dynamic parameters on the

disease, atherosclerosis and finally proposes a concept,

from the idea of basic flow characteristics in constricted

arteries, for the assessment of mass deposition in the

arterial wall to some extent. The effect of Reynolds

number and percentage of restriction on pressure drop

through stenosis, velocity contour, velocity vector, and

mass deposition in the wall is studied for the rectangular

as well as half circular restrictions. Reynolds numbers

are chosen as 100, 200, 300 and 400 and percentages of

restrictions as 30%, 50%, 70% and 90% respectively.

2. METHOD

The governing Navier-Stokes and continuity equations

are solved in the artery lumen with the commercial CFD

code ANSYS 12.1. The pressure-velocity coupling equa-

tions are solved by SIMPLE (Semi-Implicit Method for

Pressure-Linked Equations) algorithm. Least square cell

based gradient, pressure: standard, momentum: first or-

der momentum, are chosen for spatial discretization. The

under relaxation factors for pressure as 0.3, density as

1.0 and momentum as 0.7 are considered during simula-

tion. The flow under consideration has been assumed to

be steady, two-dimensional, laminar and axisymmetric,

and fluid is considered to be Newtonian and incom-

pressible. Uniform velocity at inlet, no slip condition at

wall and zero pressure at exit are used in our simulation.

Since coronary artery is an important artery for the dis-

ease of atherosclerosis, therefore the coronary artery (dia

= 4 mm) is taken for simulation. The density of blood

and viscosity are considered as 1056 Kg/m3 and 0.0035

Pas respectively. The schematic diagrams of the compu-

tational domain selected for our study are illustrated in

Figures 1(a) and (b) respectively. Total length of the

computational domain is taken as 0.2 m. Restriction is

placed at the middle of the computational domain.

The results are generated for different Reynolds num-

bers of 100, 200, 300 and 400 and percentage of restric-

tion of 30%, 50%, 70% and 90%. The details of nodes

and elements, considered during our study, are as follows

in Table 1.

3. RESULT AND DISCUSSIONS

One of the most serious consequences of an arterial

stenosis is the large pressure loss which may develop

across a severe stenosis. The reduced pressure distal to

the stenosis significantly alters the blood flow to the pe-

ripheral blood supplied by the artery. Atheromatuos

plaques appear in the regions of low pressure because a

suction action exerted on the surface endothelium even-

tually causes the layer to be selectively separated from

adjacent tissue. This tearing action is thought to cause

damage, in turn, to the endothelium and adjacent wall

layers, with subsequent thickening of the intima and

eventual plaque development [12]. The pressure loss is

primarily dependent on the flow rate and the geometry of

the stenosis due to relatively constant fluid properties of

density and apparent viscosity. Moreover, the initiation

and progression of atherosclerosis are dependent on the

accumulation of LDL in the artery wall. One of the bio-

mechanical forces of the chance of the deposition is de-

pending on transmural flux. Moreover, the recirculation

zone in the post stenotic region is considered to be an

important phenomenon for fluid flux [13]. Since the fluid

flux also depends on pressure of the blood, therefore, the

pressure of blood at any section of the concerned artery

and the pressure drop across the restricted zone may be

thought to offer an idea to some extent regarding the

formation and propagation of atherosclerosis. The physi-

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