ARTERIAL CALCIFICATION AND THE CLINICAL IMPLICATIONS ON STENT FUNCTION MELISSA YOUNG. Submitted in partial fulfillment of the requirements

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1 ARTERIAL CALCIFICATION AND THE CLINICAL IMPLICATIONS ON STENT FUNCTION by MELISSA YOUNG Submitted in partial fulfillment of the requirements For the degree of Master of Science Thesis Adviser: Dr. Linda Graham Department of Clinical Research Scholars Program CASE WESTERN RESERVE UNIVERSITY May, 2013

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Melissa Young, Ph.D. Candidate for the Master of Science degree (signed) Linda M. Graham, M.D. (chair of the committee) Geoffrey D. Vince, Ph.D. James Spilsbury, M.P.H., Ph.D Dennis Stacey, Ph.D (date) March 15 th, 2013 *We also certify that written approval has been obtained for any proprietary material contained therein. 2

3 Table of Contents List of Tables...5 List of Figures.6 Acknowledgements.. 10 Abstract.11 Chapter 1: Introduction.12 Chapter 2: Background Peripheral Arterial Disease Intravascular Ultrasound Stent Interventions Computational Modeling...16 Chapter 3: Clinical Analysis of Patient with Peripheral Arterial Disease Study Population Geometrical Data Captured with IVUS In Vivo Plaque Morphology Geometric Properties Captured with CT.20 Chapter 4: Finite Element Simulation Stent Models Stent Mesh Convergence Artery Models Homogenous Artery Model Patient Specific Artery Model Combined Stent-Artery Models..57 3

4 4.3.1 Patient Specific Models Patient Specific Model with Low Calcium Patient Specific Model with High Calcium Stent Prediction...67 Chapter 5: Clinical Relevance Computer models for Stent Design Personalized Medicine 73 Chapter 6: Conclusion 75 References.76 4

5 List of Tables Table 1: Summary of geometric and morphological values for PAD cohort (n=75)...18 Table 2: Association of clinical factors with plaque burden.20 Table 3: Association of clinical factors with geometric lumen and vessel measurements.20 Table 4: Descriptive statistics for PAD cohort (n=75). 25 Table 5: TASC II classification measurements for PAD cohort...27 Table 6: Comparison of computational cost for wire, shell and solid stent models (Intel Xeon, 3.2 GHz, single processor). 44 5

6 List of Figures Figure 1: Distribution of mean vessel diameter for PAD cohort..19 Figure 2: A diagram displaying measurement locations taken from CT imaging on aortic-common iliac artery bifurcation. The right and left take off angles (θ R, θ L ) are defined by the longitudinal centerlines of the distal abdominal aorta and the centerline of the iliac artery 23 Figure 3: A representative patient CT image displaying the take-off angle measurement technique, where the left image shows the take-off angle measured from the centerline of the abdominal aorta to the centerline of the left common iliac, and the right image shows the take-off angle measured from the centerline of the abdominal aorta to the centerline of the right common iliac...24 Figure 4: A representative patient CT image displaying the lumen diameter measurement technique, where the top images capture the measurements for the right iliac diameter adjacent to the aortic bifurcation and the bottom images capture the right iliac diameter adjacent to the internal iliac artery...24 Figure 5: The relationship between take-off angle and age is clearly shown. Take-off angle for both the right and left common iliac artery had significant correlation when compared to the subject s age. As the subject s age increased, take-off angle increased...28 Figure 6: Illustration depicting the impact of age on disease severity (TASC II classification). Age was found to be significantly different for TASC II classifications (P <.05). As the patient s age increased, the disease severity increased

7 Figure 7: Take-off angle comparing subjects with and without AIOD. There was a significant difference between the two populations, but no significant difference amongst the TASC II classifications (Type A/B v. Type C/D) for the subjects with AIOD...29 Figure 8: Plot revealing the minimum common iliac artery diameter and its relationship to disease severity (TASC II classification). Lumen diameter tended to decrease with increasing TASC II categories, where Type C/D lesions have the smallest diameters.30 Figure 9: Process flow to generate finite element (FE) simulations.33 Figure 10: Geometry for (a) a portion of a full stent, (b) the joint used to compare the responses for different model types, and (c) the analogous wire, shell, and solid models 34 Figure 11: Representational meshes for the (a) wire, (b) shell, and (c) solid joint models 35 Figure 12: Von Mises stress in the full (a) wire, (b) shell and (c) solid models...37 Figure 13: Local Von Mises stress at the joint in the (a) wire, (b) shell and (c) solid models...38 Figure 14: Strain in the full (a) wire (linear), (b) shell and (c) solid models (logarithmic)..39 Figure 15: Comparison of the model responses for converged mesh densities for the wire, shell and solid, all with a seed size of 0.01 mm. Plots are shown for (a) reaction forces vs. displacement, (b) the percent change in reaction force between different model types vs. displacement, and (c) Von Mises stress vs. displacement...40 Figure 16: Sensitivity analysis for the transverse shear parameter in the wire model. Plots are shown for (a) reaction force vs. displacement for all wire models and the mesh 7

8 converged solid models, with increasing transverse shear, and (c) the relative percent error in reaction force between each wire model and the solid model..41 Figure 17: Von Mises stress for different values of transverse shear in the wire model for integration points (a) 1, (b) 5, (c) 21, and (d) Figure 18: The percent change in the stress for different values of transverse shear in the wire model for integration points (a) 1, (b) 5, (c) 21, and (d) Figure 19: Simplified cylindrical artery mesh..45 Figure 20: Von Mises stress of a 25mm length homogenous artery at 120mmHg with varying mesh densities of (a) 2x32 and (b) 4x Figure 21: Example of a few successive IVUS VH images from a patient with high plaque.47 Figure 22: Boundaries extracted from IVUS VH images shown in Figure Figure 23: Material mesh of 25mm length artery with a density of 4 elements (radial) x 64 elements (angular).49 Figure 24: Filtered meshes for 25mm length artery, retaining every slice (n span = 1) and filtering every 5 slices (n filter = 5), for in-plane mesh densities of (a) 2x 32 and (b) 4 x 64 (radial x angular) 51 Figure 25: The compressive stress-strain relationship for each material property, colored to correspond to the color-code in the IVUS VH images. Zooming in from (a) to (b) 54 Figure 26: Von Mises stress of a 25mm length patient specific artery (with average calcium) at 120mmHg with varying mesh densities of (a) 2x32 and (b) 4x Figure 27: (a) initial state of stent and artery (b) final state of stent after radial compression of 2.2mm

9 Figure 28: Stent and artery at (a) maximal expansion at 5 seconds, and (b) the end of the 10 second simulation at 120mmHg 59 Figure 29: Patient specific model boundary conditions.62 Figure 30: Outer nodes fixed angularly through axial section to boundary plane 62 Figure 31: Stent deployed in patient specific artery representative of low calcium at (a) maximal expansion and (b) zoomed in on the stent region of high stress concentration...64 Figure 32: Stent deployed in patient specific artery representative of high calcium at (a) maximal expansion and (b) zoomed in on the stent region of high stress concentration..66 Figure 33: Force vs. radial expansion curve demonstrating the beneficial radial resistive force and chronic outward force for nitinol stents. Stents can exert a gentle force in vivo as shown by the low chronic outward force, but provide large resistive forces when subjected to external crushing forces...69 Figure 34: Typical uniaxial stress strain response for nitinol

