Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Katul, Ramsey
Master of Applied Science - MASc
University of British Columbia
Atherosclerosis is a deadly cardiovascular disease that is one of the leading causes of mortality in North America. It slowly progresses over the course of a person’s life starting as a streak of fatty cells on the endothelial lining of arteries into a fibrous capped atherosclerotic plaque with a highly thrombotic necrotic core. It is generally asymptomatic until the plaque ruptures causing acute potentially fatal events such as stroke or myocardial infarction. A plaque’s likelihood to rupture is based on an elaborate relationship between physiological, biomechanical and geometric factors. This thesis aims develope methods to study and understand the relationship between these factors and gain a better understanding of plaque rupture. A computational study was performed and published to study the effects of the viscoelastic properties of atherosclerotic plaque on rupture. Material models were chosen to reflect the viscoelastic nature of plaque. Realistic models were obtained from medical imaging, and idealized geometries were created using shapes typically formed by necrotic cores. The computational study showed that higher heart rates led to higher stresses in the plaques. Differing viscous properties affect the stress too, as lower viscous models generated higher stress, and so more prone to rupture. The study illuminated just how limited studies like this are, and how much more there is to know. In addition to computational simulations, physical tests can help close the gap in knowledge to better treat atherosclerosis and predict plaque rupture. Arterial phantoms developed here at the Heart Valve Performance Laboratory can be utilized as they mimic the material properties of arterial tissue. They can be injected with a lipid mixture to simulate atherosclerotic plaque. The missing element is a testbed to pressurize the phantoms between a max and min at different frequencies to simulate the heart. With this testbed, a large number of arteries can be pressurized until plaque rupture, helping gain insight into the events that precede plaque rupture. This testbed is designed, built, and tested, and ready to be used in further studies to learn about atherosclerosis. The computational study and the testbed are initial stepping stones to understanding plaque rupture. By investigating further, a plaque’s stability may eventually be measurable to an accuracy suitable for a clinical setting.
Towards the Detection of Vulnerable Atherosclerotic Plaques by Ramsey Katul B.A.Sc., University of British Columbia 2018 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) January 2021 © Ramsey Katul, 2021 ii The following individuals certify that they have read, and recommend to The College of Graduate Studies for acceptance, a thesis/dissertation entitled: Towards the Detection of Vulnerable Atherosclerotic Plaques submitted by Ramsey Katul in partial fulfillment of the requirements for the degree of Master of Applied Science in Mechanical Engineering Examining Committee: Dr. Hadi Mohammadi, Faculty of Applied Science Supervisor Dr. Ray Taheri, Faculty of Applied Science Supervisory Committee Member Dr. Zheng Liu, Faculty of Applied Science Supervisory Committee Member Dr. Ayman El Naggar University Examiner iii Abstract Atherosclerosis is a deadly cardiovascular disease that is one of the leading causes of mortality in North America. It slowly progresses over the course of a person’s life starting as a streak of fatty cells on the endothelial lining of arteries into a fibrous capped atherosclerotic plaque with a highly thrombotic necrotic core. It is generally asymptomatic until the plaque ruptures causing acute potentially fatal events such as stroke or myocardial infarction. A plaque’s likelihood to rupture is based on an elaborate relationship between physiological, biomechanical and geometric factors. This thesis aims develope methods to study and understand the relationship between these factors and gain a better understanding of plaque rupture. A computational study was performed and published to study the effects of the viscoelastic properties of atherosclerotic plaque on rupture. Material models were chosen to reflect the viscoelastic nature of plaque. Realistic models were obtained from medical imaging, and idealized geometries were created using shapes typically formed by necrotic cores. The computational study showed that higher heart rates led to higher stresses in the plaques. Differing viscous properties affect the stress too, as lower viscous models generated higher stress, and so more prone to rupture. The study illuminated just how limited studies like this are, and how much more there is to know. In addition to computational simulations, physical tests can help close the gap in knowledge to better treat atherosclerosis and predict plaque rupture. Arterial phantoms developed here at the Heart Valve Performance Laboratory can be utilized as they mimic the material properties of arterial tissue. They can be injected with a lipid mixture to simulate atherosclerotic plaque. The missing element is a testbed to pressurize the phantoms between a max and min at different frequencies to simulate the heart. With this testbed, a large number of arteries can be pressurized until plaque rupture, helping gain insight into the events that precede plaque rupture. This testbed iv is designed, built, and tested, and ready to be used in further studies to learn about atherosclerosis. The computational study and the testbed are initial stepping stones to understanding plaque rupture. By investigating further, a plaque’s stability may eventually be measurable to an accuracy suitable for a clinical setting. v Lay Summary Atherosclerosis is a deadly disease caused by the buildup of fatty plaque in arteries. Plaques can rupture and release blood clots into the bloodstream, causing further complications. For this reason, plaque stability is of great interest to researchers. Many numerical studies have been published simulating plaque rupture to learn more. A finite element analysis was performed that explored the effects of heart rate and viscosity on plaque rupture. It found that increased heart rates and lower viscous properties have the potential to cause plaques to become unstable. To verify these results and perform more extensive experimentation a testbed is needed. This testbed will pressurize arterial substitutes to try and provoke plaque rupture. The design, fabrication, and testing of this testbed are described within this thesis vi Preface This thesis presents research work published by the author. Part of the work in the current research was developed in collaboration with other other researchers including Hadi Mohammadi and Mehrdad Zareh of the Heart Valve Performance Laboratory at the University of British Columbia’s Okanagan campus. This work was also published in the journal Cardiovascular Engineering Technology. Chapters 2 and 4 include portions of: Zareh, M., Katul, R. & Mohammadi, H. Mechanics of Atherosclerotic Plaques: Effect of Heart Rate. Cardiovasc Eng Tech 10, 344–353 (2019). https://doi.org/10.1007/s13239-019-00413-6 I researched background information of relevance and contributed to the editing and revision of the manuscript. vii Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ........................................................................................................................ vii List of Tables ................................................................................................................................ xi List of Figures .............................................................................................................................. xii List of Abbreviations ................................................................................................................. xiv Acknowledgements ......................................................................................................................xv Chapter 1: Introduction ................................................................................................................1 1.1 Purpose and Overview .................................................................................................. 2 1.2 Causes and Risk Factors ............................................................................................... 4 1.3 Plaque Development and Necrotic Core ....................................................................... 5 1.4 Fibrous Tissue Formation ............................................................................................. 6 1.5 Arterial Remodeling...................................................................................................... 7 1.6 Thrombosis and Plaque Rupture ................................................................................... 8 1.7 Healing .......................................................................................................................... 9 1.8 Mechanics of Atherosclerotic Plaques .......................................................................... 9 1.8.1 Composition ............................................................................................................ 9 1.8.2 Factors of Vulnerable Plaques .............................................................................. 10 1.8.3 Mechanical Properties of Plaque Components ..................................................... 11 1.8.3.1 Collagen (Types 1&3)................................................................................... 11 1.8.3.2 Elastin ........................................................................................................... 12 viii 1.8.3.3 Smooth Muscle Cells .................................................................................... 12 1.8.3.4 Lipids ............................................................................................................ 12 1.8.4 Plaque Calcification .............................................................................................. 13 1.8.5 Types of Plaque..................................................................................................... 14 1.8.6 Residual Stress in Blood Vessels .......................................................................... 15 1.8.7 Hemodynamics ..................................................................................................... 15 1.8.8 Stable Vs Unstable Plaques .................................................................................. 17 1.9 Risks of Plaque ........................................................................................................... 17 1.9.1 Coronary Artery Disease....................................................................................... 17 1.9.2 Carotid Artery Disease .......................................................................................... 19 1.10 Methods of Detection .................................................................................................. 20 1.10.1 Physical Test ................................................................................................. 20 1.10.2 Computed Tomography Scan (CT Scan) ...................................................... 21 1.10.3 Magnetic Resonance Imaging Scan .............................................................. 22 1.10.4 Optical Coherence Tomography (OCT) ........................................................... 22 1.10.5 Intravascular Ultrasound (IVUS) .................................................................. 23 1.10.6 Positron Emission Tomography (PET) ......................................................... 23 1.11 Methods of Treatment ................................................................................................. 24 1.11.1 Percutaneous Coronary Intervention................................................................. 24 1.11.2 Coronary Artery Bypass Grafting ..................................................................... 25 1.11.3 Carotid Endarterectomy (CEA) ........................................................................ 25 1.12 Summary ..................................................................................................................... 26 Chapter 2: Engineering Perspective...........................................................................................27 ix 2.1 Computational Fluid Dynamics .................................................................................. 28 2.2 Finite Element Methods .............................................................................................. 30 2.3 Methodology ............................................................................................................... 33 Chapter 3: Test Bed Design and Fabrication ............................................................................37 3.1 Control Module ........................................................................................................... 37 3.2 Static Pressure Module ............................................................................................... 39 3.2.1 Hardware ............................................................................................................... 40 3.2.2 Electric Circuit ...................................................................................................... 42 3.2.3 Arduino Code ........................................................................................................ 43 3.3 Dynamic Pressure Module .......................................................................................... 44 3.3.1 Hardware ............................................................................................................... 46 3.3.2 Electric Circuit ...................................................................................................... 48 3.3.3 Arduino Code ........................................................................................................ 50 Chapter 4: Tests and Results ......................................................................................................51 4.1 Computational Results ................................................................................................ 51 4.2 Physical Test Results .................................................................................................. 55 Chapter 5: Conclusion .................................................................................................................60 5.1 Discussion and Future Work ....................................................................................... 60 5.2 Future Applications ..................................................................................................... 61 5.3 Concluding Remarks ................................................................................................... 62 Bibliography .................................................................................................................................65 Appendices ....................................................................................................................................78 Appendix A: Calculation of Volume Change in Arterial Phantom ...................................... 78 x Appendix B: Resultant Total System .................................................................................... 80 Appendix C: Hydraulic System Diagram ............................................................................ 81 Appendix D: Solidworks Diagrams of 3D Printed Parts ...................................................... 82 Appendix E: Arduino Code .................................................................................................. 87 xi List of Tables Table 1: Progression of Atherosclerotic Plaque [43] .................................................................... 14 xii List of Figures Figure 1: Atherosclerotic Artery vs Healthy Artery [6].................................................................. 2 Figure 2: Disrupted flow leads to leads to conditions favorable to atherosclerotic progression through the production and release of various signaling molecules that begin various biochemical processes. Reprinted by permission from Springer Nature: Laboratory Investigations [50] © 2004............................................................................................................................................... 16 Figure 3: Blocked Coronary Artery [54] ...................................................................................... 18 Figure 4: Cross Section of Artery Obtained Through IVUS [69] IVUS of CAD © Ksheka CC BY-SA 2.5..................................................................................................................................... 23 Figure 5: Variations of Geometries in Models Used [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. 34 Figure 6: Viscoelastic Models [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. ........................................... 35 Figure 7: Tubing Connection for the Static Pressure Module ...................................................... 41 Figure 8: Circuit Diagram of the Static Pressure Module............................................................. 42 Figure 9: Components of the Static Pressure Module .................................................................. 44 Figure 10: Electric Circuits to Flip Current Across the Linear Actuator ...................................... 48 Figure 11: Enhanced Electric Circuit to Flip Current Across the Linear Actuator ...................... 49 xiii Figure 12: Peak Cap Stresses in Idealized Geometries [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. 53 Figure 13: Peak Cap Stresses in Realistic Geometries [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. 54 Figure 14: Pressure Profile Without Limits .................................................................................. 55 Figure 15: Pressure Profile with Upper Limit............................................................................... 57 Figure 16: Pressure Profile of Second Test................................................................................... 58 Figure 17: Labeled Picture of the Testbed .................................................................................... 80 Figure 18: Diagram of Hydraulic Connections ............................................................................. 