DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS
STOCKHOLM SWEDEN 2018
A Study of Vascular Plaque
in the Carotid
EXAMENSARBETE TEKNIK, GRUNDNIVÅ, 15 HP
STOCKHOLM SVERIGE 2018
A Study of Vascular Plaque
in the Carotid
In 2015, cardiovascular diseases caused the death of 17.7 million people - 31 % of all deaths globally - making it deadlier than any other cause.
Cardiovascular diseases often result from Arteriosclerosis, a disease where plaque builds up and clogs arteries. As this occurs in the carotid arteries and the plaque material is subject to forces caused by blood pressure and flow, the stress that occurs within could lead to rupture of the material. The ruptured particles could then travel to the brain and cause a stroke.
To identify and prevent these strokes, computed tomography and ultrasound scans are used today. With the help of such examination, it’s possible to see how much of the artery that is clogged and decide whether or not to operate on the patient. Another way of analyzing the plaques vulnerability of rupture is with the help of biomechanics. Based on the geometry and material composition of the plaque, and using a finite element analysis, the stresses and risk of rupture can be estimated.
This thesis invetigates how different plaque geometries, with focus on plaque length and cross-section area coverage, affects the resulting stress in the material. The study was carried out in a total of 12 different plaque models. The models were based on two different lengths, 3 mm and 10 mm and four different cross-sectional coverages.
With computed tomography as reference, models of the carotids and plaque were built using a computer-aided design program. The models were imported to the finite element program COMSOL and analyzed using fluid-mechanical and solid-mechanical simulations. The simula-tions were executed on non-linear solid-state simulasimula-tions and linear-elastic tissue models and the Newtonian fluid assumption.
based on the investigated plaque functionalities, this study found that the stress in the plaque tissue shows a peak at 50-60% plaque coverage of the cross-sectional area, such that the risk of rupture seems to be the highest at this area coverage.
2015 var hjärt- och kärlsjukdomar orsaken till 17,7 miljoner människors död - 31 % av alla dödsfall världen över - vilket gör det till världens vanligaste dödsorsak.
Hjärt- och kärlsjukdomar resulterar inte sällan från Ateroskleros, en sjukdom där plack byggs upp längs blodkärlsväggar och är än mer farlig om det sker i halspulsådern. När plackmaterialet utsätts för krafter från blostrycket och flödet uppkommer spänningar som kan leda till bristning i materialet. Partiklar färdas då till hjärnan vilket kan orsaka stora skador.
I dagsläget används datortomografi för att identifiera och bedöma denna sjukdom. Det är hur stor del av artären som är blockerad av plack som avgör huruvida patienten bör opereras eller inte. Ett annat sätt att avgöra detta är med hjälp av biomekanik. Då står plackets geometri och materialkomposition till grund för analysen och de uppkomna spänningarna och risken för bristning kan beräknas med ett finita elementprogram.
Denna uppsats behandlar olika plackgeometriers påverkan på.de resulterande spänningarna och därmed också.risken för bristning. Studien fokuserar på.skillnader i plackens längd och tvärsnittsarea där totalt 12 stycken fall studeras. Modellerna är gjorda i två olika längder, 3 mm och 10 mm, med varierande grad av plackens tvärsnittsarea.
Med hjälp av datortomografi som referens modellerads halspulsådern och placken i ett design-och konstruktionsprogram. Dessa modeller importerades sedan till ett finita elementprogram och analyseras med hjälp av fluid- och struktursimuleringar. Simuleringarna gjordes med linjärt elastiska material och en ickelinjär stationär studie.
Slutsatsen av denna studie är att vid 50-60 % täckning av tvärsnittsarean nås en maximipunkt då.spänningen är som störst, vilket också.innebär högst risk för att placken brister.
