Computational Analyses and Simulations of Fluid-structure Interactions Applied to Stented Abdominal Aortic Aneurysms

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ABSTRACT

LI, ZHONGHUA. Computational Analyses and Simulations of Fluid-structure Interactions Applied to Stented Abdominal Aortic Aneurysms (under the direction of Dr. Clement Kleinstreuer)

An abdominal aortic aneurysm (AAA) is the localized dilation, bulging, or ballooning of an abdominal aorta segment due to a degenerative arterial disease causing local wall weakness. Sudden AAA rupture could result in mortality up to 80%. Approximately 200,000 people in the United States are diagnosed to have AAAs and 15,000 Americans succumb every year. Since the introduction of endovascular techniques in the early 90s, endovascular aneurysm repair (EVAR) has stimulated considerable interest. In EVAR, starting from the femoral artery, a stent-graft is deployed into the affected segment thereby forming a new blood vessel and shielding the weakened AAA-wall from the pulsatile blood flow. There are clear benefits compared with conventional open surgery in terms of minimal incision, early-recovery, reduced mortality and morbidity. However, post-operative complications, such as stent-graft migration, endoleaks, endotension and device failure may still occur.

Because blood vessels and stent-grafts are flexible, interactions between blood flow and wall deformation can involve a wide range of fluid-mechanical phenomena. The flow will affect movement of the walls and wall movements in turn influence the flow field. Hence, simultaneous fluid-structure interactions (FSIs) should be considered when studying the hemodynamics and biomechanics of stented aneurysms. Presently, FSIs relevant to non-stented aneurysms have been only discussed by a few investigators; but, so far there are no publications of computational FSI results for stented AAAs. The complex fluid-structure interactions occur between the lumen blood, stent-graft, cavity blood with possible intraluminal thrombus, and AAA wall. Post-operative problems, such as endoleaks, stent-graft migration, endotension as well as device failure are all examples of FSI dynamics. Hence, transient 3D FSI is very important to study the hemodynamics and biomechanics of stented AAAs.

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migration, mechanism of endotension, proper stent-graft placement as well as optimal surgical recommendations; and (iv) improved stent-graft design.

The AAA-rupture risk analysis shows that the most likely rupture site is located near the anterior distal side for anterior-posterior asymmetric AAAs and the right distal side in lateral asymmetric AAAs. The rupture risk of lateral asymmetric AAAs is higher than that of anterior-posterior asymmetric AAAs. The neck angle impacts flow fields and wall-stress distributions remarkably, while the iliac bifurcation angle affects blood flow patterns insignificantly but plays an important role in wall-stress contributions. The aneurysm monitoring program based on eight biomechanical risk factors can evaluate the severity of AAA-rupture risk and hence provides useful recommendations for endovascular surgeons.

The transient 3D FSI simulations demonstrate that a secure stent-graft placement can significantly reduce sac pressure, mechanical stress, pulsatile wall motion, and maximum AAA diameter, and hence may prevent AAA rupture effectively. However, in spite of the absence of endoleaks, a certain sac-pressure level may be caused by fluid-structure interactions between the luminal blood, stent-graft, cavity blood, and AAA wall. The multi-factorial, time-varying sac (or cavity) pressure can be predicted by the stent-graft/ AAA compliance ratio.

The simulation results indicate that stent-graft migration depends on multi-factors, including blood flow conditions, stent-graft and aneurysm geometries, as well as wall mechanical properties. Excessive AAA neck angle, iliac bifurcation angle, neck aorta-to-iliac diameter ratio, stent-graft size, aorto-uni-aorta-to-iliac stent-graft, hypertension, and blood waveform are the key factors causing stent-graft migration.

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depends on the pressure difference between AAA cavity and lumen/branches. At elevated sac-pressure due to endoleaks, they may mitigate the risk of stent-graft migration.

In the present stent-graft models, a higher von Mises stress is observed near the bending point of stent wires with large curvatures. Nitinol diamond-shaped stents can produce more than 20% of neck oversize and generate hoop forces of 10 to 15N. In contrast, stainless steel is not suited for diamond stents because it cannot provide sufficient neck-oversizing to secure stent-graft anchoring. A z-bend stent is very ductile and suitable for largely angulated necks; but, its hoop force is very low, which implies that hooks or barbs should be considered to secure the neck anchor. The ultra-thin 0.1mm ePTFE graft material is not suited for z-bend stent-grafts due to its low yield stress. Woven polyester (PET) graft is appropriate for both diamond and z-bend stent-grafts. Z-bend stent-grafts have a large wall-compliance and are good at matching irregular necks or aneurysm geometries, while PET stent-grafts are better in reducing the level of endotension. Stents with a PET graft sheath generate minimum axial shortening and are suitable for precise device-deployment in aneurysms with complex geometries.

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BIOGRAPHY

The author was born on Setp.16, 1970 in Shandong Province of P.R.China. After graduating high school, he was admitted to China University of Mining&Technology in 1990 and studied in the Department of Mechanical Engineering. He continued his graduate study in the same university focusing on fluid mechanics and power engineering and received his master degree in 1997. Afterwards the author was employed as a teaching&research assistant in the same department and worked on thermal energy and power engineering for two years. From 1999-2001, the author worked as a research assistant in Institute of Refrigeration & Cryogenics in Shanghai Jiaotong University.

The author enrolled as a doctoral student under the direction of Dr. Clement Kleinstreuer in August, 2002 in the Department of Mechanical and Aerospace Engineering at North Carolina State University in Raleigh, NC. His dissertation research focused on Computational Analyses and Simulations of Fluid-structure Interactions applied to Stented Abdominal Aortic Aneurysms.

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ACKNOWLEDGMENTS

I express my gratitude to my committee chair and advisor, Dr. Clement Kleinstreuer, for his vision, ideas, guidance, and generous support. I thank the other members of my committee, Drs. Farber, Seelecke, Lyons and Echekki, for their contributions to this work through excellent teaching, constructive reviews, and supportive comments. As the collaborator of the project, Dr. Farber, an endovascular surgeon at UNC-CH, provided insightful suggestions, useful CT-scan models, and clinical data sets.

I am grateful to both past and present members of Dr. Kleinstreuer’s research group, including Dr. Zhe Zhang, Dr. Sinjae Hyun, Dr. Worth Longest, Dr. June Mo Koo, Huawei Shi, Zheng Li, and Burton Kennedy for their nice suggestions, helpful discussions, and critical analyses. Dr. Hyun has offered me very useful resources, providing insightful constructions and encouragement. I thank these aforementioned research colleagues.

Special thanks must be given to my parents for their support and assistance. I sincerely thank Dr. Jeffrey Weirbaugh and his family for their nice help, persistent support and great encouragement.

I am personally grateful to my wife, Yunzhen, for her patience, love, and support throughout my graduate career. Special debt of gratitude goes to my lovely son, David Li, who has spent most days and nights without staying with his father.

