CFD Simulation of Carotid Artery Stenosis –...

Proceedings of the 2012 ASEE North-Central Section Conference

Copyright © 2012, American Society for Engineering Education

CFD Simulation of Carotid Artery Stenosis – simplified model

Allen Page a and Wael Mokhtarb

a Graduate Assistant

b PhD. Assistant Professor Grand Valley State University, Grand Rapids, MI 49504

E-mail: , [email protected]

Introduction

Today, stroke is the third leading causes of death and the leading cause of paralysis in the

United States. A person has a stroke every 40 seconds, totaling 795,000 stroke cases each year1.

Of these, 610,000 are first time stroke occurrences and 185,000 are reoccurring strokes1. Stroke

is responsible for about $74 billion of cost on the Health Care System1. A solution for this

problem is required.

Stroke is defined as the interruption of blood supply to the brain. There are two main

types of stroke, hemorrhagic and ischemic. Hemorrhagic stroke is caused by a rupture in an

artery in the brain, resulting in blood entering the brain. Ischemic stroke is caused by a blood

clot. Ischemic stroke is classified into two subclasses, thrombotic stroke and embolic stroke.

Thrombotic stroke is caused by a clot formed at the stenosis site, a result of narrowing arterial

walls and atherosclerotic plaque rupture. Embolic stroke is caused by a clot breaking off and

logging in a smaller artery near the brain. 87% of all strokes are ischemic. The origin of the

ischemic stroke is most common in the carotid artery bifurcation region. This region is

comprised of three arteries, the Common Carotid Artery (CCA), the Interior Carotid Artery

(ICA), and the External Carotid Artery (ECA). These three arteries are joined by the Carotid

Bifurcation. This region is the most effected by atherosclerosis in the vascular system.

Atherosclerosis

Atherosclerosis is characterized by the patchy thickening and hardening of the arterial

wall due to fatty material deposits. The process begins with lipid deposits in the deep arterial

wall followed by a series of complex responses involving white blood cells (WBC) and smooth

muscle cells (SMC). Low Density Lipoproteins (LDL) penetrates the endothelium, deposit

inside the intima, and become oxidized. LDLs do not naturally occur within the intima so are

therefore identified as foreign objects, generating a WBC response. Macrophages and T –

Lymphocytes penetrate the endothelium and enter the intima to neutralize the LDL.

Macrophages consume the LDLs through phagocytosis. The combined macrophage and

oxidized LDL form a foam cell, characterized as a large cell with high lipid content. Foam cells

become “trapped” in the intima due to their large size. A collection of foam cells form,



generating a response from SMCs. SMCs migrate to the collection site and form a barrier

around the plaque region. This barrier is called the fibrous cap. The fibrous cap in turn starves

the foam cells and they die, creating a necrotic core within the plaque region. When foam cells

die they become calcified, begin to form calcium crystals. Over time the fibrous cap weakens

due to hemodynamic stresses. The fibrous cap may rupture leading to thrombosis, a clotting of

the artery at the rupture site, or an embolism, a clotting further downstream.

Literature Review

A study completed in 1991, by Lee et al, was designed to examine the relation

between the mechanical properties of fibrous caps from human atherosclerotic plaques and the

underlying histological appearance by light microscopy and to examine the dynamic nature of

these properties in the range of frequencies carried by a pressure wave at physiological heart

rates.2 The study was conducted using various samples of atherosclerotic plaque harvested from

patients within 12 hours of surgery. The plaque samples were collected from various locations

throughout the body. The sample fibrous caps were classified into three categories: cellular,

hypocellular, and calcified. To simulate the radial stress experienced by the arterial wall, an

applied static load of 0.33N was applied to produce a compressive stress normal to -9.3 KPa.2 A

dynamic stress of 0.5KPa was superimposed on the sample at varying frequencies.2 This

procedure allows one to test the stiffness at different frequencies. The frequencies used were 0.5

Hz, 1.0 Hz, and 2.0 Hz. The results showed that the hypocellular cap was 1-2 times stiffer than

the cellular cap, and the calcified caps were 4-5 times stiffer than the cellular cap.2 The results

also show that the stiffness of all compositions increased with the increase of frequency.2

A study completed in 2004, by Tang et al, was conducted in order to investigate the

quantifying effects of plaque structure and material properties on stress distribution in human

atherosclerotic plaques using 3D FSI modeling.3 The goal was to use a MRI based computational

model to quantify the effects of the three main factors on stress/strain in atherosclerotic plaque:

pulsating pressure, plaque structure, and material properties. Inspiration for the study came from

prior studies that concluded that plaque ruptures were closely associated with large lipid cores, a

thin fibrous cap, and weakening of the plaque cap, superficial plaque inflammation, and

erosion.4-8 The decision to use MRI based information was based on a study by Hatsukami et al.