10 Acknowledgements I would like to express my deepest appreciation to my research advisor, Dr. Linda Graham. I would never have been able to accomplish my thesis without her excellent guidance. I would also like to thank my committee members, Dr. Geoff Vince and Dr. James Spilsbury for their advice and time on this project. I would like to acknowledge Craig Bennetts, Dr. Ahmet Erdemir, and Dr. Milton Deherrera for their work in the development of the computational modeling platform. Computational modeling documentation was adapted from the reports provided by the Computational Biomodeling (CoBi) Core at the Lerner Research Institute, Cleveland Clinic under my leadership. I would also like to thank Matt Streicher, Paul Bishop and the Peripheral Vascular Core Laboratory at the Cleveland Clinic who provided image data and analysis support throughout the project. My research would not have been possible without this multidisciplinary team and all of their support. And finally, I would like to recognize the clinical translational research scholars program which provided funding for this research work and the National Institutes of Health, National Center for Research Resources, CTSA KL2RR024990, Cleveland, Ohio. 10

11 Arterial Calcification and the Clinical Implications on Stent Function Abstract by MELISSA YOUNG For patients with peripheral arterial disease (PAD), endovascular stenting can be a promising therapy that alleviates plaque obstruction and restores blood flow. However, stent fracture is a serious problem and it can lead to vascular complications, including restenosis. Stent fracture can be affected by type of stent and local mechanical forces that are influenced by arterial wall composition. In this study, an automated computer model platform was devised with meshes inferred from patient specific intravascular ultrasound (IVUS) data, which defined the histological disease condition of the arteries. Combined with stent modeling, this platform is targeted at the development of virtual evaluation of stent performance in a specific arterial setting. Arterial calcification, observed clinically with mild to severe levels, was investigated to determine the impact on stent performance. The analysis demonstrated that arterial calcification does significantly affect stent function, resulting in a 60% increase in logarithmic strains within the stent. 11

12 Chapter 1: Introduction Endovascular stenting of the superficial femoral artery (SFA) is sweeping the world. As promising as these stent therapies are, there have been a significant number of stent fractures observed during patient follow-up. This research identifies the anatomical morphology of the SFA in patients with peripheral arterial disease (PAD) utilizing IVUS (Intravascular Ultrasound) technology in order to understand the implant environment. A patient-specific computer model was developed and used to evaluate a representative uncalcified and severely calcified SFA with disease features observed from human data. The stent fatigue for each calcific condition was studied and compared. The hypothesis that arterial calcification adversely affects stent durability, leading to increased stent fracture was tested and proven. To accomplish this a detailed clinical analysis looking at several aspects of the disease was undertaken for patients with PAD. The shape and size of vessel, types of calcification, and calcification locations were evaluated. Artery calcification was characterized, and the information was used to generate a computer model of the artery and the stent. Bishop et. al found that with progression distally, dense calcium increased on average at a rate of 0.02 mm 2 /cm in popliteals and 0.13 mm 2 /cm in tibials. 1 Despite this, stent designs are developed assuming no calcification, which may lead to design flaws and stent failures. In this study, we developed a computer model system that utilizes patient-specific IVUS virtual histology data to generate a realistic in silico artery model including the range of calcification in the diseased SFA vessel. The model incorporated vessel eccentricity and calcification relevant structures ie. material properties and distribution of the calcium, which were used to assess the stent fatigue performance. 12

13 The stent fatigue life can be detrimentally lowered depending on the disease condition and mechanical forces of the surrounding vessel. The comparison of model stresses and strains of the stent were quantified, and have improved our understanding of how calcification affects stent fatigue life. Chapter 2: Background 2.1 Peripheral Arterial Disease Peripheral arterial disease (PAD) includes diseases caused by obstruction of blood flow of the large arteries primarily in the leg and affects approximately eight million Americans including 12-20% of the population 65 and older. 2 If not treated, PAD can cause ischemic ulcerations and gangrene, which could eventually lead to amputation. Approximately, 25% of patients with PAD have worsening limb symptoms over 5 years, 7% requiring revascularization, and 4% requiring amputation. 3 More than 50% of all PAD involve the Superficial Femoral Artery (SFA) extending to the proximal popliteal artery. 4 The Trans-Atlantic Inter-Society Consensus Document on Management of Peripheral Arterial Disease (TASC) was originally published in January 2000 and modified in 2007 (TASC II) to provide an international consensus on the diagnosis and treatment of PAD. 5 According to TASC II definitions, these stenoses and occlusions can be classified as Type A, B, C, and D lesions, dependent on disease severity and location. Understanding changes in geometry and calcium composition of the diseased state is essential to develop realistic models for designing and testing endovascular devices. 13

14 2.2 Intravascular Ultrasound Intravascular ultrasound (IVUS) imaging technology provides information on arterial morphology and plaque composition. Different types of plaque can be identified using radiofrequency backscatter data and IVUS virtual histology (VH) software. The 3D path of the patient specific vessel is obtained from biplane arteriographic X-ray images, which are used to localize the spatial position of the diseased segment during the treatment. VH begins with ultra-audible frequency data provided from the IVUS catheter, and the amplitude is evaluated from grayscale images. The VH performs a spectral analysis of the signal and maps the resulting profiles to a database, resulting in a cross sectional image where different plaque components can be identified. Nair et al. reported an accuracy greater than 93% with this technique Stent Interventions Endovascular therapies, mainly stenting via self expanding or balloon expandable devices offer promising treatment for patients with peripheral arterial disease, but require further design improvements. Stenting achieves a larger and smoother lumen, minimizing artery elastic recoil and arterial remodeling. 7 Recently nitinol stents were shown to offer improved primary patency rates in SFA after percutaneous transluminal angioplasty (PTA) compared with stainless steel stents. 8,9 However, there are concerns about long term device durability after nitinol stent fracture frequency 25% was observed during 10, 11, 12 follow-up. Poor performance of intravascular devices can result in undesirable clinical conditions such as thrombosis and intimal hyperplasia. Furthermore, stent fracture can lead to vascular complications such as restenosis, stent occlusion, and result in the need for re-interventional procedures. Long term primary patency rates for 14

15 percutaneous transluminal angioplasty (PTA) and stenting remain disappointing, where one and two year primary patency rates of 76 to 97% and 60% to 84% have been reported with nitinol stents. 13 Stent durability maybe lower in the femorpopliteal region because of the diseased environment and the mechanics of the implant location. Stent fracture can be influenced by issues such as vessel stiffness including arterial wall composition and degree of calcification. It has been shown that there is a higher percentage of calcium in the peripheral arteries compared to the coronary arteries. 1 The larger amounts of calcium in the peripheral arteries make it a more challenging environment for stents. Since each patient may have varying disease severity, calcification, and geometry, personalized stent designs may be necessary to uniquely fit a patient s anatomy and achieve optimum device performance. Additional factors in the SFA that may attribute to this lower device lifespan include complicated deformations that occur in multiple directions by leg movement, and exposure to many mechanical forces such as compression, torsion, and elongation during daily activities. 14,15 The mechanical environment of the peripheral arteries could be one of the predominate causes of high restenosis rates. 16 A robust artery computational model is desirable to consider these unique individual characteristics for stent design and development. For an adequate device prediction tool, both the stent and artery need to be modeled. While stent modeling has been studied elaborately, artery modeling with realistic in vivo stiffness has been only attempted by a handful of researchers. 17, 18,19 Stent designers have previously evaluated structural performance of self expanding nitinol stents, developed user-defined material subroutines, and used the UMAT for nitinol 15

16 developed by ABAQUS. 20, 21 Mortier et. al developed an automated mesh generation using triangulated surface representations of the stent geometry from micro CT images. 22 But, stent modeling is still limited by the time consuming nature of finite element models. With the increasing demand for virtual prototyping, researchers have confirmed that the use of beam elements for stent modeling instead of solid elements can shorten simulation time without compromising results Computational Modeling Traditional approaches to artery modeling have assumed a homogenous conduit with uniform thickness. 24 Many models of arterial walls are characterized by nearly incompressible, anisotropic, hyperelastic material behavior. 25 However, this does not accurately represent the in vivo artery performance because arteries consist of several layers including the tunica media and the tunica adventitia. In addition, depending on the diseased condition of the artery, there may exist regions of stenosis with plaque, which may be more dense, fibrous, or calcified and in turn results in varying mechanical responses within the artery. Plaques classified as cellular, hypocellular, or calcified have been shown to have different compressive stiffness. 26 Artery stiffness can directly impact the stress observed on the stent 27 and therefore an automated method for establishing in vivo artery models is critical to better design stents and provide the best therapies to patients. Once the stent is deployed into the in vivo artery model, the mechanical properties and fatigue performance of the stent device can be evaluated. Since each patient may have vessel differences, it will be essential to build a model that can account for 16