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LIST OF TABLES

Chapter 1

Table 1.1 Composition of normal aorta and aneurysm...9

Table 1.2 Stent-graft system ...31

Table 1.3 Comparison between open surgery and EVAR ...32

Table 1.4 Stent-graft specifications ...34

Table 1.5 Mechanisms of endotension from literature review ...44

Table 1.6 Attributes to stent-graft failure ...46

Chapter 2 Table 2.1 Comparison of results between simulations and theoretical analyses ...72

Table 2.2 Experimental parameters for stented aneurysm...75

Chapter 3 Table 3.1 Parameters required in the simulation ...80

Table 3.2 Assumptions for blood flow and structure characteristics...81

Chapter 4 Table 4.1 Validation of the modified Laplace’s equation...113

Table 4.2 Parameters used in AAA rupture prediction ...114

Table 4.3 Severity parameters for AAA rupture...116

Table 4.4 Validation of severity parameters for AAA rupture prediction ...123

Table 4.5 Rupture rate and surgery repair attitude ...124

Chapter 5 Table 5.1 Parameters required in the simulation ...131

Table 5.2 Assumptions for blood flow and structure characteristics...146

Table 5.3 Parameters required in the simulation ...147

Chapter 6 Table 6.1 Relationship between neck angle and migration risk ...183

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Chapter 7

Table 7.1 Assumptions for blood flow and structure characteristics...192 Chapter 8

Table 8.1 Parameters required in the simulation ...219 Chapter 9

Table 9.1 Comparison of axial shortening between different stent-grafts

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LIST OF FIGURES

Chapter 1

Figure 1.1 Schematic of thoracic aortic aneurysm...2

Figure 1.2 Dissecting aortic aneurysm...3

Figure 1.3 Abdominal aortic aneurysm ...3

Figure 1.4 Brain aneurysms ...4

Figure 1.5 Endovascular repair for aortic aneurysms ...6

Figure 1.6 Endovascular repair for cerebral aneurysm...7

Figure 1.7 AAA growth and rupture ...8

Figure 1.8 Schematic structure of artery...8

Figure 1.9 Collagen and elastin fibers in artery wall ...9

Figure 1.10 Comparison between AAA and normal aorta ...10

Figure 1.11 Three stages of AAA degeneration ...11

Figure 1.12 Stiffness of abdominal aortic aneurysm in men and women ...12

Figure 1.13 Effect of yield stress decrease on AAA ...13

Figure 1.14 Breaking stress decreases with age in a thoracic aorta ...13

Figure 1.15 Tensile strength of ascending thoracic aortic aneurysm ...15

Figure 1.16 Effect of ILT on tensile strength ...15

Figure 1.17 Open sugary...27

Figure 1.18 Endovascular repair for abdominal aortic aneurysm...29

Figure 1.19 Effect of endovascular repair for abdominal aortic aneurysm ...30

Figure 1.20 Schematics of stent-grafts...30

Figure 1.21 Schematics of AAA anatomy ...33

Figure 1.22 Schematic of stent-graft migration ...35

Figure 1.23 Enhanced neck fixation with hooks...36

Figure 1.24 Schematics of endoleaks...39

Figure 1.25 Fracture of stent wire...47

Figure 1.26 Metal corrosion...48

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Figure 1.28 Stent row separation caused by suture fracture ...50

Chapter 2 Figure 2.1 Flow chart of numerical FSI procedure...67

Figure 2.2 Flow chart of CFX-ANSYS coupling solver...68

Figure 2.3 Coupled CFX-ANSYS procedure ...69

Figure 2.4 ANSYS ALE FSI Solution algorithm ...71

Figure 2.5 Comparison of velocity distributions between coupled CFX-ANSYS results and Womersley’s theory...74

Figure 2.6 Comparison of local velocity variations with time between coupled CFX-ANSYS simulations and Womersley’s theory...74

Figure 2.7 Comparison between simulation and experimental data ...75

Figure 2.8 Comparison between simulation and experimental data ...76

Chapter 3 Figure 3.1 Schematics of AAA models ...79

Figure 3.2 Boundary conditions...81

Figure 3.3 Model mesh ...82

Figure 3.4 3D contours of blood pressure, wall deformation and stress (t/T=0.2) ...86

Figure 3.5 Contours of pressure and wall deformation (mid-plane, t/T=0.1)...87

Figure 3.8 Contours of velocity and wall stress and velocity vector (mid-plane, t/T=0.1)...90

Figure 3.11 Contours of velocity and wall stress and velocity vector at slice A-A...93

Figure 3.12 Contours of velocity and wall stress and velocity vector at slice B-B ...94

Figure 3.13 Contours of velocity and wall stress and velocity vector at slice C-C ...95

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Figure 3.15 Comparison between symmetric and asymmetric AAAs

(contour: wall stress, MPa) ...102

Figure 3.16 Effect of iliac angle on lateral asymmetric AAA (contour: wall stress, MPa) ...103

Figure 3.17 Effect of neck angle on lateral asymmetric AAA (contour: wall stress, MPa) ...104

Figure 3.18 Effect of iliac angle on anterior-posterior asymmetric AAA (contour: wall stress, MPa) ...105

Figure 3.19 Effect of neck angle on anterior-posterior asymmetric AAA (contour: wall stress, MPa) ...106

Figure 3.20 Wall stress and deformation distributions ...107

Chapter 4 Figure 4.1 Schematic of abdominal aortic aneurysm ...111

Figure 4.2 Relationship between wall stress and maximum diameter...112

Figure 4.3 Relationship between wall stress and thickness ...112

Figure 4.4 Relationship between wall stress and blood pressure...112

Figure 4.5 Relationship between wall stress and ILT/AAA area ratio ...112

Figure 4.6 Relationship between wall stress and asymmetry index ...113

Figure 4.7 Program of monitoring AAA-rupture risk...120

Figure 4.8 Interface of basic information input ...120

Figure 4.9 Input measurement data...121

Figure 4.10 Table of analyzed results ...121

Figure 4.11 Example of patient-I ...122

Figure 4.12 Example of patient-II...122

Chapter 5 Figure 5.1 Schematic of stented AAA model with inlet/outlet profiles ...130

Figure 5.2 Mesh of stented-AAA model...133

Figure 5.3 Comparison between stented and non-stented AAAs ...140

Figure 5.4(a) Comparison of AAA wall deformation changes with time (t/T=0.2) ...141

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Figure 5.4(c) Sac pressure changes with time ...141

Figure 5.5 Profiles of Von Mises stress, velocity and sac pressure for stented AAA model...142

Figure 5.6 Relationship between maximum stent-graft fixation force and friction coefficient...143

Figure 5.7 Relationship between maximum stent-graft fixation force and neck...143

Figure 5.8 Relationship between maximum stent-graft fixation force and blood pressure ...144

Figure 5.9 Relationship between maximum stent-graft fixation force and neck dilation...144

Figure 5.10 Influence of neck configuration on maximum stent-graft fixation force ...145

Figure 5.11 Schematic of stented aneurysm model ...146

Figure 5.12 3D contours of blood pressure and wall stress (t/T=0.2) ...151

Figure 5.13 Contours of blood pressure and wall deformation in mid-plane (t/T=0.1)...152

Figure 5.14 Contours of blood pressure and wall deformation in mid-plane (t/T=0.2)...153

Figure 5.15 Contours of blood pressure and wall deformation in mid-plane (t/T=0.27).154 Figure 5.16 Contours of velocity and wall stress and velocity vector mid-plane (t/T=0.1)...155

Figure 5.17 Contours of velocity and wall stress and velocity vector mid-plane (t/T=0.2)...156