1 Introduction 1
1.1 Arteriosclerosis . . . 1
1.2 Carotid Artery Disease . . . 2
1.3 Risk assessment . . . 2
1.4 Objectives . . . 3
2 Method 4 2.1 Study and Modeling of the Carotid . . . 4
2.2 Modeling of the Plaque . . . 6
2.3 Finite element analysis . . . 7
3 Result and Conclusion 12 3.1 Results . . . 12
3.2 Conclusions . . . 15
3.4 Future Work . . . 17
Appendices 18 A.1 Coordinates of the centerline of the carotid . . . 19
A.2 Different models of plaque . . . 22
A.3 Results of COMSOL-studies . . . 23
A.4 Mesh of vessel and plaque . . . 24
Arteriosclerosis is a progressive cardiovascular disease where plaque builds up inside the arteries over time. The plaque consists of fat, cholesterol and calcium. As the disease progresses it leads to narrow blood vessels with thick and stiff vessel walls. The narrow blood vessel restricts the flow of blood to organs and other parts of the body. See Figure 1.1
There isn’t an exact known cause for the disease. One accepted theory is that the build-up of plaque begins when the arteries are damaged. There are some risk factors that are known to cause damage to the arteries and these are, to mention some, high blood pressure, high cholesterol and smoking. 
Arteriosclerosis is the main reason behind heart attacks and strokes. It is consequently the leading cause of deaths and disabilities in the developed world. Preventing and treating cardi-ovascular diseases requires the highest share of health care costs in the western world.
2 Chapter 1. Introduction
Figur 1.1: Cartoid vessel with plaque in yellow that restricts the blood flow through the anas-tomosis. 
Carotid Artery Disease
Arteriosclerosis that affects the carotid arteries is called Carotid Artery Disease, and might have fatal consequences for the patient as it could lead to a stroke. The great risk lies in when the plaque material ruptures, which causes parts of the plaque tissue to travel into the brain. This has possibly fatal consequences if the tissue would get stuck, blocking the blood flow and thus causing a stroke, as illustrated in Figure 1.2.
1.4. Objectives 3
Figur 1.2: This shows how the brain and carotid artery relates to one another, it also depicts a plaque rupture with the following broken-free piece of plaque that travels to the brain and leads to blocked blood vessels, in other words, a stroke. 
variables such as the plaque material composition and the geometry of the vessel. With many unknown variables it is nearly impossible to individualize a risk assessment. This might lead to unnecessary operations of patient not in the risk of having a stroke.
Study and Modeling of the Carotid
In order to conduct a study on the Carotid, a model was created based on Computed Tomograp-hy scans (CT-scans) received from Karolinska Institutet. CT is a common imaging method used in a variety of diagnostic purposes. The images produced by this method are cross-sectional, slices", of the body . In total, three sets of CT-images from male patients were received and studied.
The pictures were analyzed in a medical image viewer  showing cross sectional images of the head. Figure 2.1 shows one of these images. As reference, the teeth are visible in the top of the picture and the throat is seen as the black area in the middle. The Carotids are in the same picture marked with red arrows, one on each side. It was put into a coordinate system, after which the coordinates of the center line could be read from different points on the z-axis.
As seen in Figure 2.1, the centerline was pointed out by its z-, y-, and x-coordinates. The same was done for several scans around the branching in order to plot a approximation of the Carotid in 3D. All coordinates can be found in appendix A.1. The results were plotted in MATLAB (Figure 2.2), with the red line representing the smaller branch. Note that the measures are given in millimeters and the coordinate system is given according to the CT-scans.
2.1. Study and Modeling of the Carotid 5
Figur 2.1: A CT-scan showing a cross-sectional image of the head. In the picture, the teeth can be seen in the top and the throat in the middle as a black area. The carotids, one on each side, are marked with arrows. The figure illustrates the measuring method used for pointing out the z-, x-, and y-coordinates of one of the carotid’s centerline. The same is done for several cross-sectional images in order to create a 3D-image of the center line.
6 Chapter 2. Method
Figur 2.3: The pictures shows the lumen i.e. the domain where the blood flows. The 3D-models of the carotid were created using the CAD software Solid Edge. For this, the centerlines measured from CT-scans were used, and in addition diameters of the inlet and outlets, measured from CT-scans as well. The lines that are visible in the models represents the centerlines
The next step was to turn the centerline into a 3D model using the computed aided design (CAD) software Solid Edge . For this, the centerlines from Figure 2.2 were used, as well as the diameters of the inlet and the two outlets. The inlet and outlets were measured at the first and last cross-sectional view that were used to plot the centerline. The resulting 3D-models represent the lumen and are shown in Figure 2.3. In addition, a vessel wall was created outside of the lumen. The vessel wall was assumed to be solid and have a constant thickness of 1.00 mm .
