Design and Simulation of a Magnesium Based Biodegradable Stent for Hemodialysis Application

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2 Design and Simulation of a Magnesium Based Biodegradable Stent for Hemodialysis Application A thesis submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in the School of Dynamic Systems of the College of Engineering & Applied Sciences by Chenhao Xu Bachelor of Science in Mechanical Engineering University of Washington Seattle, WA, 2012 July 2015 Committee Chair: Dr. Mark Schulz

3 Abstract Stents are widely used as blood vessel scaffolding in medical applications, e.g., coronary stents. Stents can provide early stage scaffolding, increase blood flow, and optimize hemodynamics. Stainless steel is the most popular material for conventional stents and it has excellent mechanical behavior. High yield stress and high ductility allow stainless steel stents to expand safely. On the down side, stainless steel stents remain in the body permanently and may cause complications or lead to occlusion of the vessel. Biodegradable stents that eventually dissolve and disappear from the body are being developed to overcome these shortcomings. However, biodegradable materials, such as a magnesium alloy, also have limitations. Magnesium based materials have lower mechanical strength and stiffness than stainless steel, and biodegradable stents lose strength as they dissolve. Thus the design of magnesium biodegradable stents is complicated and computational validation is needed to optimize their design. Computational analysis is a time-saving and low-cost approach to evaluate biodegradable stent designs before expensive manufacturing of the stent and experimental tests are performed. Computational analysis is able to examine the mechanical performance, predict potential problems, and guide stent optimization. In this thesis, two designs (Design #1 and #2) of magnesium stents were evaluated. A computational analysis using Abaqus software simulated the expansion and recoiling process for both designs. Stent design #1 expanded from 6.0 mm to 10.0 mm in the radial direction with a strut perimeter to lumen diameter ratio of Stent Design #2 has a strut perimeter to lumen diameter ratio of Stent Design #2 expanded to 76% of the expansion of Design #1 stent. The peak strain and stress values safely stayed under the upper limit of the stent material. Stent i

4 Design #1 was selected as a better structural design because of its larger expansion ratio and greater coverage of the struts in the stent which inhibits restenosis (tissue ingrowth). A number of stents were fabricated for in-vivo testing in a pig. A new application for stents proposed by medical collaborators is considered in this thesis. The application is biodegradable stenting for hemodialysis access. Our medical collaborators implanted stents into pigs for in-vivo verification of the design. The right and left symmetrical femoral blood vessels were used to evaluate the stents. One side was a control vessel with no stent, and the other side was a vessel that was stented. Computer tomography and ultrasound were used to record changes of the vessels and blood flow during weeks to months of testing. On average, the biodegradable stents increased the blood flow and retained a larger lumen diameter as compared to the non-stented vessels. Also, the majority of the stent dissolved within 1-2 months. In summary, in this study a biodegradable magnesium stent was designed, analyzed using computational simulation, and evaluated in a pig model. It is demonstrated that the stent Design #1 is a proper design for the hemodialysis access application. The stent meets the mechanical requirement, provides adequate medical function, and degrades at a proper rate. ii

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6 Acknowledgments It is an honor to have experience on scientific research and how to do academic research. I would like to express my sincere gratitude to my academic and research advisors, Dr. Mark J. Schulz and Dr. Zhangzhang Yin, by giving me the opportunity, guidance, and financial support for my master research in the graduate school of University of Cincinnati. Dr. Schulz s persistence on his work has become my best teacher for my behavior on the research, especially the difficult time when I felt discouraged. My future career will be benefited from him. Dr. Yin s rigorous working attitude is always a model in front of me to achieve each task and each step. His knowledge on medical science which was not his background on his career surprises me and motivates me confidence to keep moving forward. Dr. Prabir Roy-Chaudhury and Dr. Vesselin Shanov are specially needed to be thankful. Dr. Roy-Chaudhury leads the medical team and provides all the possible resources to advance the studies. His opinions and suggestions inspire the experiment. Dr. Shanov isn t just a professor but a generous gentleman and even a friend who often gives me encouragements. I would also like to thank the excellent surgeons and technicians, Dr. Yang Wang, Dr. Begona Campos-Naciff, Patricia (Tish) A. Poe, Michelle True, and Kati LaSance, for supporting and helping the research in the medical fields. Besides, I want to thank all my friends from the Nanoworld Laboratory for sharing the happiness together in and outside the campus. I felt very grateful to join the Nanoworld Lab directed by Dr. Schulz and Dr. Shanov. It s also such an honor for me to be involved in the Engineering Research Center for Revolutionizing Metallic Biomaterials (ERC-RMB) supported by National Science Foundation (NSF). They have been to great platforms which allow me to learn a new world, gain more experience, and meet iii

