CFD STUDIES ON THE FLOW AND SHEAR STRESS DISTRIBUTION OF ANEURYSMS. A Thesis. Presented to. The Graduate Faculty of The University of Akron

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1 CFD STUDIES ON THE FLOW AND SHEAR STRESS DISTRIBUTION OF ANEURYSMS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Arun Pundi Ramu August, 2009

2 CFD STUDIES ON THE FLOW AND SHEAR STRESS DISTRIBUTION OF ANEURYSMS Arun Pundi Ramu Thesis Approved: Accepted: Advisor Dr. Guo-Xiang Wang Dean of the College Dr. George K. Haritos Faculty Reader Dr. Francis Loth Dean of the Graduate School Dr. George R. Newkome Faculty Reader Dr. Yang Yun Date Department Chair Dr. Celal Batur ii

3 ABSTRACT Rupture of cerebral aneurysms followed by subarachnoid hemorrhage is a very fatal disease condition associated with high mortality and morbidity rates. Studies show that over 10 to 15 million people in the United States harbor intracranial aneurysms. Most aneurysms do not rupture, and the management of these lesions is difficult, due to the lack of complete understanding of their natural history and the risks associated with surgery. In this work, 3-dimensional Computational Fluid Dynamic (CFD) approach has been undertaken to study and quantify the flow mechanics of aneurysms. The hemodynamic factors leading to the formation, growth and rupture of aneurysms have not been fully understood. We provide a possible hypothesis based on low WSS distribution to assess the hemodynamic environment along the dome of spherical aneuryms, prior to rupture. Our hypothesis is based on immunohistochemical findings, of rigorous remodeling attempts along the wall of the aneurysm dome, prior to rupture. We hypothesize WSS around ±0.4 Pa, to favorably initiate such remodeling and study the variation of the area prone to remodeling for varying arterial curvature and angle of tilt of dorsal aneurysms. The study is aimed towards demonstrating a better understanding of the factors that lead to the degeneration of aneurysms, by coupling findings of clinical studies with their corresponding hemodynamic causes. iii

4 Impact of size, curvature of the parent artery, and angle of tilt and pulsatility on the various dependent variables such as, the distribution of WSS along the aneurysm, the primary and secondary flow patterns, the impact zone and the area prone to vascular remodeling are quantified. iv

5 DEDICATION I would like to dedicate this work to my mother Mrs. Padma Ramu, my father Mr.Ramu, my sister Lavanya Gopal and my brother-in-law Mr.Gopalakrishnan Ramanujam. v

6 ACKNOWLEDGEMENTS I wish to sincerely express my thanks and appreciation to my academic advisor Dr. Guo-Xiang Wang. His support, guidance and encouragement throughout my tenure as a graduate student have been invaluable. I would also like to thank the members of my thesis committee Dr.Yang Yun and Dr. Francis Loth for their valuable inputs and objective review of my thesis. I wish to extend a special mention to my dearest friend Nancy Mittal for her support and encouragement and fellow graduate student and colleague Zhengpeng Qin for his support over the past two years. I am grateful to my parents, sister and brother-in-law for all their patience, support and encouragement with all my endeavors. I would like to thank the Department of Mechanical Engineering at The University of Akron, for giving me the opportunity to pursue my graduate education here. Last but not the least, I would like to thank all of my friends here at U Akron and back home. vi

7 TABLE OF CONTENTS Page LIST OF TABLES... xi LIST OF FIGURES... xii CHAPTER I. INTRODUCTION TO ANEURYSMS Introduction and Objective...1 II. LITERATURE REVIEW Aneurysm-Types Classification of Cerebral Aneurysms In Vitro: An insight into Aneurysm Hemodynamics Geometry of Simple Lobed Cerebral Aneurysms Hemodynamic Parameters Pulsatile Flow Womersley Number Disturbed Flow Wall Shear Stress Impact of High Wall Shear Stress Geometric Parameters Aspect Ratio: An Index for Predicting Rupture of Aneurysms...19 vii

8 2.6.2 Chamber Volume to Orifice Area Parent Artery Curvature Aneurysm Shape Aneurysms at Arterial Bifurcations Treatment of Aneurysms...22 III. HYPOTHESIS: AREA PRONE TO VASCULAR REMODELING Introduction and Review Hypothesis Area Prone to Vascular Remodeling...33 IV. COMPUTATIONAL SETUP Aneurysm Geometry Mesh Generation Modeling Equations Flow Parameters Computational Assumptions Rigid Vessel Model Viscosity Solution Parameters Specified (FLUENT )...44 V. HEMODYNAMICS OF LATERAL ANEURYSMS: ASPECT RATIO EFFECT Introduction Primary Flow Structure through Lateral Saccular Aneurysms Velocity Distribution along a Plane Passing Through the Dome Diameter...49 viii

9 5.4 Wall Shear Stress Distribution Summary and Discussion...54 VI. EFFECT OF ARTERIAL CURVATURE ON DORSAL ANEURYSMS Curved Arteries: Hemodynamic Environment Leading to the Genesis of Dorsal Aneurysms Dorsal Aneurysms Primary Flow Structure Wall Shear Stress Distribution Quantification of Impact zone and area prone to vascular remodeling Summary and Discussion...65 VII. EFFECT OF ANGLE OF TILT (β) ON INTRA ANEURYSMAL HEMODYNAMICS Introduction Primary Flow Structure Secondary Flow Structure Wall Shear Stress Distribution Impact Zone Impact of Asymmetric Secondary Flow Distribution on the Shear Stress along the Aneurysm Neck Area Prone to Vascular Remodeling WSS Distribution along Cross Sectional Planes X-Z (Primary), Y-Z (Secondary) Summary and Discussion...85 ix

10 VIII. EFFECT OF ANGLE (β): PULSATING FLOW HEMODYNAMICS Introduction Primary Flow Features Time Evolution of Impact zone Time Evolution of Area Prone to Vascular Remodeling Summary and Discussion...92 IX. CONCLUSION AND FUTURE WORK Conclusion Effect of Varying Aspect Ratio Effect of Arterial Curvature Impact of Angle of Tilt (β=0, β=45 and β=90 ) Scope for Future Work...97 BIBLIOGRAPHY...98 APPENDICES APPENDIX A. UDF-PARABOLIC INFLOW CONDITION APPENDIX B. UDF-TRANSIENT BOUNDARY CONDITION APPENDIX C. MODEL VALIDATION x

11 LIST OF TABLES Table Page 4.1 Aneurysm model dimensions incorporated in the study Variation of Impact zone and area prone to vascular remodeling, for the three models of spherical aneurysms on parent arteries of varying curvature Variation of maximum WSS at the distal end of the aneurysm with varying angle of tilt at Re 135 and Re Variation of Impact Zone with angle of tilt of aneurysms Distribution of WSS along the dome region as a percentage of the max wall shear stress Variation of non-dimensionalized area prone to vascular remodeling with angle of tilt for β=0, 45 and xi

12 LIST OF FIGURES Figure Page 2.1 Schematic illustration- usual locations of appearance of cerebral aneurysms Types of aneurysms found in the human arterial network Types of non bifurcation aneurysms Digital subtraction angiograms: Demonstrating a typical saccular aneurysm arising from a curved parent artery Schematic diagram: Aneurysm measurements Nomenclature of spherical saccular aneurysms Structure of a healthy artery Endovascular techniques for aneurysm occlusion Transformation of cell morphology by fluid shear stress SEM of cerebral aneurysm Percentage of rupture along the dome of aneurysms Flow Chart-Process involved in low WSS remodeling of the arterial wall Representation of lateral spherical aneurysm incorporated in the study Representation of Dorsal spherical aneurysms incorporated in the study Representation of dorsal aneurysms at various angles of tilt to the parent artery Location where velocity magnitude was extracted to perform mesh independence study...39 xii

13 4.5 Grid independence in terms of velocity distribution along the z axis for β= Variation of the inflow velocity with time (Pulsatile variation) Parabolic nature of blood flow through the artery Comparison of the velocity vectors (m/s) along the primary flow plane for Aspect Ratio of (left), (centre), 2.3 (right) Path lines extracted for a lateral aneurysm of Aspect Ratio of at Re Velocity contour along the plane passing through the centre of the dome (A-B), for aspect ratios of (left), (centre) and 2.3 (right) Velocity magnitude (m/s) along the dome diameter, for aneurysms with aspect ratio of (D/N=1.6), A.R (D/N=2.0), A.R 2.3 (D/N=2.4) WSS distribution along the dome of the aneurysm with dome to neck ratios of (a) 1.6 (b) 2 (c) Wall shear stress distribution along the circumference of the plane passing through the centre of the dome, for aspect ratio of Comparison of WSS distribution at the centre of the dome of the aneurysm, for varying dome to neck ratios Velocity Vector distribution along a curved artery of radius of curvature 12mm Velocity contour of flow along a curved artery (left) to that of a straight artery (Right) (Re 135) Comparison of velocity profile along A-B, C-D and E-F of a curved artery to the flow profile along a straight artery Flow structure along the primary symmetry plane, and WSS distribution along the distal end of the aneurysm dome, for the three models with curvature (1/R= (a1-a2), (b1-b2) and 0 (c1-c2)) Comparison of the Area Prone to Vascular Remodeling with arterial curvature...64 xiii

14 7.1 Velocity vectors along the primary and secondary flow planes Velocity path lines for β=0, showing the inflow into the aneurysm from the distal neck and the outflow along the proximal side of the dome Wall shear stress distribution along the distal end of the aneurysm. Reynolds number (Re-270 Left, Re-135 Right) Wall Shear Stress distribution at the distal end of the aneurysms for varying angles of tilt Wall shear stress distribution along the neck and the dome of the aneurysm towards the left and right of inflow direction for β= Wall shear stress distribution along the neck and the dome of the aneurysm towards the left and right of inflow direction for β= Wall shear stress distribution along the neck and the dome of the aneurysm towards the left and right of inflow direction for β= Variation of Wall Shear Stress at the dome of the aneurysm, along the primary and secondary planes. β=0, 45, 90 (a) plot of the variation in WSS at various points along the primary and secondary plane of the dome at various angle of tilts (b) figure indicates the points along which the WSS was calculated along the primary and secondary plane of the aneurysm dome Time variation of the inflow velocity Specification of pulsatile inflow into the aneurysm Variation of Velocity along the primary plane at various instants of time along the pulsatile cycle Variation of maximum wall shear stress along the distal end with time variations in the inflow condition Transient variation of Impact zone Transient variation of area prone to vascular remodeling...91 xiv

15 CHAPTER I INTRODUCTION TO ANEURYSMS 1.1 Introduction and Objective An aneurysm is a cerebrovascular disorder characterized by the ballooning of the cerebral arterial wall. It is a fatal condition, and the rupture of aneurysm lesion leads to subarachnoid hemorrhage. Approximately Americans are estimated to suffer subarachnoid hemorrhage resulting from ruptured intracranial aneurysms, each year (Schievink 1997). Nearly half these cases result in death and several others suffer severe morbidity. To date, there is very little understanding of the process that leads to the rupture of aneurysms. Various studies (Kataoka 1999, Frosen 2004) have previously assessed the pathological differences in the wall of ruptured and un-ruptured aneurysms, to help understand that process that may lead to aneurysm rupture. At the same time in vivo studies suffer from the inability to completely assess the hemodynamic variables such as velocity, WSS and pressure within an aneurysm. This is overcome by various Computational Fluid Dynamic and experimental studies that have provided an insight into the intra aneurysmal flow features. The objective of this study is to utilize Computational Fluid Dynamics as a tool to effectively assess the intra aneurysmal WSS and velocity distribution for spherical aneurysms of various aspect ratios, curvature of the parent artery and angle of tilt of the 1

16 aneurysms with respect to the parent artery. Our goal is to create a link between the complex intra aneurysmal micro environment and the process of vascular wall remodeling that may lead to the rupture of aneurysms. We device a key hemodynamic indicator, based on low WSS to identify the region along the aneurysm subjected to active vascular remodeling. We define area prone to vascular remodeling and study the variation of this area with arterial curvature and orientation of dorsal aneurysms with respect to the parent artery. We hope that our work will provide a fresh approach towards seeking indicators to predict the risk of aneurysm growth and rupture. Also a detailed analysis of the region along the aneurysm susceptible to growth and rupture would prove to be a valuable input towards the design of endovascular devices. The methodology utilizes findings of immunohistochemical studies to arrive at a hemodynamic parameter to analyze computational results. 2

17 CHAPTER II LITERATURE REVIEW 2.1 Aneurysm-Types An Aneurysm is an abnormal bulge or ballooning in the walls of arteries. Arteries are blood vessels that carry oxygen rich blood from the heart to the other parts of the body. The reason for the occurrence of aneurysms is still unclear, but a variety of risk factors such as congenital or inherited defects weakening the arterial wall, hypertension, atherosclerosis and thrombosis have been identified as possible causative factors (Liou 1999). Blood flow hemodynamics and WSS distribution along the arteries are considered to be the most important factors in the genesis, growth and rupture of aneurysms. Types of aneurysms include Aortic, cerebral and peripheral aneurysms. Aortic Aneurysms: The aorta is the main artery that carries blood from the heart to the rest of the body. The aorta comes out from the left ventricle of the heart and travels through the chest and abdomen. The two types of aortic aneurysm are thoracic aortic aneurysm (TAA) and abdominal aortic aneurysm (AAA). Cerebral Aneurysms: Aneurysms that occur in an artery in the brain are called cerebral aneurysms. This is a pathological dilation of the artery, generally found in and about the circle of Willis. They are sometimes called berry aneurysms because they are often the size of a small berry. Most cerebral aneurysms produce no symptoms until they 3