The CT-images from case No 1 (Male, 1937) had the best images for reconstruction, hence the resulting model from this case was used in further analysis.
Modeling of the Plaque
2.3. Finite element analysis 7
Figur 2.4: 3D-models made in Solid-Edge of plaque covering 50 % of cross-sectional lumen area and with the respective lengths of 3 mm and 10 mm
Atot = 45.36 mm2. The area the plaque covered in the cross-sectional view was calculated with Aplaque = Atotα, where α corresponds to the percentage of plaque in the cross-sectional view. Different geometries made with corresponding α that was to cover 25 % (α = 0.25), 50 % (α = 0.50), 75 % (α = 0.75) and 90 % (α = 0.90). Aplaque was then used to get the radius of the circle rplaque used for sweeping the plaque model rplaque =
π . In order to explore the impact of the plaque length on the stresses, the models were made in two different sizes, 3 mm and 10 mm long, as seen in Figure 2.4. In total eight resulting plaque models were made and can be found in appendix A.2.
After receiving results from the FEA, it was concluded that the highest stresses were obtained for the blood vessels with 50 % plaque coverage. To analyze this further, two more cases of 40% and 60 % stenosis cross-sectional area coverage of the lumen were examined.
Finite element analysis
8 Chapter 2. Method
The CAD 3D-models were imported to the FEA software COMSOL Multiphysics  and stu-died. First, a CFD (Computational Fluid Dynamics) was conducted to explore how the blood pressure develops in the vessel. After this, structure studies were done to find the stresses in the plaque material.
The objective of the CFD simulation was to find the pressure in the vessel. The Reynolds number Re was calculated as Re = ρbloodubloodD
µblood ≈ 1500, where the parameters ρblood, ublood and
µblood are given in Table 2.1. The carotid’s mean diameter was measured to 7.6 mm from CT-scans as described in section 2.1. As flow can be assumed laminar for Re < 2000 , the CFD was made with laminar flow.
The CFD simulation was done on a rigid wall CFD Model with a no slip condition. First, the model of the carotid (No 1, Male (1937)) was imported to COMSOL from Solid Edge using the function Livelink. In order to minimize points of singularity, the function Remove Details was used on the geometry. The material blood was added with the density ρblood and dynamic viscosity µblood. Laminar flow physics was added with the boundary conditions of inlet, outlet and wall as shown in Figure 2.5. Inlet blood pressure as well as outlet blood velocity is defined in table 2.1. The simulation was done with a rigid wall CFD Model
Meshing was done with COMSOL’s inbuilt physics-controlled mesh, using normal element size. This tool generates a linear tetrahedral mesh.
2.3. Finite element analysis 9
Next, using the pressures received from the CFD study, a solid mechanics simulation was done calculating the stresses in the plaque. The results from the CFD show that the assumption of a constant pressure P = 20 kPa throughout the vessel can be used in further studies. Because of the complex geometry that our model represents and our limited resources with regards to computing power and time, the study on the plaque in the solid mechanics simulation was done only taking into account the vessel geometry and plaque that occurs proximal to the bifurcation. This simplification saves a lot of resources because most of the complex geometry exists distal of the bifurcation.
The specific model that was to be studied was imported from Solid Edge using Livelink. The command Form Composite Faces was then used on the geometry in order to remove all the points of singularity that our complex geometry created. Linear elastic material was used for both the vessel wall and the plaque; parameters are defined in table 2.1.
The solid mechanics study was done by simulating the constant pressure acting in the lumen, this is done by inserting a constant boundary load on all the relevant faces, as seen in Figure 2.6a. The model is then fixated with Fixed constraints at the top and bottom faces of the vessel as seen in Figure 2.6b.
The vessel and plaque was then meshed in a linear tetrahedral mesh predefined in COMSOL as "extra fine", as shown in Appendix A.4.
10 Chapter 2. Method
Figur 2.5: The 3D-model of carotid (No 1, Male (1937)) imported into COMSOL with boundary conditions set for CFD simulation. Inlet marked in purple in the left figure and outlet marked in purple in the right figure. The wall condition is set for all the remaining surfaces.