17 individual geometry and topography. Unfortunately, the current finite element methods are limited because of the required preprocessing and computational effort. This research proposes an automated artery model to accurately depict vessel stiffness based on IVUS virtual histology and imaging with limited cost computing time, and accurate resolution. The computer artery model can be utilized for a stent design optimization virtual prototyping platform, which facilitates personalized medicine and individualized stent selection for patient undergoing endovascular repair. Chapter 3: Clinical Analysis of Patients with Peripheral Arterial Disease The geometry of the superficial femoral artery for patients with peripheral arterial disease was studied using IVUS and contrast enhanced computed tomography (CT) imaging modalities. The IVUS imaging provided high resolution images of the vessel wall and VH was used to quantify the arterial plaque composition. CT imaging was used to study the geometric properties and disease severity for patients with PAD. 3.1 Study Population A total of 75 patients were included in the clinical analysis to obtain geometrical and morphological information about plaque composition in patients with PAD. Demographics and medical comorbidity data were determined by reviewing electronic medical records at the time of angiography. These imaging studies included subjects aged 18 and above, with a gender and racial mix characteristic of the population with PAD, included in the IRB-approved Cleveland Clinic Foundation, Vascular Surgery Registry. The data were collected per IRB # and the inclusion criteria involved the following: a) documented symptoms of intermittent claudication, rest pain, or minor 17

18 tissue loss (Rutherford category 1-5), b) resting Ankle-Brachial Index (ABI) <0.90 or <0.80 after exercise in patients with resting ABI >0.90 in the affected lower extremity, c) patient 10cm segment of SFA with a 20-80% lesion suitable to investigate with IVUS with no evidence of prior interventions. Patients were excluded if there was evidence of acute limb ischemia, contraindications to angiography, concurrent oral anticoagulant therapy that could not be safely withheld, extensive tissue loss, or gangrene. 3.2 Geometrical Data captured with IVUS IVUS imaging was used to collect the contours defining the internal elastic lamina and external elastic lamina of the vessel 28 and were automatically detected by the post processing software (Volcano s PCVH or VIAS). Volcano s VH IVUS was used to detect the atherosclerotic plaque composition. Plaques types were characterized as: fibrous, fibro-fatty, necrotic core, or dense calcium. The gray-scale IVUS images were used to calculate geometric data including vessel, plaque plus media, and lumen cross sectional area along with diameters (minimum, maximum, mean) for lumen and vessel, see Table 1. Measurement Minimum Mean Maximum Lumen Diameter 1.5mm 4.2±0.9mm 7.5mm Lumen Eccentricity (Min/Max) ± Lumen Area 4.1mm ±6.2mm mm 2 Vessel Diameter 2.2mm 6.2±0.9mm 9.6mm Vessel Eccentricity (Min/Max) ± Vessel Area 7.0mm ±8.5mm mm 2 Stenosis (Area Reduction) 20.9% 51.7±11.3% 78.5% Fibrous Plaque 23.5% 55.3±15.0% 84.3% Fibro-Fatty Plaque 0.9% 11.2±8.9% 49.5% Dense Calcium Plaque 0.1% 14.5±11.4% 44.0% Necrotic Core Plaque 0.7% 19.0±10.8% 44.3% Table 1: Summary of geometric and morphologic values for PAD cohort (n=75)

19 The SFA was found to have mean diameters of 4.2±0.9mm and 6.2±0.9mm for the lumen and vessel respectively. The vessel minimum and maximum diameters ranged from 2.2mm to 9.6mm, and over 70% of vessel diameters were in the range of 5-7mm, Figure 1. Mean lumen eccentricity was 0.61±0.22 while the mean vessel eccentricity was 0.68±0.10, where an eccentricity value of 1.0 would indicate a uniformly circular vessel. The corresponding mean cross sectional area for the lumen and vessel were 15.2±6.4mm 2 and 31.3±8.6mm 2 yielding an overall area stenosis of 51.6±11.1%. Plaque morphology was found to be 55.3±15.0% fibrous, 19.0±10.8% to be necrotic core, 14.5±11.4% dense calcium, and 11.2±8.9% fibro-fatty plaque. Vessel Mean Diameter Diamater (mm) Figure 1: Distribution of mean vessel diameter for PAD cohort. 3.3 In Vivo Plaque Morphology The association between demographics and clinical factors is summarized in Table 2. The distribution of the demographics and medical comorbidities for the cohort was 19

20 calculated using two-sided t-tests to measure the association with plaque composition and vessel geometry. Results are shown as the mean ± standard deviation. For all statistical comparisons, P < 0.05 was considered significant. Stenosis Present Absent p Gender (Male) 54.5± ± Diabetic 52.4± ± Smoking 51.8± ± Chronic Renal Failure 50.0± ± Hyperlipidemia 50.4± ± Age > 60 Years 53.3± ± Hypertension 52.2± ± Table 2: Association of clinical factors with plaque burden. 29 Gender and age were two clinical factors that were found to be significant with the artery geometric measurements (Table 3). The male gender was found to be correlated with increased lumen and vessel diameters (P<0.001). And age also showed an association, where large vessel diameters were observed with increase in age (p=0.006). Lumen Diameter (mm) Vessel Diameter (mm) Present Absent p Present Absent p Gender (Male) 4.5± ±0.9 < ± ±0.8 <0.001 Diabetic 4.3± ± ± ± Smoking 4.3± ± ± ± Chronic Renal Failure 4.5± ± ± ± Hyperlipidemia 4.2± ± ± ± Age > 60 Years 4.2± ± ± ± Hypertension 4.2± ± ± ± Table 3: Association of clinical factors with geometric lumen and vessel measurements

21 3.4 Geometric Properties captured with CT The abdominal aorta and common iliac arteries are a frequent locality for endovascular stenting, and contralateral femoral access is used to allow antegrade approach to an iliac lesion. This requires a guide wire and sheath to traverse the tortuous vasculature adjacent to the aortic bifurcation. Thus, take-off angles and common iliac artery diameters are important geometric measurements to take into account. Similarly, the impact of clinical factors, such as gender, age, or BSA, on these geometric properties is worthy of consideration. Although aortoiliac occlusive disease (AIOD) is less common than superficial femoral disease, surgical or endovascular treatment of AIOD represents approximately 48% of all lower limb revascularizations, and this percentage increases to 55% when considering patients younger than 40 years old 30. In addition to being a frequent site of stent placement for AIOD, the common iliac arteries are traversed and often serve as the distal landing site for endovascular grafts to repair abdominal aortic aneurysms (AAA). The common iliac arteries are not as well characterized geometrically as is the abdominal aorta. Several different approaches have been used to describe the geometric properties of the aortic bifurcation vasculature. Technology used to obtain these measurements in healthy patients included: computed tomography (CT) 31,32, angiography 33,34, radiography 35, ultrasonography 36,37, whole-body magnetic resonance imaging (MRI) 38, and calipers and protractors used on cadavers in situ 39,40. Several studies have looked specifically at only the abdominal aorta or vasculature closer to the heart with very little literature including information on both the abdominal aortic bifurcation and the common iliac arteries. Aside from the research performed by Callum et al., previous research has 21