18 become large, begin to leak blood, or rupture. The rupture of cerebral aneurysms leads to subarachnoid hemorrhage (SAH). The mortality rate for aneurysms related SAH ranges from 30% to 60% and of those who survive; approximately 50% are left disabled (Schievink 1997). Figure (2.1), is a schematic illustration of the appearance of cerebral aneurysms. On the right are angiographic images of aneurysms. Figure 2.1 Schematic illustration- usual locations of appearance of cerebral aneurysms. Right- angiographic images (Paà l 2007). Saccular aneurysms are predominantly found at arterial bifurcations. Those unrelated to arterial bifurcation are further classified as dorsal, ventral and lateral type aneurysms. These generally occur along the cavernous segments of intracranial arteries (Yoshimoto 1996). Peripheral Aneurysms: Aneurysms that occur in arteries other than the aorta or the cerebral arteries are called peripheral aneurysms. 4

19 Abdominal aortic aneurysms are found in approximately 2% of elderly people while cerebral aneurysms are present in 2 to 5% of adults. Although the causes and geometries of abdominal and cerebral aneurysms differ, both may rupture. Figure (2.2) summarizes the types of aneurysms found in the human arterial network. Figure 2.2 Types of aneurysms found in the human arterial network. 2.2 Classification of Cerebral Aneurysms Cerebral aneurysms are usually called saccular aneurysms or berry aneurysms due to their spherical shape. These aneurysms are commonly found along the apex of arterial bifurcations. It has been well established that aneurysm formation generally occurs at the areas of bifurcation where the WSS is high due to flow impingement. Stehbens et al (Stehbens 1963) speculated that early or pre aneurysmal change can be regarded as degenerative in nature and may be a part of atherosclerotic process. Due to these pathogenic mechanisms, a majority of saccular aneurysms tend to occur at arterial bifurcations and those that occur at other locations are considered to be rare. However, many of the ICA (Internal carotid artery) aneurysms do not originate at arterial branching point. The occurrence of such non branching aneurysms may be 5

20 related to the hemodynamic trust and turbulence of blood flow at the hair pin-curve of the artery. Other sites of occurrence would include the cavernous segments on the basilar and vertebral arteries, and on the distal portions of anterior cerebral arteries (Marei 1981). In case of curvature induced aneurysms, the blood strikes the wall at an oblique angle near the abrupt arterial curvature, and then proceeds along the walls resulting in a high shear stress upon the endothelium (Yoshimoto 1996). This provides the necessary degenerative change that is essential to explain the initiation of aneurysms. The peculiar projection of these curvature induced aneurysms pose a challenge to their safe surgical clipping (Diraz 1993). A lot of work has been carried out in analyzing effective clipping of such aneurysms (Kyoshima 1998, Yoshimoto 1996). Such aneurysms unrelated to arterial bifurcations are classified based on their relation to the cross section of the ICA (Internal Carotid Artery) as dorsal, ventral and lateral aneurysms. Aneurysms that point towards the direction of blood flow are called dorsal aneurysms, and the ones that do not point towards the direction of blood flow are the ventral and lateral aneurysms. Figure (2.3), illustrates the types of non branching aneurysms found in the intracranial arteries. 6

21 Figure 2.3 Types of non bifurcation aneurysms. Dorsal curvature (left), ventral curvature (centre) and lateral (right) (Yoshimoto 1996). Centrifugal force of blood flow and the depletion of the elastic lamina due to increased WSS are attributed as an important hemodynamic factor in the development of dorsal aneurysms. Ventral and non curvature aneurysms disobey the traditional rule of aneurysm development, having no clear hemodynamic causes. Stehbens et al (Stehbens 1963) noted that saccular aneurysms unrelated to arterial divisions can be caused by arteriosclerosis. Irrespective of the cause of the development of aneurysms, a clear understanding of the hemodynamics is essential to make clinical decisions and to develop endovascular treatment techniques. Figure (2.4) shows a typical case of saccular aneurysm harbored on a curved artery. 2.3 In Vitro: An insight into Aneurysm Hemodynamics Hemodynamic factors such as blood viscosity, wall shear stress, velocity and pressure distribution play an important role in the pathogenesis of aneurysms. It is essential to understand the distribution of these hemodynamic factors to better relate them to the process of evolution of aneurysms. Also the geometry of aneurysms and that of the associated parent artery have an impact on deciding the nature of flow through an 7

22 Figure 2.4 Digital subtraction angiograms: Demonstrating a typical saccular aneurysm arising from a curved parent artery. Enlarged view to the right (Hoi et al 2004). aneurysm. The availability of advanced computational tools and software s, their cost effectiveness, time savings and the difficulty in conducting in vivo experiments have popularized CFD techniques. There are two ways of numerically studying the flow patterns in aneurysms. The first would be using idealized aneurysm geometries that give enough independence to compromise on the complex shape of actual aneurysms and modeling cases in which good numerical meshes are possible. Such types of studies are usually parametric in nature. In the second approach the arterial geometry is obtained in a digital format consisting of voxels (Paà l 2007,Cebral 2007). Such geometries usually result in skewed meshes of poor quality. Paà l et al (Paà l 2007) performed numerical simulations on various real and ideal aneurysm geometries and concluded that the simulations on simplified models are more accurate and they provide a basic understanding of the underlying flow patterns in typical aneurysm geometries. Also aneurysm initiation, growth and rupture, are essentially mechanically mediated events. 8

23 We summarize some of the computational fluid dynamic studies conducted on ideal aneurysm geometry and their outcome. CFD techniques using idealized 2-d computational aneurysm models have been reported as early as Burleson et al (Burleson 1995), studied 2-d lateral aneurysms of various shapes and sizes. They found the aneurysm size, shape, ostium width and Reynolds number to have a significant impact on the distribution of shear stress on the aneurysm wall. Based on their observations, they suggested that aneurysm growth and rupture occur at the ostium and not at the dome of aneurysms. CFD studies to investigate the factors that lead to the formation of aneurysms were conducted by Foutrakis et al (Foutrakis 1999). They studied the progressive formation of saccular aneurysms from curved arteries, by modeling them at different stages of growth. They theorized the formation of aneurysms along regions of curved arteries where the wall shear stress exceeded the yield stress of the arterial wall. Based on the variations in hemodynamics along the dome of the aneurysm, they too supported the claim that aneurysm growth occur from the neck and not the dome. Hoi et al (Hoi 2004) performed 3-d computational analysis on aneurysms harbored on curved arteries. Based on their studies, they postulated that aneurysms on curved arteries are subjected to higher hemodynamic stresses. They further defined Impact Zone as the most likely site for further aneurysm growth and found that aneurysms with wider necks have larger impact zones. Liou et al (Liou 2007) studied the flow fields in aneurysms arising at various angles to the curved parent artery. The WSS distribution obtained in this study showed the dome region to be more at a risk of 9

24 rupture. They also found the aneurysm placed at an angle of 45 to the curved parent artery to be the riskiest. Sato et al (Sato 2008) performed parametric computational fluid dynamic studies to demonstrate the importance of arterial geometry on intra aneurysmal hemodynamics. Their results suggested that the configuration of the aneurysm with respect to the parent artery played a more prominent role compared to the shape of the aneurysm in determining intra aneurysmal hemodynamics. Imai et al (Imai 2008) numerically investigated the inflow features of untreated aneurysms at various arterial bends and demonstrated the important role played by the secondary flow generated in the parent artery to be a dominant factor in deciding the inflow into aneurysms. Valencia et al (Valencia 2004,2006) performed several numerical simulations to understand the flow dynamics in terminal aneurysms. In recent times studies using Fluid Structure interaction are gaining popularity (Chatziprodromou 2007 a,b). Besides the above mentioned numerical studies, several in vitro experimental studies using Particle Tracking Velocimetry, Particle Image Velocimetry (Liou 1997 a,b) and streaming double refraction (Steiger 1990), have been reported. However Computational fluid dynamic techniques on patient specific aneurysms, have been gaining popularity as a tool to understand the pathogenesis of cerebral aneurysms. Very recently attempts were made by Ford et al (Ford 2008), to study the reliability of CFD simulations by comparing CFD predicted velocity fields against those measured using Particle Tracking Velocimetry. Their work has shown that CFD can accurately predict even the finer details of flow dynamics of anatomically realistic models. 10

25 Every artery in the cerebral vasculature varies in its diameter, nature of pulsation and Reynolds numbers. Shojima et al (Shojima 2004) dealt with Middle cerebral artery aneurysm. Liou et al (Liou et al 1997b, 1999) primarily dealt with PTV and CFD techniques to assess lateral aneurysms. They also looked into the aspect of placement and the impact on stents on lateral aneurysms. Saccular aneurysms display a variety of sizes and complex shapes. The majority of intracranial aneurysms are located in the anterior circulation, most commonly at the junction of the internal carotid artery and the posterior communicating artery complex. Aneurysms of the posterior circulation are most frequently located at the bifurcation of the basilar artery or the junction of the vertebral artery and the ipsilateral posterior inferior cerebrel artery. Foutrakis et al (Foutrakis 1999) conducted computer modeling on 2-d curved arteries and bifurcating arteries. The paper outlined the process of growth of the aneurysm on the basis of the hemodynamics in the absence of biological mediating factors. The paper concluded with evidence that the pressures and shear stresses that develop along the outer wall of the curved artery and at the apex of the arterial bifurcation create a hemodynamic state that promotes saccular aneurysm formation. 2.4 Geometry of Simple Lobed Cerebral Aneurysms Parela et al (Parela 1999) characterized the geometry of simple lobed cerebral aneurysms that would help future analysis and studies. With the help of measurements on angiographic tracings neck width (N), dome diameter (D), dome height (H), and the dome semi-axis height (S) were defined. The relationship between these dimensions, 11

26 offer an indication of the aneurysm geometry. These dimensions are valid assuming the lesion to be axially symmetrical. The D/N and H/N are very important in trying to decide on the size of the dome diameter and the height for a given aneurysm neck in a model. The D/H and H/S ratio indicate the general aneurysm shape. In an extensive analysis of 87 aneurysms Parela et al assessed the relative shapes of occurance of aneurysms and its frequency of occurance, justifying the choice of ideal aneurysms, for the current and future work. Figure (2.5), highlights the aneurysm dimensions as put forth by Parela et al (Parela 1999). Parela et al found a high relative occurrence of aneurysms with D/H =1 and H/S=2 (spherical aneurysms). Also the angle of tilt of these aneurysms varied between - 50 in the anterior side to 40 in the posterior side. Computational fluid dynamic studies in the past (Burleson 1995, Hoi 2004, Chitanvis 1995) have considered spherical aneurysms in their studies. The nomenclature of spherical aneurysm used in this study is highlighted in figure (2.6). H- dome height, S- the semi axis height, D- the dome diameter, N- Neck width, and d- parent artery diameter. The proximal and distal end of the aneurysm have been indicated in the figure. 2.5 Hemodynamic Parameters Hemodynamics is the study of the forces involved in the circulation of blood i.e., hemodynamics concerns the physical factors governing blood flow within the circulatory system. Hemodynamic parameters are considered to be responsible for aneurysm initiation, growth and rupture. However in majority of the computational studies, non Newtonian viscosity of blood, wall elasticity, blood particle composition 12

27 (RBC, WBC, platelets) and temperature effects are neglected, due to their secondary importance. The hemodynamic factors play a vital role in regulating the structure and functions of the endothelial layer. Hemodynamic parameters concerning this study are explained below Figure 2.5 Schematic diagram: Aneurysm measurements. D-Dome diameter, N- Neck width, H-Neck height, S-Semi axis height (Parela 1999). Figure 2.6 Nomenclature of spherical saccular aneurysms., 13

28 2.5.1 Pulsatile Flow Several authors have studied the impact of pulsatile flow of blood on aneurysm hemodynamics (Liou 1997a,1997b, 2007, Gonzalez 1992, Hoi 2004). Liou et al (Liou 1997) conducted LDV (Laser Doppler Velocimetry) measurements of pulsatile flow along lateral saccular aneurysms. They found varying WSS patterns along the intra aneurysmal wall with peak and minimal flows. Liou et al (Liou 1997a) further investigated the impact of pulsating flow on lateral aneurysms harbored on arteries with varying curvature and found that the fluid motion near the dome region, as compared with the main stream motion in the parent vessel, undergoes a phase lag for the cases of R/D = and 5, where R is the radius of curvature of the parent artery and D is the diameter of the artery. Liou et al (Liou 2007) conducted numerical and experimental unsteady blood flow simulations on curvature induced aneurysms at various angles to the parent artery. On comparison of intra aneurysmal main flow vortex strength, secondary flow strength, volumetric inflow rate and WSS from a fluid dynamics point of view, an aneurysm at an angle of 45 to the main curved artery was found to be the riskiest angle. All of the above studies have shown that during a period of cardiac cycle, transient flow developed in aneurysms is quite different from that of steady flow. Malek et al (Malek 1999) showed that, that low oscillating blood flow that changes direction with cardiac cycle results in a weak net hemodynamic shear stress. It is this oscillating WSS along the dome of aneurysms that play a vital role in the development of atherosclerosis and consequently in aneurysm rupture. A complete understanding of the variation of intra aneurysmal hemodynamics with variations in the cardiac cycle is very critical. Gonlalez et al (Gonzalez 1992) performed transient simulations along sidewall 14