(a) Boundary loads (b) Fixed constraints
2.3. Finite element analysis 11
Tabell 2.1: Defined parameters for study in COMSOL Multiphysics.  Density of blood ρblood 1060 kg/m3
Dynamic viscosity of blood µblood 0.005 Ns/m2 Inlet blood pressure 150 mmHg Outlet blood velocity 0.5 m/s Young’s modulus plaque Eplaque 500 kPa
Poisson’s ratio plaque νplaque 0.4 Density plaque ρplaque 1090 kg/m3 Young’s modulus vessel wall Ewall 1000 kPa
Result and Conclusion
This study has been carried out by first creating a 3D-model of a section of the blood vessel with plaque of different geometries. The vessel was then analyzed in a CFD Simulation and then in a quasi-static structure analysis.
Result of fluid simulation
The CFD that was used in order to find the pressure along the vessel from the blood flow, resulted in pressures between 19.9 and 20.0 kPa. The resulting von Mises stress distribution can be seen in Figure 3.1. As there’s a small diametrical change through the vessel the near constant pressure is not surprising. The resulting flow velocity through the vessel can be seen in Figure 3.2. The resulting velocity of zero at the vessel wall is an effect from the no-slip condition used in the study.
3.1. Results 13
Figur 3.1: Units in kPa. The result of fluid simulation in order to find the pressure distribution in the plaque caused by the blood flow. As the pressure varies very little through the part examined, the pressure can be assumed to be constant. This was used in the later studies of the blood pressure’s impact on the structure.
14 Chapter 3. Result and Conclusion
Tabell 3.1: The results of the FEM-analysis. The table shows the retrieved von Mises stresses depending on the geometry.
Plaque length [mm] 3 10
Plaque coverage [%] 25 40 50 60 75 90 25 40 50 60 75 90 Maximum stress [kPa] 208 185 182 239 153 138 246 287 369 217 216 306
Figur 3.3: The von Mises stress received from the FEA plotted as a function of the plaque coverage. The green and red line show the results for 3 mm respectively 10 mm long plaque. The blue line shows the percentage for when surgery is carried out today. The results show that stresses can be expected to be higher for plaque covering a longer section. They also show an increase of stress at 50 - 60 % for both lengths.
Result of the structure analysis
The resulting peak von Mises stresses from the structure analyses on surfaces in the plaque can be seen in table 3.1 as well as plotted in Figure 3.3. The results are presented in appendix A.3.
3.2. Conclusions 15
The results show that the highest stresses in the plaque material are found in plaque with 50-60% lumen cross-sectional area coverage. This founding is quite surprising, since we expected the stresses to increase with increased plaque coverage. This result might be caused by the geometry of the models studied and in particular the bending of the plaque.
Figure 3.4 illustrates two types of plaque geometries, one thin and one thicker, viewed in a longitudinal section. The black marks show where the highest stresses were found. A thin plaque tissue is easily bent which means that it doesn’t take up as much stress as a thicker one would. A very thick plaque on the other hand is too stiff to bend and won’t cause the same bending stress. At around 50 % plaque area coverage there is a peak stress, which means that the plaque is thick enough to take up stress but not too rigid that it doesn’t bend.
The results from our study in Figure 3.3 doesn’t just only show that peak stresses occurs in plaque with 50-60% lumen coverage but also that after the peak, the more plaque the less the stress, this is especially evident in the 3 mm long plaque (green line). This suggests that surgery done today at 50% coverage (blue line) is done when the risk of rupture is at the highest and an operation is the most crucial in order to prevent a stroke.
Source of Error
The study that has been carried out in this thesis has shortcomings that needs to be taken into consideration when reviewing the results.
• The blood model used in the study is a Newtonian viscosity model, when in fact blood is non-Newtonian.
16 Chapter 3. Result and Conclusion
Figur 3.4: An explanation of the tissue stresses in the plaque. The Figure shows an example of a blood vessel with little plaque (left) and one with a lot (right). The vessel is viewed in a longitudinal section with the red and yellow area representing the vessel wall respectively the plaque. The black marks show where the highest von Mises stresses were found.