7 other faculties and students from different backgrounds. I am also appreciating to NIH and the University of Cincinnati for the generous financial support and UGS scholarships that provided a colorful foreign life for me and let me realize my own value after years of study. Finally, my deeply heartfelt thanks belong to my parents, grandparents, and my grand-uncle & grand-aunt for their unconditional love and great brief that supports me on my college studies and graduate research. I learned all my daily life tips from my grand-aunt. My parents on the other side of the Pacific Ocean loves me and think of me all the time even if I didn t realize that. Though my parents and I had contradictions during our talk sometimes, we all understood that it came from the deeply love. Recently, my grandpa passed away and I wasn t able to go back to see him. I hope this thesis will be a good way as my return for my parents (Mr. Lining Xu and Ms. Bingyi Huang), grandparents (Mr. Angju Han and Ms. Qi Huang), grand-uncle Mr. David Liu, and grand-aunt Mrs. Janne F. Liu. iv

8 Table of Contents Abstract... i Acknowledgments... iii Table of Contents... v List of Figures... vii List of Tables... xiii List of Equations... xiv 1. Background and Introduction Stent Category and Design Material and Form Geometry Classification Biodegradable Stent Advantages of Biodegradable Stent Material Type Stent Computational Analysis Stent Manufacturing Application and Project Goal Problem Statement Project Goal Stent Structure Design Design Requirement Structure of the Design #1 Stent Structure of the Design #2 Stent v

9 3. Design Simulation and Evaluation Mathematical Mechanics Material Properties Evaluation of the Design #1 Stent Expansion Analysis of the Design #1 Stent Recoiling Analysis of the Design #1 Stent Evaluation of the Design #2 Stent Stent Manufacturing Tubing Machining and Laser-cutting Electrolytic Polishing SEM (Scanning Electron Microscope) In Vivo Experiment and Validation Surgery CT scan Ultrasound Micro CT SEM Analysis Conclusion and Future Study Conclusion Future Study Reference Appendix Expansion Process of the Design #1 Stent Expansion Process of the Design #2 Stent vi

10 List of Figures Figure 1.1: The Cordis Crossflex stent made from tantalum... 2 Figure 1.2: A stent made from nitinol... 3 Figure 1.3: The Wallstent... 3 Figure 1.4: Medinol s NIR stent... 4 Figure 1.5: Stent structure classifications... 5 Figure 1.6: A typical example of coil stent... 5 Figure 1.7: A typical helical stent design... 6 Figure 1.8: Cook ZA self-expandable stent... 7 Figure 1.9: A typical structure of closed-cell designs... 8 Figure 1.10: The appearance of Palmaz Stent... 8 Figure 1.11: Abbott's self-expandable Xact Stent... 9 Figure 1.12: A typical structure of open-cell designs... 9 Figure 1.13: The self-expandable peak-to-peak IntraStent Figure 1.14: The peak-to-valley Premier Stent Figure 1.15: The Von Mises stress distributions of a Codix BX-Velocity stent Figure 1.16: Six different stents expanding simulations by Abaqus Figure 1.17: The entire system layout of the stent implantation in artery Figure 1.18: (a) the strain-stress curves of the artery and plaque, (b) the strain-stress curve of the balloon Figure 1.19: (a) the tilted stent after expansion by balloon, (b) the stress on the contact of the distal-end stent and artery Figure 1.20: The original stent structure design by Wu et al vii

11 Figure 1.21: The morphing procedure of shape changing Figure 1.22: The optimized geometry design Figure 1.23: The comparisons between (a) original and (b) optimized designs Figure 1.24: The location of the femoral artery and vein Figure 2.1: The 3-dimentional Design #1 stent model made in Solidworks, (a) the standard version of 6 peak-to-valley wavy units with 8 struts, (b) the alternative version of 4 peak-tovalley wavy units with 6 struts Figure 2.2: The complete 2-dimensional drawing of the Design #1 stent Figure 2.3: The Design #1 stent detailed drawing in 2-dimension (a) the major components of the stent structure, (b) the design details Figure 2.4: The bridge layout design, draft #A Figure 2.5: The bridge layout design, draft #B Figure 2.6: The bridge layout design, draft #C Figure 2.7: The bridge layout design, draft #D Figure 2.8: The Lekton Magic stent Figure 2.9: The stent model after wrapping into a tube in Solidworks Figure 2.10: The gap at the closure after wrapping in Solidworks Figure 2.11: The 3-dimentional Design #2 stent model made in Solidworks Figure 2.12: The complete 2-dimensional drawing of the Design #2 stent Figure 2.13: The design details of the Design #2 stent Figure 3.1: The true strain-true stress curve of AZ 31 alloy and other common stent materials. 41 Figure 3.2: The 2-struts stent model created in Solidworks Figure 3.3: The original stent model in Abaqus after importing from Solidworks viii