29 aneurysms and found the flow pattern to vary during the cardiac cycle with a reverse flow near the diastole near the aneurysm. They then hypothesized that along the area of the largest shear stress along the walls of the aneurysm, the wall tends to weaken and this leads to the growth of aneurysms Womersley Number Dimensional analysis of unsteady Navier-Stokes equation yields a non dimensional number called Womersley number. Womersley number is the ratio of unsteady force to the viscous force, given by α=r (2.1) where R is the radius of the tube, ω is the angular frequency and ν is the kinematic viscosity (Ku 1997). Low Womersley number, less than 10 is usually preferred to simulate blood flow. Inertial forces dominate in low Womersley number flows and the velocity profiles are parabolic in nature Disturbed Flow The geometry of aneurysms leads to a particular pattern of disturbed flow. The flow impingement along the distal neck of the aneurysm and the subsequent inflow into the aneurismal sac is the disturbed flow pattern seen in aneurysms. Hashimoto et al used the disturbed flow pattern to successfully explain increased leukocyte adhesion along the walls of the aneurysm (Hashimoto 2006). 15

30 Disturbed flow is generally used to describe re-circulating flow in a cavity or wall expansion. The WSS is low owing to slow velocity but the changes in direction are frequent (Cheng 2003). This condition enhances the residence time of the blood particles and increases interactions between circulating leukocytes and the wall endothelial layer ultimately resulting in inflammation and the atherosclerotic changes along aneurysm walls (Chiujj 2003). Such recirculation flows are evident along the impingement point at the distal neck of the aneurysm and can be confirmed by the numerous numerical simulations that have been conducted by various authors. There is a high spatial variation of WSS owing to this pattern of flow Wall Shear Stress As blood flows through an artery, a shear is generated to retard the blood flow across the endothelium. The wall shear stress WSS for a Newtonian fluid is proportional to the velocity gradient at the wall and the fluid viscosity. τ=µ(du/dr) (2.2) where, µ - fluid viscosity kg/m-s and du/dr- velocity gradient at the wall. For a Newtonian fluid with a steady, laminar flow through a straight tube, the wall shear stress is given by, τwall=(32*µ*q)/(π*d 3 ) (2.3) where, Q-flow rate (m 3 /s), d-artery diameter (m) Hemodynamic stresses are considered to have profound effects on the development of cerebral aneurysms (Steiger 1990). The WSS acts directly on the vascular endothelium as a biological stimulator that modulates the cellular function of 16

31 the endothelium (Malek 1999). Therefore WSS has been a very important focus of studies. It has been demonstrated that the WSS plays a pivotal role in the initiation of aneurysms (Kosierkiewicz 1994). The wall shear stress (WSS) may also play a major role in the growth and rupture of cerebral aneurysms. Shojima et al (Shojima 2004) presented results of statistical analysis of the magnitude of WSS in and around anatomically correct cerebral aneurysms. The study shows the magnitude of the wall shear stress to be the highest along the neck of the aneurysm and not at the tip or the bleb of the aneurysm Impact of High Wall Shear Stress Since the intra aneurysmal flow demonstrates areas of high and low WSS, it is important to understand the role played by each of these in deciding the fate of aneurysms. The WSS acts directly on the endothelial layer and modulates the cellular function of endothelium (Malek 1999). It has been found that the vascular endothelium regulates the arterial wall properties through a blood shear stress activation mechanism and maintains the WSS within physiological baseline limits of 15 to 20 dyn/cm 2. This is accomplished by the endothelial cells that play a large role in regulating the arterial WSS to these physiological limits by initiating a process of vascular remodeling (Gibbons 1994). This remodeling process helps the arteries to adapt to changes in blood flow conditions. Initiation of aneurysms is mainly attributed to the failure of endothelium to perform the above function (Hashimoto 2006). Currently the most important pathogenic factor in the formation of aneurysm is considered to be an area of 17

32 wall degeneration in regions of hemodynamic shear stress. Figure (2.7) shows the schematic of a healthy arterial wall. The artery consists of three layers, intima, media and adventitia. The intima consists of the endothelial layer and the elastic lamina, while the media consists of the smooth muscle cells that play a vital role in maintaining the wall shear stress to physiological limits. Hemodynamic studies on models of saccular aneurysms are very important in order to obtain quantitative values of hemodynamic stress. Based on the above mentioned premise Hoi et al (Hoi 2004), defined Impact Zone as locations in an aneurysm where the WSS is greater than 20 dyn/cm 2. They speculate that large impact zones along aneurysm walls would be the most important location for further adaptive remodeling and active growth and re growth of treated aneurysms. The impact zone was observed to increase linearly with parent artery curvature (1/R) and the third order of aneurysm neck. Endovascular techniques aim at effectively reducing the impact zone along an aneurysm (Hoi 2004). 18

33 Figure 2.7 Structure of a healthy artery. 2.6 Geometric Parameters Aneurysm sac diameter, aspect ratio, chamber volume to orifice area, aneurysm shape and parent artery diameter are the various parametric factors known to influence the nature of blood flow within an aneurysm. In CFD as well as experimental studies intra aneurysmal flow is studied as a function of these geometric parameters Aspect Ratio: An Index for Predicting Rupture of Aneurysms Aspect Ratio is defined as the ratio of the maximum height of the aneurysmal sac from the inlet plane to the diameter of the inlet of the aneurysm. Ujiie et al (Ujiie 2001), studied aspect ratio, as an index for predicting the rupture of aneurysms. His study was based on a sample of 129 patients with ruptured aneurysms and 72 patients with 78 unruptured aneurysms. His studies showed over 90% of patients with unruptured 19

34 aneurysms having an aspect ratio of less than 1.6, and over 80% of the ruptured cases, having an aspect ratio greater than 1.6. Such factors to determine the critical point of rupture are very important in cases of cerebral aneurysms where rupture does not usually happen easily. The medical examiner has to make a critical judgment on the requirement of endovascular procedure on such patients. Hence it is important to look for a critical value of a certain parameter where rupture would occur. Also risk of rupture is associated with a low flow rate, and usually the critical value of 1.6 leads to a low flow rate at the dome of the aneurysm. Wiebers et al (Wiebers 1987) reported that out of 44 aneurysms they studied, no aneurysm less than 10 mm ruptured. And 8 out of 24 aneurysms of size greater than 10 mm ruptured. Contradicting results were obtained by Ujiie et al, wherein they observed several aneurysms less than 10mm that bled. However all the aneurysms that ruptured, irrespective of their size, had an aspect ratio greater than 1.6. Since the neck and the size of the aneurysm have a definite relation to the flow into the aneurysm, i.e, the neck size is instrumental in deciding the amount of flow entering the aneurysm sac and the volume of the aneurysm deciding on how sluggish the flow in the aneurysm sac would be. Hence a combination of both these factors seems to be a good way of predicting rupture Chamber Volume to Orifice Area It is the volume contained in the aneurysm to that of the area of the inlet orifice. A number of studies consider the orifice to be elliptical in shape (Chatziprodromou 2007). Other studies consider a circular orifice (Liou 1997 a,b, 2004,2007,2008, Burelson 1995). 20

35 2.6.3 Parent Artery Curvature Aneurysms occur at arterial bifurcations or cavernous segments of arteries. Hence investigating aneurysms on curved arteries has gained prominence. Foutrakis et al (Foutrakis 1999), conducted 2-d CFD analysis of aneurysms along curved arteries. Liou et al (Liou 1997a) studied arterial curvature effects using particle tracking velocimetry. Similar studies were computationally conducted by Hoi et al (Hoi 2004) using computer simulations. Extensive parametric studies on the inflow through saccular aneurysms at arterial bends were investigated by Imai et al (Imai 2008). In their blood flow simulation through 22 models of varying arterial curvatures and bends, they have clearly demonstrated the impact of parent artery geometry in significantly influencing the inflow pattern and flux through aneurysms Aneurysm Shape Various CFD studies have used aneurysms of varying shapes. Almost all models are axially symmetrical. (i.e.., the object can be created as a volume of revolution). The models vary in the location of their fundus (the maximum external diameter of the aneurysm), neck width and the shape of their neck. Based on angiographic measurements Parela et al (Parela 1999), defined aneurysms to be either pear shaped, spherical or bee hive shaped. The measurements were carried out on 87 simple-lobed lesions located at the basilar bifurcation (BB), middle cerebral (MCA), anterior communicating (AcomA), posterior communicating (PcomA), superior cerebellar (SCA), and posterior cerebral (PCA) arteries. Their study found a relatively high occurrence of spherical aneurysms. 21

36 2.7 Aneurysms at Arterial Bifurcations It has been well established that atherosclerotic plaque formation generally occurs at areas of bifurcation and high curvatures in the human arterial system. A vast percentage of aneurysms occur at such bifurcation regions, saccular lateral aneurysms at non bifurcation regions are seldom found. Valencia et al (Valencia 2004, 2006) quantified flow through terminal aneurysms by using CFD techniques. Liou et al (Liou 1994), conducted Laser Doppler Velocimetry measurements on terminal aneurysms, as early as They reported that with uneven branch flow, in terminal aneurysms the flow activity inside the aneurysm and the shear stress acting on the intra aneurysmal wall increase with increasing bifurcation angle. There also exists a middle range in the aneurysmal size, above and below which the forced vortex inside a terminal aneurysm is weaker, where as in the middle range of the aneurysmal size, the forced vortex is stronger, and the fluctuation level is higher near the dome. In other words, the dome of a midsized aneurysm is subjected to higher wall stress and vibrations. The endovascular treatment of aneurysms may benefit from an accurate pretherapeutic evaluation of flow patterns in the aneurysm neck and dome using Computational Fluid Dynamics. 2.8 Treatment of Aneurysms With the advancement of non-invasive imaging technology for diagnosis, aneurysms are being detected before rupture. The traditional treatment is the surgical clipping of the aneurysm from the main circulation at the adventitial side of blood vessel. This is an invasive technique and is usually recommended for treating large accessible aneurysms. Also clipping is insufficient for the complete closing of the 22

37 aneurysm having a wide or calcified orifice. Metallic clipping is usually performed on non branching aneurysms along the internal carotid artery. (Diraz 1993, Kyoshima 1998) Coil embolization is an endovascular technique used to treat aneurysms. A small catcher is introduced either from carotid or femoral artery, and placed inside of an aneurismal sack, in case of a cerebral aneurysm. Micro coils are introduced through the catcher and placed into an aneurismal sac. The coils packed into the aneurysm sac induce blood stasis and thrombus is formed. It is not easy to completely fill an aneurysm sac with coils in case of a giant aneurysm and a multilobular aneurysms. Byun et al (Byun 2004) studied CFD modeling of cerebral aneurysms following such coil embolization. An ideal model of aneurysm was modeled and computations were conducted assuming the coil to be a sphere placed at various locations in the aneurismal sac. Figure (2.8) demonstrates the occlusion of a spherical aneurysm using endovascular coil. For the endovascular treatment of saccular aneurysms with wide opening or fusiform aneurysms in which the packing agents such as balloon and/ or platinum micro coils are likely to migrate from the aneurysm into the parent vessel, an alternative approach is intravascular stenting. The placement of stents in the arteries harboring aneurysms is intended for effectively altering the intra aneurysmal flow, promoting the formation of thrombus inside the aneurysm, and, in turn excluding the aneurysm from cardiac circulation. Various groups have investigated the influence of stent parameters, like filament size, design, porosity etc. Aenis et al (Aenis 1997) investigated the influence of intravascular stenting on cerebral side walled aneurysm using a square 23

38 Figure 2.8 Endovascular techniques for aneurysm occlusion. Coil procedure for cerebral aneurysms. mesh stent and found that the flow activity inside the stented aneurysm model is significantly diminished and flow inside the parent vessel is less undulated and directed past the orifice of the aneurysm. A high pressure zone at the distal neck of the aneurysm prior to stenting, diminished after stenting. Lieber et al (Lieber 2002) conducted in vitro experimentation using PTV techniques to assess the influence of stent design on intra aneurismal flow. By varying the filament sizes for a constant porosity filament, they concluded that a filament size of 127µm, was the ideal size to promote thrombosis. Following his work Stuhne et al (Stuhne 2003), further conducted detailed mesh convergence analysis for steady flow, by varying the node spacing near the stent and conducted physiologically realistic pulsatile simulations. The NURBS (non uniform rational-b-spline) geometry was used to create, the stent in this method. The method yielded more detailed results on the complex flow dynamics. Liou et al (Liou 2004) conducted particle tacking velocimetry measurements on a curved aneurysm model, with stents of varying blocking ratios-c α and concluded that C α =75% is the most favorable in attenuating the risk of aneurismal rupture and promoting thrombosis. Porosity of a stent 24

39 is the most important parameter that affects the ability to impede or modify flow through an aneurysm. More porosity results in less flow blockage, but if the porosity is too low, then the stent might inadvertently block perforating vessels or become too rigid for deployment. Because of these constraints, the endovascular stents used these days are high porosity stents. In fact, the current FDA approved stents for cerebral applications have only slight variations with porosity between 80% and 90%. Kim et al (Kim 2006) investigated the hemodynamics of two high porosity commercial stents (Tristar stent and Wall stent) using CFD. Finally all of these endovascular techniques carry a high risk rate. Hence, it is very important that only those aneurysms that carry a high risk of rupture be subjected to surgery.. 25