81 xiv List of Abbreviations LDL Low Density Lipoprotein HDL High Density Lipoprotein SMC Smooth Muscle Cell ECM Extracellular Matrix CAD Coronary Artery Disease STEMI ST Segment Elevation Myocardial Infarction NSTEMI Non-ST Segment Elevation Myocardial Infarction ECG Electrocardiogram CT Computed Tomography OCT Optical Coherence Tomography IVUS Intravascular Ultrasound PET Positron Emission Tomography PCI Percutaneous Coronary Intervention CABG Coronary Artery Bypass Graft CFD Computational Fluid Dynamics FEM Finite Element Method PVA Polyvinyl Alcohol IDE Integrated Design Environment PVC Polyvinyl Chloride DPDT Double Pole Double Throw xv Acknowledgements The first to be acknowledged would have to be Dr. Hadi Mohammadi for giving me this opportunity, and for pushing and encouraging me always. This couldn’t have happened without my friends and colleagues at the HVPL who were always there with help and advice. Most importantly, my friends and family in Lebanon and Canada who helped keep me going and saw me through to the end. Thank you1 Chapter 1: Introduction Atherosclerosis affects millions of people all over the world. It is the leading cause of mortality in the developed world and is on its way to the top globally [1]. It is a disease characterized by the growth of plaques on the interior arterial wall. Atherosclerotic plaques begin as a fatty streak -also called a xanthoma- inside the arteries. The lipids that form the fatty streak begin to oxidize and turn cytotoxic, eliciting an immune response [2]. Macrophages absorb the oxidized lipids and become so laden with lipid molecules that they change into foam cells and signal for more immune cells to repeat the process. At this point smooth, muscle cells -that form a layer of the arterial wall- migrate to the inner layer, and proliferate to form fibrous connective tissue to hold the plaque in what is known as the fibrous cap [3]. It varies on a case-to-case basis, but fibrous caps can have extremely thin sections prone to rupture. Plaques in this state are considered unstable. Once the fibrous cap forms, the foam cells undergo necrosis and disintegrate into a soft lipid-filled cavity known as the necrotic core. This all results in heavy remodeling of the arteries which occurs in several stages [4]. The area available for blood flow does not change at first. The outer walls of the artery expand until they become hard and stiff. Once the arteries harden, the fibrous cap grows inward and obstructs blood flow. Calcium deposits can form in the plaques, and cause areas of stress concentration that increase the risk of unstable plaques. The rupture of an unstable plaque can be catastrophic. The cytotoxic necrotic core leaks into the blood flow [5]. Platelets and blood clotting factors aggregate to seal the wound, and form a thrombus to seal the plug. If the thrombus doesn’t dislodge and cause an embolism or stroke, it causes a severe obstruction of the artery. This process is summarized and illustrated in figure 1 2 below. Atherosclerosis is a complicated disease to study, and requires a thorough understanding of its causes, progression, and consequences. Figure 1: Atherosclerotic Artery vs Healthy Artery [6] This figure compares a healthy artery to an artery partially blocked by atherosclerotic plaque. In addition to blocking off the lumen, the plaque contains a necrotic core that could cause many issues if ruptured. 1.1 Purpose and Overview The purpose of this thesis is to narrow the gap in knowledge when it comes to atherosclerotic plaque rupture by studying the effects of heart rate and tissue viscoelasticity on plaque stability through a finite element analysis, and to design and fabricate a testbed that will allow for physical experiments on plaque rupture. This thesis contains multiple sections that discuss this need further 3 and methods taken to better understand plaque rupture. There are five chapters to this thesis including this introduction; • Chapter 1 (Introduction): Describes atherosclerosis from a medical perspective. Literature is reviewed to discuss the origins of atherosclerosis its progression and its rupture. The risk factors that help cause it, how it is found in the human body, and possible treatments that can be recommended. • Chapter 2 (Engineering Perspective): Provides a literature review of how researchers with engineering backgrounds study atherosclerosis and the techniques they use. It also describes the methodology used in the numerical simulation to study the effects of heart rate and viscoelasticity on plaque stability. • Chapter 3 (Testbed Design and Fabrication): Discusses the design process and decisions behind the testbed, and how it was fabricated. The desired specifications of the testbed are explored, and how they are achieved by the testbed • Chapter 4 (Tests and Results): Presents the results of the finite element method study, and discusses their implications. Testbed pressure profiles are also presented to show how effective the testbed is at meeting the desired specifications. Issues that came in between meeting the testbed’s goals are also examined, and the way they were overcome is also explained. • Chapter 5 (Conclusion): Summarizes the dangers of atherosclerosis and the gaps in knowledge when it comes to predicting plaque stability. Examines the results of the numerical study, and the testbed pressure profiles and discusses further work needed to enhance our understanding of atherosclerotic plaque stability. 4 1.2 Causes and Risk Factors There are many factors that lead to the buildup of plaque in the arteries, including age, gender, genetics, diet, smoking cigarettes, high blood pressure, diabetes, and stress. These factors help determine the overall risk of a person developing plaques, but individual susceptibility is still unpredictable [1]. There are also theories that try to predict why plaques form in specific locations. Wall shear stress has been known to influence plaque formation, but this arises from other biological factors that play a role in arterial wall shear stress. These factors promote atherosclerosis through one of two mechanisms; the injury and dysfunction of the endothelial cells that line the inside of blood vessels, and the accumulation and modification of low-density lipoprotein (LDL) cholesterol [7]. A lesion in the endothelial lining creates an ideal location for the LDLs to accumulate and begin the progression of atherosclerosis. Quantifying the effects of different risk factors is pointless because one factor can compound the effects of another [8], and no single factor is ever solely responsible for plaque formation. The more important risk factors include high cholesterol, cigarette smoking, hypertension (high blood pressure), diet, and level of exercise. High concentrations of LDL and total cholesterol have been shown to impair endothelial function [8]. A high LDL to total cholesterol ratio impairs endothelial production of superoxide radicals and other oxygen-free radicals that prevent the oxidation of LDL, which is one of the first steps of plaque formation. Cigarette smoke has many effects on endothelial function [7]. Nicotine causes the constriction of blood vessels, elevates blood clotting factors, blood viscosity, and reduces the levels of high-density lipoproteins (HDL) in the blood (raising LDL to total cholesterol ratio). This imbalance between oxidant and anti-oxidants in the body is known as oxidative stress, and is associated with degeneration in the biological function of various systems [9]. Hypertension is another factor that induces oxidative stress in the 5 endothelium. Additionally, the high blood pressure causes vascular remodeling that decreases shear stress and stimulation of the endothelium causing further damage. A high-fat diet compounds these factors by increasing LDL levels and impairing flow-mediated dilation of arteries. These factors create an environment that stimulates plaque growth. These risk factors help explain how plaques form, but not why they mainly form in certain areas of certain arteries. Specifically, they form in areas where the arteries curve, bifurcate, or branch. This shows that complex vessel geometries, and the hemodynamic conditions they cause play a role in plaque formation [10]. High magnitude variations of blood flow direction are measured through wall shear stress. The wall shear stress is also subject to periodic variations based on the cardiac cycle. This is known as the oscillatory pattern of wall shear stress. It is measured through the use of what is known as the oscillatory shear index [11]. Since endothelial cells line the blood vessel wall; they are highly directional. They tend to be elongated parallel to the direction of flow but are rounded when consistently exposed to multidirectional flow. This changes their effectiveness at their roles and impedes the endothelial ability to produce factors that inhibit coagulation, smooth muscle cell (SMC) proliferation, and promote endothelial cell survivability. 1.3 Plaque Development and Necrotic Core The disruption of the endothelial layer allows for the accumulation of LDL in vessel walls. Once within the vessel walls, the LDL begins to oxidize since they lose their exposure to antioxidants in the bloodstream [2]. This oxidation makes LDLs proinflammatory cytotoxic molecules. They cause the endothelium to activate signaling molecules to attract monocytes that transform into macrophages to destroy the toxic oxidized LDLs through the process of phagocytosis. Once the macrophages begin absorbing LDL, they secrete further signaling factors that attract more macrophages and increase endothelial dysfunction in the surrounding areas [12]. The macrophages 6 absorb so much oxidized LDL that they become known as foam cells. Their presence indicates inflammation driven by lipoproteins, and once a few layers form, they are visible as a yellow fatty streak known as a xanthoma. The fatty streak can still subside at this point by reducing exposure to risk factors. Once the xanthoma thickens, the foam cells begin to break down and form a lipid pool beneath the surface [2]. This compounds with the apoptosis of SMCs and results in the formation of the necrotic core. The dead cells have no pathway to move out of the core, causing it to grow [1]. Furthermore, SMC and macrophage apoptosis release cytokines that signal for more macrophages, repeating and compounding the process [13]. The necrotic core ends up as a cavity filled with soft lipid-laden cells and cholesterol. Its presence indicates that the vessel has been irreversibly remodeled. In addition to macrophages, SMCs also play a role in forming the necrotic core. Some of the lipid-laden cells are thought to have been SMCs. SMCs associated with atherosclerosis exhibit differences from when found in other places [3]. Instead of expressing proteins involved in their contractile functions; these ‘synthetic’ SMCs are in a better capacity to synthesize proteases, cytokines, and extracellular matrix, a material that holds tissue together. They also synthesize proteoglycans that bind to lipids and enhance the cells’ lipid-binding capabilities [14]. Synthetic SMCs are also better suited for migration and proliferation. They play a big role in the next stage of atherosclerotic progression. 1.4 Fibrous Tissue Formation At this point, the plaque consists of a fatty streak with the lipid pool of the necrotic core being formed. SMCs migrate and proliferate to cover the necrotic core. The synthetic SMCs begin to produce collagen, fibronectin, and elastin to form an extracellular matrix (ECM) [3]. This ECM is only formed of type 1 collagen while type 3 is usually present in healthy ECM. This resultant 7 fibrous tissue is stiffer and functions to separate the necrotic core from the rest of the area in the artery available for blood flow also known as the lumen. Fibrous tissue is a major component of plaque. It forms as a response to the remodeling of the arterial wall. The fibrous tissue is responsible for the structural integrity of the plaque and improves its tensile strength and viscoelastic properties [15]. The outermost layer that isolates the core from the bloodstream is known as the fibrous cap. Calcification often occurs within the plaque. Small aggregates form and grow over time into larger nodules or plates of calcium deposits [14]. Osteoclast-like arterial cells begin to form in response to the cytokines released during the initial formation of plaque, and respond to potent osteogenic factors to form the deposits [16]. The presence of calcified nodules indicates progression of the disease. Over a person’s lifetime, the entire necrotic core may calcify. This improves the mechanical stability of the plaque, but until that occurs, the calcified nodules destabilize the plaque and increase the likelihood of rupture. The osteoclast-like cells are capable of resorbing the deposits, but that takes place at a much slower pace due to an imbalance in cytokines signaling for calcium formation or resorption [17]. 1.5 Arterial Remodeling SMCs will usually play a role in regulating blood flow. They can expand or restrict blood vessels based on the hemodynamic conditions of the bloodstream [4]. This is known as Glaglov’s phenomenon. This means that atherosclerotic arteries do not obstruct blood flow immediately. The outer walls of the artery expand first so that there is no change in the cross-sectional area of the lumen. This is known as lumen area compensation. Once the arteries exceed approximately 40% stenosis, the artery cannot expand further and stiffens [18]. This is problematic in itself because healthy arteries expand as a part of their regular function. Their inability to do so results in higher 8 stresses in the artery walls, unnecessarily burdening them. Once lumen compensation is no longer possible, the plaque begins growing inward, narrowing the lumen area. The arterial positive remodeling index is used to quantify the degree of remodeling done by the artery [19]. 1.6 Thrombosis and Plaque Rupture As the plaque grows, structural defects exacerbate and contribute to plaque instability. Rupture prone plaques generally have a large necrotic core covered by a thin inflamed fibrous cap [20]. This is brought about by an increase in the concentration of macrophages in the fibrous cap. They secrete inhibitors and proteases that stop collagen production by SMCs and break down the cap [12]. Most ruptured caps are less than 65 microns thick. While plaque rupture is a single acute event with disastrous consequences, plaques can be unstable for years before breaking. A single adverse event will tip the plaque over the edge and cause it to rupture. This is most commonly brought about by an irregular increase in stress in the plaque [21]. The stress increases mainly due to changes in heart rate or blood pressure brought about by emotional or physical stress. The rupture of the fibrous cap exposes the necrotic core to the bloodstream. This triggers the coagulation cascade due to the lipids and tissue factors contained in the core [5]. The thrombus forms quickly and seals the rupture. It also results in further constriction of the lumen but rarely blocks off flow completely. This increases plaque burden and the risk of cardiovascular complications. The thrombus now occupies most of the lumen and is subject to considerable hemodynamic forces [20]. It can dislodge and cause a stroke even if the plaque remains sealed. Thrombi can also form without a rupture event [22]. This process is known as plaque erosion. If macrophages do not migrate and deteriorate the fibrous cap, it remains stable and doesn’t inflame. When this occurs, hyaluronan -a compound common in the ECM- accumulates and promotes the 9 deterioration of the endothelial layer. The lack of an endothelial layer is cause enough for coagulation. Platelets and other coagulation factors accumulate and form a thrombus [12]. Similar to the thrombus formed by plaque rupture, it obstructs the lumen -increasing plaque burden- and can dislodge causing further complications. 1.7 Healing The formation of a thrombus over the plaque does not need to be lethal. In the best cases, the thrombotic response mediates SMC recruitment [23]. These SMCs have differentiated, however, into the regular ‘contractile’ cells. This means that they synthesis type 3 collagen in addition to type 1, elastin, and ECM. The type 3 collagen makes the new cap more stable and far less likely to rupture but the risk is always there. The healed cap means the plaque has progressed to its final stage. The new cap is thicker and more obstructive to blood flow [24] [25]. This is still burdensome to the cardiovascular system as severely stenosed arteries are major health risks. 1.8 Mechanics of Atherosclerotic Plaques A large component of plaque rupture is mechanical. Biological factors play a role, but they translate into the mechanical properties of the plaque. This section will discuss the mechanical phenomena related to plaque rupture and how they affect plaque stability 1.8.1 Composition Plaques are mainly composed of SMCs, collagen, immune cells, and macrophages with a necrotic core composed of cytotoxic lipids and calcified nodules. The exact composition of a plaque is variable, and even plaques physically close to each other can have very different compositions [1]. A plaque can fibrous with dense calcifications, soft with a large necrotic core and a thin cap, or any other variety possible. Plaques have a wide range of values for material properties [26]. The major component of a plaque is the fibrous tissues. It makes up around 70% of the total material. 10 The necrotic core and calcium deposits account for approximately 25% and the last 5% is accounted for by foam cells. The variation is due to a myriad of reasons. A person’s lifestyle can have a role, in addition to the location and loading conditions the plaque is subjected to over its lifetime [27]. As discussed earlier, shear stress irregularities play a role in plaque formation. Two kinds of irregularities exist; low shear stress and oscillatory shear stress [11]. They induce the production of different biochemical signaling compounds that result in different compositions. Low shear stresses induce less stable and larger plaques than those induced by oscillatory shear stress. 1.8.2 Factors of Vulnerable Plaques An important aspect of atherosclerotic studies is differentiating between stable and unstable plaques. The ability to correctly determine one from the other can have a large impact on patient health [12]. Unstable plaques are defined as those prone to developing into a major adverse cardiac event in the near future. It is important to note however, that most plaques remain without symptoms or rupture and very few grow to be dangerously unstable [12]. The challenge is determining the risk before an event occurs. There are three characteristics used to determine plaque vulnerability, size of the necrotic core, fibrous cap thickness, and the degree of stenosis [28]. Expansive remodeling can disguise the vulnerability of a plaque. A study by Garcia et al. performed post mortem analyses on victims of cardiac arrest and determined that vulnerable plaques have fibrous caps less than 55 microns, and appropriate stability is attained with a fibrous cap thicker than 85 microns [29]. Macrophage infiltration is another important part of this factor of plaque stability [30]. Their presence in fibrous tissue leads to the breakdown of the fibrous cap. They inhibit SMC production of ECM while secreting enzymes that target collagen. 