12 Figure 3.4: The meshed stent model with tetrahedron element Figure 3.5: An example of the function of virtual topology, combining unexpected boundaries 44 Figure 3.6: Stent model appearance after virtual topology and partition Figure 3.7: The stent model after complete meshing Figure 3.8: Stent expansion by radial displacement Figure 3.9: The real-time pressure data between the high-pressure balloon and the Design #1 stent. Data provided by Dr. Zhangzhang Yin Figure 3.10: The stent model after the load setting Figure 3.11: The expansion results of the Design #1 stent, (a) the strain distribution and (b) the stress distribution at diameter of 10.0 mm Figure 3.12: The selected region of the highest strain & stress of the Design #1 stent during expansion Figure 3.13: The growth of the equivalent plastic strain during the expansion in the selected region of the Design #1 stent Figure 3.14: The growth of the stress intensity during the expansion in the selected region of the Design #1 stent Figure 3.15: The design #1 stent failure test after over expansion Figure 3.16: The Design #1 stent plastic strain distribution at the diameter of 10 mm along the strut Figure 3.17: The stress comparisons of the single-arc and double-arc crown designs Figure 3.18: A fixed segmentation of the Design #1 stent before the recoiling analysis Figure 3.19: The recoiling results of the Design #1 stent, the radial displacement (a) before and (b) after the recoiling ix

13 Figure 3.20: The recoiling results of the Design #1 stent, the plastic strain distribution (a) before and (b) after the recoiling Figure 3.21: The recoiling results of the Design #1 stent, the stress distribution (a) before and (b) after the recoiling Figure 3.22: The recoiling results of the Design #1 stent, the radial stress Figure 3.23: The recoiling results of the Design #1 stent, stress comparisons of both crowns after recoiling Figure 3.24: The expansion results of the Design #2 stent, (a) the strain distribution and (b) the stress distribution at diameter of 13.8 mm Figure 3.25: The selected region of the highest strain & stress of the Design #2 stent during expansion Figure 3.26: The growth of the equivalent plastic strain during the expansion in the selected region of the Design #2 stent Figure 3.27: The growth of the stress intensity during the expansion in the selected region of the Design #2 stent Figure 4.1: The AZ31B-TP ingot Figure 4.2: The manufactured AZ31 tubes, (a) the top view, (b) the front view Figure 4.3: The manufactured Design #1 stents Figure 4.4: The schematic diagram of electropolishing Figure 4.5: The operating principle introduction of electropolishing Figure 4.6: A final processed Design #1 biodegradable stent Figure 4.7: Hitachi SEM (Scanning Electron Microscope) Figure 4.8: 50 times zoomed in Design #1 stent before electropolishing x

14 Figure 4.9: (a) 200 times zoomed in (b) 150 time zoomed in Design #1 stent before electropolishing Figure 4.10: 40 times zoomed in Design #1 stent after electropolishing Figure 4.11: (a) 200 times zoomed in (b) 120 time zoomed in Design #1 stent after electropolishing Figure 5.1: The comparisons of two AVFs with and without a stent Figure 5.2: An example of ultrasound image Figure 5.3: Pig #3 ultrasound data, diameter of the anastomosis Figure 5.4: Pig #3 ultrasound data, diameter of the outflow vein at 3 cm away from the anastomosis Figure 5.5: Pig #3 ultrasound data, volume flow in outflow vein Figure 5.6: Pig #3 micro CT image, the remaining of the Design #1 stent after 63 days of experiment Figure 5.7: Analysis of the degraded stent by SEM Figure A.1: Design #1, (a) the strain and (b) the stress distribution at diameter of 6.0 mm Figure A.2: Design #1, (a) the strain and (b) the stress distribution at diameter of 6.5 mm Figure A.3: Design #1, (a) the strain and (b) the stress distribution at diameter of 7.0 mm Figure A.4: Design #1, (a) the strain and (b) the stress distribution at diameter of 7.5 mm Figure A.5: Design #1, (a) the strain and (b) the stress distribution at diameter of 8.0 mm Figure A.6: Design #1, (a) the strain and (b) the stress distribution at diameter of 8.5 mm Figure A.7: Design #1, (a) the strain and (b) the stress distribution at diameter of 9.0 mm Figure A.8: Design #1, (a) the strain and (b) the stress distribution at diameter of 9.5 mm Figure A.9: Design #1, (a) the strain and (b) the stress distribution at diameter of 10.0 mm xi

