COMPUTATIONAL MODELING OF FLOW INSIDE A DISEASED CAROTID BIFURCATION

One of the leading causes for death after heart diseases and cancer in all over the world is still stroke. Most strokes happen because an artery that carries blood uphill from the heart to the head is clogged. Most of the time, as with heart attacks, the problem is atherosclerosis, hardening of the arteries, calcified buildup of fatty deposits on the vessel wall. The primary troublemaker is the carotid artery, one on each side of the neck, the main thoroughfare for blood to the brain. Only within the last twenty-five years, though, have researchers been able to put their finger on why the carotid is especially susceptible to atherosclerosis. In this study, the fluid dynamic simulations were done in a diseased carotid bifurcation under the steady flow conditions computationally. Reynolds numbers representing the steady flow were 300, 1020 and 1500 for diastolic, average and systolic peak flow represented by pulsatile flow waveform, respectively. In vivo geometry and boundary conditions were obtained from a patient who has stenosis located at external carotid artery (ECA) and internal carotid artery (ICA) of his common carotid artery (CCA). The location of critical flow fields such as low wall shear stress (WSS), stagnation regions and separation regions were detected near the highly stenosed region and at branching region.


INTRODUCTION
The formation of atherosclerosis has been reported due to the low or high shear regions.These regions develop at the downstream of the carotid bifurcation that is located in bifurcation part of the carotid arteries in humans.The low and high shear regions correlation with the atherosclerosis region were discussed by [1], [2] and stated the close correlation to the formation of lesions [2], [3], [4], and [5].Arterial bifurcation studies have shown that the stress level in the bifurcating areas is several times higher than that in a straight segment.The effect of the arterial wall tension in the formation of atherosclerosis was proposed by [6], who suggested that atherosclerotic plaques occurred more frequently at wall locations where wall tension would be expected to be elevated.More researchers such as [7] and [8] reported that increased tensile stress predisposes tissue to atheroschelerosis.Nevertheless, most of theses studies have been confined to either the arterial wall itself ignoring the pulsatile flow of blood, or the blood flow domain alone assuming non-distensible walls.There only a few numerical studies that have treated both pulsatile flows and compliant walls, [9], [10], and [11].

MATERIALS AND METHODS
The in vivo geometry data and flow conditions were obtained from a male patient, who has two-sided atherosclerosis, at Cerrahpasa Medical School, Istanbul, Turkey, Figure 1.His age was 50 years old.He was smoker and normotensive.Imaging of the left carotid artery was done with color Doppler ultrasound.After imaging the flow in color Doppler scan mode, a static Doppler sample volume was deposited in the center of the carotid artery and the bifurcating vessels, spanning approximately one third of the vessel diameter.A marker was aligned with the vessel axis, and the angle between the Doppler line of sight and the vessel axis was computed.The velocity trace for the graft showed much higher velocities than in normal arteries, with a low pulsatility index since the sonograph trace remained well above zero throughout the cycle.For the patient shown in Figure 2, the instantaneous mean of the sonograph trace at the inlet was estimated to be 0.68 m/s average, maximum 1m/s and 0.2 m/s minimum.

Computational grid
All geometrical data were input into a specialized preprocessing program for grid generation.In total, 60,803 grid nodes were utilized giving rise to 286,848 computational tetrahedral.Figure 4 shows details of the utilized non-structured grid of the human carotid artery.