Figure 5.18 Contours of velocity and wall stress and velocity vector mid-plane (t/T=0.27)...157

Figure 5.19 Contours of velocity and wall stress and velocity vector in Slice...158

Figure 5.20 Contours of velocity and wall stress and velocity vector in Slice ...159

Figure 5.21 Contours of velocity and wall stress and velocity vector in Slice...160

Figure 5.22 Benefits of stent-graft placement on blood flow and AAA wall (t/T=0.27)...162

Figure.5.23 Wall stress levels and blood flow directions between non-stented and stented AAA s (t/T=0.1)...163

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Figure 5.25 Wall stress levels and blood flow directions between non-stented

and stented AAA s (t/T=0.27)...165

Figure 5.26 Changes in maximum AAA diameter and wall stress as a function of time ...166

Figure 5.27 stent-graft migration force changing with time ...167

Figure 5.28 Sac pressure changing with time ...168

Figure 5.29 Influence of sac thrombus on AAA wall stress and stent-graft drag force (t/T=0.27) ...169

Figure 5.30 Influence of sac thrombus on AAA wall and blood flow (t/T=0.27) ...170

Chapter 6 Figure 6.1 AAA-systems with inlet/outlet profiles...174

Figure 6.2 Schematics of stent-graft models...175

Figure 6.3 Effect of aorto-uni-iliac stent-graft and hypertension on migration...177

Figure 6.4 Effect of stent-graft size on migration...178

Figure 6.5 Effect of main-body/iliac-leg diameter ratio on migration...179

Figure 6.6 Effect of main-body/iliac-leg length ratio on migration...179

Figure 6.7 Effect of iliac bifurcation angle on migration ...180

Figure 6.8 Effect of neck angle on migration force ...181

Figure 6.9 Effect of neck angle on migration value...184

Figure 6.10 Effect of neck angle on migration rate ...184

Figure 6.11 Effect stent-graft compliance on migration force...185

Figure 6.12 Effect of blood viscosity on migration force...186

Figure 6.13 Effect of sac pressure on migration force...187

Figure 6.14 Effect of pressure waveform on migration force...188

Chapter 7 Figure 7.1 Schematics of stented AAA model...191

Figure 7.2 Inlet and outlet boundary conditions ...192

Figure 7.3 Effect of Type I-a endoleak on stented AAA (Mid-plane, t/T=0.27) ...197

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pressure distributions (t/T=0.27)...198

Figure 7.6 Effect of Type I-a endoleak on sac pressure ...199

Figure 7.7 Effect of Type I-a endoleak on maximum AAA wall stress ...199

Figure 7.8 Effect of Type I-a endoleak on stent-graft migration force ...200

Figure 7.9 Effect of Type I-a aperture size on leakage rate...200

Figure 7.10 Effect of Type I-a aperture size on sac pressure...200

Figure 7.11 Effect of Type I-a aperture size on maximum AAA wall stress ...201

Figure 7.12Effect of Type I-a aperture size on stent-graft migration force...201

Figure 7.13 Effect of Type I-b endoleak on stented AAA (Mid-plane, t/T=0.27) ...202

Figure 7.14 Sac pressure comparison between different Type I endoleaks...203

Figure 7.15 Sac pressure and leakage rate vary with time (Type II-a endoleak)...205

Figure 7.16 Effect of Type II-a endoleak on stented AAA (Mid-plane, t/T=0.12) ...206

Figure 7.17 Maximum AAA wall stress and stent-graft migration force vary with time (Type II-a endoleak) ...207

Figure 7.18 Effect of Type II-b endoleak on stented AAA (Mid-plane, t/T=0.27) ...208

Figure 7.19 Sac pressure and leakage rate vary with time (Type II-b endoleak) ...209

Figure 7.20 Maximum AAA wall stress and stent-graft migration force vary with time (Type II-b endoleak)...209

Figure 7.21 Sac pressure and leakage rate vary with time (Type II-c endoleak)...211

Figure 7.22 Effect of Type II-c endoleak on stented AAA (Mid-plane, t/T=0.27) ...212

Figure 7.23 Maximum AAA wall stress and stent-graft migration force vary with time (Type II-c endoleak) ...213

Figure 7.24 Effect of Type III endoleak on stented AAA (Mid-plane, t/T=0.27) ...214

Figure 7.25 Sac pressure and leakage rate vary with time (Type III endoleak) ...215

Figure 7.26 Maximum AAA wall stress and stent-graft migration force vary with time (Type III endoleak)...215

Chapter 8 Figure 8.1 Schematic of stented aneurysm and boundary conditions...218

Figure 8.2 Relationship between EVG lumen pressure, sac pressure and aneurysm wall stress ...221

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Figure 8.4 Mechanism of endotension generation...222

Figure 8.5a Midplane view of a typical asymmetric aneurysm ...223

Figure 8.5b Artery neck (dashed line) projected onto the plane of maximum aneurysm cross section. ...223

Figure 8.6 Influence of aneurysm asymmetry on sac pressure and wall stress ...224

Figure 8.7 Influence of aneurysm wall Young’s modulus on sac pressure and aneurysm wall stress ...226

Figure 8.8 Influence of EVG wall Young’s modulus on sac pressure and aneurysm wall stress ...226

Figure 8.9 Influence of aneurysm volumes on sac pressure and aneurysm wall stress ..227

Figure 8.10 Influence of aneurysm wall thickness on intra-sac pressure and aneurysm wall stress ...229

Figure 8.11 Influence of aneurysm EVG thickness on intra-sac pressure and aneurysm wall stress ...229

Figure 8.12 Influence of ILT volume on the intra-sac pressure and aneurysm wall stress ...231

Figure 8.13 Relationship between sac pressure and EVG/aneurysm wall compliance and saccular index ...233

Chapter 9 Figure 9.1 Balloon-expandable stent and self-expandable stent...236

Figure 9.2 Characteristics of shape memory alloy...239

Figure 9.3 Geometry and mesh of diamond stent-graft model ...241

Figure 9.4 Geometry and mesh of z-bend stent-graft model ...242

Figure 9.5a Two common loading modes for stents...243

Figure 9.5b Schematic of hoop force caused by neck oversize ...244

Figure 9.6 Wall stress (von Mises) distribution in diamond stent with 20% of oversize ...245

Figure 9.7 Comparison of stress between different stent materials (diamond stent )...246

Figure 9.8 Comparison of hoop force between different stent materials (diamond) ...247

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Figure 9.10 Comparison of stress between different stent materials (z-bend stent)...249

Figure 9.11 Comparison of hoop force between different stent materials (z-bend stent) ...249

Figure.9.12 Stress (von Miese) distributions in diamond stent-graft model (p=120 mmHg) ...251

Figure 9.13 Comparison of stent-stress in different stent-graft materials ...252

Figure 9.14 Comparison of graft-stress in different stent-graft materials ...252

Figure 9.15 Stress (von Mises) distributions of z-bend stent-graft (p=120 mmHg)...253

Figure 9.16 Comparison of stent-stress in different stent-graft materials (z-bend)...254

Figure 9.17 Comparison of graft-stress in different stent-graft materials (z-bend)...255

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PART I: BACKGROUND INFORMATION

CHAPTER

1

1 INTRODUCTION AND OVERVIEW

1.1 Occurrences and Causes of Aneurysms

1.1.1 Aneurysms

An aneurysm is a local blood vessel ballooning greater than 50% of its nominal

diameter with a risk of sudden rupture. Aneurysms may result from local

weakening/deterioration of blood vessel walls, caused by disease, sudden injury, or

from birth. Aneurysms usually appear fusiform or saccular (see Fig.1.4). A thrombus is

often lined on the inside wall of an aneurysms. The patient could bleed to death in case

of a sudden aortic aneurysm rupture. If a cerebral aneurysm bursts, a stroke may occur.