22 been focused on geometric properties of the vasculature in healthy individuals 35. Geometric variables related to individual aortic bifurcation anatomy, disease pattern (patient-dependent), and stenting configuration (operator-dependent), may have an impact on long-term stent patency 41. This analysis provided the average geometric properties of the common iliac arteries in conjunction with the abdominal aortic bifurcation using CT imaging in individuals with PAD. Geometry changes with increasing severity of PAD were explored. According to TASC II definitions for AIOD, these stenoses and occlusions can be classified as Type A, B, C, and D lesions, dependent on disease severity and location. Endovascular management is preferred to open surgery in the presence of TASC A and B lesions, and surgical reconstruction is the recommended treatment for TASC C and D lesions in good-risk patients 42. Understanding changes in geometry from the undiseased state to increasingly severe AIOD, based on TASC II classification, is essential to develop realistic models for designing and testing endovascular devices. Seventy-five consecutive subjects with PAD, 64 of which had AIOD, were selected and had intravascular contrast enhanced abdominal and pelvic CT. Those patients with previous arterial bypass, aneurysmal disease, or stenting in the aortoiliac region were excluded. Basic demographic, diabetic status, and tobacco use data were abstracted from the subject s electronic medical record. This analysis was approved by the Cleveland Clinic Institutional Review Board (IRB ). Contrast enhanced CT imaging was volumetrically reconstructed with slice thickness of less than 2 mm and measured by the Peripheral Vascular Core Laboratory (Cleveland Clinic, Cleveland, OH) utilizing TeraRecon Intuition Software (Foster City, 22

23 CA). The take-off angle for both the right and the left common iliac artery was measured using a multiplanar reformatted view (MPR) that best exposed the maximum angulations of the abdominal aorta and common iliac arteries (Figure 2). This measurement can be best described as the angle between the extended centerline of the distal abdominal aorta and the centerline of the common iliac artery (Figure 3). In addition, external and lumen vessel diameters of the left and right common iliac arteries were measured orthogonal to centerline flow views in the 75 subjects (42 male and 33 female). As shown in Figure 4, diameters were measured at two specific locations along the common iliac arteries: adjacent to the aortic bifurcation (1-3 mm immediately downstream from the aortic bifurcation where there were two distinct vessels) and adjacent to the internal iliac artery (1-3 mm prior to reaching the internal iliac artery in typical circulation). Figure 2: A diagram displaying measurement locations taken from CT imaging on aortic-common iliac artery bifurcation. The right and left take off angles (θ R, θ L ) are defined by the longitudinal centerlines of the distal abdominal aorta and the centerline of the iliac artery. 23

24 Figure 3: A representative patient CT image displaying the take-off angle measurement technique, where the left image shows the take-off angle measured from the centerline of the abdominal aorta to the centerline of the left common iliac, and the right image shows the take-off angle measured from the centerline of the abdominal aorta to the centerline of the right common iliac. Figure 4: A representative patient CT image displaying the lumen diameter measurement technique, where the top images capture the measurements for the right iliac diameter adjacent to the aortic bifurcation and the bottom images capture the right iliac diameter adjacent to the internal iliac artery. 24

25 The 75 subjects were stratified into three separate TASC II groups: 50 were identified as having Type A/B lesions, 14 with Type C/D lesions, and the remaining eleven subjects had no lesions associated with the aortic bifurcation and common iliac arteries, but had disease at a more distal location. This can be termed as infrainguinal occlusive disease (IIOD) which is caused by atherosclerosis involving the femoral, popliteal, and/or infrapopliteal arteries. Descriptive statistics for the PAD cohort population are displayed in Table 4. The mean ages of the men and women for this study were fairly similar (Males: 64.8 ± 13.1 years; Females: 68.4 ± 12.5 years). Height measurements were only available for 66 of the 75 subjects (Males: ± 6.5 cm; Females: ± 6.9 cm) and weight values were provided for all but five (Males: 88.0 ± 11.7 kg; Females: 76.1 ± 21.2 kg). Diabetic information and tobacco use was available for 72 of the 75 individuals. Diabetes was present in 27.8% and tobacco use was present in 66.7% of the study s population. Neither diabetes nor smoking history had a significant impact on the take-off angle or iliac diameter measurements in this cohort. Characteristics of Male Female All Subjects (N = 42) (N = 33) (N = 75) Age (Mean (SD)) 64.8 (13.1) 68.4 (12.5) 66.4 (12.9) Height (cm) (6.5) (6.9) (9.4) Weight (kg) 88.0 (11.7) 76.1 (21.2) 82.4 (17.8) Body Surface Area (m 2 ) 2.05 (.16) 1.83 (.24) 1.95 (.22) Yes Diabetic No Unknown Yes Tobacco No Use Unknown Table 4: Descriptive statistics for PAD cohort (n=75)

26 External and luminal diameter measurements, as well as common iliac artery take-off angles obtained from the CT images are summarized in Table 5. Both right and left iliac artery take-off angles had a significant correlation with the subject s age. The take-off angle tended to show an increase on both the left and right sides as the subjects age increased (Figure 5). For all diameter measurements recorded, maximum and minimum diameters adjacent to the aortic bifurcation and adjacent to the internal iliac artery, males had a larger diameter compared to females (P <.05). The external and luminal diameters for males were approximately mm larger than the diameters for the female population. All external and luminal diameters showed no effect based upon the age of the subject except the maximum external left common iliac artery adjacent to the aortic bifurcation. All of the external and luminal diameter measurements showed a weak, yet significant statistical correlation to body surface area (BSA) (P <.05), with diameter increasing as BSA increased. 26

27 TASC II Classifications External Diameters (mm) Rt. Iliac Adjacent to Bifurcation Rt. Iliac Adjacent to Internal Iliac Lt. Iliac Adjacent to Bifurcation Lt. Iliac Adjacent to Internal Iliac Luminal Diameters (mm) Rt. Iliac Adjacent to Bifurcation Rt. Iliac Adjacent to Internal Iliac Lt. Iliac Adjacent to Bifurcation Lt. Iliac Adjacent to Internal Iliac Take-Off Angle ( ) Right Iliac Take-Off Angle ( ) Left Iliac Take-Off Angle ( ) Type A/B Lesions (N = 50) Type C/D Lesions (N = 14) Minimum Mean (SD) Maximum Mean (SD) No Lesions (N = 11) 13.0 (3.0) 14.8 (3.4) 12.0 (2.2) 13.7 (1.9) 12.1 (1.9) 13.6 (1.9) 13.1 (2.9) 14.3 (3.0) 12.2 (2.2) 13.5 (1.9) 12.7 (2.0) 14.0 (2.1) 13.6 (3.3) 15.4 (3.4) 12.6 (2.6) 14.1 (2.2) 11.6 (1.6) 13.1 (2.2) 13.4 (2.8) 14.6 (2.8) 13.0 (3.0) 14.6 (3.0) 12.3 (2.4) 13.5 (2.7) Minimum Mean (SD) Maximum Mean (SD) 9.5 (2.9) 11.6 (3.2) 6.8 (2.3) 9.4 (2.2) 9.9 (1.4) 11.3 (1.6) 9.7 (2.7) 11.1 (2.8) 7.4 (1.6) 9.6 (1.8) 10.5 (1.7) 11.2 (1.7) 9.7 (3.3) 11.9 (3.4) 6.8 (2.3) 9.4 (2.3) 9.6 (1.6) 11.0 (1.8) 9.8 (1.6) 11.1 (3.0) 8.6 (3.8) 10.8 (3.7) 10.3 (2.2) 11.5 (2.5) Mean (SD) 29.1 (13.2) 30.5 (15.7) 18.6 (8.3) 26.0 (11.2) 28.3 (15.5) 13.6 (6.4) Table 5: TASC II Classification Measurements for PAD cohort