40 CHAPTER III HYPOTHESIS: AREA PRONE TO VASCULAR REMODELING 3.1 Introduction and Review Frosen et al (Frosen 2004) and Kataoka et al (Kataoka 1999), in their immunohistochemical studies have observed a large amount of inflammation along the walls of ruptured aneurysms. This is mainly due to the low flow conditions along the dome of the aneurysm leading to the proliferation of inflammatory cells such as macrophages, leukocytes and SMC (Smooth Muscle Cells) that destroy the extra cellular matrix proteins, i.e., collagen. These extracellular matrix proteins perform the cellular function of preferentially relaxing the endothelial layer to maintain the WSS levels within physiological limits. The presence of these inflammatory cells leaves the artery stiffer and unable to cope with the condition of increasing WSS. Hashimoto et al (Hashimoto 2006) described the disturbed flow pattern in an aneurysm that leads to a recirculating zone along the dome of the aneurysm, to result in inflammatory cell invasion. Clinical studies have related this disturbed flow pattern in an aneurysm to the increased leukocyte adhesion to endothelial cells and ultimately to the observed inflammation along the aneurysm walls (Chiu 2003) Hence inflammatory changes occur in growing aneurysms with low velocity recirculating flow, owing to the increase in aspect ratio with growth. Also Kazuo et al (Kazuo 1999), in order to better understand the pathological differences between. 26

41 ruptured and unruptured aneurysms, studied the inner walls of 44 ruptured and 27 unruptured aneurysms, under a scanning electron microscope. They found vast amount of difference in the structural integrity of ruptured and unruptured aneurysms. One of the pointers in this study included, scoring the walls of the aneurysm for inflammatory cell invasion. They found a significant amount of macrophage and leukocyte invasion along the walls of ruptured aneurysms accompanied by a fragile wall and widespread disruption of the endothelial layer. They also found a significant co-relation between the degree of inflammatory cell invasion and the level of fragility of the wall. Thus, macrophage infiltration and the resulting inflammation along the aneurysm wall may play a role in further deteriorating the wall of the aneurysm prior to rupture. They concluded that the proteases derived from inflammatory cells may help to compromise the structural integrity of the aneurysm and lead to rupture. Further Frosen et al (Frosen 2004), in his study of snap frozen fundi resected after microsurgical clipping of 66 aneurysms suggested that, before rupture the wall of saccular cerebral aneurysms becomes unstable and undergoes morphological changes that start at an undefined time interval before rupture. The morphological changes that result from the matrix destruction are called vascular wall remodeling. This is an adaptation mechanism of arteries to hemodynamic stress. In case of subarachnoid hemorrhage patients, for undefined reasons the vascular wall remodeling would be insufficient to prevent aneurysm rupture. Similar to Kataoka et al s (Kataoka 1999) findings Frosen et al (Frosen et al 2004) found the walls of ruptured aneurysms to show a high degree of inflammation. Hence the degree of inflammatory remodeling along the wall of an aneurysm could serve as an indicator to predict aneurysm rupture. 27

42 Malek et al (Malek 1999) showed that atherogenesis involves points of blood flow re-circulation and stasis where the fluid shear on the wall is significantly lower in magnitude and exhibits directional changes. In other words this is the case of disturbed flow in an aneurysm. Direct measurements and fluid mechanical models of these susceptible regions have revealed shear stress of the order of ±4 dyn/cm 2 in these regions. A WSS much less than 4 dyn/cm 2 covered a wide area of the aneurysm sack, in the parametric computational studies by Sato et al (Sato 2008).Clinical studies (Frosen 2004, Kataoka 1999) have suggested that such vascular remodeling changes in the aneurysm wall may lead to the development and rupture of aneurysms. Shojima et al (Shojima 2004), conducted a study on twenty mathematical models of MCA (Middle Cerebral Arteries) aneurysms constructed by 3-d computed tomographic angiography and subjected the samples to CFD analysis. They found the WSS along the tip of ruptured aneurysms to be remarkably decreased <5 dyn/cm 2, while for unruptured aneurysms the WSS was of the order of 17dyn/cm 2. These results have established that the magnitude of WSS of well developed aneurysm is very low, in accordance to the previous hypothesis that the strength of the WSS of the aneurysm is not sufficient to mechanically tear the wall of the aneurysm (Steiger 1990). Also the WSS along the tip of the aneurysms was very low. These results suggest that in contrast to the pathogenic effect of high WSS leading to the initiation of aneurysms, it is actually the low WSS along the dome of the aneurysm that triggers the pathogenic mechanism that leads to the rupture of aneurysms. Hence the low WSS of the aneurysm may be of some help towards predicting rupture. 28

43 Fluid shear stress transforms polygonal, cobblestone-shaped endothelial cells of random orientation into fusiform endothelial cells aligned in the direction of flow. The persistence of physiological level of WSS reduce endothelial turnover by decreasing proliferation and apoptosis (Malek 1999). The physiological shear stress aligns the fusiform shaped endothelial cells along the direction of flow. Shear stress levels of dyn/cm 2 also decrease the endothelial turnover rate by preventing proliferation and apoptosis. The transformation of cell morphology by Fluid shear stress is shown in figure (3.1). (Malek 1999). Figure (3.2), shows a similar disorientation observed along the walls of ruptured intracranial aneurysms, as seen under the scanning electron microscope (Kataoka 1999). The figure to the left shows macrophage infiltration and disorganized endothelial layer along a ruptured middle cerebral artery aneurysm. Figure to the right indicates organized endothelial cells along the direction of blood flow. Focalized vascular remodeling continues with increasing inflammation. When the inflammation is intense, the structural components of the vascular wall may be destroyed and lead to the rupture of aneurysms (Hashimoto 2006.) 29

44 Figure 3.1 Transformation of cell morphology by fluid shear stress. Left - Physiological wall shear stress. Right- Low wall shear stress (Malek 1999). Figure 3.2 SEM of cerebral aneurysm. Left- (Kazuo et al 1999) Ruptured middle cerebral artery aneurysm. Disruption of endothelial cells and adherence of blood cells to inter endothelial cell gaps. Right -(Kazuo et al 1999) Normal shape of longitudinal endothelial layer of an incidentally discovered middle cerebral artery aneurysm. Crawford et al (Crawford 1959) pointed the percentage fraction of local rupture along the aneurysm. His studies showed about 64% of aneurysms to rupture at the dome. The dome region of the aneurysm is exposed to very low WSS of less than 5 dyn/cm 2, in case of ruptured aneurysms (Shojima 2004). These indications co-relate well 30

45 with the theory of low WSS leading to the rupture of aneurysms. Also rupture always occurred at the distal portion of the aneurysm dome, where the effects of oscillatory WSS are experienced. The proximal side of the aneurysm dome of considerable aspect ratio is devoid of any oscillating WSS. Figure (3.3) represents the percentage of rupture along the dome of saccular aneurysms as indicated by Crawford et al from the analysis of 163 ruptured aneurysms. Figure 3.3 Percentage of rupture along the dome of aneurysms. (Crawford 1959). 3.2 Hypothesis From comprehensive literature review, we have shown that the low WSS mediated processes play a vital role in degenerating the structural integrity of the aneurysm wall. Histochemical studies have shown a high inflammatory score on the walls of ruptured aneurysms and have speculated that this could orchestrate the rupture of aneurysms. Hence, we find it important to quantify the region along the dome of aneurysms that is susceptible to low WSS mediated vascular remodeling. We study the distribution of this area for various orientations of dorsal aneurysms. We summarize the 31

46 process of endothelial turn over and proliferation of SMC s leading to inflammatory cell response (figure 3.4). The hemodynamic shear stress affects the endothelium, and initiates a vascular remodeling process. Vascular endothelial cells and smooth muscle cells produce extracellular matrix proteins, in the aneurysm wall that help maintain the structural integrity of the aneurysm against the pressure forces acting on the intra aneurysmal wall. To the left leg of the flowchart, the process of adaptive remodeling of the arterial wall at WSS above the physiological limits of dyn/cm 2 is demonstrated. When the WSS along the arteries exceed the physiological WSS limits, the vascular endothelium release NO (Nitric Oxide) based vasodilators that result in the relaxation of the smooth muscle cells restoring the WSS back to its physiological limits. In contrary along the dome of the aneurysm, where the WSS distribution is low, a vascular remodeling process owing to the low WSS response of endothelium is initiated. The presence of, inflammatory cells such as macrophages and leukocytes affect the vascular pathology; they secrete many kinds of proteases that destroy the extracellular matrix proteins. The layer of extra cellular matrix proteins contributes to the tensile strength of the aneurysm wall. Along the dome region of an aneurysm, a slow recirculating flow exists, where the WSS is low. This flow pattern increase the residence time of blood along the dome region resulting in enhanced mass transfer. The slow flow results in the disorientation of the layer of endothelial cells along the dome wall and results in leukocyte infiltration. The inflammatory cells secrete proteas such as cathepsin, that play a vital role in digesting the SMC s and collagen fibers, that result in the loss of structural integrity of the arterial wall. Hence the aneurysmal wall would no longer be able to cope with the intra aneurysmal pressure. The morphological changes 32

47 that result from the destruction of the matrix wall at low WSS are collectively called remodeling of the vascular wall (Intengan 2001). Figure 3.4 Flow Chart-Process involved in low WSS remodeling of the arterial wall. 3.3 Area Prone to Vascular Remodeling Vascular wall remodeling is a low WSS mediated process in the dome of the aneurysm. It is now clear that the low WSS along the dome of the aneurysm triggers the proliferation of Smooth Muscle Cells towards the luminal surface. Low wall shear stress in the range of ±4 dyn/cm 2 plays a vital role in degenerating the endothelial layer, resulting in an inflammatory response by initiating an atherosclerotic cell response 33

48 (Malek 1999). We define area prone to vascular remodeling as the region that is most susceptible to inflammatory changes initiated by vascular remodeling where the WSS ranges between ±4 dyn/cm 2.We hypothesize that the distribution of this area along the dome of aneurysms would indicate the risk of rupture. Aneurysms with large area prone to vascular remodeling would indicate larger areas along the dome showing characteristics that may lead to rupture. With this, we attempt to couple findings of clinical studies with their corresponding hemodynamic cause and quantify the region along the dome where such changes are possible. 34

49 CHAPTER IV COMPUTATIONAL SETUP 4.1 Aneurysm Geometry We have clearly demonstrated the vital role played by CFD techniques in providing a better understanding of aneurysm hemodynamics. The difficulties in conducting in vivo clinical studies on aneurysms have further popularized CFD techniques. In the current study, we computationally model 3-d spherical aneurysms to understand the flow features in lateral aneurysms and further assess the effect of arterial curvature and angle of tilt of the aneurysm sac on intra aneurysmal flow. The current study comprises of the following aneurysm geometries, a) Lateral aneurysms models b) Sidewall aneurysm model on curved parent artery c) Sidewall aneurysm models placed at various angles of tilt to the parent artery. The above 3d model geometries were constructed using Pro-e or Gambit. The model dimensions were obtained from previous studies (Ujiie 2001, Parela 1999). Figure (4.1), represents the geometry of lateral aneurysms. The dimensions that characterize the aneurysm geometry are N- neck width, H- dome height, D- dome diameter and d-artery diameter. 35

50 Figure 4.1 Representation of lateral spherical aneurysm incorporated in the study. (D)- Dome diameter, (N)-Neck width, (H)-Neck height, (d)-artery diameter. Figure 4.2 Representation of Dorsal spherical aneurysms incorporated in the study. (D)- Dome diameter, (N)-Neck width, (H)-Dome height, (R)-Radius of curvature of the parent artery, (d)-artery diameter. 36

51 Figure 4.3 Representation of dorsal aneurysms at various angles of tilt to the parent artery. Left- Mesh structure and co-ordinate axes representation. Right (Top), angle of tilt of the aneurysm β=0,45 and 90. Right (Bottom) - Model representation for the cases of β=0, 45 and 90. Figure (4.2), represents the geometry of aneurysms harbored on curved arteries where R, represents the radius of curvature of the parent artery. Figure (4.3) represents curved artery aneurysms at various angles of tilt to the parent artery. Table (4.1) indicates the dimensions of various geometries incorporated in the study. The dome diameter (D) is maintained at 10mm and the diameter of the parent artery (d) is maintained at 3mm for all the models. Model 1, Model 2 and Model 3 are constructed on the basis of figure (4.1), to study the impact of aspect ratio on intra aneurysmal hemodynamics. The neck width, which is defined as the major axis length of the aneurysm orifice of the models was varied to obtain an aspect ratio of 1.424, and 2.3 (D/N ratio 1.6, 2.0 and 2.4). Model 4, Model 5 and Model 6 are constructed on the basis of figure (4.2), to study the impact of arterial curvature on intra aneurysmal 37

52 hemodynamics. The radius of curvature of the models were varied as R=, 16 and 12 (R -1 = 0, and ). Model 6, Model 7 and Model 8 are dorsal aneurysms harbored at various angles of tilt to the parent artery. (β= 0, 45 and 90 ). The values selected for D/N ratios were based on a statistical study by Ujiie et al (Ujiie 2001). Table 4.1 Aneurysm model dimensions incorporated in the study. D-Dome H-Dome N-Neck d R -1 H/N D/N MODEL β Height Width Diameter (mm) (mm -1 ) Ratio Ratio (mm) (mm) (mm) Model Model Model Model Model Model Model Model Mesh Generation The mesh for the various geometries was generated using Gambit. The lateral aneurysm models consisted of approximately hexahedral grid elements. The curved artery models consisted of unstructured and structured hybrid grid elements. The elements constituting each of the models comprised of hexahedral, tetrahedral and wedge elements. 38