11 1.8.3 Mechanical Properties of Plaque Components The mechanical properties of plaque are difficult to quantify since it is a heterogeneous structure [31]. The properties are also known to change due to the position of the plaque in the intima – the inner lining of blood vessels-, and the conditions the plaque was formed in. The formation of the plaque can also affect its properties, such as the composition, and its ratios vary during the development, as well as any external forces that can influence the plaque. Although the overall properties of the plaque are difficult to determine, the individual components can be tested and amalgamated. The main components of the plaque are comprised of collagen [31], SMCs, and elastin in the fibrous cap, with lipids comprising the necrotic core. 1.8.3.1 Collagen (Types 1&3) Collagen is the most abundant protein in the animal kingdom [32]. It is characterized by its triple helical structure formed by 3 chains of amino acids, the building block of proteins. There are more than 19 different types of collagen that differ from each other through functional blocks of amino acids along the collagen fibrils also formed by a repeating pattern of 3 amino acids. Collagen has many important roles throughout the body, mainly providing tissue with strength as a part of the ECM, a material that holds cells together. It can do this due to the crosslinking of amino acids [33]. Some nonconsecutive amino acids form crosslinks that provide stability. This role makes it responsible for the integrity and material properties of human tissues and systems. Type I and Type III are the most common forms of collagen found in vessel walls, and subsequently, atherosclerosis. Collagen is produced by SMCs, and stabilizes the fibrous cap. It was found that for individual collagen fibrils, the fracture strength was between 5GPa – 11.5GPa. The tests comprised of the nanoindentation of collagen I from rat tails [34]. The collagen fibers are distributed all over the plaque but in the cap as the plaque progresses. The stability of the 12 plaque itself cross-linked structure of the fibers [35]. As the cross-linked structure of the fibers increases the stiffness of the cap increases with it. As Collagen is one of the main components of the fibrous cap, the stiffness of the fibers directly impacts the mechanical properties of the plaque. 1.8.3.2 Elastin Elastin is another key component of the human body. It is typically found in the ECM of tissue. While collagen provides strength, elastin provides elasticity and allows tissues to return to their shape after stretching [36]. They are prominent in blood vessels as they allow for the contraction and expansion of blood vessels as pressure varies. Using an Atomic Force Microscope (AFM), single fibers of elastin were tested to the breaking point [37]. It was found that for small strains uncrosslinked and crosslinked fibers had a Young’s modulus in between 0.5 MPa – 1.0 MPa. The amount of elastin usually found is not large, but it plays a large role in the mechanical properties of plaque due to the effect of SMCs. 1.8.3.3 Smooth Muscle Cells SMCs form a significant layer in blood vessels. As such, they also make most of the fibrous cap. Most of the SMCs in the fibrous cap change their phenotype to generate ECM, changing their function [38]. They become known as synthetic muscle cells, and lose their anisotropic contractile mechanical properties, becoming less stiff. They also form an enzyme called metalloproteinase that breaks down collagen and the ECM in late plaques. Their elasticity varies from 21.6 kPa to 3.5 kPa [39]. This low value means that many collagen fibers are necessary for the ECM to avoid plaque rupture. 1.8.3.4 Lipids Lipids form the majority of the necrotic core. Thus, they are mainly responsible for the viscoelastic mechanical properties of the core [40]. There are different components to the necrotic core which 13 affect the overall mechanical properties. The necrotic core can be composed of LDL, calcium deposits, and cholesterol esters and crystals. The core is soft and viscous. It is described as having a similar feel to toothpaste by some surgeons. Two parameters are used to describe viscoelastic materials. They are the storage and loss modulus. The storage modulus represents the elastic component and quantifies the elastic restoring force of the material. The loss modulus is used for the viscous component and quantifies the energy dissipated due to viscosity. Loree et al have measured these properties of plaques with different levels of cholesterol [41]. Storage moduli ranged from 20 to 300 GPa, increasing along with the cholesterol. The storage modulus increased from 50 to 250 GPa with increases in cholesterol. This range is due to the proportions of esters (which are soft) and crystals (which are stiffer). The makeup of the lipid core greatly affects the properties of the plaque plays a role in plaque rupture. 1.8.4 Plaque Calcification The exact role of calcification when it comes to the vulnerability of plaques is not well known. Generally, plaques become stiffer as they calcify, but they can harm the vulnerability of a plaque to rupture before the calcium deposits grow large enough to stabilize the plaque [42]. The calcification happens due to an increased amount of calcium crystals within the plaque which precipitate into solids [43]. These deposits grow in size and eventually take over the plaque, solidifying it. However, when small individual deposits exist, they create stress concentrations that can burst the plaque. The stiffness of the calcium between 0.1 to 20 GPa, but on average are around 2 GPa [37]. 14 1.8.5 Types of Plaque Plaque can go through different stages, which are not exactly a linear process varies, nevertheless, the type has a direct impact on plaque properties [44]. There are different classifications for plaques as they progress, and are summarized below in table 1. Type I and II are characterized as an early lesion containing only LDL and foam cells. They are reversible if appropriate lifestyle changes are made. Once the LDL and foam cells form into a pool of extracellular lipids; changes to the arterial wall become non-reversible. The plaque moves on from type III when a cap develops. The type IV and Va have a lipid core separated from the bloodstream by the fibrous cap [45]. The type V subtypes are used to describe the predominant features of the late-stage plaque. Va is a stable plaque with no significant calcification and a stable ECM in the cap. Vb is a largely calcified plaque that still has a lipid core, while type Vc consists largely of fibrous tissue. When a plaque ruptures, it becomes a type VI that is hemorrhaging into the bloodstream or gone on to form a thrombus. Type I Initial lesion with foam cells Type II Fatty streaks with multiple foam cell layers Type III Pre-atheroma with extracellular lipid pools Type IV Atheroma with a unified lipid pool Type Va Fibroatheroma Type Vb Calcified plaque with lipid core or large calcification Type Vc Fibrotic plaque with large fibrotic tissue, and no lipid core Type VI Complex plaque with hemorrhage or thrombus Table 1: Progression of Atherosclerotic Plaque [45] 15 1.8.6 Residual Stress in Blood Vessels Blood vessel walls are comprised of three main layers, the intima, media, and externa. These layers are made so that they experience stress even when there are no external loads. This phenomenon is extremely important to the function of blood vessels and the mechanics of the arterial wall. The wall will expand and contract as blood flows, to regulate pressure and flow as the blood gets farther from the heart [46]. Blood vessels need to be able to withstand a variety of conditions and keep functioning over the lifespan of the subject. This is known as residual stress/strain. It is most easily demonstrated when an artery is cut along its length. When this happens, the artery springs open due to the residual stress. Many computational methods ignore the residual stress/strain of blood vessels. A study that explored how this affected the results showed that they help decrease stress in fibrous caps since the lining experiences a compressive state at zero loadings [47]. The residual stress/strain help change the dimensions of blood vessels to suit the environment and pressure experienced [48]. Plaque buildup in a blood vessel will severely hinder the ability of a blood vessel to deform and accommodate a higher heart rate. This phenomenon is what causes initial arterial remodeling where the arteries expand outwards to maintain the original area for blood flow. Plaque affects the remodeling by causing the blood vessels to stiffen, putting a direct impact on both the geometry and composition of the vessel walls. 1.8.7 Hemodynamics Hemodynamic is the study of blood flow, this area of study focuses primarily on the fluid mechanics of blood in the blood vessels. Overall, blood is a non-Newtonian fluid but in certain cases such as large arteries, it can be modeled as laminar Newtonian flow [49]. Hemodynamics is used to explain the effects of disrupted blood flow on plaques and vice versa. Using Computational Fluid Dynamics (CFD), blood flow was examined over the region affected by 16 plaque. It was found that the mean wall shear stress increased over the plaque shoulder where the flow is most disrupted. The plaque and walls are not able to expand to accommodate the flow due to the wall hardening effects of the plaque. Downstream of the plaque is a flow reversal and a recirculation zone. Oscillatory flow occurs due to flow separation. This puts the plaque at further risk due to stresses with large spatial wall shear stress oscillations that rapidly occur over short distances [49]. This concept is shown in figure 2. Figure 2: Disrupted flow leads to leads to conditions favorable to atherosclerotic progression through the production and release of various signaling molecules that begin various biochemical processes. Reprinted by permission from Springer Nature: Laboratory Investigations [50] © 2004 Irregular blood flow also helps initiate the growth of atherosclerotic plaque. Lower shear stresses cause endothelial cells to activate an inflammatory response from the mechanical stimulus. Endothelial cells begin expressing adhesion molecules for lipids to begin accumulation and other factors that begin oxidizing the LDLs [51]. This mainly occurs where blood flow is non-uniform, mostly due to a blood vessel segment with complex geometry such as the inner curve of a bend, or a bifurcation. 17 1.8.8 Stable Vs Unstable Plaques With the understanding of some of the factors that go into the mechanical properties of plaque, the challenge is to determine the stability of a plaque. A stable plaque has a very small risk of bursting, mostly due to large calcification or large fibrous cap to core ratios. In all intents and purposes, it means that if the core is properly protected, it will prevent it from bursting, thus preventing the creation of a thrombus [20]. Typically, vulnerable plaques are determined by their large cores (>40%), thin caps (<65µm), and large obstruction of blood flow (stenosis). Plaques may have large cores and thin caps, but are not particularly vulnerable until they obstruct blood flow. The study by Garcia et al. also found that 70% of ruptured plaques closed off more than 75% of the cross-sectional area of the vessel. Furthermore, less than 5% occupied less than 50% of the area [29]. Plaques that have grown and expanded the artery walls won’t rupture until at least some degree of stenosis occurs. There are many techniques to image plaques, but they are not easily accessible. They also do not allow for an accurate determination of plaque vulnerability. Determining plaque vulnerability properly requires the use of computational methods to fully account for plaque geometry and stress concentrations. 1.9 Risks of Plaque Plaque in a blood vessel has various risks associated with it; the main risk is that the plaque in itself will burst to create a thrombus, potentially blocking blood flow to an important area of the body. In this section, the different diseases associated with atherosclerosis are explained. 1.9.1 Coronary Artery Disease Coronary artery disease (CAD) is the leading cause of death in North America, affecting the lives of 16.5 million Americans and killing over 370,000 people every year [52]. It is classified as the 18 thickening of the coronary arterial wall that supplies oxygenated blood to the heart. The thickening plaque begins to stenose the lumen – the empty area in an artery available for blood flow. Ischemia occurs when the heart does not receive enough oxygen. After thirty seconds of oxygen deprivation, cardiac cells begin to die. There are two main types, Non-ST segment elevation myocardial infarction (NSTEMI), and ST segmented myocardial infarction (STEMI). The former is typically less damaging to your heart [53]. The term comes from the change in ECG (electrocardiogram) readings in the ST segment of the PQRST wave of the electrical measurements of the heart. Figure 3: Blocked Coronary Artery [54] This figure shows the effects of coronary artery disease on the heart. The flow of oxygenated blood is obstructed due to the buildup of plaque and blood clotting. This leads to the death of heart muscle cells causing further complications if not death. In the case of a STEMI, a plaque will grow, rupture, clot, and end up completely blocking blood flow to heart muscles. Immediate medical intervention is required to resume blood flow to the 19 heart. Failure to do so will result in death [55]. NSTEMI is a partial blockage of blood to the heart. It has the potential to permanently damage the heart and even kill, but since the heart is still receiving some blood, it may not be totally lethal. An NSTEMI is shown in figure 3. Plaques blocking blood flow can cause damage to any organ based on their location. Peripheral arterial disease is a blanket term for this phenomenon in other organs. 1.9.2 Carotid Artery Disease Carotid artery disease is a major cause of long-term disabilities and the third leading cause of death [56]. Similar to coronary artery disease, this disease is characterized by the thickening of arterial walls leading to a major organ. Two carotid arteries -on the left and right side- supply blood to the head. They bifurcate into internal and external carotid arteries that provide blood to the brain and the face respectively. The geometry of the bifurcation causes blood flow conditions that promote plaque growth. If the plaques rupture, they will likely cause a stroke, the fifth leading cause of death in the US. There are three types of stroke, bruit, transient ischemic attack, and stroke [57]. Bruit is a whooshing sound caused by reduced blood flow. It is rarely detected and mainly by a stethoscope. A transient ischemic attack is also known as a mini-stroke. It has all the symptoms of stroke, but they are temporary. Strokes however, can cause serious permanent damage including death. A stroke is caused by a lack of blood flow to the brain. When it occurs due to a blood clot in the carotid artery, it is termed thrombotic stroke. An embolic stroke occurs when the blood clot forms outside the carotid artery but makes its way through blood vessels into the brain. Once the brain loses its supply of oxygen, brain cells begin to die. The main symptoms of a stroke are, a drooping face, arm weakness, speech difficulty, trouble with sight, and sudden severe headache [58]. The death of brain cells means that surviving a stroke can leave a person with permanent damage. 20 1.10 Methods of Detection Atherosclerosis can lead to coronary artery disease, which is the worldwide cause of death and other possibly fatal conditions. Methods of detecting the disease are not exact but constantly improving. Many methods do not fully determine whether a person has a plaque or not. There are physical tests that help doctors assess the probability of plaque and justify further testing such as medical imaging. 1.10.1 Physical Test During a physical test, the doctors will be looking for anything that would signify a narrowed or enlarged artery. Using a stethoscope, they will listen for whooshing sounds across arteries. A physical test also looks for a weak or absent pulse in the limbs, and a decrease in blood pressure of the affected limbs. With these physical tests, a doctor may also request further testing, including a blood test, doppler ultrasound, ECG, ankle-brachial index, or a stress test. Physical Exams are always the initial method of diagnosis and allow doctors to determine any initial severity and plan any next step [59]. They do not however, allow the ruling out or diagnosing arterial disease. There are several physical tests and are not always given altogether. The results of a test may warrant further physical testing or the doctor may want images taken. Blood tests are an invasive form of physical testing. They can be used to check for signs of atherosclerosis, and to justify further procedures. The fat, cholesterol, and blood sugar levels are measured after a 12-hour fasting period [60]. The blood tests determine the probability of a plaque and the patient’s risk level. The ankle-brachial index compares the blood pressure at the ankle to that in the arms. It is especially useful for atherosclerosis in the peripheries and limbs of the body. Comparing the pressures allows doctors to have an idea of any obstructions to blood flow. If the ratio of the ankle 21 blood pressure to the arm's blood pressure is between 1 and 1.4, then there is no blockage and a low probability of peripheral arterial disease. An index of less than 0.9 indicates arterial stenosis in the lower leg. An index greater than 1.4 indicates rigid blood vessels and necessitates further testing. The index is very limited in the information it gives, but it can be a starting point to justify further testing. The stress test is used to detect irregularities in a patient’s heart rhythm. An ECG is used while the patient walks on a treadmill. They are constantly asked if they feel discomfort or fatigue. The goal is to stress the heart and have it beat faster. Medication can be used if a patient is incapable of physical exertion. The ECG shows the electrical pulses of the heart, and are examined for irregularities as the patient’s heart rate increases. Technological advances have made the stress obsolete for the most part. It can show if a patient’s artery is more than 70% blocked, which is not useful because strokes and coronary events can occur due to less stenosis than that. 1.10.2 Computed Tomography Scan (CT Scan) The CT scan uses a rotating X-ray to take multiple 2D image slices in 360 degrees [61]. The patient is positioned on a table and moved through a donut-shaped motorized scanner called a gantry. The gantry has an x-ray scanner that shoots beams through the patient. It is then picked up on the opposite side. The source and receiver rotate around the patient to create 2D slices at different angles. These slices can be viewed individually, or combined to create a 3D model of the patient. These slices can range from 1-10mm thick. CT Scans are effective at finding spots before symptoms develop and can find calcium deposits in the plaque. Some risks that follow from using a CT scan is the risk of radiation exposure [62]. A CT angiogram uses a contrast agent to image blood vessels. The agent contains iodine, which blocks x-rays. This makes it very easy to visualize blood vessels; 22 specifically, any narrowing of blood flow. However, since the angiogram picks up the contrast in the blood, it doesn’t image vessel walls, so it cannot recognize arteries undergoing expansive remodeling due to plaque growth. 