28 Figure 5: The relationship between take-off angle and age is clearly shown. Take-off angle for both the right and left common iliac artery had significant correlation when compared to the subject s age. As the subject s age increased, take-off angle increased. Take-off angles did not differ significantly between Type A/B and Type C/D lesions, while age was statistically significantly different among the classifications (P <.05) (Figure 6). The average take-off angles were however, significantly larger for arteries with AIOD than those without (i.e. those in patients with IIOD, more distal disease). The subjects with AIOD had mean take-off angles of 29.4 and 26.5 degrees for the right and left sides respectively, and the angles for individuals without AIOD were 18.6 and 13.6 degrees (Figure 7). 28

29 Figure 6: Illustration depicting the impact of age on disease severity (TASC II classification). Age was found to be significantly different for TASC II classifications (P <.05). As the patient s age increased, the disease severity increased. Figure 7: Take-off angle comparing subjects with and without AIOD. There was a significant difference between the two populations, but no significant difference amongst the TASC II classifications (Type A/B v. Type C/D) for the subjects with AIOD. 29

30 As expected, the minimum luminal diameters decreased with increasing disease severity noted by the TASC II classifications (P <.05) (Figure 8), except for the minimum left iliac artery adjacent to the internal iliac. External diameters showed no significant difference amongst the TASC II classifications at both locations near the bifurcation and internal iliac artery, suggesting no compensatory dilation or remodeling. Age was found to gradually increase with increasing disease severity. Subjects without AIOD averaged 51.5 (SD: 11.9) years old, Type A/B lesions 67.2 (11.1), and Type D lesions 75.1 (9.8). There was not a statistically significant difference in BSA amongst the TASC II classifications. Figure 8: Plot revealing the minimum common iliac artery diameter and its relationship to disease severity (TASC II classification). Lumen diameter tended to decrease with increasing TASC II categories, where Type C/D lesions have the smallest diameters. 30

31 The external and luminal diameter measurements are essential to determine ideal stent implant size. Previous research has focused on the geometry of the aortic bifurcation and common iliac arteries in healthy individuals, and provided a range for luminal and external diameter measurements of the common iliac artery that varied with different technologies. For example, ultrasound measurements yielded a mean common iliac luminal diameter of 9.9 ± 1.6 mm in men and 8.8 ± 1.2 mm in women. 36 Right common iliac artery luminal diameters of 10.4 ± 1.8 mm and left common iliac artery luminal diameters of 9.8 ± 1.9 mm were found using standard angiography. 33 According to the Subcommittee on Reporting Standards for Arterial Aneurysms of the Society for Vascular Surgery, using computed tomography methodology, the normal luminal common iliac diameter is ± 1.5 mm and ± 2.0 mm for females and males, respectively. 44 The data provide important insight as to how the common iliac artery differs in size and shape between patients with AIOD and distal occlusive disease (IIOD). As expected, the luminal diameter decreased as the TASC II classification increased with regards to disease severity from Type A/B to Type C/D lesions. In comparison to the previous literature, the external diameter measurements for individuals with PAD were slightly larger than the measurements observed in healthy individuals. For all individuals with PAD, mean diameters measured at the four specific locations ranged from 13.5 to 14.0 mm, as compared to outside caliper measurements in cadavers which averaged 12.0 ± 1.9 mm in the right common iliac artery and 11.8 ± 2.1 mm in the left common iliac artery. 39 However, external diameter measurements did not vary with increased disease severity based on the TASC II classifications. The increase in 31

32 diameter for our measurements can possibly be attributed to a combination of both age and PAD whereas the previous caliper measurements were done on healthy individuals. With the development of arterial stenoses, positive remodeling can occur in which there is an expansion in the external elastic membrane of the vessel to accommodate the plaque buildup so that the luminal diameter remains the same, as noticed in the coronary arteries in previous literature. 45 The data showed that there was no statistically significant difference in external diameter with increased disease severity, suggesting that positive remodeling is very limited for the common iliac artery in patients with PAD. However, an increased sample size, especially for subjects with Type C/D lesions, would be beneficial to strengthen this observation. On the other hand, regional differences in remodeling have been previously observed, and conduit arteries such as the iliac and femoral arteries have less tendency to enlarge in response to plaque formation compared to the common carotid, coronary, and renal arteries. 46 Common iliacs do not have the elasticity 47, and thus may be less able to remodel during atherogenesis. From the take-off angle, to the arterial diameter, to the disease severity of the common iliac arteries and the abdominal aortic bifurcation, all facets of the geometry are important to properly treat individuals with PAD. The measurements obtained in this study from contrast enhanced CT images provide valuable information regarding vessel geometry in the diseased population. Knowing these characteristics of the vasculature can help interventionalists and medical device designers improve the technology and devices used to treat vascular disease. The vessel geometry can be used to develop valid in vitro bench test models and provide a more robust, clinically relevant test paradigm for all endovascular devices. 32

33 Chapter 4: Finite Element (FE) Simulation The goal of developing a computer model for this patient population is to be able to determine the impact of calcified anatomical configurations on stent fatigue. Having a robust tool that can be utilized by stent designers for improving device durability will be very important to reduce patient re-interventional procedures. The computational modeling analysis will be used for predicting in vivo structural reliability performance of stents deployed into patients with calcified environments. Figure 9 demonstrates the process flow and relationship between the model and clinical analysis of the diseased population. Figure 9: Process flow to generate finite element (FE) simulations. 4.1 Stent Models It was important to determine the mechanical consistency between different geometrical representations of the stent model (solid, shell, and wire) and their associated material definitions for nitinol. The geometrical stent models are illustrated in Figure 10, and were defined for a single joint taken from the full stent geometry, which is half the amplitude of the stent pattern. 33

34 (a) (b) (c) Figure 10: Geometry for (a) a portion of a full stent, (b) the joint used to compare the responses for different model types, and (c) the analogous wire (black), shell (dark yellow) and solid (transparent yellow) models Stent Mesh Convergence Mesh convergence for the different geometrical stent models (solid, shell, and wire) was performed. For the wire model, sensitivity analysis was conducted for the transverse shear parameter (required to be specified by the user for the section of the beam element). Mesh convergence was performed for each type of model (wire, shell, solid), see Figure 34

35 11 for mesh representations. Beam elements were used to mesh the wire model. Quadrilateral elements were used to mesh the shell model. Hexahedral elements were used to mesh the solid model. The range of seed sizes included in the mesh convergence study were 0.005, 0.01, 0.02, and 0.04 mm. (a) (b) (c) Figure 11: Representational meshes for the (a) wire, (b) shell and (c) solid joint models. The following nitinol material properties were assigned to all models: E A = Austenitic Elastic Modulus = 40,000 MPa ν A = Austenitic Poission's ratio = 0.33 E M = Martensitic Elastic Modulus = 32,000 MPa 35

36 ν M = Martensitic Poission's ratio = 0.33 Abaqus has a special user material sub-routine to implement nitinol materials. However, it does not automatically define the transverse shear for shell and wire models. For both of these model types, the transverse shear was calculated from the material properties corresponding to the Austenitic region of the nitinol (E A = 40,000 MPa, ν A = 0.33). The components of the transverse shear for the shell model were determined to be: G = Bulk Modulus = E A / 2(1+ν A ) = 15, K 11 = K 22 = (5/6)Gt = , K 12 = 0 = shell thickness = 0.25 mm The components of the transverse shear for the wire model were determined to be: K 13 = K 23 = = = 0.85 for rectangular cross-sectional profiles = area of cross-sectional profile = 0.03 value = 0.25 Sensitivity analysis was performed for the transverse shear parameters in the wire model. The range of values used for sensitivity analysis of the transverse shear were ¼, ½, 1, 2, 4 times the value calculated from the Austenitic region: , , , , respectively. The cross-sectional ends of the stent joint model were tied to rigid bodies of corresponding cross-sectional geometry. All degrees of freedom were held fixed for one of the cross-sectional ends in each model. A compressive displacement of mm was applied along the line of action between centers of the terminal ends of the joint model. This prescribed displacement collapses all models to the point past which self-contact 36