53 The boundary wall of each of the models consisted of closely placed hexahedral grid elements to resolve high velocity gradients at the wall. Detailed mesh convergence analysis was performed to ensure that the solutions obtained were independent of the grid size. Mesh independence was investigated by checking the velocity magnitude distribution along the line passing through the centre of the dome as shown in the figure (4.4). Hybrid multi block grids of , , and were examined and mesh independence was attained for the mesh sizes of and The maximum difference in velocity distribution calculated for these two meshes were around 3.6% (Figure 4.5). Consequently, results presented in the following are for a grid size of Figure 4.4 Location where velocity magnitude was extracted to perform mesh independence study. Along the z axis for β=0. 39

54 u/u in Curve Length (m) Figure 4.5 Grid independence in terms of velocity distribution along the z axis for β= Modeling Equations The incompressible form of the Navier Stokes equation was selected for the numerical solution. The continuity and momentum equation for incompressible, constant property flow without body forces are given by, (4.1) (4.2) where, µ is the dynamic viscosity, p is the pressure and V is the velocity. 40

55 For our studies, the process is isothermal, hence the energy equation has not been considered. Fluent Version was used to solve the equations using Finite Volume Approach. 4.4 Flow Parameters The density of blood was specified as 1050 kg/m 3. The viscosity of blood was considered as kg/m-s, as obtained from previous studies (Hoi 2004). A UDF (Appendix A), for the fully developed parabolic inflow was specified at the inlet. The Reynolds number was maintained at 135 and 270 (maximum velocity 0.3 m/s and 0.6 m/s). The Fourier series expansion for the pulsatile waveform was given by the first six terms of the series (Mulay 2002 ), (4.3) The maximum and minimum Reynolds number of pulsatile flow was and respectively. The duration of the pulse was 0.75 sec and the peak systole was attained at sec. Based on the radius of the parent vessel, the Womersley Number of flow was Figure (4.6) shows the variation of the inflow velocity with time. 4.5 Computational Assumptions Certain computational assumptions are made to facilitate the computational modeling of blood flow in aneurysms. Several authors have validated the impact of these assumptions on the obtained computational results. 41

56 Figure 4.6 Variation of the inflow velocity with time (Pulsatile variation) Rigid Vessel Model Healthy arteries are highly deformable complex structures having a non linear stress strain curve with exponential rigidity at high shear rates. The rigidity effect is typically due to the rough collagen fibers that show anisotropic behavior (Paà l. 2007). Distensible arterial wall models and its impact on aneurysm initiation and growth have been studied from as early as 1987 (Steiger 1987). Owing to difficulties in computationally modeling the distensible wall motion, not much work was done on this front to determine its impact on aneurysms. Recently studies have been conducted by using coupled fluid structure approach to study the impact of wall distensibility (Chatziprodromou 2007a). 42

57 Kobayashi et al (Kobayashi 2004) studied the impact of wall pulsation on ICA and MCA (middle cerebral artery) aneurysms. In their small orifice model the flow entering the aneurysm was higher in the pulsatile flow model. In models with the wide orifice there was no significant difference in the rigid and pulsatile conditions. In case of small orifice aneurysms and pulsating wall conditions, the inflow into the aneurysm is increased in the systolic condition due to the additional volume created due to expansion, hence reducing the outflow. During the diastolic phase the out flow would increase with the contracting sac. But in case of wide orifice aneurysms (3mm neck width, done to neck=1.7) the orifice is roomy enough to accommodate both the inflow and outflow simultaneously. Hence, rigid wall assumption is an acceptable model for wide orifice aneurysms Viscosity Blood viscosity decreases with increasing shear rates, that is increasing differences of flow velocity between adjacent laminae. The flow velocity profile in arteries is blunter than one would expect for Newtonian fluids. The non Newtonian property profoundly affects flow in small size vessels such a as arterioles and capillaries while in large caliber vessels the effect is not all that prominent (Steiger 90). At shear rates above 100 s-1, the viscosity of blood is relatively constant and the value for the logarithm of viscosity increases linearly as a function of the hematocrit and blood is considered a Newtonian fluid at such shear rates (Yun 1999). The shear rates in the arterial system are typically considered larger than this value. The non Newtonian nature of blood is limited to conditions of very low shear rates or very small vessels 43

58 (diameter < 0.1mm). These conditions are seldom present at the site of an aneurysm; although the wall of the aneurysm sac in certain regions may exhibit values lower than this. Perktold et al (Perktold 89) considered a large artery model under physiological flow conditions. The comparison of Newtonian and non Newtonian results indicated no essential differences for the high shear rates. In the present study we use the Newtonian model of viscosity to study blood flow through aneurysms. 4.6 Solution Parameters Specified (FLUENT ) The incompressible Navier Stokes equation was solved using Fluent developed by Ansys, Inc - Santa Clara, CA A pressure based implicit solver was used for our steady and unsteady simulations. The pressure velocity coupling was achieved using the simple algorithm (semi-implicit method for pressure linked equations). The SIMPLE algorithm uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field. The procedure is based on a cyclic series of guess-and-correct operations to solve the governing equations. The momentum equations are solved using a guessed pressure value to obtain velocity components. The pressure value is then corrected so as to satisfy the continuity equation. The procedure continues until the solution converges. In this procedure, the actual pressure p is given by equation (4.4) 44

59 (4.4) where, is the estimated value of pressure and is the pressure correction. The pressure correction is obtained using, (4.5) where, is the estimated velocity vector obtained by solving the momentum equations. The spatial discretization is performed using the Second Order Upwind Scheme for both the steady and unsteady cases. The temporal discretization for the unsteady case was performed using the Second Order Implicit Algorithm. The under relaxation factors for pressure and momentum were specified as 0.3 and 0.7. For the unsteady computations, a time step size of sec was specified, yielding 150 steps per pulsatile cycle of 0.75 sec. A fixed time stepping was specified with a maximum of 70 iterations per time step to ensure convergence. Data was stored at every time step, in order to obtain required values at a later stage. The simulations were run for three complete cycles, and the values obtained in the third cycle were considered for post processing. The simulations were run on a x86 Family Genuine Intel ~ 3800 Mhz processor. 45

60 CHAPTER V HEMODYNAMICS OF LATERAL ANEURYSMS: ASPECT RATIO EFFECT 5.1 Introduction In this section, we investigate the impact of aspect ratio on lateral spherical aneurysms. The aneurysm sac is spherical in shape. The dome diameter is maintained at 10mm and the neck width is varied to maintain a dome to neck ratio of 1.6, 2.0 and 2.4 which translates to aspect ratios of 1.424, and 2.3. Ujjie et al (Ujjie 2002) had earlier predicted an aspect ratio of 1.6 to be a critical value in predicting rupture of aneurysms. Hence aspect ratio values around this range were chosen to study the variations in hemodynamics. Figure 5.1 Parabolic nature of blood flow through the artery. A steady flow UDF was specified at the inlet to obtain a fully developed flow profile. Figure (5.1) represents the parabolic steady blood flow through lateral aneurysms. The plot was extracted along an aneurysm with an aspect ratio of at a 46

61 Reynolds Number of 270, with a UDF for the parabolic steady flow specified at the inlet (Attached- Appendix A). The parabolic nature of flow is maintained throughout the length of the artery. The presence of the aneurysm sac does not cause much of a deviation from the parabolic flow profile, downstream of the artery. 5.2 Primary Flow Structure through Lateral Saccular Aneurysms The flow into the aneurysms is essentially shear driven. The inflow into the aneurysm is along the distal neck. It can be seen (figure 5.2) that the intra aneurysmal flow in the three aneurysms is characterized by a single counter rotating vortex towards the distal end of the aneurysm. With an increase in aspect ratio the vortex moves closer to the distal neck of the aneurysm. The flow features for all the three aspect ratios consists of a low velocity inflow into the aneurysm sac at the distal end of the aneurysm. The flow velocity in the aneurysm sac is one order of magnitude less than that in the artery harboring the aneurysm. From the path lines that were extracted (figure 5.3) for an aspect ratio at Re 270, it can be seen that only a few path lines along the upper wall of the artery enter the aneurysm at the distal end. The inflow region into the aneurysm sac is really small compared to the outflow that occurred through a major portion of the aneurysm neck. 47

62 y z Figure 5.2 Comparison of the velocity vectors (m/s) along the primary flow plane for Aspect Ratio of (left), (centre), 2.3 (right). The flow direction in from left to right. Reynolds number-270. y z Figure 5.3 Path lines extracted for a lateral aneurysm of Aspect Ratio of at Re 270. The flow direction is from left to right. The path lines are color mapped according to their velocity (m/s). 48

63 5.3 Velocity Distribution along a Plane Passing Through the Dome Diameter The disturbed flow in the aneurysm leading to a low velocity re circulating zone along the aneurysm sac is considered a major factor in the degeneration and rupture of aneurysms (Hashimoto 2006). The flow pattern along a plane passing through the centre of the dome of the aneurysm (A-B) had been presented in the figure (5.4). This will enable us to assess the flow entering and exiting the upper region of the aneurysm dome where rupture usually occurs (Cawford 1959). The velocity contour along the plane passing through the dome diameter, for aspect ratios of 1.424, and 2.3 are shown from left to right. The upper end represents the distal side of the dome (side B) and the lower end the proximal side (side A). The aneurysm with an aspect ratio of has the highest inflow into the upper region of the aneurysm with a maximum velocity of 0.45 m/s. With the increase in aspect ratio the flow into the upper region of the aneurysm decreases and the velocity of inflow drops. Hence the neck size here plays an important part in deciding the amount of flow into the aneurysm sac. The other factor in deciding the sluggish nature of flow in the aneurysm sac would be the volume of the sac which would be a function of the dome diameter, the dome height and the semi axis height. Hence for a given neck width the shape of the aneurysm would decide the nature of flow within the aneurysm sac. In the case of spherical aneurysms modeled here, as the neck width decreased from 6.25 mm to 4.166mm, the flow in the aneurysm sac was more stasis like. The dome height (H) for the three cases was 8.9 for A.R-1.424, 9.33 for A.R and 9.5 for A.R-2.3. The flow rate along the plane passing through the centre of the aneurysm dome was highest in case of the aneurysm with the smallest aspect ratio of 49

64 1.424 and decreased with increasing aspect ratio. The flow rate was 2.79*10-10 m 3 /s for A.R-1.424, *10-10 m 3 /s for A.R and 1.177*10-10 m 3 /s for A.R-2.3 respectively. A DISTAL A A B B PROXIMAL B e-2 Units-m/s Y Z Figure 5.4 Velocity contour along the plane passing through the centre of the dome (A- B), for aspect ratios of (left), (centre) and 2.3 (right). Side A represents the proximal side and B represents the distal side of the aneurysm. The upper and lower sides of the contours indicate the distal and proximal sides. The velocity magnitude along line AB passing through the centre of the plane is extracted. Figure (5.5) shows the variation of velocity magnitude along the line passing through A-B. The velocity magnitude is one order of magnitude less than that in the artery. The magnitude of inflow velocity is found to be the highest for the smallest 50

65 aspect ratio. The maximum inflow velocity is obtained along the distal side of the aneurysm dome for all the aspect ratios investigated. Figure 5.5 Velocity magnitude (m/s) along the dome diameter, for aneurysms with aspect ratio of (D/N=1.6), A.R (D/N=2.0), A.R 2.3 (D/N=2.4). Distance (m) represents the diameter of the spherical aneurysm. (m) 5.4 Wall Shear Stress Distribution The Wall Shear Stress (WSS) along the artery was ~3.7 N/m 2. The WSS along the models was maximum at the distal end increasing with an increase in aspect ratio. The maximum WSS at the distal end was more than double the arterial WSS. The WSS distribution along the dome was very low compared to that of the artery. Also, the region of the aneurysm dome exposed to elevated values of WSS increased with a decrease of aspect ratio from 2.3 to as shown in the figure (5.6). Figure (5.7) demonstrates the 51

66 WSS variation on either sides of the dome of the aneurysm, along the plane passing through the dome diameter for an aspect ratio of at a Reynolds number of 270. The WSS values were extracted at various points along the intersection of the plane, and the dome of the aneurysm. Capital letters (A,B S), are the values along the dome to the left of the inflow direction and small letters (a,b,c..s) are the values to the along the dome to the right of the inflow direction. The WSS at the proximal and distal end of the dome diameter are denoted by Prox (Proximal), and Distal respectively. The plot shows the symmetric distribution of WSS along either sides of the dome. The WSS is found to increase from the proximal to the distal end, where the impact of impinging flow is felt. The WSS increases from Pa at the proximal end to at the distal end. (a) (b) (c) Units-Pascal Figure 5.6 WSS distribution along the dome of the aneurysm with dome to neck ratios of (a) 1.6 (b) 2 (c)

67 Aspect Ratio Left Aspect Ratio Right y Wall Shear Stress (Pascal) z Prox A,a B,b C,c D,d E,e F,f G,g H,h I,i J,j K,k L,l M,m N,n O,o P,p Q,q R,r S,s Distal X-Z Plane Figure 5.7 Wall shear stress distribution along the circumference of the plane passing through the centre of the dome, for aspect ratio of Figure shows the location of capital (A,B..S) and small (a,b.s). We further extract the WSS along the line passing through the circumference of the plane passing through the dome diameter, towards the right of the inflow direction (figure 5.8). The plots show a higher value of WSS for the smallest aneurysm of aspect ratio The WSS distribution decreases with the increase in the aspect ratio. The WSS at the distal end reduces from Pa (A.R or D/N 1.6) to Pa (A.R 2.3 or D/N 2.4). Further a steep WSS gradient was observed along the line, between points P and the distal end of the aneurysm. 53