1.10.3 Magnetic Resonance Imaging Scan Magnetic Resonance Imaging Scan (MRI Scan) uses a combination of radio waves, and strong magnetic field gradients to create images [63]. It is a non-invasive imagining method that maps locations of water and fat in the human body using nuclear magnetic resonance. It is a non-invasive procedure with no radiation, but the powerful magnetic fields mean that any magnetic objects will interfere with the image. The MRI is a very powerful tool for imaging plaques due to its very high resolution. It can be used to assess the size and shape of the plaque, and differentiate between components of the plaque [64]. It can be used to measure the dimensions of the arterial wall, fibrous cap, lipid core, and any calcium deposits. However, it is not capable of imaging coronary arteries due to their rapid motion and the long imaging times associated with the technique. 1.10.4 Optical Coherence Tomography (OCT) OCT is an optical imaging technique that can image coronary arteries with high resolution. An optical fiber catheter is inserted into the patient and infrared light is used at ranges between 1250-1350nm to image the inside of the cross-sectional area of the artery [65]. Red blood cells can interfere with the signal and cause scattering. To deal with this, the immediate area is flushed with saline. This allows for great resolution at a tissue penetration of 1-3 mm. OCT can allow for the identification of a plaque as fibrous, calcified, or lipid-rich [66]. More crucially, it can accurately identify a thin fibrous cap. 23 1.10.5 Intravascular Ultrasound (IVUS) IVUS is another widely used imaging technique similar to OCT as it requires a catheter to be inserted into a vein and wired through to the location of diagnosis. IVUS uses an ultrasound catheter to visualize plaque along the arterial wall. IVUS uses an ultrasound transducer that uses sound waves to image deeper into the vessel wall than light-based techniques such as OCT. This means it has a penetration depth of 4-8mm. IVUS is used to assess the diameter of the lumen and the vessel. This allows doctors to determine if intervention is required [67]. It can also determine the composition of the plaque buildup. IVUS is also capable of determining the composition of plaque, by analyzing the attenuation of the ultrasound. Figure 4 displays a cross-sectional image of an artery taken using IVUS. The poor spatial resolution of IVUS does not allow for the determination of relatively small lengths such as a thin fibrous cap [68]. Figure 4: Cross Section of Artery Obtained Through IVUS [69] IVUS of CAD © Ksheka CC BY-SA 2.5 The yellow line shows the lumen and the blue line shows where the plaque has formed on the arterial wall. The area highlighted in green shows the atherosclerotic plaque build-up. 1.10.6 Positron Emission Tomography (PET) PET is a nuclear imaging technique used for heart conditions. A radioactive tracer is injected into the bloodstream with the help of glucose and travels all over the body emitting gamma rays. Similar to CT angiography, a gamma-ray detector rotates around the chest taking 2D slices of the 24 heart. The slices are combined to form a 3D model of the heart. PET scans help doctors understand to what extent a cardiac procedure will help a patient, but it still has drawbacks. It images the inside of the arteries but not the arteries themselves. It can be difficult to understand how stenosed an artery is, or how thin a fibrous cap may be [70]. Multiple imaging techniques are often used in conjunction with one another to make up for their individual disadvantages and help doctors get a clear picture. 1.11 Methods of Treatment Treatment of Atherosclerosis depends on the severity of each case. For mild cases, patients will be told to pursue a healthier lifestyle. A healthy lifestyle is portrayed as eating heart-healthy foods and staying away from red meat, not smoking, physically active, aiming for a healthy weight, and managing stress. Most cases will also require patients to go on medications. Medications that may be used would affect cholesterol levels, blood pressure, blood clotting, blood thinning, and inflammation [6]. All medications will either target the artery themselves or the makeup of the blood. Intense cases require surgical 1.11.1 Percutaneous Coronary Intervention Percutaneous Coronary Intervention (PCI) is a short-term procedure also known as coronary angioplasty. It is recommended for patients that can’t endure an open-heart surgery such as a coronary artery bypass graft since up to 40% of patients will experience symptoms again. The procedure involves directing a balloon-tipped catheter into the blood vessel to the location with the plaque. Using an x-ray scanner, surgeons will move the catheter into place and inflate the balloon to expand the artery and improve blood flow. A stent is often used to keep the plaque from expanding into the lumen again. The balloon is inflated to compress the built-up plaque and to expand the stent into place. The balloon is then deflated and retracted, leaving the stent behind. 25 This procedure is minimally invasive, common, and considered low risk making it an attractive first step in treating atherosclerosis. 1.11.2 Coronary Artery Bypass Grafting Coronary Artery Bypass Grafting (CABG) is the most common type of open-heart surgery. It can alleviate any issue the patient was facing due to atherosclerosis [71]. This is because a donor blood vessel is taken and used to totally bypass an obstruction in the coronary artery. The most common source for a donor vessel is the saphenous vein in the leg which can provide donors for multiple grafts. The heart may be stopped while a pump is used to keep blood flowing, but the surgery can be performed “off-pump” while the heart is still beating [72]. The off-pump procedure is preferable since it has less of a recovery time and side effects, but is significantly more complex. A newer even less invasive technique is also available that uses robotics to perform the surgery through chest incisions. Either way, it is still a hard procedure that takes its toll on patients, but can keep them symptom-free for 10-15 years. 1.11.3 Carotid Endarterectomy (CEA) CEA is another invasive surgery where surgeons remove the entire endothelial layer to reverse plaque growth and return regular blood flow to the brain [73]. Carotid arterial plaques are formed where the artery forks into the interior and exterior carotid arteries. The procedure involves pinching off the arteries before and after the plaque while placing a shunt to ensure blood flow to the brain. Incisions are made to access and remove the plaque before stitching everything back together. This procedure does not usually use general anesthesia so that the patient’s neurological condition can be monitored in real-time. There are more significant risks with CEA than with CABG [74]. With a mortality rate of 15%, this procedure is recommended for patients with severe cases that have already had a stroke as it will greatly reduce the chances of further strokes. 26 1.12 Summary Atherosclerosis is a potentially deadly disease traditionally characterized by the hardening and narrowing of arteries. Tears and defects in arterial walls allow for the accumulation of LDLs to form xanthomas. As they grow; a necrotic core forms sealed by a fibrous cap. This is the atherosclerotic plaque. The lumen narrows, affecting blood flow, and the plaque may rupture. Plaque rupture is a catastrophic event that can lead to heart attacks, strokes, organ failure, or even death. Treating atherosclerosis depends on the severity of each case. For mild cases and even after surgery for severe ones, patients will be directed towards a healthy lifestyle. A healthy lifestyle is portrayed as eating healthy, such as cutting out processed foods or eating in moderation, adding physical activity, and reducing their weight if they weren’t already at a healthy one. Most cases will also require patients to go on medications. Forms of medications that might be used but not exclusive to cholesterol, blood pressure, blood clot, and inflammation. All medications will either target the artery themselves or the makeup of the blood. Atherosclerosis is very interesting for engineers. Hemodynamic factors have roles in its progression, and plaque rupture is a highly mechanical event that can be studied. In the following chapter, atherosclerosis is examined from an engineering perspective. Numerical methods and techniques used to study plaque rupture are discussed, including one such numerical study by the author in an effort to learn more. 27 Chapter 2: Engineering Perspective The problem of plaque rupture has received a lot of attention recently as an issue that can be tackled by engineers due to its mechanical nature. There is a lot of interest in detecting and predicting plaque ruptures. The most common methods for this; computational fluid dynamics (CFD) and finite element methods (FEM) are techniques known as mechanistic modeling [75]. They assume prior knowledge of the system through the appropriate governing equations. The governing equations are discretized and fitted to the geometry and boundary conditions of the problem at hand to determine the response of the system. This technique relies on an intimate knowledge of the behavior of all components of the system. Statistical modeling doesn’t require any knowledge of the system. Instead, methods such as machine learning are used to find relationships between the input and output of the system, treating it as a black box. Machine learning is a relatively new tool to use for purposes pertaining to atherosclerosis, but recent studies have shown promise; using machine learning algorithms to different ends. Terrada et al. developed an algorithm to predict and classify the progression of atherosclerotic plaques [76]. The developers see it being used as a medical decision support system by doctors. Xie et al. performed a similar study to predict and discover risk factors of carotid atherosclerosis for clinical applications [77]. In an approach closer to the engineering side of things, Madani et al. bridged FEM and machine learning to predict the location and magnitude of peak stresses [75]. The study used a database of twelve thousand finite element simulations as training data, and their algorithm was able to predict the max stresses and their location within 10% error. This study shows how statistical methods can be developed using mechanistic methods such as finite elements, or computational fluid dynamics. 28 2.1 Computational Fluid Dynamics CFD is a numerical method that uses the Navier-Stokes equation -which itself is derived from Newton’s second law- to solve dynamic fluid problems. Computer programs use algorithms to perform the hundreds of thousands of calculations necessary to simulate the behaviour of fluids under certain conditions known as boundary conditions [75]. CFD is applicable to blood flow in arteries and has been used to gain a better understanding of the formation of atherosclerosis. The key to using CFD for blood flow applications is to have the right assumptions depending on the purpose of the study. Blood is formed of a suspension of red blood cells, white blood cells, and platelets within the plasma. This makes it a non-Newtonian fluid whose viscosity changes with the shear [78]. Interestingly it has a Newtonian nature when the shear rate is above 100 s-1 [79]. This is generally the case in large arteries, which can simplify the simulation. However, CFD studies have determined that modeling it as newtonian can lead to relative differences up to 50%. The non-Newtonian characteristics of blood are emphasized in cases with small length scales and where blood flow becomes highly pulsatile. Furthermore, red blood cells can store energy through elastic deformation [80]. This makes blood viscoelastic, another characteristic of its non-newtonian nature. The Weissenberg number is used to characterize viscoelastic flow. It is a dimensionless number defined as the ratio between elastic and viscous forces, and is used along with the widely known Reynolds number. The viscoelasticity of blood is confirmed through the measurement of its loss and storage moduli, which quantify the viscous and elastic components of blood respectively. The loss modulus is greater than the storage; indicating liquidlike behaviour, but the difference gets smaller at high frequencies showing that the elastic effects of blood are not negligible depending on the case being studied. Modeling the non-Newtonian aspects of blood is 29 critical for accurate results in the carotid and peripheral arteries but less necessary in the larger coronary arteries and aorta. Boundary conditions are also critical for CFD simulations of blood flow. Generally, a velocity inlet boundary condition is used. This helps simplify simulations, but determining the inlet velocity profile is difficult, especially when considering the periodic nature of blood flow and irregular geometries at the inlet [80]. A workaround for determining the velocity profile is to use a pressure boundary condition. Pressure in this application is uniform and mainly depends on the distance of the artery from the heart [81]. By extending the domain to upstream of the irregular geometry and defining pressure as the boundary condition, CFD will determine the velocity profile at the location of interest and solve the rest of the flow as initially desired at the same time. Another critical boundary condition is that of the arterial wall. Generally, the arterial walls are defined as rigid or linearly elastic for simplicity when in fact they are viscoelastic, storing energy from blood flow, and dissipating some [82]. This assumption can be used when studying the patterns and characteristics of blood flow, but will lead to inaccurate approximations of other characteristics such as wall shear stress. This is due to the fluid-structure interaction (FSI) between blood and the artery wall. FSI -in arteries specifically- requires three assumptions at the fluid-structure interface [83]. The first and second conditions are that the displacement and traction are at equilibrium at the boundary between fluid and structure. The third is the no-slip condition typical of CFD which is that the velocity of blood at the arterial wall is equal to the velocity of the arterial wall, or zero in most conventional studies. This accounts for the change in arterial diameter due to blood pressure variations in the cardiac cycle; allowing for more accurate results. CFD is a powerful tool that can be used to determine and analyze blood flow characteristics in a variety of ways that can be applied to help treat and detect atherosclerosis. One study by Saha et 30 al. for example; used CFD to study the effects of blood viscosity on ultrasound imaging to allow for more accurate imaging of atherosclerotic plaques [84]. Another by Ilegbusi et al. used CFD to begin the development of a fluid-structure interaction index to help predict plaques critically prone to rupture [85]. The complex nature of blood flow can be simplified to allow for reduced computation time, but the nature of the problem determines which simplifications can be made without reducing the accuracy to unacceptable errors. Fluid-structure interaction can be used to determine the effect of artery walls on the flow, but to properly determine the effect of the flow on arteries, a different numerical technique is better used; the finite element method. 