37 would occur in the solid model. Representative output results are shown in Figures Von Mises stress, local Von Mises stress at the joint, and strain. (a) (b) Figure 12: Von Mises stress in the full (a) wire, (b) shell and (c) solid models. (c) 37

38 (a) (b) Figure 13: Local Von Mises stress at the joint in the (a) wire, (b) shell and (c) solid models. (c) 38

39 (a) (b) (c) Figure 14: Strain in the full (a) wire (linear), (b) shell and (c) solid models (logarithmic). Wire, shell and solid models were each found to be convergent for the reaction force and displacement at a seed size of mm. A comparison of the relative mechanical reactions between the different model types is shown in Figure

40 (a) (b) (c) Figure 15: Comparison of the model responses for converged mesh densities for the wire, shell and solid, all with a seed size of 0.01 mm. Plots are shown for (a) reaction force vs. displacement, (b) the percent change in reaction force between different model types vs. displacement, and (c) Von Mises stress vs. displacement. Sensitivity analysis was performed for the following specific transverse shear values in the wire model with the converged seed size of 0.01 mm: , , , , (Figure 16). The relative percent error in reaction force was calculated between pairs of models, successively along the range of included transverse shear values. The relative percent error was also calculated between each of the wire 40

41 models (with varying transverse shear) and the converged solid model, with a seed size of 0.01 mm. (a) (b) (c) Figure 16: Sensitivity analysis for the transverse shear parameter in the wire model. Plots are shown for (a) reaction force vs. displacement for all wire models and the meshconverged solid model, (b) the relative percent error in reaction force between each successive pair of models, with increasing transverse shear, and (c) the relative percent error in reaction force between each wire model and the solid model. For the wire model, the resultant Von Mises stress at the joint returns 4 values, assumed to be at the corner integration points of the beam element in the corresponding 41

42 section. The stress and percent change in stress are plotted vs. displacement in Figure 17 and 18 respectively. Large variations in the transverse shear values for the wire model produced little effect on the mechanical response of the joint, demonstrating that the wire model is not that sensitive to transverse shear. (a) (b) (c) (d) Figure 17: Von Mises stress for different values of transverse shear in the wire model for integration points (a) 1, (b) 5, (c) 21, and (d)

43 (a) (b) (c) (d) Figure 18: The percent change in the stress for different values of transverse shear in the wire model for integration points (a) 1, (b) 5, (c) 21, and (d) 25. Table 6 shows a comparison of the computational cost for each type of model for the converged seed size of 0.01 mm. The wire and shell models have the default transverse shear values of and , respectively. The values for the wire model were not readily available for a seed size of 0.01 mm, so those for a seed size of 0.02 mm are presented, which should have a similar computational cost. A seed size of 0.01 mm was found to provide meshes that converge for values of reaction force and therefore this seed size was deemed suitable for future stent designs/models. 43

44 MODEL Wire (seed = 0.02) Shell Solid Memory (MB) CPU Time (s) Wallclock Time (s) Table 6: Comparison of computational cost for wire, shell and solid stent models (Intel Xeon, 3.2 GHz, single processor). Comparing the converged meshes (seed size = 0.01 mm) shows that there is still significant difference in the mechanical response of the different representations of the model (wire, shell, and solid). This must be taken into account when using each type of model. The general trend is that the wire responds as if it were softer than the shell, which is softer than the solid. 4.2 Artery Models Models of the superficial femoral artery were generated from intravascular ultrasound (IVUS) virtual histology (VH) images, labeled to identify distinct material components of arterial wall and plaque. Software was developed to automatically generate finite element (FE) meshes from IVUS VH images with arbitrary mesh density and averaged, elementspecific material properties Homogenous Artery Models A cylindrical artery geometry was used to simplify the simulation to focus on determining contact settings between the stent and artery, Figure 19. The artery model corresponds to the arterial wall with an inner (lumen) diameter of 4.0 mm, a thickness of 0.4 mm, and a length of 12.4 mm (twice the length of the corresponding 3-layer solid stent model = 6.2 mm). The linear wire stent geometry was meshed with a seed size of 44

45 0.01 mm. This seed size was used based on the results of mesh convergence studies in chapter The artery mesh seed size was defined to be a third of the arterial wall thickness, 0.4 mm / 3 = mm. This gives three elements through the thickness of the artery to properly capture mechanical effects while providing a minimum overall number of elements to reduce computational cost. Figure 19: Simplified cylindrical artery mesh. Material properties for the simplified artery model were determined and an average value for Young's modulus of 25 dynes/cm 2 was selected from the provided range of dynes/cm 2, with an assumed Poisson ratio of 0.5 (completely incompressible). 49 Converting this to appropriate units for the model (in mm) gives 2.5 N/mm 2 (= MPa). A Poisson ratio of 0.49 was used instead of 0.5 to ease the constraint of complete incompressibility. The automatically generated filtered meshes were built for two selected inplane(xy) mesh densities of 2x32 and 4x64. The Von Mises stress concentrations (at 120 mmhg) indicate slight differences (approximately 4%) in the resulting stress outputs in the artery Figure

46 (a) Figure 20: Von Mises stress of a 25mm length homogenous artery at 120mmHg with (b) varying mesh densities of (a) 2x32 and (b) 4x64. 46

47 4.2.2 Patient Specific Artery Model IVUS images are used to provide the geometric input to generate FE meshes for the SFA. The IVUS images were taken at the same point in the cardiac cycle. The distance between images is recorded during pull-back (rate ~0.5 mm/s). However, the true relative 3D spatial rotation and translation between images is not known. Brands et al. inserted a reference wire during IVUS imaging where the relative position was shown in successive slices. No significant differences in positions were seen in rotation or torsion of the IVUS catheter. 19 Image processing is used to generate color-coded VH images (.bmp) that identify different material components of the SFA. The arterial wall is gray and the different types of plaque are white, red, light green, and dark green. A few example IVUS VH images from a patient with high dense calcium (~44%) are shown in Figure 21. These images had a 10 mm field-of-view with an image size of 400 x 400 pixels, giving a resolution of mm. Figure 21: Example of a few successive IVUS VH images from a patient with high plaque. 47

48 A python script was developed to extract ordered sequences of points from the inner (lumen) and outer (arterial wall) boundaries for an arbitrary number of successive IVUS VH images. The connectivity between boundary pixels was determined using the 4-neighborhood (i.e. edge-to-edge, not diagonally corner-to-corner). The user specified a number of pixels to skip (n skip = 6, for the following examples) when outputting the boundary points to the text file in order to eliminate jagged or overlapping edges from the boundary points. The boundaries extracted from the IVUS VH images shown in Figure 21 are shown in Figure 22. Figure 22: Boundaries extracted from IVUS VH images shown in Figure 14. Two hexahedral meshes are generated for each model. One mesh exactly fits the original boundaries to determine material properties for the elements and the other is a mesh that is filtered to remove discontinuities from slice to slice. The user defines the mesh by specifying the number of elements in the radial and angular dimensions, the number of slices for elements to span in the z dimension (n span = 1, for the following examples), and the number of slices to filter in the z dimension (n filter = 5, for the following examples). 48

49 The material mesh (Figure 23) was created from a desired number of contiguous slices. The boundary points were scaled by the image resolution to convert from image indices to physical dimensions. The relative spacing between boundaries in the image plane (xy) is not altered from that of the IVUS VH images. The relative spacing out of the image plane (z) is defined from the recorded pull-back data (typically ~0.3 mm/slice). The centroids of the lumen boundary points for all slices were averaged together to best center all boundaries about the origin. The inner and outer boundaries, represented by a series of line segments connecting the boundary points, were resampled at evenly spaced angles to determine the inner and outer nodes of the mesh. The appropriate number of interior nodes (to give the desired number of elements in the radial dimension) were found by linearly interpolating between the inner and outer boundary nodes at each angle, so that they were evenly spaced. Figure 23: Material mesh of 25mm length artery with a density of 4 elements (radial) x 64 elements (angular). 49