• The Plaque and wall models used in the study are linear models, when in fact they’re both non-linear.
• The composition of the plaque material is approximated to be one homogeneous material, when in fact it is a complex inhomogeneous material made up by cholesterol and calcium.
• The CT-scans provided was hard to decipher and the resulting geometry of the vessel is a severe simplification.
• The geometry of the plaque is an approximation as in reality it is not evenly covering the sides of the cross-sectional view of the vessel. The plaque usually builds up from one side and the coverage is irregular with respect to the cross-sectional view.
• The boundary conditions in the study is a simplification that doesn’t represent reality.
3.4. Future Work 17
Suggestions for future work based on this report is to do the analysis on different geometries with more relevance to patients, since this seems to have significant impact on the stresses. The plaque modeled in this work is evenly spread out on the walls, which is an approximation that might be misleading as plaque rarely builds up in an even manner.
Further work would also be modeling of the plaque material more accurately. There are many types of plaque material, such as soft and hard tissue as well as different matrix compositions, with great variations from person to person. These variations all play a big role in the stress levels and the risk of rupture.
From this study the progress of future work could go two ways according to us:
1. To individualize the data in order to create more patient specific models.
***** Coordinates of the Centerline no 1***** Anonymous male 1937 --- z-led -70.052 y-led 54.7 x-led 82.5 --- z-led -68.804 y-led 54.7 x-led 82.5 --- z-led -66.932 y-led 55.2 x-led 83.0 --- z-led -64.748 y-led 55.7 x-led 83.5 --- z-led -62.252 y-led 56.6 x-led 82.0 --- z-led -57.26 y-led 58.1 x-led 77.1 --- z-led -54.14 y-led 59.1 x-led 75.7 --- z-led -52.258 y-led 60.1 x-led 75.2 --- *** Branching *** --- z-led -51.02 y-led 60.1 y-led 60.1 x-led 75.7 x-led 75.7 --- z-led -50.084 y-led 60.1 y-led 59.6 x-led 75.2 x-led 79.1 --- z-led -49.148 y-led 60.5 y-led 59.6 x-led 75.2 x-led 79.6 --- z-led -47.588 y-led 61.0 y-led 60.1 x-led 75.2 x-led 79.6 --- z-led -45.716 y-led 60.5 y-led 60.1 x-led 73.7 x-led 79.1
A.1. Coordinates of the centerline of the carotid 19
***** Coordinates of the Centerline no 3***** Anonymous male 1950 --- z-led -284 y-led 49.6 x-led 61.7 --- z-led -281 y-led 50.5 x-led 61.7 --- z-led -279 y-led 51.0 x-led 60.4 --- z-led -276 y-led 50.5 x-led 59.9 --- z-led -273 y-led 51.9 x-led 59.9 --- z-led -270 y-led 52.8 x-led 59.0 --- z-led -268 y-led 53.7 x-led 59.9 --- z-led -267 y-led 52.8 x-led 59.0 --- z-led -266.5 y-led 53.2 x-led 59.0 --- *** Branching *** --- z-led -264 y-led 53.2 y-led 55.9 x-led 58.1 x-led 63.1 --- z-led -262 y-led 52.3 y-led 57.7 x-led 56.8 x-led 63.1 --- z-led -259 y-led 52.8 y-led 58.1 x-led 56.8 x-led 64.9 --- z-led -256 y-led 53.2 y-led 59.5 x-led 56.4 x-led 65.3 --- z-led -254 y-led 53.2 y-led 59.5 x-led 57.3 x-led 57.3 ---
25 %, 3 mm 50 %, 3 mm 75 %, 3 mm 90 %, 3 mm
25 %, 10 mm 50 %, 10 mm 75 %, 10 mm 90 %, 10 mm
25 %, 3 mm 25 %, 10 mm 40 %, 3 mm 40 %, 10 mm 50 %, 3 mm 50 %, 10 mm 60 %, 3 mm 60 %, 10 mm 75 %, 3 mm 75 %, 10 mm 90 %, 3 mm 90 %, 10 mm
A.3. Results of COMSOL-studies 23
Mesh of vessel and plaque
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