68 y AR 1.42 WSS (Pascal) z AR AR INFLOW 0 Proximal b c d e f g h i j k l m n o p q r s Distal X-Z Plane Figure 5.8 Comparison of WSS distribution at the centre of the dome of the aneurysm, for varying dome to neck ratios. The points are at the intersection of the plane and the wall of the aneurysm. 5.5 Summary and Discussion The study of lateral aneurysms provides a basic insight on the distribution of hemodynamic parameters along the aneurysm dome. The primary flow features were found to be similar for the three aspect ratios of lateral aneurysms. A single counter rotating vortex is a common feature. The velocity of flow in the aneurysm dome is one order of magnitude less than that in the parent artery. With the increase in aspect ratio of the spherical aneurysm, the inflow into the aneurysm sac reduces. The resulting re circulating flow in the aneurysm sac becomes more stasis like. Also the area along the 54

69 distal side of the dome occupied by increased wall shear stress reduces, exposing a larger area of the aneurysm dome susceptible to inflammatory changes. This condition enhances the residence time of the blood particles and increases the interactions between circulating leukocytes and the wall endothelial layer. The macrophage infiltration into the endothelial layer results in wall fragility and further promoting proliferation of extracellular matrix proteins. In spherical aneurysms, increasing aspect ratio, promotes factors that promote vascular wall remodeling. The maximum WSS is found at the distal neck of the aneurysm at the zone of impingement of the inflow into the aneurysm sac. Further the maximum WSS at the distal neck is found to be more than double that of the arterial wall shear stress for lateral aneurysms. The phenomenon of aneurysm growth is associated with elevated wall shear stress at the distal end of the aneurysm. Wall shear stress greater than 2 Pa, results in growth related remodeling of the aneurysm wall (Hoi 2004). The area occupied by elevated WSS along the distal side of the aneurysm is also reduced with an increasing aspect ratio. Also, the WSS distribution along the dome of the aneurysm is found to be symmetric along the primary flow plane, with decreasing WSS from the proximal end to the distal end of the aneurysm. A high WSS gradient is observed closer to the distal end of the aneurysm dome. There is considerable evidence that the spatial variation in shear stress along the in the disturbed flow region exert significant influences on the endothelial cells (Da Palora 1992, Chiu JJ 2003).The large shear stress gradient not only increases monocyte adhesion to endothelial cells but also cause a net migration of endothelial cells away from the region of high shear gradient (Tardy 1997). 55

70 CHAPTER VI EFFECT OF ARTERIAL CURVATURE ON DORSAL ANEURYSMS 6.1 Curved Arteries: Hemodynamic Environment Leading to the Genesis of Dorsal Aneurysms Flow through curved tubes is usually complicated to assess. This is mainly because the particles of flow cannot be parallel to the artery along the curvature. Secondary (or transverse) components would be present. For a fluid particle to move along a curved tube of radius R, with speed u, it must be acted upon by a lateral force provided by the pressure gradients. The radius of curvature of the particles at the core would be higher than that at the walls. This results in a secondary circulation, where the fluid in the core region is swept towards the walls, and the fluid in the wall region moving towards the centre. This leads to a complex interaction in the flow with a prominent secondary flow that is very different from the flow in a straight pipe or artery. In this chapter we study the role of arterial geometry in the pathogenesis of saccular aneurysms. We study the impact of arterial curvature on aneurysm hemodynamics and highlight its implications relative to aneurysm genesis, growth and rupture. The conditions of flow are similar to that specified in case of lateral aneurysms. The Reynolds number of flow was 135 and 270, with a fluid viscosity of cP and fluid density of 1050 Kg/m 3. The diameter of the arterial segment was maintained at 56

71 3mm and the radius of curvature of the curved artery was 12mm. The U shaped artery has an entrance region twice the diameter of the artery to the inlet and from the outlet. Figure (6.1), demonstrates the velocity contours along plane A-B for the curved arterial segment. The centrifugal effects of the curvature induced flow are evident in case of the curved arterial flow. The high velocity components of flow shift from the core to the upper wall of the artery. Owing to the change in momentum of the impinging velocity along the curvature of the artery, the WSS along the curvature increases to 2.25 Pa compared to 1.4 Pa along the straight artery. The WSS along the curvature increases with increase in curvature of the artery. The elevated WSS along the cavernous segments play a vital role in the genesis of aneurysms (Yoshimoto et al 1996, Hashimoto 2006). The location of occurrence of dorsal and ventral aneurysms with respect to the curved parent artery has been indicated in the figure. Figure (6.2), compares the velocity contour along a straight artery 20 mm from the inlet to that of a curved artery along plane A-B for Re 135. The shift in the region of increased velocity from the centre of the straight artery (right) to the dorsal region of a curved artery is shown. Also the peak velocity magnitude along the curved artery is slightly lesser compared to the maximum velocity in the straight artery. This can be clearly seen from the velocity color map. Parela et al (Parela 1999) in his study of 87 aneurysms found the angle of tilt of aneurysms to vary from -50 in the anterior side to 40 in the posterior side. The influence of the centrifugal effects of curvature along the curved arteries are found between +90 and -90, as shown in figure (6.3) below. This region experiences an elevated WSS ranging from 2.20 Pa at point B to 1.87 Pa along point F for Re 135 (Ref figure 6.3). In the figure, points B, D and F denote dorsal aneurysms placed at an angle 57

72 Dorsal A Inflow z x z B A B z y Ventral Unit-m/s y x Figure 6.1 Velocity Vector distribution along a curved artery of radius of curvature 12mm. Artery diameter 3mm. Vectors are extracted along plane A-B (Top Left). Arterial model with the co-ordinate description (Bottom Left). Velocity Contours A-B (Top Right). Unit-m/s Figure 6.2 Velocity contour of flow along a curved artery (left) to that of a straight artery (Right) (Re 135). The plots are extracted along A-B for the curved artery and 30 mm from the inlet, Straight Artery. Direction of flow (Paper to the reader). 58

73 of tilt β=0, 45 and 90. This is in accordance to the nomenclature illustrated by Parela et al (Parela 1999). We further extract the velocity profiles along lines A-B, C-D and E- F along the curved artery to draw a comparison with that of a parabolic velocity profile along a straight artery that harbors a lateral aneurysm. The maximum velocity is found to be highest in case of a straight artery, followed by A-B, this is in good agreement with the results published by Krams et al (Krams 2005), where they study the impact of arterial curvature on fluid flow. Their results using Computational fluid dynamic technique and Doppler ultrasound agree well with the results obtained here. Velocity profiles along C-D and E-F show a maximum velocity lesser that A-B. Also the velocity profile along E-F, that would harbor an aneurysm at β=90, shows a symmetric variation along the diameter of the artery. The arteries above simulate conditions prior to pre aneurysmal change along straight and curved arteries. We speculate that in the absence of any disease causing process, the initiation of dorsal aneurysms could be mediated by the increased hemodynamic WSS along the curved arterial segment. It is now clear that dorsal aneurysms are initiated on sites prone to elevated WSS. The WSS along curved arteries decrease as we move from β=0 to β=90. Unlike a straight artery that shows a parabolic velocity profile along all directions with the peak velocity along the core of the artery, curved arteries show a variation in the velocity distribution along lines passing through β=0, 45 or 90. We further consider curvature induced dorsal aneurysms to assess impact of arterial curvature on intra-aneurysmal hemodynamics. 59

74 Figure 6.3 Comparison of velocity profile along A-B, C-D and E-F of a curved artery to the flow profile along a straight artery. Position B is where dorsal aneurysms are formed 60

75 6.2 Dorsal Aneurysms We model dorsal aneurysms harbored on arteries with varying radius of curvature. The geometry of the aneurysms has been explained earlier (Chapter IV). Model 3, Model 4 and Model 5 have been incorporated in this study, and a description of their geometry is available in Table (4.1) (Chapter IV). The impact of arterial curvature on the distribution of impact zone and area prone to vascular remodeling has been assessed Primary Flow Structure Figure (6.4), represents the primary flow structure along the symmetry plane, and the WSS distribution along dorsal aneurysms. (a1) represents the primary flow structure and (a2) represents the WSS distribution at the distal end of the aneurysm harbored on an artery with radius of curvature of R=12mm or 1/R= m -1, similarly (b1-b2) for R=16mm or 1/R= m-1 and (c1-c2) for R= or 1/R=0. The flow impingement intensified with an increase in curvature of the parent artery. The flow impinges along the distal end of the neck before entering into the aneurysm, demonstrating the effect of centrifugal force of flow due to the arterial curvature. For the case where the curvature was zero, the flow weakly entrained the aneurysm dome. A single counter clockwise rotating vortex was a feature similar among all the models investigated. The circulating flow in the aneurysm dome was one order of magnitude less than that in the artery harboring the aneurysm. 61

76 6.2.2 Wall Shear Stress Distribution The WSS at the distal end of the dorsal models, increase with increase in arterial curvature (figure 6.4). Also the impact zone enlarged with the increase in the curvature of the parent artery harboring the aneurysm. The area prone to vascular remodeling was found to decrease with the increase in curvature of the parent artery. The area prone to vascular remodeling was found to be the largest in case of the lateral aneurysm where the curvature was zero. 6.3 Quantification of Impact zone and area prone to vascular remodeling Table 6.1, shows the variation of Impact zone and the area prone to vascular remodeling for the three models of spherical aneurysms on parent arteries of varying curvature. The values have been non-dimensionalized with the total area of the dome and the neck of the aneurysm. The impact zone increases with the increase in the curvature of the parent artery and the area prone to vascular remodeling decrease with the increase in parent artery curvature. The area along the dome of the aneurysm that is susceptible to adaptive remodeling increases with the curvature of the parent artery harboring the aneurysm. Aneurysms harbored on straight arteries (lateral aneurysms), showed the largest area that is prone to vascular remodeling owing to the weak entraining flow into the aneurysm sac as against centrifugal force induced flow into curved artery aneurysms (figure 6.5). Almost the entire dome region of the aneurysm is occupied by low WSS congenial to initiate remodeling. This feature demonstrates the risk of increased leukocyte adhesion and inflammation along the larger areas of lateral spherical aneurysms. 62

77 a1 a2 b1 b2 z c1 c2 z y x Figure 6.4 Flow structure along the primary symmetry plane, and WSS distribution along the distal end of the aneurysm dome, for the three models with curvature (1/R= (a1-a2), (b1-b2) and 0 (c1- c2)). 63

78 Table 6.1 Variation of Impact zone and area prone to vascular remodeling, for the three models of spherical aneurysms on parent arteries of varying curvature. 1/R (Curvature) (mm -1 ) Impact zone Area Prone to Vascular Remodeling Figure 6.5 Comparison of the Area Prone to Vascular Remodeling with arterial curvature. 1/R=0 (Left), 1/R= (Centre), 1/R= (Right). The blue region along the aneurysm dome represents the region where WSS < 4 dyn/cm 2. 64

79 6.4 Summary and Discussion We study the impact of curved arteries on the pathogenesis of aneurysms. Our studies demonstrate that the flow features along curved arteries are remarkably different compared to that along straight arteries. We speculate that the curvature induced centrifugal force could play an important role in the initiation of dorsal aneurysms. Also the curvature induced elevated WSS is experienced along the upper surface of the artery (-90 to +90 ).However we could not provide any noticeable variation in the hemodynamic environment of lateral arteries to explain the initiation of lateral aneurysms. The maximum WSS at the distal end was found to be more than 7 times the value along the artery, for the model with the highest curvature. The maximum WSS was just twice as much along the straight artery for lateral aneurysms. We further demonstrate that the impact zone increases with the increase in arterial curvature. The large impact zones along the dome of aneurysms placed on arteries of high curvature show that the area susceptible to adaptive remodeling along the dome of the aneurysm increase with the increase in curvature of the parent artery. Also, lateral aneurysms where the curvature was zero showed the highest area prone to vascular remodeling, suggesting the possibility of increased vascular remodeling and leukocyte infiltration resulting in an inflammatory cell response along a large area of the dome. Hence the low flow conditions along lateral aneurysms result in a larger area along the dome of the aneurysm that is susceptible to vascular remodeling processes that further deteriorate the wall of the aneurysm. Previous clinical studies speculate the increased vascular wall remodeling to play a prominent role in deteriorating the 65

80 structural integrity of the intra aneurysmal wall, which may lead to degeneration of the arterial wall and finally rupture. 66

81 CHAPTER VII EFFECT OF ANGLE OF TILT (β) ON INTRA ANEURYSMAL HEMODYNAMICS 7.1 Introduction We model dorsal aneurysms placed at various angles of tilt to the parent artery, in order to understand the impact of such geometric arrangement on the intra aneurysmal hemodynamics. We consider three cases of aneurysms placed at β=0, 45 and 90 to the parent artery. At these locations the centrifugal effect of arterial curvature are experienced that results in the high WSS along curved arteries. We utilize these models to demonstrate the impact of angle of tilt on the primary and secondary velocity profiles and WSS distribution along the aneurysmal sac. We further quantify the Impact Zone and area prone to vascular remodeling with the variation in the angle of tilt of aneurysms. 7.2 Primary Flow Structure Figure (7.1 a1, b1, c1) demonstrates the intra aneurysmal primary flow pattern at Re 270, for the three cases β=0, 45 and 90. The primary flow pattern mainly consists of high velocity inflow into the aneurysm impinging at the distal neck and flowing along the distal region of the aneurysmal sac. The distal side of the aneurysm neck acts like a flow divider. A single counter rotating vortex along the dome is a common feature among the three cases of β modeled. The flow velocity is an order of magnitude less 67