2.2 Finite Element Methods FEM is well-suited for solving the partial differential equations that govern systems’ responses to various stimuli. Phenomena that can be modeled include heat transfer, electrostatics, and stress distribution among many others. FEM works by dividing a system into elements with nodes, and applying the discretized differential equations to each element. This results in a vast system of equations that provide the physical system’s response to external stimuli. FEM has a large role in atherosclerosis research, especially in predicting plaque rupture. However, the difficulty in its application to this field; is in accurately modeling the material properties of plaques and their components. The mechanical properties of plaque components can be found in literature, and they have been discussed in the previous chapter. Despite a good understanding of the mechanical properties of plaque, they are simplified in FEM studies to make the problem easier and save on computation time. This is especially common when a study is looking at the effect of a specific factor and won’t be looking at the effects of certain material parameters. Despite this, these studies still help close the knowledge gap in predicting cap stability. One particular study by Karimi et al [86] in 2012 performed a physical study and 31 computer simulation side by side. Healthy and atherosclerotic arteries were extracted and tested for the difference in their material properties [86]. These material properties were then used in numerical simulations to study the effect of stenosis and calcification on plaque stability and rupture. The arteries were tested assuming a neo-hookean hyperelastic material, and measured for the hyperelastic coefficients. These material parameters were then used in the finite element analysis of the effects of arterial hardening and stenosis as atherosclerosis progresses. Different levels of stenoses were tested with different levels of arterial hardening. The study determined that plaques are most stable when they are calcified, and most vulnerable in a hypocellular state when the fibrous cap is thinnest due to the deterioration of the ECM in the fibrous cap. Interestingly, the study found that plaque is more stable at high levels of stenosis (80-90%) due to the subsequent thickening of the plaque. Another interesting study using FEM was performed by Pazos et al. This study also combined numerical simulations with experimental data. The study aimed to develop a method to test the material properties of lipid pools and arterial walls of atherosclerotic plaque [87]. Arterial substitutes were made from polyvinyl alcohol (PVA), and pressurized. An IVUS catheter was used to measure the geometry and reaction of the PVA. These experiments were performed side by side with numerical simulations of the same case. The resultant data was used to predict the material properties of the substitute itself. A basic single-walled artery was used at first. Once the material parameters were properly determined, a more realistic double-walled arterial substitute with a lipid pool between the layers to simulate the necrotic core. The substitutes are pressurized, measured, and compared to the simulation results to determine material parameters [88]. With the results, the material parameters of the arterial substitute were accurately determined, including the elasticity of the lipid pool as a whole. The authors wanted to use this method to estimate material properties 32 of atherosclerotic plaques while they are still in vivo. This is badly needed in a clinical setting to determine the stability of plaque. The most comprehensive study examined was performed by Gholipour et al. in 2018 [88]. This study aimed to study the effects of arterial bifurcation on plaque stability. Additionally, the study went further and combined CFD with FEM to consider many factors such as solid-fluid interaction, artery viscoelasticity, arterial hyperelasticity, pulsatile blood flow, non-newtonian blood, bifurcation shape, arterial layers, medial layer contraction, calcification, stenosis level, and fibrous cap thickness [88]. To model the hyperelastic viscoelasticity, a 5 parameter Mooney-Rivlin hyperelastic model was used, along with a five-term relaxation model using material coefficients of a Prony series shear relaxation model. The results of the study showed that plaques in specific bifurcations are more unstable than others. It confirmed previous claims in literature about plaque shoulder regions having highest stresses, and showed that microcalcification increases stresses and makes plaque more likely to rupture. This study considered the viscoelastic properties of plaque, but did not specifically examine its effects on plaque stability. These studies are very helpful in gaining insight into atherosclerosis. Much has been learned from them, and they promise more. However, they have their limitations. These studies, along with others studied were limited in their accuracy to real-world conditions. Some studies used static pressure conditions, and the ones that considered oscillating pressure used only one heart rate. They also considered arterial tissue to be elastic or hyperelastic at best. Viscoelastic properties have only recently begun to be considered in finite element studies. These deviations from reality mean that much insight into atherosclerosis is lost. In an effort not to lose this insight, a finite method analysis is performed -for the first time to the best of our knowledge- to examine and study the effects of variable heart rate and viscoelasticity on atherosclerotic plaque rupture. Additionally, 33 a testbed for an experimental set up is constructed to supplement the numerical results. The details of this study are described in detail in the next section. 2.3 Methodology FEM is a good candidate for investigating the effects of viscoelasticity and heart rate on atherosclerotic plaque stability. It is preferred over CFD because that is more suited for studying flow features and other fluid problems. Since plaque rupture occurs due to the pressure, this is a problem of structural stresses. To that end, idealistic and realistic geometric 2D models of a slice of the blood vessel with the plaque were obtained. The realistic models were obtained from OCT and IVUS imaging methods. The idealistic models were designed based on different kinds of shapes of the necrotic core; nodal, linear, or curvilinear. Two fibrous cap thicknesses were chosen for the idealistic models; 70 and 100 microns [28]. The 70-micron thickness was chosen since it is in a grey area for fibrous caps. Below 50 is critical, while above 85 is considered stable. The second thickness of 100 microns was chosen to be well in the stable zone. This can be used to assess how appropriate it is to consider thicknesses over 85 microns stable. It may also provide insight into how the different factors od plaque stability interplay. The results of the two thicknesses compared can show also how cap thicknesses will affect plaque rupture and stability. Examples of the models are shown below in figure 5. As the figure above shows, a relatively simple assumption of the geometry of the plaque is made for the idealistic models. The models consist of the arterial fibrous plaque stenosing the whole artery, with a simple necrotic core close to the lumen. Three different shapes were chosen for the necrotic cores, nodal, linear, and curve-linear. These different shapes were observed in medical imaging of real plaques and used to show the effect of the necrotic core’s shape on plaque stability. Prior to rupture, the necrotic core can be modeled as isotropically elastic, and incompressible with 34 a poisson’s ratio of 0.49 [89]. The fibrous cap’s elastic components are anisotropic and have different elasticities depending on whether the direction is circumferential, radial, or axial. Figure 5: Variations of Geometries in Models Used [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. This figure illustrates the three idealized geometries chosen for the necrotic core. It also shows examples of how these idealized shapes look in real images of plaques. The viscoelastic properties of the fibrous cap can be modeled as a configuration of dampeners (viscous element) and springs (elastic elements). Possible viscoelastic models are shown in figure 6. The Weichert model is chosen for this application. It most accurately describes the creep and relaxation behavior of the fibrous cap [90]. The branch with the single spring element accounts for the elastic portion of the tissue’s material properties. The branches with dampeners each account for different components of the fibrous cap that relax at different rates. Two cases were considered; one with a higher viscosity to account for a higher concentration of SMCs at different stages of plaque development. Lowering the viscoelasticity of a material brings it closer to hyperelastic material models. A key factor for the study is the plane-stress assumption. This 35 assumes that axial stress is negligible compared to the circumferential and radial stresses that are responsible for plaque rupture [90]. Some studies use the plane-strain assumption, which accounts for no strain in the axial direction. An important condition for this is a uniform cross-section, which is not the case due to the plaque. The boundary conditions were set as cyclic pressure oscillation between 10 and 20 kPa. This pressure range is chosen because it is at the extreme ends of recorded blood pressures in humans. Figure 6: Viscoelastic Models [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. The Maxwell, Kelvin-Voight, and standard linear solid configurations shown in figure 6a, 6b, and 6c respectively are too simplistic to be accurate. The Weichert model in 6d is ideal for the applications of this study. 36 Four frequencies were tested; at 60, 90, 120, and 150 beats per minute [28]. Similar to the pressure, these heart rates encompass the extremes observed in vivo. The outer boundary of the fibrous plaque was prescribed a displacement boundary condition of zero. A commercially available FEM code; ANSYS 2017 was used to obtain the stress distribution and peak cap stresses for each case. The models were meshed with triangular elements, taking care to increase the mesh density in critical areas like the area of the fibrous cap between the necrotic core and the lumen. To ensure that errors due to space discretization are reduced, a mesh independency study is performed. Three realistic models were chosen at random for the test. Realistic models were chosen because testing the idealized models may hide meshing issues or other problems due to their smooth shapes. By the last iteration of the test, the three models went from three-four thousand elements to five-six thousand. The relative errors between the two iterations were less than 2%. With mesh independency achieved, we could go forward with other tests knowing that there are minimal errors due to spatial discretization. With this major source of error out of the way, the simulations are performed with confidence in their results and are presented later in chapter 4. 37 Chapter 3: Test Bed Design and Fabrication The numerical simulations are not enough. To gain real insight into the factors behind plaque rupture, a large data set is needed. This requires many tests and is computationally expensive. Furthermore, the simulations themselves are simplified to decrease computing time, so there is a gap between the simulation results and real life. Physical experimentation can fill this gap and verify the assumptions and results of the computational studies. Synthetic arteries produced at the Heart Valve Performance Laboratory mimic the mechanical properties of arteries in vivo. A fatty plaque substitute can be placed within to simulate a real section of artery affected by atherosclerosis. The proposed experiment would need a specialized testbed to pressurize the arteries until they rupture. The testbed would need to have several capabilities to be suitable for its experimental purpose. It would need to oscillate the pressure in the arterial sample between a specific maximum and minimum pressure, operate over a physiological range of heart rates, and record and store the pressure profile within the arterial section. This chapter will discuss the initial design process of the testbed and its subsequent fabrication. One feature of the testbed is its modularity. Its functionality is broken down and performed by three different modules to dynamically pressurize the mock artery and plaque. Minor design choices will be explored first, and design options explored. The module as fabricated is then presented. There are several aspects to the fabrication of each module; the hardware involved, the electrical circuit, and the Arduino code. 3.1 Control Module The control unit is the brain of the simulator. It is responsible for running the previously mentioned components in coordination with the intent of the user. It should allow the user to adjust the systolic 38 and diastolic pressures, and heart rate. To do this, it must apply the inputs to the system through the dynamic and static pressure units. Using a microcontroller such as Arduino is the easiest solution. Arduinos are made for applications such as this. They have analog and digital input/output pins to control electronics. It comes with its unique integrated development environment (IDE) to easily code it from a computer. This makes it easy to adjust the machine and add any features as needed. However, the Arduino is rated 5 V for its input/output pins which won’t be enough for some of the other components. Relays are used to control a high voltage circuit using the Arduino board’s low voltage. The control module consists of the Arduino UNO purchased for this application. The individual codes for each component described previously are compiled together to be uploaded into the Arduino. Part of the code relies on a pressure reading, so a pressure sensor is connected to the Arduino. The sensor is rated for a max of 25 psi, and has 3 wires. Two are connected to the 5V and ground pins on the Arduino. The third wire is connected to an analog input pin. As the pressure changes, the voltage difference between the third wire and the ground changes proportionally from 0 to 5 volts. The Arduino can read this change in voltage as an analog signal. The analog signal is presented by the Arduino as a number ranging from 0 to 1,023 which corresponds with the acceptable range of 0 to 5 V input on the pin. In addition to using the pressure readings in the code, the pressure readings need to be stored for later analysis. The Arduino has a serial.print() command that allows it to send text or values to display on the Arduino IDE’s serial monitor and serial plotter. The serial monitor simply displays the values desired while the plotter plots them on a graph. By using the delay() function, and setting a value of 50 milliseconds the time values can be extrapolated since that is the time between each 39 pressure value. The IDE does not allow for any data to be saved. To read and save the values from the Arduino, a free program called Terra Term is used. 3.2 Static Pressure Module The function of the static pressure unit is to raise the pressure of the arterial system to the lower pressure the system will oscillate from. Increasing water pressure is conceptually tricky since water is not compressible. It is therefore helpful to think of the simulator as a hydraulic system. Increasing the pressure then becomes a question of transmitting a force through the water to the inner walls of the arterial system. There are many ways to do this, each one with its pros and cons. The simpler method uses a piston and cylinder to apply a force to the water. As the piston moves through the cylinder, it displaces water from the cylinder into the arterial system and increases the pressure. Despite the simplicity, there are complications to consider. The force needed by the piston to displace the water depends on the cross-sectional area of the cylinder. Furthermore, the volume of water the cylinder needs to displace is related to the volume of the arterial system since the arteries will bulge in response to the pressure to accommodate the added volume. The various geometric variables affect each other. As the area of the cylinder increases, the necessary stroke length decreases. This makes it less robust and limits the size of the arterial system that could be successfully pressurized. Another configuration is inspired by domestic water pressure boosters. They use an expansion tank and pump to increase the water pressure in homes. The tank is a pressure vessel with a bladder to separate the air and water in the tank. The pressure is built by pumping water into the tank to compress the air portion, and the compressed air pushes back on the water and pressurizes the system. However, the pressure decreases once pressurized water is released into the system when a tap is opened. This system can be adapted to suit the needs of the simulator. 40 By pumping air in to pressurize the tank while already connected to the system, a constant pressure can be reached and maintained. There is also no need for a bladder to separate the air and water in the tank since the air is being added to pressurize the system instead of water. The chamber is connected to the system from a port at the bottom. A port at the top allows air to be pumped in to compress the air portion of the chamber. The pressurized air pushes on the water interface to displace water into the system. The pressure of the water at its interface will be equal to the pressure of the compressed air. The air-and-water chamber is preferable since it is not limited by its geometry. It is limited by the performance of the air pump and the pressure rating of the chamber. 3.2.1 Hardware The pressure module will use a clear polyvinyl chloride (PVC) hose as a conduit for water and air. Two diaphragm pumps were salvaged from portable blood pressure monitors. The pumps are powered by 6-volt DC motors, and connected and to the air/water chamber using a T-shaped hose barb that can be seen in figure 8. The chamber was then connected to the rest of the system from the bottom so that only water would continue into the rest of the system. Additionally, the pumps need to be mounted since they are not stable on their own and vibrate considerably. To get around this, rings made of silicon rubber were cured to slip around the motors. The rubber rings helped to absorb the vibration of the motors, and Velcro strips were attached to fix the motors in place. A diagram of the hose connections is shown below in figure 7. The air chamber was difficult and frustrating to obtain. At first, a box was 3D printed with acrylic panes put in and sealed with silicone putty. Its stability was difficult to maintain, as were airtight connections at the inlets and outlets. A second solution was to use plastic food containers. Certain brands of containers are designed with airtight lids to preserve freshness, and ports were created by attaching hose couplers. Unfortunately, the containers weren’t as airtight as hoped for. Under 41 pressure, the lids began to leak. This was observed by rubbing soapy water around the lid and any connections to the containers. As the system is pressurized, bubbles form where the air leaks. The containers couldn’t handle the pressure. To find an appropriate solution, the basic function of the air/water chamber was re-examined. The chamber provides an interface for the air to push on the water as the air compresses. As the volume of the chamber decreases, so too does the volume of air that needs to be pumped in to achieve a certain pressure. A chamber with as little volume as possible is ideal. It becomes clear that the best chamber is no chamber. The air/water interface could be easily located within a section of hose. In the case of an air pressure drop, a check valve could prevent water from backing into the air pumps and possibly destroy them. Isolating the section of tubing with the check valve creates an ideal chamber. Figure 7: Tubing Connection for the Static Pressure Module This diagram shows how the tubing is connected for the static pressure module. Air is pumped into a chamber with an air-water interface. This will pressurize the water to raise the base pressure. 42 3.2.2 Electric Circuit The electrical components for the simulator are simple. They simply consist of two DC motors powering the pumps. The motors are rated for 6 volts, so they are connected in series to the 12-volt power supply. A switch is placed in the circuit to allow the user to turn the static module on or off separately from the rest of the simulator. To allow the Arduino to control the circuit, a relay is also added in series. A relay allows for two circuits to interact while still totally isolated. It will protect the Arduino from the high voltage of the power supply. Relays are composed of a switch that is electromagnetically flipped open or closed when an electrical current runs through the coil within the relay. Figure 8 shows the circuit with all components in series on one loop. Figure 8: Circuit Diagram of the Static Pressure Module This is the electric circuit for the static pressure module. The air pumps are placed in series with the DC supply. The circuit is open due to a relay that is controlled by the Arduino. 