Approximately 2,200,000 people in the United States are annually diagnosed with

aneurysms and 18,000 Americans are killed by all types of aneurysms.

1.1.2 Causes

Presently, causes of aneurysms include mainly atherosclerosis, atheroma, syphilis,

congenital defects, heart attacks, smoking, obesity, hypertension, trauma, inflammation

and/or hereditary conditions (e.g., Marfan's syndrome), as well as hemodynamics and

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the arteries" called arteriosclerosis. At least 80% of aortic aneurysms are from

arteriosclerosis. However, the exact reason leading to aneurysm generation and rupture

is not very clear. It seems that aneurysm formation and rupture is a multi-factorial

problem. Many controversies still exist in this research field.

1.1.3 Types

Although aneurysms can occur in any blood vessel, i.e., artery or vein, there are

mainly four types of aneurysms with life-threatening risks: brain aneurysms, thoracic

aortic aneurysms, dissecting aortic aneurysms and abdominal aortic aneurysms (AAAs).

Thoracic Aortic Aneurysms. Thoracic aortic aneurysms (Fig.1.1) occur in the chest and can be detected with chest X-rays or CT-scans. Most thoracic aortic aneurysms

have no symptoms. Sudden rupture can cause rapid blood loss and death. Clinically,

thoracic aneurysms are not as common as brain or abdominal aortic aneurysms.

Hereditary conditions (e.g., Marfan's syndrome) are believed to be the main reason

causing thoracic aortic aneurysms.

Normal aorta

Descending aorta

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Fig.1.2 Dissecting aortic aneurysm (Source: http://www.mayoclinic.org)

Fig.1.3 Abdominal aortic aneurysm (Source: http://www.mayoclinic.org)

Dissecting Aortic Aneurysm. A dissecting aneurysm (Fig.1.2) results from a tear between

the tissue layers of the aorta, caused by blood

flow pumped from the heart. This tear usually

occurs in the aorta close to the heart. Clinically,

the aorta is seldom dilated before the dissection

occurs. Risk factors include high blood pressure,

particularly high diastolic blood pressure.

Abdominal Aortic Aneurysm. As shown in Fig.1.3, abdominal aortic aneurysms are located

in abdominal aorta (below renal arteries and

above iliac bifurcation). 75% of abdominal aortic

aneurysms occur in people over 60 years of age.

The AAA shapes are irregular, including bulge,

prism, zigzag, boat, cylinder etc. Different

patients have different AAA shapes.

Brain Aneurysms. A brain aneurysm is a weak ballooning in the brain’s blood vessels (Fig.1.4).

Clinically, it is also called a cerebral or intracranial aneurysm. Brain aneurysms usually

occur at a branch of the brain arteries. If the brain aneurysm reaches a certain size (i.e.,

>2.5cm), the aneurysm may generate pressure on the surrounding brain tissue and cause

progressive problems. If an aneurysm ruptures and bleeds into the brain, stroke or death

may occur. 60% of people with ruptures will die within a year.

Tissue layer tear

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1.1.4 Symptoms and Diagnosis

Symptoms of aneurysm will depend upon the location of the aneurysm. Most

aneurysms have no symptoms and can be detected with X-rays or Ultrasound images

during a routine examination. When symptoms occur, they could include a pulsing

sensation, pain, difficult swallowing, coughing or hoarseness. A ruptured aneurysm can

cause a severe pain. Most aneurysms have thrombi in the aneurysm cavities, which

probably leads to the danger of embolisms in distant organs.

(http://www.healthscout.com/ency/197/198/main.html).

Aneurysms can be detected by simple physical examination, e.g., X-rays or

Ultra-sonography. Angiography, Computed Tomography (CT) and Magnetic Resonance

Imaging (MRI) are commonly used for detecting AAAs. CT scans can detect the

location and shape with precision.

Fig.1.4 Brain aneurysms (Source: 2001 eCureMe.com)

Saccular Fusiform

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1.1.5 Treatments

Open Surgical Repair. For aortic aneurysms, an incision is made in the patient’s chest and/or abdomen, the thrombus in the aneurysm is removed and the weakened portion of

the aorta is replaced with an artificial implant, called a graft (PTFE or Dacron). The

graft forms a new channel and allows blood to pass through it without causing a bulge.

When treating a cerebral aneurysm via open surgery, a section of the skull has to be

removed. To block blood flow into the aneurysm region, a tiny metal clip is usually

placed across the aneurysm neck

(http://www.brainaneurysm.com/aneurysm-treatment.html). In conventional open repair of an aneurysm, the patient must face a

large incision and possible pain. Hospitalization and recovery time are quite long.

Serious complications may occur.

Minimally Invasive Endovascular Repair. Minimally invasive endovascular repair is a new technology developed in the 1990s. Instead of open aneurysm repair, minimally

invasive treatment is performed inside the patient’s body using long catheters guided by

X-rays or other screens. For aortic aneurysms, the surgeon makes a small incision in

femoral artery and then passes the stent-graft through the leg artery to the aneurysm site.

After it is correctly positioned in the abdominal aorta, the stent-graft is released and

restores to its original shape under self-expandable or balloon-expandable mechanisms.

After expansion of the stent-graft, the delivery catheter is withdrawn. The aneurysm

cavity is excluded via the stent-graft. Blood flows though a new synthetic vessel

protecting the weakened aneurysm wall (http://www.vascularweb.org). Thus, the blood

pressure load is carried by the stent-graft and the aneurysm rupture is prevented

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In case of a cerebral aneurysm, a catheter is also delivered starting from the

femoral artery to the head and into the aneurysm. To block blood flow into the

aneurysm and prevent rupture, tiny platinum coils are threaded through the catheter and

deployed into the aneurysm cavity. This endovascular coiling of the aneurysm is also

called embolization. If the opening of the aneurysm is too wide, a stent is often used to

prevent the coils from descending into the main artery (see Fig.1.6). More than 125,000

patients with cerebral aneurysm worldwide have been treated with detachable platinum

coils. (http://www.brainaneurysm.com).

Stent-graft

Fig.1.5 Endovascular repair for aortic aneurysms (Source: http://www.vascularweb.org; http://www.xueguan.net; http://www.slrsurgery.org/programs/aneurysm.html)

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1.2 The Biomechanics of Abdominal Aortic Aneurysms

90 % of aortic aneurysms are located between renal arteries and iliac bifurcation,

called abdominal aortic aneurysms (AAAs). AAAs occur in 5-7% of people over 60.

About 200,000 patients are diagnosed with AAAs every year in the United States. It is

estimated that 15,000 patients die each year from ruptured AAA in the US, i.e., 80% of

total deaths caused by all types of aneurysms. AAA rupture is the 12th to 13th leading

cause of death in the US. The AAA characteristics are as follows:

z The ratio of male to female is 4:1; but, the rupture risk is four times in females than

in males even for the same AAA size.

z 75% of AAA patients are over the age of 60.

z The AAA wall distensibility decreases significantly with the increase in size.

z 80% of AAAs include thrombi;

z 90% have calcification in the wall.