It reported that MRI was capable in distinguishing intact thick fibrous caps from intact thin and

ruptured fibrous caps in the carotid artery in vivo.9 From the analysis of data, a conclusion was

made that vessels and plaque material properties, plaque structure, component volume and

pressure conditions have large impacts on stress/strain behaviors.3 It was found that

considerably higher stress/strain variations occurred in plaque with thin fibrous caps under

pulsating pressure.3 Weakening fibrous caps lead to large strain increases, but the stress levels

did not show a drastic difference.3 Maximal stress levels rose as plaque material stiffness

increased.3 Although the study posted significant results, a final conclusion is made that large



patient studies are required to identify and validate potential stress/strain risks for plaque fibrous

cap rupture.3

A study completed in 2006, performed by Li et al, created a flow - plaque interaction

model to examine the how critical fibrous cap thickness is to carotid plaque stability10. The

study is the first attempt to create a theoretical model to describe the plaque rupture mechanism

and to show that luminal stenosis and fibrous cap thickness are critical to plaque rupture.10 To

achieve the objective Li et al simulated pulsatile flow through a stenotic artery and the

interaction with atherosclerotic plaque. The variation on stress due to different degrees of

stenosis and fibrous cap thicknesses was the intended data. The simulation was conducted using

the assumptions that flow is laminar, Newtonian, viscous, and incompressible.10 The laminar

flow was given a parabolic velocity profile and the shape of the plaque was declared by a

sinusoidal function.10 The luminal stenosis was varied from 10% to 95% and the fibrous cap was

varied from 0.1mm to 2mm.10 Fluid velocity, plaque deformation, and plaque internal stress

was calculated. A stress of 300 KPa was used as the threshold to indicate high risk of plaque

rupture.10 Data was analyzed using a 1-sample t test. After data analysis, Li et al concluded that

there is a direct correlation between the degree of stenosis and the thickness of the fibrous cap.10

It is common practice for physician to perform surgery for stenosis greater than 70% due to high

rupture risks.11,12 Li et al, shows in the results that there is still a high risk for rupture of stenosis

between 30% and 70% depending on the thickness of the fibrous cap.10 The critical thickness for

this range of stenosis was showed to be 0.5mm.10

A study completed in 2009, performed by Barrett et al at the University of Cambridge,

sought to measure the stiffness of the human fibrous cap13. Carotid atherosclerotic plaque

samples harvested from patients were used for this study. Due to the irregular shape and small

size of the samples, indentation tests were considered the appropriate method of stiffness

measurement.13 The indentation test is a well-established method for testing material properties

of soft tissue.15-17 The samples thickness ranged between .25mm and .75mm and samples were

tested within 3 hours of surgery. A Zwick 3103 hardness testing machine was used to indent the

samples with a tungsten sphere with radius 0.5mm. Results from sample measurement were

used in a FIA study, after which the results were validated using synthetic rubber samples. The

results of the study were that the inferred shear modulus was found to be in the range of 7 – 100

KPa with a median value of 11 KPa.13

C.G Caro wrote an article in the Journal of the American Heart Association titled,

“Discovery of the Role of Wall Shear in Atherosclerosis.” The article described the initial

suggestions made on the importance of wall shear in atherosclerosis. For more than one hundred

years it was thought that fatty deposits within arteries were found in regions experiencing

mechanical damage due to high wall shear stresses.14 Since the 1960’s a plethora of studies have

since suggested the contrary. It is now widely accepted that fatty deposits occur at arterial



regions where wall shear stress is low.14 The regions found to have low wall shear also

experienced secondary flow recirculation, and where distal to points of flow separation.

Method

Gaining a better understanding of atherosclerosis and how it effects the environment of

the carotid artery is the first step in solving the problem of stroke. A greater understanding can

be achieved through computer simulations. The issue is that atherosclerosis is a highly complex

phenomenon. It involved the interaction of hemodynamics on the stenosis of the arterial wall

deformation and the interaction of the deformation on the hemodynamics. Both the flow of

blood affects the stenosis region and the stenosis region affects the flow. It is this interaction that

first creates the stenosis and eventually causes the stroke. Using a combination of computational

fluid dynamics (CFD) and finite element analysis (FEA) techniques allows one to study the

physics involved with atherosclerosis. Due to the aforementioned complexity of atherosclerosis,

however, one simply cannot study all the different aspects in one study. Therefore the solution

has been to study individual aspects of the problem and use the results of many different studies

to create overall assumptions. In order to study an individual aspect of the problem, it is

common practice to first establish a viable hypothesis.