82 than that in the artery. Also β=45 shows the highest inflow into the aneurysm, a result co-relating well with experimental as well as numerical simulations of Liou et al (Liou 2007). From figure (7.2), velocity path lines for the case of β=0⁰, at Re 270, it is clear that the particles exiting the aneurismal sac do so from the proximal side of the aneurysm neck, occupying a large area compared to the area occupied by the blood flowing into the sac at the distal end. The path lines also show the high velocity inflow into the aneurysm at the distal end, gradually decreasing in velocity as it reaches the recirculation region towards the centre of the dome. The low velocity circulating flow in the aneurysm is shown by the blue colored path lines in the aneurysmal sac. The maximum inflow velocity in case of the aneurysm with β=0 is along the distal neck is about 51% of the maximum velocity in the parent vessel. 68

83 a1 a2 b1 b2 c1 c2 m/s m/s Figure 7.1 Velocity vectors along the primary and secondary flow planes. For the models with β=0⁰ (a1-primary, a2-secondary), β=45⁰ (b1-primary, b2- secondary), β=90⁰ (c1-primary, c2-secondary). 69

84 7.3 Secondary Flow Structure Figure (7.1 a2, b2, and c2) demonstrates the secondary flow pattern along the orientations of the aneurysm sac considered i.e., for β=0⁰,45⁰,90⁰ at a Reynolds Number of 270. The secondary flows in the models are essentially due to the induced centrifugal force due to curvature. The result is a pair of symmetric counter rotating vortices for β=0 (figure 7.1 a2).the vortices originate from the side wall boundary layer before flowing back into the inner core region of the dome. However for β=45⁰ and β=90⁰ (figure 7.1 b2, c2) the aneurysm orifice is located off the plane of curvature and show a varying pattern of secondary flow compared to β=0⁰. For β=45⁰ and β=90⁰, the secondary flow consists of a single counter rotating vortex initiating towards the Dorsal side and flowing towards the opposite side of the dome. This is mainly due to the skewed inflow into the aneurysm along the neck and the dome wall facing the dorsal side. The plots are extracted along the inflow direction from the reader into the paper. The high velocity inflow into the aneurysm shifts towards the dorsal side with an increase in the angle of tilt β. This skewed region of high velocity at the dorsal region accompanied by a change in the secondary flow pattern should impact the wall shear stress distribution along the secondary direction of flow 70

85 Unit-m/s Figure 7.2 Velocity path lines for β=0, showing the inflow into the aneurysm from the distal neck and the outflow along the proximal side of the dome. 71

86 7.4 Wall Shear Stress Distribution Figure 7.3 Wall shear stress distribution along the distal end of the aneurysm. Reynolds number (Re-270 Left, Re-135 Right). WSS is found to be maximum along the distal neck of the aneurysms. The distal end acts as a flow divider to the impinging flow from the parent artery. This is in agreement with the results of Shojima et al (Shohima 2004), based on CFD analysis of magnitude of WSS in and around twenty anatomically correct cerebral aneurysms and studies pertinent to idealized aneurysm geometry (Hoi 2004, Liou 1997, 2007, 1999 Burleson 1995).Figure (7.3) shows an increase in the maximum WSS at the distal end with an increase in Reynolds number. Owing to this high hemodynamic stress at the distal end, aneurysms may tend to expand further along this region (Hoi 2004). Also it can be seen that the area occupied by elevated WSS increases with an increase in Reynolds number of flow. The impact of arterial curvature on the maximum WSS at the distal neck was studied earlier (Chapter VI) and has been shown that the flow 72

87 impingement led to increase in WSS at the distal neck with an increase in the arterial curvature. Table 7.1 Variation of maximum WSS at the distal end of the aneurysm with varying angle of tilt at Re 135 and Re 270. Angle of Tilt (β) Maximum Wall Shear Stress (Pa) Re 135 Re 270 β= β= β= Impact Zone We utilize the premise put forth the by Hoi et al (Hoi 2004), to calculate the area of impact zone for the three models considered in this study by quantifying the area along the dome and the neck of the aneurysm with WSS greater than 20 dyn/cm 2 (2 Pascal), for Re 135 and Re 270.Table (7.2), consists of the Impact zone to the angle of tilt for Re of 135 and 270. The values were non-dimensionalized with the total area of the dome and neck of the aneurysm. The impact zone increases with increase in the angle of tilt β, from 0 to 90. This is due to the skewed secondary flow pattern along the dome in cases of β=45 and β=90, as shown previously in figure (7.1 b2, c2). This skewed inflow profile leads to an increase in the WSS along the dome wall facing the dorsal side of the aneurysm. Also the skewed inflow into the aneurysm sac, coupled with 73

88 the complex secondary flow pattern leaves β=90, with the highest distribution of elevated WSS. It can also be seen that the variation in impact zone is greater for the first two models, demonstrating the impact of offsetting the aneurysm sac from the primary flow plane. Table 7.2 Variation of Impact Zone with angle of tilt of aneurysms. Aneurysm Model Impact zone Re 135 Impact zone Re 270 β= β= β= (a) (b) (c) Figure 7.4 Wall Shear Stress distribution at the distal end of the aneurysms for varying angles of tilt. Left-β=0, Centre-β=45, Right-β=90. Direction of flow is from paper to the reader. 74

89 Figure (7.4) shows an increase in the area occupied by elevated wall shear stress along the dome of the aneurysm for cases of (a) β=0, (b) β=45 and (c) β=90. The direction of flow is from the paper towards the reader. With an increase in the angle of tilt, more shear along the dome of the aneurysm is observed. The amount of increase in the area occupied by the elevated WSS is higher between β=0 to β=45 when compared that between β=45 and β=90. The skewed impinging flow profile away from the plane of symmetry results in the WSS distribution being oriented away from the symmetry plane (A-B), towards the dorsal region. Unlike the impact of curvature on Dorsal aneurysms, where the maximum WSS at the distal end and the Impact zone increase simultaneously (Hoi 2004), in case of angle of tilt effect, the maximum value of WSS decreases from β=0 to 90, while the Impact zone increases. In case of dorsal aneurysms of β=0, the WSS distribution along the dome and neck is symmetrical about A-B. The cases with β= 45 and 90, experience an asymmetrical distribution of WSS along the dome and neck region. The WSS value along the neck region where the flow impingement occurs is higher compared to the region free of flow impingement. 7.6 Impact of Asymmetric Secondary Flow Distribution on the Shear Stress along the Aneurysm Neck When the WSS distribution along the neck of the aneurysm was assessed for the case of β=0, the distribution was found to be symmetric along the neck of the aneurysm towards the left and right of the inflow region. This can be attributed to the symmetric secondary flow pattern along the dome of the aneurysm. When this feature was assessed for the cases of β=45 and 90, the WSS distribution along the neck was found to be 75

90 asymmetric. The WSS towards the neck region facing the left of the inflow direction (towards the dorsal region) was found to be higher compared to the neck region facing the right of the inflow region (towards the ventral region). This is predominantly due to the skewed secondary flow profile and the impinging flow towards the left or dorsal wall. The shift of the maximum velocity from the core to the upper wall of the artery and the location of the aneurysm neck for cases of β=45 and 90 favor an impingement of high velocity particles at the neck region facing the dorsal side. Figure (7.5, 7.6 and 7.7), represent the WSS distribution along the neck towards the right and the left of the inflow region. In each of the figures (7.5, 7.6 and 7.7), top centre- represents the distal end of the aneurysm neck. The flow direction is from the paper towards the reader. Figures to the left and right bottom represent the WSS distribution along the neck and dome region towards the left of the inflow plane and right of the inflow plane respectively. The color map points towards the WSS distribution along the neck. 76

91 Figure 7.5 Wall shear stress distribution along the neck and the dome of the aneurysm towards the left and right of inflow direction for β=0. 77

92 Figure 7.6 Wall shear stress distribution along the neck and the dome of the aneurysm towards the left and right of inflow direction for β=45. 78

93 Figure 7.7 Wall shear stress distribution along the neck and the dome of the aneurysm towards the left and right of inflow direction for β=90. 79

94 Table 7.3 Distribution of WSS along the dome region as a percentage of the max wall shear stress. Aneurysm Model Left-% of max WSS Right-% of max WSS β=0 7.5%-26% 7.5%-26% β= %-30% 2%-15% β=90 32%-60% 6.4%-16.3% Table (7.3), shows the WSS distribution along the neck of the aneurysm, towards the left and right sides of the inflow direction, as a percentage of the max wall shear stress. The wall shear stress along the left of the inflow direction increases up to 60% the value of max wall shear stress for the case where β=90. The pattern confirms an increase in the wall shear stress distribution along the region facing the dorsal side with an increase in the angle of tilt from 0 to Area Prone to Vascular Remodeling Since, low wall shear stress in the range of ±4 dyn/cm 2 plays a vital role in degenerating the endothelial layer, and resulting in an inflammatory cell response by initiating vascular wall remodeling (Malek 1999). We quantify the area of the aneurysm that is susceptible to this process for various angles β. Hence we define area prone to vascular remodeling as the region that is most susceptible to inflammatory changes initiated by vascular remodeling. Table (7.4), shows the area prone to vascular 80

95 remodeling for the three angles of tilt studied, at Re 135 and 270. The area has been non dimensionalized with the total area of the dome and neck of the aneurysm. Table 7.4 Variation of non-dimensionalized area prone to vascular remodeling with angle of tilt for β=0, 45 and 90. Aneurysm Model Area Prone to Remodeling Re 135 Area Prone to Remodeling Re 270 β= β= β= It is seen that the area prone to vascular remodeling increases with decrease in Reynolds number. At low Reynolds number, the flow along the dome of the aneurysm is more sluggish and the WSS along the dome of the aneurysm drops increasing the risk of leukocyte adhesion. Further the area prone to vascular remodeling decreases with an increase in the angle of tilt β. At a low Reynolds Number of 135 and angle of tile β=0, almost 90% of the surface area of the dome and the neck of the aneurysm are prone to vascular remodeling. High Reynolds number and higher angle of tilt of the dorsal aneurysm with respect to the parent artery result in the decrease of area prone to vascular remodeling. 81

96 7.8 WSS Distribution along Cross Sectional Planes X-Z (Primary), Y-Z (Secondary) It has been shown, that the velocity distribution along the primary flow plane, was similar for all the cases of tilt angles (β=0, 45 and 90 ). However the flow features along the secondary plane varies with the angle of tilt. The flow degenerates, from a dual counter rotating vortex pattern for β=0, to a single clockwise rotating vortex for β= 45 and 90. This is mainly due to the skewed inflow velocity profile in the later cases. The direction of flow creates a higher shear along the face of the aneurysm oriented towards the dorsal side. The wall shear stress distribution along the plane of symmetry Y=0, (Primary flow plane) and X=0 (Secondary flow plane) at various points along the dome were extracted for varying angle of tilt. In the figure (7.8) point A represents the distal end of the aneurysm neck and point S represents the proximal neck. The wall shear stress is found to be maximum at the distal end of the aneurysm neck, for all the case of tilt angles. The WSS distribution along the primary plane Y=0, is found to be similar, for all the cases of β. The region from point A to D, is subjected to WSS greater than 2 Pa (20 dyn/cm 2 ) in all the cases. This is the active region where remodeling would take place. The region of the aneurysm exposed to this high wall shear stress is where the aneurysm is most susceptible to growth (Hoi 2004). We had earlier defined this region as the impact zone. Further we extract points along the dome at the secondary flow plane. Point (a), starting along the dome to the left of the inflow direction and point (s), to the right of the inflow direction. For the case of dorsal aneurysm with β=0⁰, the distribution of WSS along the primary flow plane is in agreement with experimental results along curved artery aneurysms published by Liou et al (Liou 1997). The secondary flow in our 82

97 computational studies for β=0, show a WSS variation between positive and negative values of almost equal magnitude towards either side of the tip of the aneurysm, corelating well with PTV (Particle Tracking Velocimetry) results published by Liou et al (Liou 1997). For angles greater than β=0⁰, the WSS along the secondary flow plane shows an increase in magnitude. Also flow separation is seen in case of β=0 at the tip of the aneurysm dome (Point J). 83

98 (a) (b) SECONDARY PRIMARY Figure 7.8 Variation of Wall Shear Stress at the dome of the aneurysm, along the primary and secondary planes. β=0, 45, 90 (a) plot of the variation in WSS at various points along the primary and secondary plane of the dome at various angle of tilts (b) figure indicates the points along which the WSS was calculated along the primary and secondary plane of the aneurysm dome. Counter clockwise arrow indicate the direction of positive WSS. 84

99 7.9 Summary and Discussion We modeled dorsal aneurysms placed at various angles of tilt β=0, 45 and 90, to the parent artery and demonstrate the variation in primary flow patterns, secondary flow patterns and WSS distribution The aspect ratio for each of the models was maintained constant with a fixed neck width and dome diameter. The radius of curvature of the parent artery was maintained at 12mm (R/d=4). These models at varying angles of tilt were modeled in accordance to the location along the artery where the impact of centrifugal force due to curvature of the artery is felt. The orientation of aneurysms along curved arteries and the secondary flow pattern in the parent artery, influence the intra aneurysmal hemodynamics. Aneurysms placed at varying angles of tilt (β), experience a major difference in the nature of secondary flow. The dual counter rotating vortex in β=0, degenerates to a single counter rotating vortex for β=45 and 90.Owing to this the WSS distribution along the secondary plane is unidirectional in the later two cases. β=0 shows the highest area that is prone to vascular remodeling. Dorsal aneurysms with lower angles of tilt and lower flow rates show larger areas along the dome and neck that are likely to show vascular wall remodeling due to low WSS. Also there exists a flow separation point along the dome of the aneurysm sac placed at β=0. We speculate that β=0, that demonstrates the highest area prone to vascular remodeling accompanied by a flow separation point along the tip of the dome carries an increased risk of leukocyte adhesion and consequently inflammation along the aneurysm sac. 85