50 The filtered mesh (Figure 24) was obtained by averaging (equally weighted) the xy-coordinates for the specified number of slices (n filter ) centered about a each slice at each angle for both the inside and outside nodes of the material mesh. Only the nodes on every n span number of slices were contained in the filtered mesh. Each of the two meshes was written to a different Abaqus input file (.inp). Nodes and elements were numbered in the following order: radial (increasing), angular (0->360 degrees), z (0.0->z max ). Node and surface sets were defined bottom (z=0.0), top, inner (lumen) and outer (outer arterial wall) surfaces. 50

51 (a) (b) Figure 24: Filtered meshes for 25mm length artery, retaining every slice (n span = 1) and filtering every 5 slices (n filter = 5), for in-plane mesh densities of (a) 2x 32 and (b) 4 x 64 (radial x angular). 51

52 The IVUS VH image identifies different materials by labeling each material plaque type with a different color. A third Python script was written to determine element-specific material properties by finding a weighted average of material property coefficients associated with each color in the IVUS-VH images for the set of pixels lying within (or on the surface of) each element. The material properties used for different components in the model were hyperelastic and incompressible. The arterial wall material properties were described with 2nd order polynomial coefficients. 50 The material properties for each type of plaque were determined by finding 3rd order reduced polynomial coefficients to fit experimental compression data 51, and the compressive stress-strain relationship is exponential, defined to be: Stress (MPa)= (1 MPa/1000 kpa) ((1 kpa) e k*strain -1) The color [R,G,B], material type, material description, and exponential stress-strain coefficient (k) for each type of plaque materials were defined as follows: 1) BLACK [0,0,0] = background k background = k adipose = 2.8; stress background = 0.001*stress adipose 2) GRAY [136,136,136] = arterial wall k wall = 5.2 3) RED [255,0,0] = plaque (minor) necrotic core, dead cells (no nuclei), very soft, toothpaste consistency (similar to adipose tissue) k adipose = 2.8 4) DARK GREEN [0,170,0] = plaque (major) fibrous, collagen matrix, few smooth muscle cells 52

53 k fibrous = 5.9 5) LIGHT GREEN [187,255,0] = plaque (minor) softer collagen matrix, intertwined with foam cells (macrophages), fatty structures k fatty = 6.7 6) WHITE [255,255,255] = plaque (minor) dense, calcium-based (similar to osteoporotic bone) k calcified = 12.6 Stress values were calculated for each material type over a range of strains from 0.0 to 0.5, in increments of Abaqus was used to determine coefficients for reduced polynomial materials for orders N=1 to 5 with negated stress-strain values, to delineate compression. N=3 provided the best fit while limiting the number of coefficients for all material types. Background pixels were assigned a material property 1000 times softer than the softest material (red) in case there were background pixels included in the element due to the discrete approximation of the boundaries by the mesh. The reduced polynomial coefficients (order N=3) [C10,C20,C30,D1] for each material type were: BLACK:[4.81E-06, 2.19E-07, -2.30E-07, ] GRAY:[9.56E-04, 7.64E-04, -2.51E-04, 21.05] RED: [4.81E-04, 2.19E-05, -2.30E-05, 41.83] DARK GREEN:[1.10E-03, 1.22E-03, -3.63E-04, 18.31] LIGHT GREEN:[1.27E-03, 1.93E-03, -5.06E-04, 15.92] WHITE:[2.49E-03, 1.64E-02, 6.98E-03, 8.09] 53

54 The stress-strain relationship for these coefficients were plotted in Abaqus and are shown below in Figure 25. (a) Figure 25: The compressive stress-strain relationship for each material property, colored to correspond to the color-code in the IVUS VH images. Zooming in from (a) to (b). (b) 54

55 A range of meshes were generated to assess convergence of the interdependent effects mesh density and material averaging on arterial stiffness for a patient specific artery representative of average calcium (14% dense calcium). A set of 32 successive slices (giving 31 elements in z) were used to generate two meshes, with in-plane element dimensions of 2x32 and 4x64 (#radial x #angular). Spatial smoothing was applied between every 5 neighboring slices. A systolic pressure of 120 mmhg (0.016 MPa) was applied to the inner lumen surface. For the given mesh densities, the Von Mises stress concentrations at 120 mmhg indicate inhomogeneities in the artery with stress differences (approximately 14%) with the two mesh densities (Figure 26) studied. 55

56 (a) Figure 26: Von Mises stress of a 25mm length patient specific artery (with average calcification) at 120mmHg with varying mesh densities of (a) 2x32 and (b) 4x64. (b) 56

57 4.3 Combined Stent-Artery Models Several studies were conducted to establish settings to simulate the interaction between the stent and artery. The overall simulation for the interaction between the stent and the simplified artery was achieved using 2 successive simulations. The first simulation performed in Abaqus Implicit was used to crimp the stent into the artery. The second simulation was performed in Abaqus Explict and was used to deploy the stent into the artery. The stent was compressed radially inwards by 2.2 mm, from its initial diameter of 8.25 mm to 3.85 mm, so that it was just inside the lumen boundary (diameter = 4.0 mm), see Figure 27. The stent is oversized by 10%, and contact between the stent and inner surface of the arterial wall was defined. The Normal Behavior of the contact interaction property was set to the Default constraint enforcement method with Linear pressureoverclosure and a contact stiffness of In the explicit step, densities need to be classified for the materials properties. The nitinol material for the stent was assigned a density of 6.45 tonnes/mm 3. The artery material was assigned a density of 1.0 tonnes/mm 3 selected between the density of muscle (1.03E-08 tonnes/mm 3 ) and the density of fat (0.95E-08 tonnes/mm 3 ). 49 These densities are 10 8 times more dense than the actual material densities, which was done to give a reasonable increment size of ~10-5 for the simulation, since the mass of the stent is so low. Future work will involve using mass scaling features within Abaqus to accommodate the differences seen in the artery and stent materials. The stent was released to allow it to expand. The explicit simulation step was run for a time period of 10 seconds, results are displayed in Figure

58 (a) Figure 27: (a) initial state of stent and artery (b) final state of stent after radial compression of 2.2 mm. (b) 58

59 (a) (b) Figure 28: Stent and artery at (a) maximal expansion at 5 seconds and (b) 10 seconds. 59

60 A different model was used for each stage of the simulation because a single model cannot contain both the implicit and explicit steps. The first model runs the implicit compression of the stent and the second model runs the explicit expansion and interaction with the simplified artery. The explicit model is created by making a copy of the implicit model and making the following modifications: 7) The Restart attributes of the explicit model are modified to read data from the implicit job, giving the name of the compression step, and specifying to restart from the end of the step. 8) A density material behavior is added to each of the material definitions. NOTE: The material naming convention for properly calling nitinol material subroutines in explicit is: solid: ABQ_SUPER_ELASTIC_N3D shell: ABQ_SUPER_ELASTIC_N2D wire: ABQ_SUPER_ELASTIC_N1D This is not the case in implicit, which just requires that the name begins with ABQ_SUPER_ELASTIC. Therefore, the explicit naming convention can be used for both implicit and explicit. 9) The implicit step is deleted and an explicit step is created for the desired simulation time period. 10) A contact interaction is defined 11) The implicit compression boundary condition is deleted (allowing the stent to expand). 12) A Predefined Field is created for the stent from last frame of the compression 60