43 3.2.3 Arduino Code Now that the circuit is constructed, it needs to be controlled. The simplicity of the circuit means a simple code. The circuit is switched open and closed by the Arduino through a relay. Arduino pins are voltage based, and do not run enough current to energize the relay’s coil. Special relays were found that could switch relays based on a digital signal from the Arduino. A digital signal from an Arduino consists of a 5-volt output from the pin. The state of the pin is either high (5V) or low (0V). Setting the pin to high while the manual switch is closed will run the motors and pressurize the system. The module now needs to know when to start and stop. A momentary button that connects the Arduino’s 5-volt pin to an input pin will allow the user to signal the simulator to start pressurizing. A pressure sensor allows the system to know the pressure and stop when necessary. It is difficult to change the value of the base pressure. It is determined by a preset value within the code. To get a different base pressure, the value of the variable should be changed and the code reuploaded to the Arduino. The only interface with the testbed is through the IDE on a computer. To increase functionality in the future, a number pad and liquid crystal display screen can be added to the Arduino, and the code modified to allow better user interfacing. There are two sections in an Arduino code. The first is a setup section, indicated in the code with the void setup () command. This section is for declaring initial variables, declaring pins as output or input, or setting the serial rate. The serial rate sets the data transmission rate to the serial monitor. It is needed when you want to read a data value being used while the Arduino is in operation. For this module, a digital input pin was declared and hooked up to a button to be able to start pressurization. An analogue pin was used to read the value from the pressure sensor. A digital pin was declared as an output to turn the pumps off and on as needed. 44 The next section is the looping portion of the code. This part follows the void loop () command. An IF statement is used to determine whether the button has been pressed. Once it is pressed, an IF/ELSE statement turns the pumps as long as the pressure is less than the desired pressure in the code. A picture of the entire static pressure module is found below in figure 9. 3.3 Dynamic Pressure Module Once the static pressure unit has pressurized the system, the dynamic unit kicks in and starts oscillating the pressure between the diastolic and systolic pressures. The oscillation of pressure makes the air and water tank unsuitable for this application. The time it takes to reach the desired Figure 9: Components of the Static Pressure Module This is a labeled picture of the static pressure module. The Arduino controls the circuit through a relay not in the picture. The two air pumps are connected to each other and the rest of the system through the T-shaped hose barb in the center. 45 systolic pressure would depend on the air pump’s performance. This affects the heart rate being simulated and decreases the range of systolic pressures achievable. The higher the systolic pressure, the longer it will take to be reached. Furthermore, bringing the pressure back down during the oscillation will need careful control of the depressurization, or the air pressure in the tank risks going below the desired diastolic pressure and the system will need to repressurize. This will make achieving the desired pressure profile very difficult. When it comes to cyclically pressurizing the system, a piston and cylinder configuration is more suitable. The parameters of the piston correlate to those of the heartbeat. The frequency of the piston is the same as the heart rate. The systolic pressure is proportional to the piston’s stroke. While not appropriate for increasing the static pressure of the system, this configuration is ideal for dynamic pressure oscillation. The issue now lies with finding a system to drive the piston back and forth that allows control over the different parameters of the heartbeat. The first design to achieve the controlled oscillation of a piston involves using a crank driven by a spinning wheel. The key feature of this configuration is the ability to adjust the radius of the wheel. That way, the systolic pressure can be changed by adjusting the radius, and the heart rate can be adjusted by changing the speed of the wheel. This design is easy to control but hard to build. Changing the radius of the wheel is the difficult part. The peg could be removed from a slot on the wheel and placed into a different slot at another point on the radius. The radius would need to be manually changed without much of an idea as to how the systolic and diastolic pressures will change. The other option would be to use a device to move the crank up or down the radius of the wheel such as a stepper or servo motor. This would allow for almost any radius to be implemented instead of the incremental basis of the manual configuration. However, there are some technical difficulties associated with the design. The first 46 is that the force will be transmitted to the crank through the motor. A bending moment will be applied to the motor’s shaft which is not how it is designed to be loaded. This means the simulator will require more frequent and expensive maintenance. Furthermore, the motor would be spinning on the wheel and require wiring. The spinning and twisting of the wires with the wheel would require more expensive measures. Another option for oscillating the piston is a linear actuator. Linear actuators work by having a motor drive a lead screw to move a rod axially. Tying the parameters of the heartbeat to the linear actuator is more complicated. The heart rate of the testbed is the same as the frequency of the actuator, but the frequency is not adjusted so easily. It depends on the speed of the actuator and the stroke length. Since the stroke of the actuator also affects the systolic pressure, changing a parameter is more complicated. The speed of the actuator can be adjusted with a motor speed controller, and the stroke length can be determined by the control system. The performance of the actuator affects the maximum frequency and pressure of the simulator. 3.3.1 Hardware The dynamic pressure module is centered around the linear actuator. A high-speed 12-volt actuator was purchased from Firgelli Automations. It can handle a 44 lb static load, and 22 lb dynamic loading. At max loading, it travels at 4.5 inches per second, and can go up to 9 inches per second with no load. The maximum pressure required of the system 200 mmHg or approximately four psi. To power it, a 12-volt DC power supply was purchased. The surface area of the piston in the cylinder will determine the force of the linear actuator. In place of a piston and cylinder, a large 60 ml syringe was obtained. With a surface area of 0.785 in2. This would apply a force of 2.6 lb. This is a small portion of the max loading so a minimal speed reduction is expected. To get an accurate sense of the speed-and thus frequency- the system 47 should be built and tested, but at this point, the linear actuator can do everything it needs to do. For the moment, the size of the cylinder is due to the availability of material. Further calculations to determine the volume change of the phantom can be found in appendix A. This can be helpful when optimizing the geometry of the cylinder in later stages. Varying the surface area and stroke length while maintaining the stroke volume changes the speed needed from the linear actuator to maintain the required heart rate. The system pressure can be made more or less sensitive to the change of position of the linear actuator. The same kind of tubing from the static module was used to connect the dynamic module to the rest of the system. The tubing attaches through the use of hose couplers that allow for various hosing configurations to be achieved. The components still needed to be connected physically. Mounting brackets were available for the linear actuator. The rear of the actuator was bolted to the bottom of the plastic tub with a bracket, while the rod was attached to the plunger of the syringe through a second mounting bracket, and a 3D printed coupler. A second piece was 3D printed to be able to mount the syringe and hold it in place. Diagrams of the 3d printed parts can be found in appendix D. Electrical components were also sourced for the electric circuit. There are two limit switches mounted side by side at each end of the actuator’s stroke. One is to break the circuit and stop the actuator from moving past the max stroke of the cylinder plunger. The other is for the Arduino to know that the actuator has reached one end of its stroke. The next section goes into further detail concerning the electrical components of the dynamic pressure module. 48 3.3.2 Electric Circuit To change the direction of the linear actuator, the flow of current through it must be reversed. The most feasible way to do this is to have two single-pole double-throw switches at each pole of the actuator. Each switch can change which end of the battery is connected to that pole. If they are not switched almost simultaneously, then a short circuit will occur. Using one double pole-double throw (DPDT) switch will prevent that, and a relay is used to allow the Arduino to control the switching. This relay requires 12 volts to switch, and is not compatible with the Arduino. The same compatible relay from the static module was used to switch a circuit that activates the DPDT relay. The Arduino controls this relay through another relay. A manual switch is added between the and the positive pole of the power supply to allow a person to start and stop the oscillation. Figure 10 shows how the relay switches the direction of the current. Figure 10: Electric Circuits to Flip Current Across the Linear Actuator This electric circuit is used to reverse the current across the linear actuator through the use of a double-pole double-throw relay. The relay has two switches that operate simultaneously to flip the connections across the actuator. 49 The length of the syringe is less than the stroke of the linear actuator. To prevent a failure, limit switches were mounted on 3D printed parts. The limit switches are single pole -double throw switches. A diode is placed across the pole and the normally open end of the switch. When the actuator reaches the end of the syringe’s stroke and activates the switch, the current is stopped. The diode is placed so that it will stop the current, but allow it to flow the other way. When the relay switches the current, it is able to flow the other way to reverse the direction of the actuator. A second limit switch was mounted next to each one, but without a diode. The second set of limit switches connect the Arduino 5-volt output to digital input pins. When they are activated, they close the circuit and input pins read a value of “high”. This lets the Arduino know when to switch the current. Figure 11 below shows where the limit switches are placed in the circuit to control the actuator. Figure 11: Enhanced Electric Circuit to Flip Current Across the Linear Actuator This circuit is the same as the previous figure, but normally closed limit switches have been added. They partially open the circuit when the actuator reaches one of its limits. The diode across the switch keeps the circuit closed, but current can only flow in one direction. When a limit switch is activated, the linear actuator stops moving until the Arduino activates the relay and reverses the flow of current. 50 3.3.3 Arduino Code The Arduino code is initially simple since it is only trying to achieve a simple oscillatory pressure wave. The length of the stroke for now, is determined by the position of the limit switch. When the Arduino receives a high digital signal from a limit switch, the linear actuator is at one of its extreme positions. The polarity of the power source was matched to the limit switches and Arduino. Energizing the relay coil will cause the polarity to retract the actuator. When the limit switch at the extended position is activated, the Arduino will activate the relay and cause the actuator to change direction. The other limit switch will do the opposite. This way the actuator will go back and forth between the limit switches. The algorithm block diagram shown in figure 14 shows how the code will function. To start, three digital pins were used. Two were declared as inputs. One from each limit switch. The third pin is an output. It controls the direction of the actuator. When the relay is not energized, the actuator extends. When the relay is activated, it switches the polarity across the actuator to make it retract. The code does this through if statements. When one of the limit switches activates, it sets the pin to high or low if the actuator is fully extended or retracted respectively. 51 Chapter 4: Tests and Results Two sets of results are discussed. The first set of results are for the FEM study that looked at the effects of heart rate and viscoelasticity on plaque stability. Two viscoelastic material models were applied along with different heart rates to several idealized and realistic plaque geometries. In addition to the FEM study, a testbed was built to verify future numerical simulations. This test bed has three criteria; oscillate pressure between a maximum and minimum value, operate at frequencies normal for a human heart, and record the pressure within the arterial system. The results for the testbed correspond to tests undertaken to make sure it meets the criteria set. 4.1 Computational Results Once the geometries were obtained and boundary conditions assigned, mesh independence was investigated to ensure that the size of the mesh did not affect the results. The mesh independency study determined that the numerical results were not affected by the mesh. Following that, tests were run with all the different combinations of heart rate, viscosity, and fibrous cap thickness. The results in figures 12 and 13 below show the peak cap Von-Mises stresses (PCS) for each case of the idealistic and realistic geometries. The results show that the heart rate has a notable effect on peak cap stresses. In every case, the peak cap stress rises then -in some cases- plateau as the heart rate increases. The range of stresses across the heart rates increases from 15-25 kPa to 35-45 kPa along with viscosity for the seventy-micron cap thickness models. When the thickness is increased to one hundred microns, the ranges decrease to 14-15 kPa and 20-35 kPa respectively. The higher viscosity models had lower peak cap stresses, but wider ranges. This indicates that at higher viscosities, the fibrous cap can handle pressures better, but is more sensitive to changes in heart rate. 52 Despite the variability in the material properties of fibrous caps, as mentioned previously, 300 kPa is considered the standard breaking point in numerical simulations. Half of the idealistic models had peak cap stresses above that limit. In one case, the stress was below 300 kPa for 60 and 90 BPM, but then increases above 300 when the heart rate increases to 120 and 150 BPM. Only one model from the 100-micron tests had stresses over 300 kPa. Despite being above the 85-micron ‘safe zone’, the plaque is still vulnerable. The factors affecting plaques’ susceptibility to rupture affect each other, and even if one factor is not vulnerable, the other factors may compound to form a plaque highly prone to rupture. This study shows the importance of viscosity and heart rate on plaque rupture. Numerical studies need to be comprehensive in the factors being studied, and use a range of heart rates instead of just one. One’s heart rate is never constant throughout the day. Heart rate increases during exercise, when under stress, or during anxiety. Emotional shocks can spike heart rates, and even how well-rested one is can have an effect [91]. The precise viscoelastic nature of the fibrous cap is also important. As seen in the results, it can have a role in how sensitive the plaque is to heart rate. The viscoelastic nature of the fibrous cap varies depending on the exact composition of the plaque, which depends on how far it has progressed. SMCs and macrophages increase the viscous effects of the viscoelastic plaque. The viscosity of the plaque affects the impact of heart rate on plaque stability. This makes them important markers in determining plaque stability along with cap thickness, necrotic core size, and plaque morphology. These factors all interplay to affect one another and must all be taken into consideration. No one factor can determine a plaque's likelihood to rupture. They must all be studies together. This is where the testbed can apply itself to future research. 53 Figure 12: Peak Cap Stresses in Idealized Geometries [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. These results show the PCS in each idealized geometry. The top graph shows the results for caps with thicknesses of 70 microns. For each geometry and cap thicknesses, two levels of viscosity were tested. 54 Figure 13: Peak Cap Stresses in Realistic Geometries [28] Republished with permission of Springer Nature BV, from Mechanics of Atherosclerotic Plaques: Effect of Heart Rate, Mehrdad Zareh, Vol 10, No 2, 2019 Permission conveyed through the Copyright Clearance Center, Inc. These are the results for the realistic geometries. The shapes of the necrotic cores were taken as is, along with the calcification in model H2. Two levels of viscosity are tested for each geometry. 