stenosis paper final
DESCRIPTION
A thesis paperTRANSCRIPT
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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,
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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 1960s a plethora of studies have
since suggested the contrary. It is now widely accepted that fatty deposits occur at arterial
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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
Figure 2: 2-D longitudinal cross section and cross section at stenosis for 50% case.
Table 2: Geometry for 50% stenosis case. Area blockage is the area taken away from the tube by the
spherical infraction.
~50% Stenosis
Length (L) 90.0mm
Diameter (D) 6.0mm
Radius (r) 3.375mm
Area Blockage 13.47mm2
Figure 3: 2-D longitudinal cross section and cross section at stenosis for 70% case.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
Table 3: Geometry for 70% stenosis case. Area blockage is the area taken away from the tube by the
spherical infraction.
~70% Stenosis
Length (L) 90.0mm
Diameter (D) 6.0mm
Radius (r) 4.250mm
Area Blockage 19.32mm2
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.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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.
Figure 5: Velocity streamlines over 50% spherical infraction.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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.
Figure 6: Velocity streamlines over 70% spherical infraction.
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.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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.
Figure 9: Wall shear stress magnitude and distribution along the arterial tube and across the stenosis for
50% stenosis.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
Figure 10: Zoomed view of the wall shear stress distribution across the stenosis for 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.
Figure 11: Wall shear stress magnitude and distribution along the arterial tube and across the stenosis for
70% stenosis.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
Figure 12: Zoomed view of the wall shear stress distribution across the stenosis for 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 14 depicts the total pressure magnitude and distribution on the arterial tube and
stenosis for 50% stenosis. A decrease in total pressure is found downstream of the stenosis. The
pressure difference between upstream and downstream flow was 314.94 pa, see Figure 12.
Maximum total pressure was 259.27 pa and was located between 48% and 46% of total distance
proximal to the center of stenosis, see Figure 12.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
Figure 14: Total pressure magnitude and distribution for 30% stenosis.
Figure 15 depicts the total pressure magnitude and distribution on the arterial tube and
stenosis for 70% stenosis. A decrease in total pressure is found downstream of the stenosis. The
pressure difference between upstream and downstream flow was 911.9 pa, see Figure 12.
Maximum total pressure was 649.29 pa and was located between 48% and 46% of total distance
proximal to the center of stenosis, see Figure 12.
Figure 15: Total pressure magnitude and distribution for 30% stenosis.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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 LDLs 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.
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Proceedings of the 2012 ASEE North-Central Section Conference
Copyright 2012, American Society for Engineering Education
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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