100 The impact zone being the highest for the case of β=90, the aneurysm is subjected to a large area of adaptive remodeling to maintain the WSS within physiological limits and we speculate this to have the highest growth potential among the three models. Due to the skewed inflow along the wall facing the dorsal side, in case of aneurysms placed at β=45 and 90, the WSS distribution along the neck as well as the dome of these models are asymmetrical about the primary flow plane (Y=0).The highest variation in WSS along the neck towards the left and right of the inflow plane is found in the case of β=90.this could be a valuable pointer in the design of intravascular stents using computational studies. Our studies show that β=0, demonstrates the maximum area prone to vascular remodeling owing to low WSS and β=90 has the highest impact zone. It is likely that the aneurysm at β=0 is more likely to develop proliferation of SMC s and inflammatory cell invasion along a large region of the dome and neck of the aneurysm. β=90 owing to its high impact zone, contains a larger area capable of growth and expansion of the aneurysm sac. We have quoted sufficient evidence (Chapter II) to further elucidate the prominent role played by low WSS in deciding the fate of aneurysms. 86

101 CHAPTER VIII EFFECT OF ANGLE (β): PULSATING FLOW HEMODYNAMICS 8.1 Introduction We investigated intra aneurysmal flow dynamics in saccular aneurysms, placed at various angles of tilt to the parent artery, under steady flow conditions. However, physiological flow is pulsatile in nature. We extend our analysis to unsteady flow simulations and plot the variation of high and low WSS regions along the aneurysm dome. Figure (8.1), shows the time variation of the inflow velocity along the inlet of the aneurysm. (UDF-Appendix B) Figure 8.1 Time variation of the inflow velocity Specification of pulsatile inflow into the aneurysm. 87

102 8.2 Primary Flow Features We extract the pulsatile velocity flow field for a dorsal aneurysm at β=0 at different instants of time. The time instants and the corresponding inflow velocity along the cardiac cycle along which the plots are extracted are shown in the figure (8.1).Figure (8.2 b) and figure (8.2 e), indicate the flow profile at peak systole and end diastole respectively. (a) (b) (c) (d) (e) Figure 8.2 Variation of Velocity along the primary plane at various instants of time along the pulsatile cycle. Figures (8.2 c and 8.2 d) are plots at intermediate diastole phases. There is no change in the direction of flow along the aneurysm with progress in the cardiac cycle. The single vortex remains intact throughout the cycle. A slight phase lag was observed 88

103 in the evolution of inflow into the aneurysm when compared to the time evolution of inlet velocity. Also the variation of maximum WSS at the distal end of the aneurysm when plotted with cardiac cycle, showed variation similar to the pulsatile cycle. Figure 8.3 Variation of maximum wall shear stress along the distal end with time variations in the inflow condition. We calculate the variation in Impact zone and area prone to vascular remodeling with cardiac cycle. For idealized dorsal aneurysm geometry, there was no change in the inflow pattern or flow reversal features observed along the dome of the aneurysm. 8.3 Time Evolution of Impact zone It has been shown that the impact zone increases with increase in the flow rate into the aneurysm (Figure 8.4). However in case of the pulsatile model there is a phase lag between peak systole and the instant of occurrence of maximum Impact area. This feature is common to the three models studied in this work (β=0, 45 and 90 ). The 89

104 impact zone at the distal side of the aneurysm change dramatically with the pulsatile cycle. Maximum impact area is attained at approx t=0.3.the velocity vector of inflow into the aneurysm shown in figure (8.2), extracted at t=0.3 sec (t/t=0.4) for the case of β=0 shows an increased inflow into the aneurysm at this instant co relating well with the impact zone plot. However the overall variation of impact zone with the cardiac cycle was assessed irrespective of the phase lag. For the case of β=0, the area of the aneurysm subjected to remodeling was found to be lesser at any instant of time compared to the models at β=45 and 90. Figure 8.4 Transient variation of Impact zone. 90

105 8.4 Time Evolution of Area Prone to Vascular Remodeling We assess the variation of area prone to vascular remodeling with time variations in the cardiac cycle (figure 8.5). Area along the dome and neck of the aneurysm where the WSS was less than 0.4 Pa (4 dyn/cm 2 ) was extracted at various time instants along the cardiac cycle. The area along the aneurysm dome that is prone to vascular remodeling was the highest for the case of β=0, throughout the pulsatile cycle. Within a pulsatile cycle β=0 showed the highest area prone to vascular remodeling, followed by β=90 and finally β=45. The peak values were attained at almost the same instant of time. Figure 8.5 Transient variation of area prone to vascular remodeling. 91

106 8.5 Summary and Discussion Physiological flows are pulsatile in nature. Hence, we simulate cases of dorsal aneurysms with pulsatile inflow conditions. The geometry of the aneurysms was the same as those considered in the steady flow simulations for various angles of tilt. The time evolutions of the inflow into the aneurysm showed a slight phase lag when compared to the inflow velocity profile. Peak inflow was achieved at the intermittent diastole phase. The variation of impact zone with the cardiac cycle showed β=0, to have the least area subjected to wall remodeling. Although a phase lag was observed between the peak systole and the attainment of maximum impact zone, the feature remained consistent with any orientation of the aneurysm with respect to the parent artery. Aneurysms offset from the primary direction of the centrifugal force, show larger areas along the dome of the aneurysm that is subjected to increased WSS that lead to adaptive remodeling along the wall of the aneurysm sac. We speculate that aneurysms that are offset from the direction of centrifugal force in the dorsal side would be exposed to sustained remodeling along a large area of the aneurysm sac and might show quicker growth rate compared to the aneurysms along the direction of centrifugal force (β=0 ). The time evolutions of the area prone to vascular remodeling indicate that the case of β=0, to have a larger area along the dome of the aneurysm throughout the pulsatile cycle that is prone to inflammatory changes. However the effects of oscillating hemodynamic parameters have to be taken into consideration more strongly. Comparing the results to the studies put forth by Crawford et al 1959 (refer to figure 3.3), it is seen that the frequency of rupture is high along regions where the oscillatory effects of fluid flow are felt, the highest being the region where the fluid 92

107 shear stress on the vessel wall is least in magnitude and exhibits directional changes. Pre procedural planning of endovascular techniques would benefit from the comprehensive study of flow patterns that we have put forth in this computational study. Finally, it is very essential to corroborate clinical and physiological concepts with numerical studies to understand not just the nature of flow, but its impact on the pathophysiology of aneurysms. 93

108 CHAPTER IX CONCLUSION AND FUTURE WORK 9.1 Conclusion We have performed numerical simulations on spherical aneurysms to assess the impact of aspect ratio of the aneurysm sac, curvature of the parent artery, angle of tilt of the aneurysm with respect to the parent artery and unsteady blood inflow condition on, the WSS distribution along the aneurysm sac, primary and secondary velocity distribution, Impact zone and area prone to vascular remodeling. The studies are aimed at providing a better understanding of the variation of hemodynamic variables along the dome of the aneurysm as a function of several geometric variations of the aneurysm sac and artery orientation. Histochemical studies (Kataoka 1999, Frosen 2004) have observed severe inflammatory changes along the dome of the aneurysm prior to rupture. The inflammatory changes along the walls of the artery are remodeling efforts initiated by the vascular endothelium at low WSS. Based on this observation we have hypothesized the area prone to vascular remodeling as the region along the dome of the aneurysm where the WSS is less than 4 dyn/cm 2. These are the sites that are most susceptible to leukocyte infiltration and subsequent inflammation. The growth of an aneurysm is due to the remodeling along the distal neck (Impact zone) and rigorous amount of vascular remodeling coupled with inflammation is 94

109 a feature that is seen prior to rupture. The hemodynamic environment associated with aneurysms are likely to constitute a disturbed flow pattern leading to low flow conditions along the dome resulting in high particle residence time that enable complex cell interaction leading to inflammatory cell proliferation (Hashimoto 2006).Here we reiterate some of the most important conclusions drawn from this study, Effect of Varying Aspect Ratio The area prone to vascular remodeling increase with increase in aspect ratio of spherical aneurysms. Higher aspect ratios lead to very low velocity re-circulating flow that promotes vascular wall remodeling, over a larger area of the aneurysm dome. A high wall shear stress gradient is observed closer to the distal end of the aneurysm dome. Also the WSS distribution is found to be symmetric about the primary flow plane of the aneurysm Effect of Arterial Curvature For aneurysms harbored on curved arteries, the impact zone increases with increase in arterial curvature. Also, the WSS distribution along the dome of the aneurysm is found to be symmetric along the primary flow plane, with decreasing WSS from the proximal end to the distal end of the aneurysm. We speculate that the curvature induced centrifugal force could play an important role in the initiation of dorsal aneurysms. 95

110 9.1.3 Impact of Angle of Tilt (β=0, β=45 and β=90 ) The wall shear stress distribution is symmetrical for dorsal aneurysms oriented at β=0 and asymmetric for β=45 and β=90. The offset of the aneurysm sac from the primary flow plane drastically changes the secondary flow pattern within the dome of the aneurysm, from a pair of counter rotating vortices to a single counter clockwise rotating vortex. Dorsal aneurysms with lower angles of tilt and lower flow rates show larger areas along the dome and neck where the WSS is less than 4 dyn/cm 2, we speculate that these are the likely sites of vascular remodeling. Our studies show that β=0, demonstrates the maximum area prone to vascular remodeling owing to low WSS and β=90 has the highest impact zone. It is likely that the aneurysm at β=0 is more likely to develop proliferation of SMC s and inflammatory cell invasion along a large region of the dome and neck of the aneurysm. The time evolutions of the area prone to vascular remodeling indicate β=0, to have a larger area along the dome of the aneurysm throughout the pulsatile cycle that is prone to inflammatory changes. The time evolutions of impact zone indicate β=90, to have a large area with WSS greater than 20 dyn/cm 2 throughout the pulsatile cycle. 96

111 9.2 Scope for Future Work Clinical decisions to conduct endovascular procedures are faced with remarkable amount of uncertainties. Management of these lesions remains controversial. In some patients the risk of surgical treatment may be higher than the risk of rupture (Wiebers 2003). This is primarily due to the lack of understanding of the factors that lead to the rupture of aneurysms. Aneurysm size, which was earlier an indicator for aneurysm rupture, is now replaced by the aspect ratio of aneurysms. Several observational and experimental studies have attributed the vascular wall remodeling and inflammation to play a vital role in degenerating the structural integrity of the aneurysm wall, which may lead to rupture Further computational simulations have to be carried out to understand the role played by oscillating wall shear stress, towards initiating vascular remodeling. The next logical step is to model Ventral aneurysms and study the variation of intra aneurysmal hemodynamics. The distribution of the low wall stress region has to be further analyzed for patient specific aneurysms of various sizes and orientations. Image acquisition techniques have to be incorporated to enable a longitudinal follow up of the changes in aneurysm geometry coupled with a study of the corresponding hemodynamic changes, which is possible by creating patient specific computational models. 97

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117 APPENDICES 103

118 APPENDIX A UDF-PARABOLIC INFLOW CONDITION /********************************************************************** parabolic.c UDF for specifying fully developed inflow condition *********************************************************************** / #include "udf.h" DEFINE_PROFILE(inlet_z_velocity, thread, position) { float x[nd_nd]; /* this will hold the position vector */ float r; face_t f; begin_f_loop(f, thread) { F_CENTROID(x,f,thread); r = sqrt(pow(x[0],2)+pow(x[1],2)); F_PROFILE(f, thread, position) = 2*0.3*(1-((r/0.0015)*(r/0.0015))); } end_f_loop(f, thread) } 104

119 APPENDIX B UDF-TRANSIENT BOUNDARY CONDITION /********************************************************************** unsteady.c UDF for specifying a transient velocity profile boundary condition *********************************************************************** / #include "udf.h" DEFINE_PROFILE(unsteady_velocity, thread, position) { face_t f; real t = CURRENT_TIME; real omega = 2* /0.75; begin_f_loop(f, thread) { F_PROFILE(f, thread, position) = 0.01*( *cos(omega*t ) *cos(2.*omega*t ) *cos(3.*omega*t ) *cos(4.*omega*t ) *cos(5.*omega*t ) *cos(6.*omega*t )); } end_f_loop(f, thread) 105

120 APPENDIX C MODEL VALIDATION It is essential to validate our models to analytical results. The validation was performed under steady state conditions along a 30 mm pipe of the same diameter as that of the parent artery (3mm) used in the simulations. The solutions were compared to the analytical distribution of velocity and WSS along the pipe. The maximum inlet velocity was 0.3m/s (Re 135). The UDF, for the fully developed parabolic velocity profile was incorporated at the inlet. The velocity distribution at a distance of 15mm and 25mm from the inlet were extracted and compared to analytical solutions. It was found that the numerical solution over predicts the velocity by 0.066%. The wall shear stress distribution along the arterial wall was extracted for a Re 135 and compared to the analytical result. The analytical value of the WSS was 1.4 N/m2. τ wall =(32*µ*Q)/(π*d3) Q is the volumetric flow rate (m 3 /s) and µ-dynamic viscosity. 106

121 L=30mm INFLOW OUTFLOW Figure C.1 Parabolic velocity profile obtained along the pipe at various lengths from the inlet. Figure C.2 Comparison of numerical and analytical results of velocity profile along a straight pipe at a distance of 15mm and 25 mm from the inlet. 107