Fig.1.6 Endovascular repair for cerebral aneurysm (Source: http://www.brainaneurysm.com) Stent

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z 90% of the patients have no symptoms before rupture (see Fig.1.7).

1.2.1 AAA Generation

The arterial wall mechanics and

integrity are mainly determined by

the matrix components of the wall.

As shown in Figs.1.8&1.9, these are

predominantly elastin, collagen and

smooth-muscle cells. The distensible

elastin is load-bearing at low

pressures and responsible for the

elastic recoil of the artery. Collagen

is 1000 times stiffer and is

load-bearing at high pressures, preventing

over-dilation and rupture of the vessel. Smooth muscle cells have the potential for

contraction and relaxation with modulation of wall mechanics. The latter seems to be of

minor importance in the abdominal aorta. Thus, the collagen-to-elastin ratio is the Fig.1.8 Schematic structure of artery (Source:

The McGROW-Hill Companies, Inc) Fig.1.7 AAA growth and rupture (Source: http://www.xueguan.net)

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principal determinant of wall

mechanics in the aorta. Changes in

composition and structure of the

arterial wall will alter wall

mechanics. The increasing

collagen-to-elastin ratio may alter

the wall structure, resulting in

increased wall stiffness and

decreased tensile strength. Clinical

observations show that most AAA

walls become progressively stiffer

as the diameter increases. This is because of biomechanical restructuring of the wall. In

the normal abdominal aorta, the collagen-to-elastin ratio is about 1.58 (Nichols&

O’Rourke 1990). However, the collagen-to-elastin-ratio is much higher in AAAs (Table

1.1).

Table 1.1 Composition of normal aorta and aneurysm (after He and Roach., 1994)

Normal aorta Aneurysm Elastin

Average Maximum Minimum

22.7 32.5 16.1

2.4 6.7 0.2

Muscle

22.6 33.6 15.5

2.2 6.4 0.4

Collagen and ground substances

54.8 63 48

95.5 98 91.4

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As shown in Fig.1.10, the σ −ε of AAA moves to the left considerably. The

elastic modulus is much higher than that in the normal aorta, while its breaking stress

decreases significantly. Fig.1.11 indicates the three stages of the AAA generation. In

Stage I, elastin begins degradation and more collagen is produced. The increase of

collagen-to-elastin ratio is the indicator of AAA beginning formation. In Stage II, even

though the collagen begins degradation but largely offset by more collagen production.

However, the remodeling ability of the AAA wall becomes weak due to the accelerating

collagen degradation. Under the load of blood pressure, the AAA wall begins rapidly

expanding and finally ruptures (Stage III). That is, the elastin degradation is the key step

in the development of AAA, whereas collagen degradation is ultimately required for

AAA rupture.

Fig.1.10 Comparison between AAA and normal aorta (after: Raghavan 2002) Breaking stress of normal abdominal aorta

Breaking stress of AAA

Elastic modulus

σ

(32)

Even though elastin and collagen degradation are the key reason to cause AAA

generation, deterioration and rupture, the exact pathophysiology to cause the

elastin/collagen degradation is still unknown. Generally, pathophysiologic processes

include:

z Atherosclerosis

z Hemodynamics

z Inherited susceptibility

z Chronic inflammation and neovascularization

z Immunologic responses and inflection

z Structural remodeling of the extracelluar matrix

z Matrix-degrading proteinases and inhibitors

z Gelatinases, stromelysins, macrophage elastase

z Regulation of MMP activeities

(33)

1.2.2 AAA Mechanical Properties

So far, many investigators try to find the AAA rupture mechanism focusing on

changes of mechanical properties in arterial wall. Sonesson et al. (1999) and Lanne et al.

(1992) declared that the aortic stiffness of aneurysm wall is exponentially increasing

with age in men and women (see Fig.1.12). However, enhanced wall stiffness is not

necessarily advantageous for preventing AAA rupture, because along with the increase

of wall stiffness, the wall yield stress will accordingly decrease. As a case in point,

Raghavan et al. (2000) stated that Young’s modulus in an AAA wall may reach 4.66

MPa, which is about three times that in normal arterial wall; whereas its yield stress is

only 50% of the normal artery. Thus, although large Young’s modulus may reduce

AAA-wall stress, the yield stress is possibly lower than the mechanical stress in the

AAA wall, i.e., AAA rupture still may occur when the wall becomes stiffer (see

Fig.1.13). Groenink et al. (1999) investigated the influence of aging and hence stiffness

on the breaking stress in the descending aorta. They found that the average breaking

(Sonesson et al., 1999)

(34)

stress was 2.7 MPa and decreasing correlated with age. Wilson et al. (2003) found that a

(35)

when compared to AAAs without wall stiffness changes. They also indicated that from

the time of AAA observation to elective repair, the wall stiffness appears to increase,

while the wall stiffness in ruptured AAAs is less than that in elective repaired AAAs. It

implies that there is a maximum stiffness before rupture. They declared that the reason

of fast expansion before rupture is due to the failure of restructuring and accelerating

degradation of collagen.Thus, the change of wall stiffness may be a strong player in

AAA rupture. Vorp et al. (2003) studied the effect of aneurysm on the tensile strength

and found that the stiffness in an aneurysm is 72% higher than in a normal artery, while

the tensile strength is 29-34% lower (see Fig.1.15) Based on experiments, Flora et al.

(2002) indicated that AAA wall mechanics contributor more significantly to peak wall

stress than pressure variations and techniques to measure the rate of deterioration may

predict AAA rupture. Thubrikar et al. (2001) tested the breaking strength in AAA and

found that different location has very different yield stress in AAA, which changes from

0.47-0.74 MPa. However, Raghavan et al. 1996 reported that the yield stress is

significantly lower for the aneurysm group than for the normal group (0.65 MPa vs. 1.2

MPa). Inzoli et al. (1993) studied the biomechanical factors in abdominal aortic

aneurysm rupture and found that atherosclerosis plaques can cause stress concentration

and a significant increase in AAA wall stress. Maybe it is one reason that the small AAA

still can rupture. Even though ILT is taken as the help to reduce the wall stress, Vorp et

al. (2001) stated that an ILT can decrease the ultimate AAA strength dramatically. They

found that the strength of an AAA with 4 mm ILT decreases 20% compared to an AAA

with ILT less than 1 mm. Hypoxia, i.e., oxygen deficiency caused by an ILT, is the main

reason for wall strength reduction (Fig.1.16).Therefore, if the degeneration of the wall

(36)

1.3 AAA Rupture Prediction

Practically, once the induced mechanical stress exceeds the ultimate strength of the AAA wall, rupture is going to happen. However, because direct mechanical stress

Fig.1.16

(Vorp et al., 2003)

(37)

measurements are not available in vivo, key biomechanical factors (BFs) influencing

AAA rupture are employed to estimate the risk of rupture and to determine when

elective repair, i.e., open surgery or endovascular repair, is necessary. Several possible

AAA-rupture indicators have been proposed in publications, including maximum AAA

diameter, expansion rate, mechanical stress, diastolic pressure, asymmetry index,

stiffness, intraluminal thrombus ratio, saccular index, wall curvature, gender, serum

elastin peptide, the ratio of AAA diameter to the third lumbar vertebral and others.