In this study, CFD techniques were used to investigate Newtonian fluid flow in a straight

tube with variable degrees of area blockage due to a spherical infraction. The spherical

infraction in this case represents stenosis within an artery. The objective is to create a hypothesis

based on the observations made on the results of the study.

A segregated flow solver was used using STAR-CCM+ to model the fluid flow through

the tube with the simulated stenosis infraction. The stenosis is represented by a sphere cut into a

straight tube. The radius of the sphere is changed to generate different degrees of area blockage.

Simulations were run for three different degrees of stenosis, 30% (Figure 1, Table 1), 50%

(Figure 2, Table 2), and 70% (Figure 3, Table 3).

The flow is assumed to be Newtonian, turbulent, viscous, and incompressible. Water

was chosen as the fluid, because it would yield results to use as a baseline for future blood flow

characteristics. The results for this study will be based on a steady state case using the mean

velocity of blood through a normal carotid artery. The inlet boundary layer is defined as a

velocity inlet using the mean velocity of 38.8 cm/s. The outlet boundary is defined as a pressure

outlet with initial pressure of 0.0 pa. All wall boundary layers were defined as no-slip walls,

resulting in a velocity of 0.0 cm/s along the wall surface.

The mesh was created using a surface re-mesher, trimmer, and prism layers. A spherical

volumetric control was introduced at the stenosis region in order to capture more meshing detail

at the region. It is important to have a fine mesh at the stenosis region as this is the main area of

focus for this study. Table 4 shows all mesh references and cell count for each case.



Figure 1: 2-D longitudinal cross section and cross section at stenosis for 30% case.

Table 1: Geometry for 30% stenosis case. Area blockage is the area taken away from the tube by the

spherical infraction.

~30% Stenosis

Length (L) 90.0mm

Diameter (D) 6.0mm

Radius (r) 2.625mm

Area Blockage 8.77mm2




~50% Stenosis

Length (L) 90.0mm

Diameter (D) 6.0mm

Radius (r) 3.375mm







~70% Stenosis

Length (L) 90.0mm

Diameter (D) 6.0mm

Radius (r) 4.250mm


Table 4: Mesh reference values for each case.

Mesh Setting Degree of Stenosis (Spherical Infraction)

30% 50% 70%

Base Size 0.0040m 0.0040m 0.0040m

Max. Cell Size (Relative to

Base)

1000.0 % 1000.0% 1000.0%

Prism Layers 10 10 10

Prism Layer Stretching 1.1 1.1 1.1

Prism layer Thickness

(Relative to Base)

10.0 % 10.0% 10.0%

Surface Curvature (#

pts/circle)

100 100 100

Surface Growth Rate 1.3 1.3 1.3

Min. Surface Size (Relative

to Base)

10.0% 10.0% 10.0%

Target Surface Size

(Relative to Base)

20.0% 20.0% 20.0%

Volumetric Custom Size

(Relative to base)

2.0% 2.0% 2.0%

Volume Mesh (# of cells) 872285 1091137 1391565

Results

The flow streamline velocity and flow reaction to stenosis are shown in Figures 4-6.

Results for the 30% stenosis simulation show a small area of recirculation distal to the stenosis.

A maximum velocity of 70.38 cm/s is present at the point of flow separation, see Figure 4.



Figure 4: Velocity streamlines over 30% spherical infraction.

Results for the 50% stenosis simulation show a large region of turbulence and flow

recirculation distal to the stenosis. The turbulence is shown to extend beyond the recirculation

region and encompass the entire volume of the tube. Downstream flow along the wall boundary

indicates a vortex. A maximum flow velocity of 90.32 cm/s is present at the point of flow

separation, see Figure 5.




Results for the 70% stenosis simulation show a large region of recirculation and

turbulence distal to the stenosis. There are two regions of recirculation, a small area along the

distal wall boundary of the stenosis and a larger region following. The turbulence extents past

the regions of recirculation and encompass the entire volume of the tube. Downstream flow

along the wall boundary indicates vortex. A maximum velocity of 144.73 cm/s is present at the

point of flow separation, see Figure 6.


Figurer 7 and 8 depict the wall shear stress on the arterial tube and stenosis for 30%

stenosis. The maximum wall shear stress on the tube is 11.34 pa, see Figure 11, and is located in

the region between 26% and 24% of total distance proximal to the center of the stenosis, see

Figure 11.



Figure 7: Wall shear stress magnitude and distribution along the arterial tube and across the stenosis for

30% stenosis.

Figure 8: Zoomed view of the wall shear stress distribution across the stenosis for 30% stenosis.

Figure 9 and 10 depicts the wall shear stress on the arterial tube and stenosis for 50%

stenosis. The maximum wall shear stress is 13.24 pa, see Figure 11, and is located in the region

between 22% and 20% of total distance proximal to the center of the stenosis, see Figure 11.