61 step of the implicit job. 13) A Full analysis job is created for the explicit model. The simulation was run in two stages: 1) implicit for stent compression, and then 2) explicit for expansion. This approach was adopted after attempting two other methods. Initially, a fully implicit approach was used, which had problems solving in the expansion phase, after contact was established between the stent and the artery. For the second attempt, a fully explicit approach was used, but the stent collapsed at the end of the compression step due to the high density required to get the simulation to solve in a reasonable amount of time Patient Specific Models Stent implantation into a patient specific artery was conducted, which includes both crimping the stent and expansion into the vessel. The boundary conditions and constraints for the model are shown in Figures 29 and 30. Both ends of the patient specific artery are fixed to the boundary plane on each end, but can translate in the z direction. The outer nodes of the artery are fixed angularly. 61

62 Figure 29: Patient specific model boundary conditions. Figure 30: Outer nodes fixed angularly through axial section to boundary plane. 62

63 Patient Specific Models with Low Calcium A patient specific artery representative of low calcium (0.1% dense calcium) was selected for the analysis. This analysis primarily focused on dense calcium plaque irregularities because it most likely had the greatest impact on stent fatigue performance. A set of 32 successive slices (giving 31 elements in z) was used to generate the 25 mm length artery mesh. The mesh density of the artery used for the analysis was 4x64, and a wire model with beam elements was used to model the stent. The maximum Von Mises stress of the stent was determined to be approximately MPa with a corresponding logarithmic strain of (Figure 31). 63

64 (a) (b) Figure 31: Stent deployed in patient specific artery representative of low calcium at (a) maximal expansion and (b) zoomed in on the stent region of high stress concentration. 64

65 Patient Specific Models with High Calcium Stent implantation into a patient specific artery representative of high calcium (44% dense calcium) was conducted for comparison to determine how a calcified environment impacts the stent. A set of 77 successive slices (giving 76 elements in z) were used to generate the 25mm length arterial mesh. The maximum Von Mises stress of the stent was found to be MPa, with a logarithmic strain of 8.48E-2 (Figure 32). In comparison to the model simulation for the patient with low calcium there was more than a 60% difference in strains observed on the stent, demonstrating the importance of accounting for patient specific anatomy and calcification morphology during stent development, design, and implantation. Anatomical environmental factors like large calcium regions or nodules do change the mechanical forces acting on the stent and determination of stent placement in a calcified artery maybe critical to achieve appropriate fixation and to minimize stent loading in vivo. The computational model shows a difference in stent performance for patients with varying calcification, but the magnitude of stresses can change depending on the mechanical properties chosen to represent the plaque morphology as well. Therefore it is critical to classify the artery mechanical properties, and perform more tissue mechanical testing on the diseased valve to provide a better representation of the artery compliance. 65

66 (a) (b) Figure 32: Stent deployed in patient specific artery representative of high calcium at (a) maximal expansion and (b) zoomed in on the stent region of high stress concentration. 66

67 The computational analysis provided a means for comparison, but as with any modeling it inherently had some limitations. The stent was designed to be deployed into a diseased anatomical environment which had varied geometry, contact interactions, and mechanical properties, yet the simulations provided only a simplified analysis of the boundary conditions. Stresses could be impacted in the model due to the influences of geometry such as artery lumen diameter size, as this would affect the loads during expansion of the stent. Additionally, some devices are deployed with a balloon, and the simulation does not attempt to model the balloon or represent the interactions of a balloon on the stent. The engineering approach taken can be improved by applying even more realistic in vivo conditions to the model such as fluid flow. To do this, it may be essential to study different imaging data such as CT (computed tomography) and MRI (magnetic resonance imaging) to reveal details about the diseased environment. This type of work could lead to knowledge about effects due to patient geometry, stent-tissue interfaces, boundary conditions, and other interactions. Future work involves computer model validation. One validation technique under consideration is to compare a stented artery from a patient with PAD under in vivo pressures to that same patient specific computer model under the same pressures and measuring the resulting diameters. 4.4 Stent Prediction One of the most promising treatment options for peripheral arterial disease is stenting, but stenting has had several clinical issues including incomplete or asymmetrically expansion, as well as stent failures. 10, 52, 53 Therefore, using the computer model to evaluate stent deployment and fatigue could be extremely beneficial for predicting patient outcomes. 67

68 The stent deployment simulations shown in sections and for patients with low and high calcium were stents made of nitinol (nickel-titanium alloy). Nitinol stents are ideal for a device used in the peripheral arteries because of the shape memory, superelastic, and kink resistance characteristics that allow the stent to conform to the vessel wall. Key design contributions include stent geometry, stent placement, and stent oversizing during deployment. The stent primary geometrical attributes are stent diameter, strut width, strut angle, and wall thickness. Stent over-sizing is an important issue because nitinol stents rely on a radial resistive force (RRF) and constant outward radial force (COF) to give adequate structural strength and ensure the calcification is pushed way from the center of the vessel, see Figure 33. Radial resistive force is the force generated by a stent when it expands from a smaller diameter towards a larger diameter. However, the constant outward force is defined as the force the stent exerts on the arterial wall when the stent is constrained by the arterial wall such that its diameter is less than the fully expanded stent diameter. 54, 55 The force balance between a stent and an artery can result in smaller strut angles after deployment. 68

69 Figure 33: Force vs. radial expansion curve demonstrating the beneficial radial resistive force and chronic outward force for nitinol stents. Stents can exert a gentle force in vivo as shown by the low chronic outward force, but provide large resistive forces when subjected to external crushing forces. The patient specific computational stent-artery simulation predicts maximum principle strains for the diametric expansion/contraction of the stent in vessel, which are indicators of fatigue life. The post processing simulation results show the peak stress and strain for the stent device and arterial wall (Figures 31 and 32). Plastic strains seen on the nitinol stent were compared against the maximum elongation of the stent material, which in-turn dictates mechanical failure. Nitinol is fully recoverable up to 6% strain and has a maximum elongation between 10 and 15%, see Figure 34 for the mechanical property stress strain response. However, stent manufactures need to account for a device safety factor, and typically like to see the stent strains be substantially <10%. Comparing the 69

70 material property strains to the patient specific simulation strain results provides valuable information about the device fatigue performance. The strains observed for the patient with low calcium (5%) would suggest good stent durability because the strains are under the recoverable strain for nitinol (~6%). However, the strain results obtained for the patient with high calcium (9%) could be problematic for implant device durability and could suggest mechanical failure because it is past the nitinol material recoverable strain and just below the final strain of the material (~10% ). There are many other critical issues when assessing the nitinol stent device fatigue besides the design and environment. For example, material processing and performance are interrelated and this is especially true for nitinol devices since it is very sensitive to its material processing. 56 Generally stents undergo a complicated manufacturing process flow. Shape-setting and electropolishing are two of the most important processes that can impact fatigue performance. 57 Shape setting is the process where the part takes its final shape and the metal mechanical properties are defined. While, electropolishing eliminates surface imperfections and removes the nickel oxide and hydrogen from the surface to provide a biocompatible and corrosion resistant TiO 2 layer. Crystallographic texture can also play an influential role in the mechanical properties of nitinol, and therefore affect fatigue performance. Robertson et al. investigated how geometry and heat treatment affect texture of nitinol. 58 Nitinol obtains its nonlinear and anisotropic mechanical properties from stress-induced martensite transformations. These transformations generate strains that affect the crystallographic orientations. 59 The FDA Guidelines recommends not only device stent testing be conducted, but also fatigue life analysis on 70

71 the material should be performed in order to establish the fatigue endurance limit and take into consideration the affect of material processing. 60 Figure 34: Typical uniaxial stress strain response for nitinol. Chapter 5: Clinical Relevance The patient specific artery and stent analysis demonstrates that there is adverse effects of calcification on stent fatigue. Future investigations to develop stents that function better in a calcified vessel using this computer modeling tool will be conducted. Additionally, there are many areas for improvement in the current model such as adding blood flow and applying more realistic loading boundary conditions that simulate daily activities. Currently, researchers are now using x-ray computer tomography and magnetic resonance angiography to evaluate causes of fractures 61, and this tool will help prevent future stent fractures by improving the design and selection process for stents. Future 71