Maximum Diameter. As established, the larger the maximum AAA diameter, the higher is the rupture risk. Clinical data showed that the rupture risk is exponentially

related to the maximum AAA diameter. For example, Myers et al. (2001) stated that for

abdominal aortas 1.9cm≤dAA≤ 2.6cm, the rupture chance in AAAs with maximum

diameters less than 4.0cm, 4.0-4.9cm, 5.0-5.9cm, 6.0-6.9 and greater than 7.0 is 2%,

3.2%, 25%, 35% and 75%, respectively. In 3-month to 10-year follow-up studies,

Darling et al. (1970&1976) found that the rupture risk in AAAs less than 4cm, 4-5cm,

5-7cm and 7-10cm in the maximum transverse diameter is 8%, 25%,50% and 64%,

respectively. Presently, the maximum transverse diameter, dAAA,max, is taken as the main

criterion for judging the necessity of surgical intervention in asymptomatic AAAs due to

its simple measurement. However, there is no consensus for a threshold value regarding

the appropriate diameter for intervention. Some investigators regarded 5.5cm as the

threshold for elective repair. To prove this point, the UK Small Aneurysm Trial showed

that there is no benefit from early surgical repair of asymptomatic AAAs of 4.0 to 5.5

cm (Myers et al., 2001). Although it is obvious that a large AAA is more prone to

rupture than small ones, there is still clinical evidence that small aneurysms can rupture

(38)

cm ruptured in their clinical investigations. Furthermore, Fillinger et al. (2003) reported

that 10-24% of the ruptured AAAs were 5 cm or less in maximum diameter. Clinically,

the maximum AAA transversal diameters of 5 cm for women and 6 cm for man are

most commonly used to recommend surgical intervention (Heikinen et al., 2002).

Because of the well-known difference in aorta diameter (1.5 cm-2.5cm) for different

patients, the simple criterion of AAA maximum diameter is not accurate to evaluate all

patients. As a case in point, the individual-independent parameter, i.e., the ratio

AA AAA

d d _,_max

=

χ seems better than the maximum AAA diameter alone. The numerical

simulation results of Li & Kleinstreuer (2005) and clinical study of Cappeller et al.

(1997) confirm that threshold values of χ =2.2and 2.2 and 3.3 for elective repair and

possible rupture prediction may provide more reasonable recommendations than AAA

size alone.

More significantly, other anatomic variables may be very influential; for

example, shape eccentricity, wall thickness, blood pressure, intraluminal thrombus and

other biomechanical properties. Thus, the maximum AAA diameter is an important

parameter but insufficient to predict AAA rupture.

Expansion Rate. Besides the maximum transverse diameter, the expansion rate is another important indicator for AAA rupture. Clinically, a high expansion rate, say from

0.5 cm per year and up, is often associated with a high risk of rupture (Thubrikar et al.,

2000; Hirose et al.,1998). According to Wolf et al. (1994), if the expansion rate reaches

more than 0.5 cm/year, elective repair should be considered even if dAAA,max < 5cm.

However, Scott et al. (1999) regarded a growth rate of more than 1cm per year as one of

the principal indicators for AAA operation. There is evidence that the growth rate is not

(39)

Vardulaki et al. (1998) found that the growth rate may differ with the initial AAA

diameter, where more rapid growth occurs in larger AAAs (i.e., 5 cm or more),

independent of gender and age. Hallin et al. (2001) reported that AAA expansion

averaged 0.2-0.4 cm per year for AAAs smaller than 4 cm, 0.2-0.5cm/year for AAAs of

4-5 cm and 0.3-0.7 cm/year for those larger than 5 cm, and the associated rupture risk at

four years was 2%, 10% and 22 % respectively. In addition, Brown et al. (2003)

described that the mean expansion rate in patients with ruptured AAAs was 0.84cm/year

compared to 0.39cm/year in non-ruptured AAAs. Hirose et al. (1998) indicated that

AAA began to grow faster at about three months before rupture. They also established a

bi-exponential correlation between AAA expansion rate and time, i.e., the closer the

time to rupture, the faster was the expansion rate. Similarly, Limet et al. (1991) fitted an

exponential model describing growth rate, and provided thresholds of 10.6% /year and

18%/year for elective AAA repair and rupture prediction, respectively. To the contrary,

Choyke et al. (1993) declared that the use of a fast expansion rate as an indication for

surgery makes sense but has never been validated for small AAAs. Based on clinical

observations, Sharp et al. (2003) found that a rapid increase in AAA diameter is not an

indicator for elective AAA repair. Combining the research results of Thompson et al.

(2000) and Bernstein et al. (1984), the rupture rate is proportionally related to the

growth rate when GR >0.5 cm/year; and that there is no significant correlation if the

GR< 0.5 cm/year.

Mechanical Stress. The general consensus is that the peak wall stress is the best indicator of AAA rupture, although the maximum AAA diameter and growth rate as

well as aortic neck asymmetry are very important and easier to measure. Generally,

(40)

in AAA rupture analyses. However, because of the complex mechanism of rupture and

often complex AAA geometries, which stress actually causes AAA rupture remains

unresolved. Furthermore, how to define the critical threshold-value and yield stress in

different patients is not clear. Because stress measurements are not available in vivo,

software packages for structural analysis, such as ANSYS, ABAQUS, ADINA, and

FIDAP are efficient tools. For example, Di Martino et al. (2001) employed the

finite-element software FIDAP to simulate fluid-structure interaction in realistic AAA models,

and indicated that the complicated AAA geometry would affect the stress distribution

considerably. Raghavan et al. (2000) used ANSYS to simulate three-dimensionally

reconstructed AAA models and found that the 5-cm AAA-diameter criterion as a

rupture predictor was not sufficient. To test the validation of wall stress as the rupture

criterion, Fillinger et al. (2002 & 2003) did in vivo analyses of mechanical wall stress

and AAA-rupture risk, and suggested that the peak wall stress seems to be superior to

maximum AAA diameter in predicting rupture risk. Thubrikar et al. (2001) found that

different regions of an AAA had different yield stresses, yield strains and other

mechanical properties. They also indicated that the rupture of an AAA was most likely

to occur on the inner surface of the wall at the anterior region in circumferential

orientation. Vorp et al. (1998) stated that, in addition to diameter, the influence of

asymmetry on mechanical wall stress in AAAs is very important. Li et al. (2005)

employed the coupled CFX and ANSYS solver to analyze the stress distribution in an

axisymmetric AAA model and found that stress analysis may yield necessary insight in

AAA-rupture prediction. At present, such stress analyses include CT scanning and

image processing, model development and computer fluid-structure-interaction (FSI).