55 4.2 Physical Test Results With the simulator built, several tests are run to test the system and its capabilities. To start, the simulator is run as-is. This means that the linear actuator will keep retracting or extending until it hits a limit switch and reverses. This test will run the actuator to the max stroke of the syringe at full speed. This test will determine the performance of the system at maximum parameters. This is mainly a test of the dynamic pressure module, so the static module is not used in this test. From there, the system can be further modified to allow the adjustment of those parameters such as frequency, diastolic and systolic pressure. The raw data of the first test are shown below in figure 14. Figure 14: Pressure Profile Without Limits For this test, the actuator oscillated the full length between the fully extended and retracted positions. It achieved a max pressure around 22 psi, and an average frequency of around 50 BPM. 56 When the test began, the position of the syringe was not at the complete end of one stroke. The actuator was moved to the fully retracted position and held there. The dynamic module was then activated fully and pressure oscillation can be observed. The first thing noticed is the noise. During the static portions of the test, oscillations occur with low amplitude and high frequency. This is noise from the sensor, and can be reduced with a low pass filter for the pressure sensor before it is read by the Arduino. Despite the noise, values are still obtainable from the graph. The maximum pressure achieved by the system can be approximately measured at around 22 psi or 1137 mmHg. The frequency is calculated by measuring the period from the graph and taking its inverse. The first few cycles were inconsistent with the rest of the test. The actuator was slower, so the peaks are farther apart. This aberration was solved by itself when the actuator becomes more consistent. The average of the frequency between every peak was calculated to obtain a value for the frequency. The frequencies averaged 0.837 Hz or 50 bpm. The frequency is too low for the scope of the project, but this is not an issue yet. For this test, the entire stroke of the syringe is being used, so by limiting the upper pressure to the desired range, the stroke is decreased, and the frequency increases. For the next test, the Arduino is coded to reverse the stroke once the pressure reaches an upper limit. For this portion, an upper limit of 200 mmHg or 4 psi is chosen. These figures are implemented by writing them into the code. An or statement is used to add a second condition to energize the relay when a specific pressure is reached in addition to when the limit switch is toggled. The system starts with the full volume of the syringe, and the static pressure module brings the system up to the desired minimum pressure of 0.75 Psi. This way, there is no need to limit the 57 minimum pressure since it occurs naturally at the bottom of every stroke. The pressure data is plotted in figure 15 below. Introducing an upper limit to the pressure greatly reduced the stroke length. This in turn increased the frequency, to an average of 66 bpm or 1.11 Hz. This is an acceptable value of heart rate in a healthy person. While the minimum pressure is relatively consistent, the max pressure overshoots the desired 4 psi with a max error of 62.5%, and an average error of 22%. This possibly results from a combination of the lag time of the Arduino and the noise from the sensor. Additionally, there is a recurring pattern in the profile. The pressure plateaus between 1.5 - 1.8 Psi every oscillation for a fraction of a second during the phase when pressure increases. During testing, it was noticed that air bubbles were remaining in the system, which is theorized to be the source of Figure 15: Pressure Profile with Upper Limit This pressure profile had an upper pressure limit of 4 psi implemented through the Arduino code. The frequency is increased to 66 BPM since the stroke length is decreased as a result of the upper pressure limit. 58 this error. As the system is pressurized, the air is compressed which delays the transmission of pressure to the system walls and pressure sensor. These issues were addressed for the next test. An upper limit of 4 psi was maintained, and the time delay decreased to 30 milliseconds to make the Arduino more responsive. There is less time between the Arduino reading a value over the max pressure, and its command to reverse the direction of the linear actuator. There should be less time for the system to overshoot. Additionally, extra care was taken to flush the system of air entirely. After these measures were taken, the system was tested again, with the results shown in figure 16 below. Figure 16: Pressure Profile of Second Test This pressure profile had the same upper limit of 4 psi. In this case, the time delay at the end of every Arduino loop was reduced from 50 ms in previous tests to 30 ms. Extra care was taken to flush all the air from the hosing system. It led to more consistent max pressure peaks and a frequency of 66 BPM. 59 These results are more promising. The max pressure peaks are more consistent, with an average error of 4.9% and a max error of 12%. The average frequency is maintained at 66 BPM. The lower pressure range was decreased further to 0.5 psi to test that limit of the system. The figure shows that it is consistent, although there are deviations due to noise. The random noise is still present in the pressure profile as it has not been addressed. So far, it has not impeded the functioning of the system. Addressing this issue remains for later work. The system performs as required by the scope of the project, and meets all the criteria set out at the beginning. 60 Chapter 5: Conclusion The results of both the testbed and the FEM study are promising. In this chapter they will be discussed and evaluated. Any future work necessary will also be examined along with any possible applications for the testbed. 5.1 Discussion and Future Work Despite the minor inaccuracies, the results are promising. So far, the testbed can pressurize the system dynamically to oscillate between two values within physiological conditions. The testbed pressurized the system up to the desired value, and was then able to oscillate at an appropriate frequency. The testbed parameters have its initial criteria, and can thus be considered a successful minimal viable product. It can be greatly improved to further facilitate the desired experimental procedures it is designed for. The main improvements include noise reduction, better pressure control, and easier interfacing. The pressure profiles show considerable noise; which can affect the control over the pressure oscillation. The noise needs to be reduced while the testbed is in operation. The best option for this is an active low pass filter. An active one is needed because passive filters do not need an external power source that can dampen the signal. This will lead to an underestimation of the pressure by the Arduino. While having the filter draw from an external power source will complicate the circuit, it is worth it to ensure accurate pressure readings. A more important improvement is finer control over the pressure. So far, the system simply oscillates between two pressures, but this is not an accurate representation of the pressure in the blood vessels of the body. Vascular pressure profiles vary based on their location in the body, and do not simply oscillate between two values the way the testbed does. While the simple oscillation is sufficient for initial testing, it would be better and more robust if it could simulate a variety of 61 pressure profiles from across the body. PID (proportional-integral-derivative) control is possible on the Arduino and open-source libraries are available online. The issue now lies with the linear actuator. Since the actuator uses a simple DC motor, the Arduino wouldn’t be controlling the pressure, but instead the rate of change of pressure -through the speed of the motor. This will require further work to ensure that the testbed isn’t applying the desired rate of change of pressure at a shifted pressure value. A good workaround to this is to use a stepper motor to control the actuator. Stepper motors spin in discrete increments, so the exact position of the actuator -and thus the pressure value- can be controlled at every point in time of the cycle. This will allow for precise control over all parameters of the pressure profile; maximum and minimum pressure, shape, and frequency. As more functionality is added to the testbed, interfacing becomes more difficult simply through the Arduino code. A need arises to be able to control the output without changing and uploading code every time a change is desired in one of the parameters. LCD screens and number pads can be compatible with Arduino microcontrollers. This would allow a user to select the maximum and minimum pressures, frequency, and pressure profile to simulate different locations in the body. The simulator would be more convenient to use especially for many experiments in a row. 5.2 Future Applications There are many possible applications for the testbed both in furthering research and for commercial purposes. Another research application could be in studying the formation of atherosclerosis. As mentioned in the literature study, shear stress is crucial to endothelial cell development and functionality. Variations in shear stress cause disruptions in the endothelium forming atherosclerotic predilection sites. The testbed could be used to study this effect in greater detail to further understand how atherosclerosis forms. Arterial phantoms could be made that are suitable 62 substrates for endothelial seed cells. The simulator would then begin pressurization to apply the necessary shear stress and develop the endothelial cells more similar to in vivo conditions than possible before. These cells could then be used for a plethora of other studies. Specifically to atherosclerosis, the response to injury theory could be tested in a lab setting by applying turbulent flow to the cells to see how they’d react. This could lead to a much deeper understanding of why atherosclerotic plaques form in the places they do, and how to recognize these predilection sites. This way, potential plaque sites can be found in patients and monitored while it is still a few fatty cells smeared on the arterial wall. This has the potential to prevent a serious decay in health before it results in thousands of dollars of invasive medical procedures and strain on the public healthcare system. Commercial applications would center around educational purposes. In medical schools, a variety of training platforms are used to teach medical skills. These are often made of unrealistic silicon or rubber materials, and are unsophisticated in their simulation of the medical procedure. When coupled with the lifelike material of the arterial phantoms, the testbed could be used to provide pressurization to the more realistic training models. Doctors would be more prepared for real procedures having practiced on the more realistic platforms. 5.3 Concluding Remarks Atherosclerosis is a deadly cardiovascular disease that is often only detected after a stroke, heart attack, or death. It affects many people worldwide and is a hard burden on the public health system. High concentrations of lipids in the bloodstream lead to the formation of a xanthoma on the arterial wall. Brought about by an unhealthy lifestyle and diet; plaques restrict blood flow and rupture when they progress too far. Plaque rupture leads to blood clotting that can completely block blood flow and cause heart attacks, stroke, organ failure, and even death. This places a huge burden on 63 public health systems and is one of the leading causes of death in North America. It is difficult to detect early, and often isn’t found until it’s too late. From an engineering perspective, there is a lot of interest in plaque rupture due to its mechanical nature. To that end, computer simulations are often used to study certain structural or flow features using computational fluid dynamics or finite element analysis. These numerical methods are powerful tools but not without their inaccuracies. To save on computational time, certain phenomena are considered negligible. In the finite element study performed, considering the usually neglected viscous material properties of the fibrous cap showed that heart rate is a major factor in plaque rupture. Many previous studies neglected the viscoelastic properties of plaque, and even those that did not; only considered a single heart rate. This computational study shows that heart rate is another factor critical to plaque rupture. Heart rate along with the other three traditional factors interplay to form conditions that affect a plaque’s likelihood to rupture. The interplay between all these factors makes it very difficult to predict the stability of a plaque to rupture. There is a large gap in knowledge for researchers trying to model atherosclerotic plaques and their rupture. Further research is much needed to better understand atherosclerosis and stopping the deterioration in health it causes. To bridge this gap in knowledge; a heart simulator is built to serve as a testbed for arterial phantoms with mechanical properties similar to arterial tissue. Phantom arteries can be implanted with a suitable plaque analogue, and pressurized as if from a heart. This would enable large scale testing of many different plaque geometries to help recognize gaps of knowledge when it comes to modeling plaque rupture. A complete understanding of plaque rupture could help develop models accurate enough to be of use in a clinical setting. This would help countless people prone to developing arterial plaque. This initial prototype oscillates between an upper and lower pressure 64 within the phantom to simulate pressure pulses from the heart. The functions of the prototype are split between several modules to allow for easy changes and upgrades as needed. Pressurization is achieved through the static and dynamic pressure modules. The static pressure module is responsible for raising the pressure of the system to the minimum required. The dynamic module then takes over and begins to oscillate the pressure as required. This is all coordinated by the control module, which keeps track of the pressure and runs the modules accordingly. The testing module for this report consists simply of an arterial phantom. Further experimentation will have the same arterial phantoms injected with a fatty material that mimics plaques. The testing module can be interchanged with other systems needed for different purposes. There are countless areas of research that can make use of the testbed, to help bring forward scientific innovations and improve lives everywhere. 65 Bibliography [1] E. Falk and V. Fuster, "Atherothrombosis: Disease Burden, Activity, and Vulnerability," in Hurst's The Heart, McGraw-Hill, 2011. [2] H. Yoshida and R. Kisugi, "Mechanisms of LDL Oxidation," Clinica Chimica Acta, pp. 1875-1882, 2010. [3] A. C. Doran, N. Meller and C. A. McNamara, "Role of Smooth Muscle Cells in the Initiation and Early Progression of Atherosclerosis," Arteriosclerosis, Thrombosis, and Vascular Biology, pp. 812-819, 2008. [4] V. A. Korshunov, S. M. Schwartz and B. C. Berk, "Vascular Remodelling Hemodynamic and Biochemical Mechanisms Underlying Glagov's Phenomenon," Arteriosclerosis, Thrombosis, and Vascular Biology, vol. 27, no. 8, pp. 1722-1728, 2007. [5] F. Otsuka, S. Yasuda, T. Noguchi and H. Ishibashi-Ueda, "Pathology of Coronary Atherosclerosis and Thrombosis," Cardiovascular Diagngnosis and Therapy, vol. 6, no. 4, pp. 396-408, 2016. [6] National Heart, Lung, and Blood Institute, "Atherosclerosis," National Intsitute of Health, 13 November 2018. [Online]. Available: https://www.nhlbi.nih.gov/health/health-topics/topics/atherosclerosis/treatment. [Accessed 20 July 2020]. [7] R. A. Vogel, "Coronary risk factors, endothelial function, and atherosclerosis: a review," Clinical Cardiology, vol. 20, pp. 426-432, 1998. [8] G. S. Berenson, S. R. Srinivasan, W. Bao, W. P. Newman, R. E. Tracy and W. A. Wattigney, "Association Between Multiple Cardiovascular Risk Factors And 66 Atherosclerosis In Children And Young Adults," The New England Journal of Medecine , pp. 1650-1656, 1998. [9] B. Uttara, A. V. SIngh, P. Zamboni and R. Mahajan, "Oxidative Stress and Neurodegenerative Diseases: A Review of Upstream and Downstream Antioxidant Therapeutic Options," Current Neuropharmocology, vol. 7, pp. 65-74, 2009. [10] A. M. Shaaban and A. J. Duerinckx, "Wall Shear Stress and Early Atherosclerosis: A Review," American Journal of Roentgenology, vol. 174, pp. 1657-1666, 2000. [11] Y. Mohamied, E. M. Rowlan, E. L. Bailey, S. J. Sherwin, M. A. Schwartz and P. D. Weinberg, "Change of Direction in the Biomechanics of Atherosclerosis," Annals of Biomedical Engineering, vol. 43, no. 1, pp. 6-25, 2015. [12] J. F. Bentzon, F. Otsuka, R. Virmani and E. Falk, "Mechanisms of Plaque Formation and Rupture," in Acute Coronary Syndromes Compendium, 2014, pp. 1852-1866. [13] G. Eelen, P. de Zeeuw, L. Treps, U. Harjes, B. W. Wong and P. Carmeliet, "Endothelial Cell Metabolism," Physiological Review, vol. 98, pp. 3-58, 2017. [14] W. Insull Jr., "The Pathology of Atherosclerosis: Plaque Development and Plaque Responses to Medical Treatment," The American Journal of Medecine, vol. 122, no. 1, pp. S3-S14, 2009. [15] A. C. Newby and A. B. Zaltsman, "Fibrous cap formation or destruction - the critical importance of vascular smooth muscle cell proliferation," Cardiovascular Research, vol. 41, no. 2, pp. 345-360, 1999. [16] T. M. Doherty, K. Asotra, L. A. Fitzpatrick, J.-H. Qiao, D. J. Wilkin, R. C. Detrano, C. R. Dunstan, P. K. Shah and T. B. Rajavashisth, "Calcification in Atherosclerosis: Bone 67 biology and chronic inflammation at the arterial crossroads," Proceedings of the National Acadamy of Sciences of the United States of America, vol. 20, pp. 11201-11206, 2003. [17] M. Abedin, Y. Tintut and L. L. Demer, "Vascular Calcification Mechanisms and Clinical Ramifications," Arteriosclerosis, Thrombosis, and Vascular Biology, vol. 24, no. 7, pp. 1161-170, 2004. [18] M. R. Ward, G. Pasterkamp, A. C. Yeung and C. Borst, "Arterial Remodeling Mechanisms and Clinical Implications," Circulation, vol. 102, no. 10, pp. 1186-1191, 2000. [19] J. Ohayon, G. Finet, A. M. Gharib, D. A. Herzka, P. Tracqui, J. Heroux, G. Rioufol, M. S. Kotys, A. Elagha and R. I. Pettigrew, "Necrotic Core Thickness and Positive Arterial Remodeling Index: Emergent Biomechanical Factors for Evaluating the Risk of Plaque Rupture," American Journal of Physiology: Heart and Circulatory Physiology, vol. 295, no. 2, pp. 717-727, 2008. [20] Z. Sun and L. Xu, "Computational Fluid Dynamics in Coronary Artery Disease," Computerized Medical Imaging and Graphics, vol. 38, pp. 651-663, 2014. [21] V. Fuster, B. Stein, J. A. Ambrose, L. Badimon, J. J. Badimon and J. H. Chesebro, "Atherosclerotic Plaque Rupture and Thrombosis Evolving Concepts," Circulation, vol. 82, no. 3, pp. 47-59, 1990. [22] T. Quillard, G. Franck, T. Mawson, E. Folco and P. Libby, "Mechanisms of Erosion of Atherosclerotic Plaques," Current Opinion in Lipidology, vol. 28, no. 5, pp. 434-441, 2017. 68 [23] J. F. Bentzon, C. S. Sondergaard, M. Kassem and E. Falk, "Smooth Muscle Cells Healing Atherosclerotic Plaque Disruptions are of Local not Blood Origin in Apolipoprotein E Knockout Mice," Circulation, vol. 116, no. 18, pp. 2053-2061, 2007. [24] A. P. Burke, F. D. Kolodgie, A. Farb, D. K. Weber, G. T. Malcom, J. Smialek and R. Virmani, "Healed Plaque Ruptures and Sudden Coronary Death," Circulation, vol. 103, no. 7, pp. 934-940, 2001. [25] S. Carr, A. Farb, W. H. Pearce, R. Virmana and J. S. Yao, "Atherosclerotic Plaque Rupture in Symptomatic Carotid Artery Stenosis," Journal of Vascular Surgery, vol. 23, no. 5, pp. 755-766, 1995. [26] C. Cheng, R. de Crom and R. Krams, "Shear Stress-Induced Changes in Atherosclerotic Plaque Composition are Modulated bu Chemokines," The Journal of Clinical Investigation, vol. 117, no. 3, pp. 616-626, 2007. [27] W. E. Hellings, W. Peeters, F. L. Moll, S. R. Piers, J. van Setten, P. J. Van der Spek, J.-P. de Vries and K. A. Seldenrijk, "Composition of Carotid Atherosclerotic Plaque is Associated with Cardiovascular Outcome," Vascular Medecine, pp. 1941-1950, 2010. [28] M. Zareh, R. Katul and H. Mohammadi, "Mechanics of Atherosclerotic Plaques: Effect of Heart Rate," Cardiovascular Engineering and Technology, vol. 10, no. 2, pp. 344-353, 2019. [29] H. M. Garcia-Garcia, I.