Flow equations, boundary flow conditions, and solution
The blood velocity was assumed uniform at the orifice of carotid.The applied inflow conditions mimic typical carotid blood flow velocity, 0.68 m/s, under resting condition.The values of the outflow discharges as percentages of the inlet flow are seventy-five percent from Internal carotid Artery Figure 4. Mesh formation for diseased carotid artery (ICA) to twenty-five percent from External Carotid Artery (ECA).All computational grid data, as well as all physical flow data determined from the boundary conditions, were imported into the main Computational Fluid Dynamics solver (FLUENT Inc.,) [12].The numerical code solves the governing Navier-Stokes flow equations.In the generality, these equations solve the mass, momentum and energy conservation.The assumptions made about the nature of the flow are that it is three-dimensional, steady, laminar, isothermal, with no external forces applied on it while the arterial wall is comprised of non-elastic and impermeable material.In their generality time dependent governing equations for incompressible flow are where ρ (kg/m 3 ) is the density, t (s) is the time, u i (m/s) are the velocity components along the x i , (m) axis, while S m is the added or subtracted mass of fluid in the flow field.Equation 1 becomes for steady flow as Unsteady conservation of momentum equation along the i direction is written as Here, ρ (N/m 2 ) is the static pressure, τ ij (N/m 2 ) is the shear stress tensor, ρg i (N/m 3 ) and F i (N/m 3 ) are gravity and externally acting forces, respectively.For steady flow equation 3 becomes The WSS, denoted by τ (N/m 2 ), is calculated as Where µ is the viscosity defined for incompressible fluid and the strain rate as The components of the WSS possibly have different effects upon endothelial cells.Some components, mainly those being diagonal, generate intercellular tension, while the off-diagonal components possibly contribute to intercellular shearing forces.

RESULTS
The fluid flow characterization of the flow inside a diseased carotid bifurcation was analyzed computationally.Figure 5 shows the velocity vectors inside the diseased carotid artery together with the ICA and ECA.SI units were used.The flow enters the model with a flat velocity profile.The peak Reynolds number was 1500 at the inlet.The flow went through ICA and ECA and accelerated through the internal and external carotid arteries due to the reduction in cross-sectional area.The flow separation region at downstream of the branching point was seen by retrograde vectors.The artery stenosis on both left and right carotid arteries was seen in these specific patients.The velocities inside the stenosis region are increased similar to the jet flow.Depending on the internal geometry of the diseased artery, the circulation regions were seen not only at the inner surface of the branches but also on the external surface of the branches.The maximum velocity was found as 2.2 m/s at the narrowest region of the flow inside the internal carotid artery.The endothelial cells inside the arteries are very sensitive to the high and low shear stress regions.The regions found here would cause the increase of the intimal hyperplasia if there was no surgery done which will also cause the increase of the thickness of the diseased region more.This will cause the sudden ischemia for the patient who may result the patient to get killed or to get his brain affected.The plots clearly show the nature of secondary flow inside these regions.The shear stress distribution on the wall is illustrated in Figure 6.The highest WSS was seen at downstream of the carotid branching.The lower WSS region was found where the fluid circulation occurs on both sides of the branches.The structure of the internal part of the carotid was highly complex after stenosis formation.

CONCLUSIONS
Computational analysis of the flow field inside diseased carotid arteries for a male patient was performed The flow was found similar to the flow inside a branching channel.The geometry of the stenosis inside the diseased carotid artery defines the flow characterization.When the inner diameter gets smaller, the flow rate will increase which will cause the high shear stress regions.The geometry due to the atheroschelerosis formation inside the internal and external branching caused the flow circulated and low WSS.The upscaled experimental model of the diseased artery will be better to study to understand the flow regions with a higher spatial resolution in future.In addition, the effect of the critical flow regions on the endothelial cells in vivo will be considered for the future studies to understand the mechanics of the real formation of the atherosclerosis.

Figure 1 .Figure 2 .
Figure 1.The geometry of the stenosed carotid artery taken by Color Doppler Ultrasound Imaging technique.

Figure 3 .
Figure 3. Physiological forcing function used to drive the inlet velocity boundary condition as a function of time.

Figure 5 :Figure 6 .
Figure 5: Velocity distribution (m/s) inside the diseased carotid artery along the bifurcation plane at various points of cardiac cycle, A) u=1 m/s, B) u=0.68 m/s, C) u=0.2 m/s