(41)

accumulation of fibrin, blood cells, platelets, blood proteins and cellular debris adhering

to the AAA inner wall. Clinically, 75% of AAAs include thrombi (Wang et al.,2002). At

present, the effect of ILT on AAA rupture is still controversial. Some investigators think

ILT may reduce the stress in the AAA wall. For example, Wang et al.(2002) reported

that the peak wall stress may be reduced from 6~38% if the ILT-AAA volume ratio

ranges from 0.29-0.72. Thubrikar et al. (2003) regarded ILT as a fibrous network

adhering to the aneurysm wall. They reported that even though the ILT allows the

transmission of luminal pressure to the AAA wall, it may prevent the AAA from rupture

by diminishing the AAA dilation by 4-15%. Vorp et al. (1996) reported that an ILT

could improve the compliance of the wall like a cushion, reduce mechanical stress, and

hence was benefital for preventing AAA rupture. Mower et al. (1997) simulated the ILT

in an AAA and found that an ILT significantly reduced AAA wall-stress if the ILT

became solid. Di Martino et al. (1998) declared that a well organized thrombus may

reduce the effect of the pressure load on the AAA wall. Li et al. (2005) found that the

maximum Von Mises stress relates inversely proportional to the ILT-AAA volume ratio

and exponentially with respect to its Young’s modulus. These correlations agree with

findings by Mantero et al. (1998&2001). In contrast, some researchers declared that

ILTs could accelerate AAA rupture. For example, Wolf et al. (1994) found that an

increased AAA-ILT volume is associated with a higher likelihood of rapid expansion.

They stated that the larger the ILT volume in the AAA cavity, the higher is the

possibility of rupture. Cappeller et al. (1997) indicated that if the ILT/AAA volume ratio

is more than 0.45, the rupture rate becomes very significant. They took the ILT/AAA

volume ratio of 0.62 as one possible indicator for AAA rupture. Stenbaek et al. (2000)

(42)

greater than 1.5cm2/year were prone to rupture. They suggested that the growth of ILT may be a better predictor of rupture than AAA diameter. Interestingly, some researchers

stated that there are no close relationship between ILT presence and AAA rupture. To

prove the point, Schurink et al. (2000) tested the blood pressure close to the inner wall

of an AAA and found that the pressure is almost the same as that in the lumen. Another

debate is that the an ILT volume in AAA sac is associated with AAA size. According to

Pillari et al. (2000), for AAAs with dAAA,,max >7cm no change in ILT volume was found

with the increasing sac diameter; however for an 5<dAAA,,max<7cm, the increase in sac

diameter was associated with an increase in ILT volume. The impact of the maximum

ILT volume before AAA rupture remains controversial. Our simulation results support

that ILT may reduce the stress in the wall, if the decrease of wall yield stress caused

by ILT is not considered (Li et al., 2005). However, Vorp et al. (2001) stated that an ILT

can decrease the ultimate AAA strength dramatically. They found that the strength of an

AAA with 4 mm ILT decreases 20% compared to an AAA with ILT less than 1 mm.

Hypoxia , i.e., oxygen deficiency caused by an ILT, is the main reason for wall strength

reduction.Therefore, if the degeneration of the wall strength is taken into account, the

net effect of ILT on AAA wall rupture may vary.

Diastolic Pressure. Hypertension is considered to be a key factor contributing to AAA rupture. It is well-known that the maximum blood pressure, i.e., systolic pressure, is the

main force to cause AAA-wall deformation. It is no doubt that AAAs in patients with

systolic hypertension are prone to rupture. The relationship between the maximum wall

stress and systolic pressure is approximately exponential. Once the systolic blood

pressure is greater than 160 mmHg, the rupture risk becomes high (Li et al., 2005).

(43)

pressure between non-ruptured and ruptured AAAs. Thus, although the systolic pressure

is the main force to cause AAA-wall stress, it alone can not be regarded as a predictor

for AAA rupture. In contrast, the diastolic pressure is found to be closely associated

with AAA rupture. For example, Hatakeyama et al. (2001) reported 72% of ruptured

AAAs in patients with diastolic hypertension. Cronenwett et al. (1985) also asserted that

diastolic hypertension must be evaluated to assess the accuracy in predicting small AAA

rupture. They defined the diastolic pressure value of 75 mmHg, 90 mmHg and 105

mmHg as the low, middle and high risk levels for AAA rupture. Powell et al. (2001)

proposed that the ankle/branchial pressure index (ABPI) is an important prognostic

indicator for AAA rupture, and patients with an ABPI below 0.87 have the highest

mortality risk. Schewe et al. (1994) declared that the AAA expansion rate is

significantly correlated with the diastolic pressure and a high diastolic pressure is an

important risk factor for AAA both expansion and rupture. Wilson et al. (1998-2003)

studied the effect of diastolic pressure on AAA rupture and found that a high diastolic

pressure may reduce the time to rupture considerably. Up to now, the correlation

between diastolic hypertension and AAA rupture is accepted by most researchers.

Change of Wall Stiffness. Clinical observations show that that most AAA walls become progressively stiffer as the diameter increases. This is because of biomechanical

restructuring of the wall. For example, He et al. (1994) investigated the composition and

mechanical properties of AAAs, and they found that AAA walls were stiffer and volume

fractions of collagen and ground substance levels were highest, whereas the volume

fraction of elastin and muscle tissue were relatively low. MacSweeney et al. (1992) also

indicated that the increasing aneurysmal aorta stiffness was associated with the loss of

(44)

et al. (1992). Enhanced wall stiffness is not necessarily advantageous for preventing

AAA rupture, because along with the increase of wall stiffness, the wall yield stress will

accordingly decrease. As a case in point, Raghavan et al.(2000) stated that Young’s

modulus in an AAA wall may reach 4.66 MPa, which is about three times that in normal

arterial walls; whereas its yield stress is only 50% of the normal artery. Also, Groenink

et al. (1999) reported that even though stiffness may become large with age, the yield

stress of the wall will decrease significantly with respect to age. Thus, although Young’s

modulus may reduce AAA-wall stress, the yield stress is possibly lower than the

mechanical stress in the AAA wall, i.e., AAA rupture still may occur when the wall

becomes stiffer (see Fig.1.13).

In case of wall stiffness decreases with time because of a failure in wall

restructuring, the risk of rupture increases significantly. For example, Wilson et al.

(2003) found that a 10% decrease in stiffness over time was associated with a 28%

increase in rupture risk when compared to AAAs without wall stiffness changes. They

also indicated that from the time of AAA observation to elective repair, the wall

stiffness appears to increase, while the wall stiffness in ruptured AAAs is less than that

in elective repaired AAAs. It implies that there is a maximum stiffness before rupture.

They declared that the reason of fast expansion before rupture is due to the failure of

restructuring; but the actual factors that determine at what point AAA restructuring fails

are unknown.Thus, the change of wall stiffness may be a strong player in AAA rupture.

Interestingly, Sonesson et al. (1999) reported that no difference was found in

aneurysmal aortic wall mechanics in ruptured AAAs compared with electively operated

AAAs. They declared that it is not possible to use aneurysmal aortic wall stiffness as a

(45)

Asymmetry Index. As a result of the local support provided by lumbar vertebrates, most AAAs are asymmetric. Generally, the anterior size is greater than the posterior size

with a larger wall thickness at the posterior side than at the anterior side. According to

Vorp et al. (1998), the shape factor has a substantial influence on the distribution of wall

stress within the aneurysm, where the magnitude of the peak stress in the wall increased

non-linearly with increasing asymmetry. Specifically, when the asymmetry index

1 max

. ₋

=

a AAA

l d

β (see Fig. 4.1) changed from 1 to 0.3, the circumferential stress

increased to 85% in their numerical AAA model. Hua et al. (2001) stated that a simple

symmetric model is unreliable in predicting the location and magnitude of peak stresses

in most AAAs. Thus, assessing the risk of rupture for typical AAAs may require

detailed three-dimensional modeling. Finol et al. (2003) studied the effect of asymmetry

in AAAs under physiologically realistic flow conditions. They graphed the peak wall

shear stress and peak wall pressure as a function of aneurismal asymmetry. The effect of

asymmetry increases the maximum wall shear stress at peak flow and induces the

appearance of secondary flows during the late diastole. Furthermore, mechanical stress

concentrations may be triggered by asymmetric and complicated AAA geometries.