50% stenosis.




Figure 11 and 12 depicts the wall shear stress on the arterial tube and stenosis for 70%

stenosis. The maximum wall shear stress is 24.04 pa, see Figure 11, and is located in the region

between 12% and 10% of total distance proximal to the center of the stenosis, see Figure 11.


70% stenosis.




Figure 13 depicts the total pressure magnitude and distribution on the arterial tube and

stenosis for 30% stenosis. A decrease in total pressure is found downstream of the stenosis. The

pressure difference between upstream and downstream flow was 165.36 pa, see Figure 12.

Maximum total pressure was 177.18 pa and was located between 48% and 46% of total distance

proximal to the center of stenosis, see Figure 12.

Figure 13: Total pressure magnitude and distribution for 30% stenosis.








Figure 11: Wall shear stress distribution for 30%, 50%, and 70% stenosis one a section place at center.

Figure 12: Total pressure distribution for 30%, 50%, and 70% stenosis one a section place at center.

Discussion

11.35

13.24

24.04

0

5

10

15

20

25

-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50%

Wa

ll S

he

ar

Str

ess

Ma

gn

itu

de

(P

a)

Percentage Location from Center

Wall Shear Stress Distribution on Stenosis Plane Section

30% Stenosis

50% Stenosis

70% Stenosis

177.19

259.27

649.29

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

700

-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50%

To

tal

Pre

ssu

re M

ag

nit

ud

e (

pa

)

Percentage Location from Center

Total Pressure Distribution on Stenosis Plane Section

30% Stenosis

50% Stenosis

70% Stenosis



The flow streamline velocity scenes displayed how the flow is affected by the stenosis.

In all cases there was a region of recirculation and turbulence distal to the stenosis. The region

of recirculation increased as degree of stenosis increased. Two separate regions of recirculation

was observed for 70% stenosis, a small region along the boundary of the stenosis followed by a

larger region similar in appearance to the recirculation observed for 30% and 50% stenosis. The

region of recirculation was always followed by a region of turbulence encompassing the entire

tube. The turbulence was found to create a vortex downstream of the stenosis. This irregularity

of flow could have adverse effects.

The wall shear stress and total pressure magnitude for 70% stenosis was significantly

greater than both 30% and 50% stenosis. An increase in magnitudes between 30% stenosis and

50% stenosis was apparent, however the increase was small. This suggests that a degree of

stenosis greater than 50% should be considered as critical stenosis development because the

magnitudes increase rapidly after this stage.

A key interest of this study was to see how the location of maximum wall shear stress and

total pressure changed or did not change. The location of maximum wall shear stress was

different for each case. The maximum location for 30% stenosis was further away from the apex

than 50% and 70%. The location moved closer to the apex as the degree of stenosis was

increased. The location for maximum total pressure did not change for each case. By analyzing

the location of maximum wall shear stress and maximum total pressure one can visualize how

deformation of the stenosis occurs. The flow simultaneously pushes in on the front of the

stenosis while pulling at the top. Such deformation combines with weakening cells over time

could lead to plaque rupture. This proposed deformation would increase greatly as the degree of

stenosis is increased.

As discussed the flow can affect the stenosis by applying stresses on it that might lead to

a rupture of the fibrous cap, but how else could the flow interact with the stenosis? Perhaps the

flow has an effect on how the stenosis is formed and what shape it would take. As explained

earlier, atherosclerosis is occurs when LDL’s penetrate the endothelium, a thin layer of skin-like

cells. But this phenomenon does not occur everywhere within the circulatory system and it

might be due to the magnitude of wall shear stress that occurs at certain points within the system,

such as the carotid artery. The wall shear stress could be an indicator of where plaque deposits

localize and build off of. The flow velocity and wall shear stress results are comparable to

results explained by Caro. The flow velocity illustrations showed that regions of recirculation

occurred distal to the stenosis. Wall shear stress results illustrated that wall shear stress was

minimal distal to flow separation and concurrent throughout the region of flow recirculation.

Caro explained that it is widely accepted that regions with low shear stress and flow recirculation

are where fatty deposits occur. By looking at these two regions, it is possible to visualize the

growth of a stenosis.



This study presents a good idea of what happens within the artery and how flow is

affected by the presence of a stenosis infraction. The study was not meant to establish any

significant data or prove any theory. This study was done to investigate Newtonian fluid flow

within a tube with an obscure infraction to create a hypothesis concerning carotid artery

atherosclerosis, and if possible, relate any observations with results found in other studies.

Future studies will include blood hemodynamics, again using CFD techniques and possible

simulated wall deformation using FEA techniques. The ultimate goal is to create a methodology

to study a specific hypothesis using patient specific artery geometries.

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