-K. Jang, P. W. Serruys and J. C. Kovacic, "Imaging Plaques to Predict and Better Manage Patients with Acute Coronary Syndrome," Circulation Research , vol. 114, pp. 1904-1917, 2014. 69 [30] A. C. van der Wal and A. E. Becker, "Atherosclerotic Plaque Rupture - Pathologic Basis of Plaque Stability and Instability," Cardiovascular Research , vol. 41, no. 2, pp. 334-344, 1999. [31] N. K. Seemantini, B. E. Bouma, J. de Boer and G. J. Tearney, "Evaluation of collagen in atherosclerotic plaques: the use of two coherent laser-based imaging methods," Lasers Med Sci., vol. 24, no. 3, pp. 439-445, 2009. [32] H. Lodish, A. Berk, S. Zipursky and e. al., "Collagen: The Fibrous Proteins of the Matrix," in Molecular Cell Biology 4th edition , New York, W.H. Freeman, 2000, p. Section 22.3. [33] S. Katsuda, Y. Okada, T. Mnamoto, Y. Oda, Y. Matsui and I. Nakanishi, "Collagen in Human Atherosclerosis Immunohistochemical Analysis Using Collagen Type-Specific Antibodies," Arteriosclerosi and Thrombosis, no. 12, pp. 494-502, 1992. [34] M. D. Shoulders and R. T. Raines, "Collagen Structure and Stability," Annual Review Biochemistry, no. 78, pp. 929-958, 2009. [35] M. P. Wenger, M. A. Horton, L. Bozec and P. Mesquida, "Mechanical Properties of Collagen Fibrils," Biophys J., vol. 93, no. 4, pp. 1255-1263, 2007. [36] A. Krettek, G. M. Sukhova and P. Libby, "Elastogenesis in Human Arterial Disease," Arteriosclerosis, Thrombosis, and Vascular Biology, vol. 23, no. 4, pp. 582-587, 2003. [37] A. C. Akyidz, L. Speelman and F. J. Gijsen, "Mechanical Properties of Human Atherosclerotic Intima Tissue," Journal of Biomechanics, no. 43, pp. 773-783, 2014. [38] G. L. Basatemur, H. F. Jorgensen, M. C. H. Clarke, M. R. Bennet and Z. Mallat, "Vascular smooth muscle cells in atherosclerosis," Nature Reviews Cardiology, no. 16, pp. 727-744, 2019. 70 [39] Q. H. T. J. S. Z. L. Z. H. Z. H. M. H. W. V. D. V. S. M. G. Zhu Y1, "Temporal analysis of vascular smooth muscle cell elasticity and adhesion reveals oscillation waveforms that differ with aging.," Aging cell, vol. 11, no. 5, pp. 741-750, 2012. [40] A. l. o. o. p. M. J. Y. J. T.Lee, "Static circumferential tangential modulus of human atherosclerotic tissue," Journal of Biomechanics, vol. 27, no. 2, pp. 195-204, 1994. [41] H. M. Loree, B. J. Tobias, L. J. Gibson, R. D. Kamm, D. M. Small and R. T. Lee, "Mechanical Properties of Model Atherosclerotic Lesion Lipid Pools," Arteriosclerosis and Thrombosis, vol. 14, no. 2, pp. 230-234, 1994. [42] G. Bailey, J. Meadows and A. R. Morrison, "Imaging Atherosclerotic Plaque Calcification: Translating Biology," Current Atherosclerosis Reports, vol. 18, no. 8, 2016. [43] 1. P. T. S. C. C. Z. S. a. J. T. a. Kelvin KL Wong, "Effect of calcification on the mechanical stability of plaque based on a three-dimensional carotid bifurcation model," BMC Cariovasc Disord., vol. 12, no. 7, 2012. [44] F. Wu, H. Song, Q. Ma and J. Xiao, "Hyperintense Plaque on Intracranial Vessel Wall Magnetic Resonance Imaging as a Predictor of Artery-to-Artery Embolic Infarction," Stroke, vol. 49, 2018. [45] H. C. Stary, A. B. Chandler, R. Dinsmore, V. Fuster, S. Glagov, W. J. Insull, M. E. Rosenfeld, C. J. Schwartz, W. D. Wagner and R. W. Wissler, "A definition of Advanced Types of Atherosclerotic Lesions and a Histological Classification of Atherosclerosis," Circulation, vol. 92, no. 5, pp. 1355-1374, 1995. 71 [46] Heart, "heart.org," [Online]. Available: https://www.heart.org/en/health-topics/high-blood-pressure/the-facts-about-high-blood-pressure/blood-pressure-vs-heart-rate-pulse. [Accessed 16 11 2019]. [47] J. Ohayon, O. Dubreuil, P. Tracqui, S. Le Floc'h, G. Rioufol, C. Lara, F. Thivolet, R. I. Pettigrew and G. Finet, "Influence of Residual Stress Strain on the Biomechanical Stability of Vulnerable Coronary Plaques: Potential Impact for Evaluating the Risk of Plaque Rupture," American Journal of Physiology; Heart and Circulatory Physiology, vol. 293, no. 3, pp. 1987-1996, 2007. [48] F. YC, "wha are residual stresses doing in our blood vessels?," Ann Biomed Eng., vol. 19, no. 3, pp. 237-249, 1991. [49] C. M. Schirmer and A. M. Malek, "Computational fluid dynamic characterization of carotid bifurcation stenosis in patient-based geometries," Brain Behav., vol. 2, no. 1, pp. 42-52, 2012. [50] K. S. Cunningham and A. I. Gotlieb, "The role of Shear Stress in the Pathogenesis of Atherosclerosis," Nature Laboratory Investigations, no. 85, pp. 9-23, 23 9 2005. [51] J. Ohayon, G. Finet, S. Le Floc'h, G. Cloutier, A. M. Gharib, J. Heroux and R. I. Pettigrew, "Biomechanics of Atherosclerotic Coronary Plaque: Site, Stability, and In Vivo Elasticity Modeling," Annals of Biomedical Engineering, vol. 42, no. 2, pp. 269-279, 2013. [52] Cleveland Clinic, "coronary artery disease," [Online]. Available: https://my.clevelandclinic.org/health/diseases/16898-coronary-artery-disease. [Accessed 18 11 2018]. 72 [53] Healthline, "healthline," [Online]. Available: https://www.healthline.com/health/nstemi#risk-factors. [Accessed 18 11 2019]. [54] National Institute of Heart, Lung, and Blood Institute, "Heart Attack," [Online]. Available: https://www.nhlbi.nih.gov/health-topics/heart-attack. [Accessed 18 11 2019]. [55] M. C. Staff, "Mayo Clinic," 5 June 2020. [Online]. Available: https://www.mayoclinic.org/diseases-conditions/coronary-artery-disease/symptoms-causes/syc-20350613. [Accessed 7 July 2020]. [56] "Stroke Statistics," The Internet Stroke Center, November 2016. [Online]. Available: https://www.ninds.nih.gov/Disorders/All-Disorders/Stroke-Information-Page#disorders-r1. [Accessed 7 July 2020]. [57] Mayo Clinic, "Mayo Clinic," [Online]. Available: https://www.mayoclinic.org/diseases-conditions/carotid-artery-disease/symptoms-causes/syc-20360519. [Accessed 19 11 2019]. [58] "National Institute of Neurological Disorders and Stroke," 27 March 2019. [Online]. Available: https://www.ninds.nih.gov/Disorders/All-Disorders/Stroke-Information-Page#disorders-r1. [Accessed 7 July 2020]. [59] "Arteriosclerosis," 2018. [Online]. Available: https://www.mayoclinic.org/diseases-conditions/arteriosclerosis-atherosclerosis/diagnosis-treatment/drc-20350575.. [60] M. C. Staff, "Arteriosclerosis," Mayo Clinic, 24 April 2018. [Online]. Available: http://www.mayoclinic.org/diseases-conditions/arteriosclerosis-atherosclerosis/diagnosis-treatment/diagnosis/dxc-20167050. [Accessed 10 July 2020]. 73 [61] M. C. Staff, "CT Scan," Mayo Clinic, 28 February 2020. [Online]. Available: https://www.mayoclinic.org/tests-procedures/ct-scan/about/pac-20393675. [Accessed 14 July 2020]. [62] "Computed Tomography," National Institute of Biomedical Imaging and Bioengineering, 2016. [Online]. Available: https://www.nibib.nih.gov/science-education/science-topics/computed-tomography-ct. [Accessed November 2019]. [63] "Magnetic Resoncance Imaging," National Institute of Health, 2009. [Online]. Available: https://www.nibib.nih.gov/science-education/science-topics/magnetic-resonance-imaging-mri. [Accessed 11 2019]. [64] J. D. Anderson and C. M. Kramer, "MRI of Atherosclerosis: Diagnosing and Monitoring Therapy," Expert Review of Cardiovascular Therapy, vol. 1, no. 5, pp. 69-80, 2007. [65] S. Geraci, C. Tamburino and A. la Manna, "Optical coherence tomography for coronary imaging," E-Journal of the ESC Council for Cardiology Practice, vol. 9, no. 12, 2010. [66] M. Terashima, H. Kaneda and T. Suzuki, "The Role of Optical Coherence Tomography in Coronary Intervention," Korean Journal of Internal Medecine, vol. 1, no. 27, pp. 1-12, 2012. [67] "Intravscular Ultrasound (IVUS)," Angioplasty.org, February 2013. [Online]. Available: http://www.ptca.org/ivus/ivus.html. [Accessed November 2019]. [68] D. Fornell, "The Advantages and Disadvantages of OCT vs. IVUS," Diagnostic and Interventional Cardiology, 18 May 2011. [Online]. Available: https://www.dicardiology.com/article/advantages-and-disadvantages-oct-vs-ivus. [Accessed 20 July 2020]. 74 [69] "Intravascular ultrasound," Wikipedia, 2009. [Online]. Available: https://en.wikipedia.org/wiki/Intravascular_ultrasound. [Accessed November 2019]. [70] B. McCall, "The big question: CT, MRI, or nuclear for coronary artery disease diagnosis," AuntMinnie.com, 7 March 2015. [Online]. Available: https://www.auntminnie.com/index.aspx?sec=ser&sub=def&pag=dis&ItemID=110358. [Accessed 20 July 2020]. [71] "Coronary Artery Bypass Grafting (CABG)," UCSF Department of Surgery, December 2018. [Online]. Available: https://cardiacsurgery.ucsf.edu/conditions--procedures/coronary-artery-bypass-grafting-(cabg).aspx. [Accessed November 2019]. [72] National Institute of Health, "Coronary Artery Bypass Grafting," National Heart, Lung, and Blood Institute, 11 February 2019. [Online]. Available: https://www.nhlbi.nih.gov/health-topics/coronary-artery-bypass-grafting#:~:text=Coronary%20artery%20bypass%20grafting%20(CABG,arteries%2C%20are%20narrowed%20or%20blocked.. [Accessed 21 July 2020]. [73] "Carotid Endarterectomy," HealthLinkBC, 22 July 2018. [Online]. Available: https://www.healthlinkbc.ca/health-topics/hw224563. [Accessed November 2019]. [74] National Institure of Health, "Questions and Answers About Carotid Endarterectomy," National Institute of Neurological Disorders and Stroke, 13 August 2019. [Online]. Available: https://www.ninds.nih.gov/Disorders/Patient-Caregiver-Education/Hope-Through-Research/Stroke-Hope-Through-Research/Questions-Answers-Carotid-Endarterectomy. [Accessed 21 July 2020]. 75 [75] A. Madani, A. Bakhaty, J. Kim, Y. Mubarak and M. R. Kofrad, "Bridging FInite Element and Machine Learning Modeling: Stress Prediction of Arterial Walls in Atherosclerosis," Journal of Biomechanical Engineering, vol. 141, 2019. [76] O. Terrada, B. Cherradi, A. Raihani and O. Bouttane, "Classification and Prediction of Atherosclerosis Diseases Using Machine Learning Algorithms," in 2019 5th International Conference in Optimization and Applications, Kenitra, Morroco, 2019. [77] J. Xie, H. Wang, Zhang, Jiyuan, C. Meng, Y. Kong, S. Mao, L. Xu and W. Zhang, "A Novel Hybrid Subset-Learning Method for Predicting Risk Factors of Atherosclerosis," in IEEE international Conference on Bioinformatics and Biomedecine, Kansas City, MO, 2017. [78] A. Baieth, "Physical Parameters of Blood as a Non-Newtonian Fluid," International Journal of Biomedical Science, vol. 4, no. 4, pp. 323-330, 2008. [79] "Non-Newtonian and Newtonian Blood Flow in Human Aorta: A Transient Analysis," Biomedical Research, vol. 28, no. 7, pp. 3194-3203, 2017. [80] L. Campo-Deano, M. S. N. Oliviera and F. T. Pinho, "A Review of Computational Hemodynamics in Middle Cerebral Aneurysms and Rheological Models for Blood Flow," Applied Mechanics Review, vol. 67, pp. 030801-1-16, 2015. [81] H. Mohammadi and F. Bahramian, "Boundary Conditions in Simulation of Stenosed Coronary Arteries," Cardiovascular Engineering, vol. 9, pp. 83-91, 2009. [82] C. A. Figueroa, I. E. Vignon-Clementel, K. E. Jansen, T. J. Hughes and C. A. Taylor, "A Coupled Momentum Method for Modeling Blood Flow in Three-Dimensional Deformable 76 Arteries," Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 5685-5706, 2006. [83] V. C. Rispoli, J. F. Nielsen, K. S. Nayak and J. L. Carvalho, "Computational Fluid Dynamics Simulations of Blood Flow Regularised by 3D Phase Contrast MRI," Biomedical Engineering Online, 2015. [84] D. K. Saha and Hossain, "A Simulation Study on Viscosity Change Effects in Ultrasound Based Carotid Atherosclerosis Diagnosis," in Proceedings of 2015 3rd Internaitonal Conference on Advances in Electrical Engineering, Dhaka, Bangladesh, 2015. [85] O. Ilegbusi and E. Valaski-Tuema, "A Fluid-Structure Interaction of Coronary Plaque Rupture," in Biomedical Simulation, Phoenix, Arizona, 2010. [86] A. Karimi, M. Navidbakhsh, S. Faghihi, A. Shojaei and K. Hassni, "A Finite Element Investigation on Plaque Vulnerability in Realistic Healthy and Atherosclerotic Human Coronary Arteries," Journal of Engineering in Medecine, vol. 227, no. 2, pp. 148-161, 2012. [87] V. Pazos, R. Mongrain and J.-C. Tardif, "Mechanical Characterization of Atherosclerotic Arteries Using Finite-Element Modeling; Feasibility Study on Mock Arteries," Transactions on Biomedical Engineering, vol. 57, no. 6, pp. 1520-1528, 2010. [88] A. Gholipour, M. H. Ghayesh and A. Zander, "Nonlinear Biomechanics of Bifurcated Atherosclerotic Coronary Arteries," International Journal of Engineering Science, vol. 133, pp. 60-83, 2018. 77 [89] H. Mohammadi and K. Mequanint, "Effect of Stress Intensity Factor in Evaluation of Instability of Atherosclerotic Plaque," Journal of Mechanics in Medecine and Biology, vol. 14, no. 5, 2014. [90] M. Zareh, G. Fradet, B. Naser and H. Mohammadi, "Are Two-Dimensional Images Sufficient to Assess the Atherosclerotic Plaque Vulnerability: a Viscoelastic and Anisotropic Finite Element Model," Cardiovascular System, vol. 3, no. 1, 2015. [91] V. Fuster, P. R. Moreno, Z. A. Fayad, R. Corti and J. J. Badimon, "Atherothrombosis and High-Risk Plaque: Part I: Evolving Concepts," Journal of the American College of Cardiology, vol. 46, no. 6, pp. 937-954, 2005. [92] Popov and E. P, Engineering Mechanics of Solids, Upper Saddle River: Prentice Hall, 1998. [93] J. C. Kohn, M. C. Lampi and C. A. Reinhart-King, "Age-Related Vascular Stiffening: causes and consequences," Frontiers in Genetics, vol. 6, no. 112, 2015. [94] D. Zhang, C. D. Eggleton and D. D. Arola, "Evaluating the mechanical behaviour of arterial tissue using digital image correlation," Experimental Mechanics, no. 42, pp. 409-416, 2002. [95] N. H. L. a. B. I. Staff, "Atherosclerosis," National Heart, Lung, and Blood Institute, 2 October 2018. [Online]. Available: https://www.nhlbi.nih.gov/health-topics/atherosclerosis. [Accessed 2020]. 78 Appendices Appendix A: Calculation of Volume Change in Arterial Phantom The arterial phantom is best modeled as a thick-walled pressure vessel. The governing differential equation for which is shown below [92]: 𝑑𝑢𝑑𝑟 +1𝑟𝑑𝑢𝑑𝑟−𝑢𝑟2= 0 (1) Where u stands for the radial displacement, at any point r. The solution for this equation is of the form: 𝑢 = 𝐴1𝑟 +𝐴2𝑟 (2) A1 and A2 are constants obtained from the boundary conditions. In this case, radial displacement can’t be used since the boundary values are unknown. However, boundary values are known for the radial stress at any given point which can also be found from the following equation: 𝜎𝑟 =𝐸(1+𝜐)(1−2𝜐)[(1 − 𝜐) (𝑑𝑢𝑑𝑟) + 𝜐𝑢𝑟] (3) Where E is the young’s modulus and ν is the poisson’s ratio. The stress at the inner radius (ri) is equal to the inner pressure (pi), and equal to the outer pressure (po) at the outer radius (ro). These relations are shown in the equations below: 𝜎𝑟(𝑟𝑖) = −𝑝𝑖 (4) 𝜎𝑟(𝑟𝑜) = −𝑝𝑜 (5) 79 The negative values indicate compressive stress. After combining equations 2 and 3, and substituting the boundary conditions yields the following values for A1 and A2: 𝐴1 = (1+𝜐)(1−2𝜐)𝐸 𝑝𝑖𝑟𝑖2−𝑝𝑜𝑟𝑜2𝑟𝑜2−𝑟𝑖2 (6) 𝐴2 = 1+𝜐𝐸(𝑝𝑖−𝑝𝑜)𝑟𝑖2𝑟𝑜2𝑟𝑜2−𝑟𝑖2 (7) Using these constants with equation 2 will allow for the calculation of the radial displacement on any point of the thick wall. These calculations may not be used with arterial walls since they are not a standard linear elastic material. The young’s modulus changes depending on the strain as the collagen and elastin activate at different points. However, under the normal ranges of the human body, the elasticity can be approximated as 1.5 MPa [93]. The poisson’s ratio of arterial tissue is known to be around 0.17 [94]. The inner and outer radii of the arterial phantoms are 0.875 and 1.75 mm respectively. The inner pressure can only be measured relative to the atmosphere, and the phantom is at equilibrium when the pressures are equal, so the outer pressure is considered 0 while two inner pressures are considered for the max and min cases. The minimum 0.5 Psi is equivalent to 3.447 KPa, and the maximum 4 Psi is 27.579 KPa. These values are plugged into the equation above to calculate the radial expansion at both pressure cases to measure the difference in area. The radial displacements are 0.00365 and 0.0291 mm for the minimum and maximum pressures respectively. The cross-sectional area of the phantom then changes from 2.4 to 2.57 square millimeters during operation (trivial equations used can be found below). This is a difference of 0.17 mm2. The arterial phantoms have a length of 100 mm, so the total change in volume can be calculated as 17 mm3 (1.0375*10-3 in3). 80 Appendix B: Resultant Total System Figure 17: Labeled Picture of the Testbed This is a picture of the entire testbed. The control, and the static and dynamic pressure modules are seen all together within the plastic tub that forms the testbed. 81 Appendix C: Hydraulic System Diagram Figure 18: Diagram of Hydraulic Connections This shows how the PVC hosing connects the testbed together. The arrows on the lines show the direction of travel of pressure pulses. 82 Appendix D: Solidworks Diagrams of 3D Printed Parts These are the engineering drawings for the parts that were 3D printed. Most of the dimensions were chosen to match the dimensions of other parts. The dynamic coupler connects the actuator to the plunger of the syringe. This lets it pull on the plunger as well as push The control panel allows for switches and LEDs to be mounted. The switches are pushed through from the bottom and washers are screwed from the top to hold them in place. The planned LEDs were only superficial and did not end up being mounted. The limit switch mount holds the limit switches in place so that they can be activated by linear actuator as it approaches one of its limits. The syringe base holds the syringe in place as the actuator retracts and extends the plunger. 83 84 85 86 87 Appendix E: Arduino Code int stat = 12; int extended = 4; int retracted = 5; int dynswitcher = 7; int startstat = 8; int pressure = A3; int statbutton = 0; int ext = 0; int ret = 0; int anre = 0; float inter = 0; float reading2 = 0; void setup() { pinMode(stat, OUTPUT); pinMode(dynswitcher, OUTPUT); pinMode(startstat, INPUT); pinMode(extended, INPUT); pinMode(retracted, INPUT); // So far the code has initialized values and declared Serial.begin(9600); // pins as output or input digitalWrite(stat, LOW); digitalWrite(dynswitcher, LOW); } void loop() { 88 inter =analogRead(pressure); // This loop sends the pressure reading2 = (inter)*(30)/(1023); //reading to the PC Serial.println(reading2); ext = digitalRead(extended); if (ext == HIGH || reading2 > 4) // This if statement causes the actuator { // to retract if it has reached its limit digitalWrite(dynswitcher, HIGH); // or the max pressure } ret = digitalRead(retracted); if (ret == HIGH || reading2 <1.5) //This if statement causes the actuator { // to extend if it has reached its limit digitalWrite(dynswitcher, LOW); // or the min pressure } statbutton = digitalRead(startstat); if (statbutton == HIGH) // This if statement starts the static { // pressure module if the pressure anre = analogRead(pressure); // is less than the minimum when the if (anre >= 350) // button is pressed { digitalWrite(stat, LOW); } else {digitalWrite(stat, HIGH);} delay(50);
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-ShareAlike 4.0 International
Graduate
Towards the detection of vulnerable atherosclerotic plaques
Text