(Fillinger et al., 2002&2003) Thus, since most AAAs are asymmetric, a shape index

should be taken into account in evaluating AAA rupture.

Saccular Index. The saccular index,

AAA AAA

L d _,_max

=

γ (see Fig. 4.1), i.e., the ratio of

maximum AAA diameter to the length of AAA region, is another novel system

parameter to express AAA characteristics. Clinical observations indicate that the smaller

the saccular index the higher is the possibility of AAA rupture. For example, Ouriel et al.

(46)

where the clinical thresholds of saccular indices for elective repair and rupture are 0.6

and 0.7, respectively. Based on clinical data, Hatakeyama et al. (2001) studied the

influence of saccular index on AAA rupture. Their results demonstrated that the saccular

index correlated significantly to AAA rupture. They also fitted an equation to express

rupture in terms of saccular index, diameter ratio and diastolic pressure. Li et al. (2005)

graphed AAA-wall stress vs. saccular index and illustrated that there are two “turning

points” at γ =0.65 and γ =0.72. The Von Mises stress increases slowly when the

saccular index changes from 0.72 to 0.65. However, once the saccular index is less than

0.65, the Von Mises stress increases quickly. It suggests that the saccular index may be

one possible predictor for AAA rupture.

Wall Curvature. Theoretically, wall stress concentration occurs at the location of highest wall curvature. The AAA-wall stress distribution is not only related to the

maximum diameter, wall thickness and mechanical properties, but also to AAA-wall

curvature. For example, Elger et al. (1996) studied the effect of wall curvature on the

wall stress in terms of exponential, parabola-exponential and consine-exponential

curvature models. They found that the maximum stress typically occurred near the

inflection point of a curve drawn coincidental with the AAA wall. They declared that

the Laplace Equation in terms of maximum diameter provided neither a qualitative nor a

quantitative understanding of the AAA-wall stress and concluded tat the wall curvature

is more important than the maximum diameter in evaluating AAA rupture. Filliger et al.

(2003) simulated the mechanical stress distributions in clinical AAA models obtained

from CT scans. They found that that the local stress may be high even when the

diameter is relatively small because of the irregular AAA shape. They also indicated that

(47)

wall curvature is high. Our research also demonstrated that the maximum Von Mises

stress is usually located near the inflection point of the AAA-wall (see Li et al. 2005).

In summary, AAA walls with very strong curvatures feature serious stress

concentrations implying a high likelihood of rupture.

Gender. Clinically, the rupture risk is four times in female than in male with the same AAA size, even though the AAA morbidity ratio of male to female is 4:1, especially in

people over the age of 60. It well-known that women have smaller aortas than men

(1.9-2.3cm vs. 2.3-2.6cm; Ouriel et al., 1992); but the same threshold diameter of 5.5cm is

currently used for elective AAA repair, which leads to underestimating the risk of AAA

rupture in women. For example, Brown et al. (2003) stated that the risk of rupture in

male patients with dAAA,max =5.0-5.9 cm is low, but the four-time higher risk of AAA

rupture in female patients with dAAA,max =5.0-5.9 cm suggests that a lower threshold

value should be considered for women. To the contrary, Vardulaki et al. (1998) reported

that the rate of AAA growth did not differ with age and sex. Similarly, Cheng et al.

(2003) compared the abdominal aortic hemodynamics between men and women and

found that no significant differences of wall shear stress, temporal flow and other

hemodynamic parameters were found between the genders. It suggests that

hemodynamics may not play a significant role in AAA disease and rupture between

genders. Sonesson et al. (1999) also reported that the stiffness of AAA wall is only

related to age, no relationship with gender. In summary, the reason for gender difference

in AAA rupture is still under investigation, and the problem to define the best diameter

threshold for women remains unresolved.

(48)

in terms of serum elastin peptides, procollagen-IIIN-terminal propeptide, and initial

AAA size. If useful, only a simple blood test may predict the AAA growth status and the

risk of rupture. But they also stated that a larger sample size was still needed for clinical

recommendations. Another method to predict AAA rupture presented by Ouriel et al.

(1992) is the standardization of the aneurysm diameter to the transverse diameter of the

third lumbar vertebral body. They declared that it may produce an accurate predictor of

rupture when a threshold ratio of 1.0 was used.

1.4 AAA Repair

1.4.1 Open Surgery

Up to now, there are no drug treatments

for abdominal aneurysms. The available

treatment requires surgical repair. The first

abdominal aneurysm was successfully

repaired in 1951 (Charles Dubost, Paris).

Conventional repair of abdominal aortic

aneurysms involves replacement of the

diseased aorta segment with a synthetic

prosthetic graft made of polyester or PTFE

(see Fig.1.17). An abdominal incision is

required to completely expose the abdominal

aorta. The procedure usually requires general anesthesia and takes 4-6 hours to

complete. The overall in-hospital mortality is less than 2-3%. Open AAA surgery has Fig.1.17 Open surgery

(Source: http://www.mayoclinic.org)

Kidney

Iliacs

(49)

been performed for the past 40 years without significant modifications. The procedure is

extremely durable and secondary surgical procedures are rarely necessary. Aside from

routine post-operative checkups, there is no long-term follow up required. Open surgery

is suitable for all kinds of AAAs. However, open repair requires a long abdominal

incision to gain access to the aorta. A large amount of blood transfusion is required. The

patient may endure great pain. Hospitalization and recovery time are substantially long.

The complications of open operation mainly include myocardial infarction, arrhythmia,

congestive heart failure, lung failure, renal failure and reduction in blood flow to legs

and other vital organs in and downward from the abdomen.

1.4.2 Endovascular Aneurysm Repair (EVAR)

Minimally Invasive Endovascular Repair. As we know, AAA is only the dilation of an artery, not a tumor. The task is to prevent it from rupturing, not get rid of it. EVAR

technology has been developed for this purpose. In EVAR, a stent-graft is installed to

exclude the AAA from blood flow, eliminate blood circulation in the AAA sac, reduce

blood pressure, and prevent AAA rupture. Dotter (1969) was the first to suggest a

stent-graft for endovascular repair. Because of the limited technology, this idea could not

come into practice at that time. Balko (1980) began to test stent-graft in animals and

obtained promising results. In 1990, Parodi successfully used an endovascular

stent-graft to repair an AAA in a patient for the first time. In 1991, he published his clinical

experience about this new technology. In 1993, Chuter designed the first bifurcated

stent-graft for AAAs. With the development of new technologies, such as new materials,

non-invasive screens and improved designs, EVAR has become one of the hottest

research fields in the world. At present, over 25,000 patients world wide with AAAs