15 Figure A.10: Design #2, (a) the strain and (b) the stress distribution at diameter of 8.18 mm Figure A.11: Design #2, (a) the strain and (b) the stress distribution at diameter of 8.9 mm Figure A.12: Design #2, (a) the strain and (b) the stress distribution at diameter of 9.6 mm Figure A.13: Design #2, (a) the strain and (b) the stress distribution at diameter of 10.3 mm Figure A.14: Design #2, (a) the strain and (b) the stress distribution at diameter of 11.0 mm Figure A.15: Design #2, (a) the strain and (b) the stress distribution at diameter of 11.7 mm Figure A.16: Design #2, (a) the strain and (b) the stress distribution at diameter of 12.4 mm Figure A.17: Design #2, (a) the strain and (b) the stress distribution at diameter of 13.1 mm Figure A.18: Design #2, (a) the strain and (b) the stress distribution at diameter of 13.8 mm xii

16 List of Tables Table 2.1: Components Design Details in the Design #1 Stent Table 2.2: Details of Design #2 Stent (unit: mm) Table 3.1: Mechanical Properties of AZ31B-TP Alloy Table 3.2: Design #1 Stent, the Highest Local Strain and Stress during the Expansion Table 3.3: Design #2 Stent, the Highest Strain and Stress during the Expansion Table 3.4: Comparisons of Both Designs Table 5.1: The Ultrasound Data on the Control Side of Pig # Table 5.2: The Ultrasound Data on the Stent Side of Pig # Table 5.3: The Degradation Rate of the Design #1 Stent Table 5.4: The Surface Elements Analysis of the Degraded Design #1 stent xiii

17 List of Equations Equation 1: Stent s Governing Equation Equation 2: Function of Acceleration Vector Equation 3: Function of Velocity Vector Equation 4: Deformation Gradient Tensor Equation 5: Cauchy-Green Tensor Equation 6: Green s Strain Tensor Equation 7: Cauchy-Green and Piola-Kirchoff Stress Tensor Relation Equation 8: Piola-Kirchoff Stress Tensor Equation 9: Strain Energy Function Equation 10: The First Invariant of Cauchy-Green Tensor Equation 11: Determinant of Deformation Gradient Tensor Equation 12: Engineering Stress to True Stress Equation 13: Engineering Strain to True Strain Equation 14: Stress Intensity Equation 15: Recoiling Ratio xiv

18 1.1. Stent Category and Design 1. Background and Introduction Stents are usually defined as small tubular structures that are implanted into a diseased region via a catheter [1]. Providing mechanical scaffolding of damaged blood vessels to restore lumen and flow conditions in these vessels is the function of stents. Cell structures of stents can support tissue and plaque against the vessel walls [2]. Recently developed stents may accumulate functions like drug delivery or treatment of bleeding esophageal varies. Clinical failures (crushing, removing, and restenosis) are the most typical and serious reasons for stent improvement [1]. According to Wholey and Finol, the stent crushing incidence is about 2% [2]. There are more than 100 types of stents available in the markets [1, 3]; coronary stents are the major variety. The 2002 Handbook of Coronary Stent includes 43 coronary stents or stent families [4, 5]. According to the survey by Stoeckel, stents can be categorized by engineering design aspects on the materials, form, fabrication methods, and geometry [3, 5] Material and Form Materials are directly associated to the stent operation methods, which distinguishes between balloon-expanding and self-expandable stents. The balloon-expanding stents that were firstly to be produced commercially are manufactured with a small diameter for implanting into blood vessels and then dilated with high pressure balloons [5]. The materials require plastic deformation capacity to allow stents substantially remaining in expanded shape through the balloon inflation and deflation. Minor recoiling caused by the elastic deforming portion is inevitable during the balloon pressure unload process [3]. Low yield stress providing large plastic deformation range and high Young s modulus for minimizing recoiling rate are features 1

19 of ideal balloon-expanding stents [1]. On the contrary, self-expandable stents are manufactured at expanded state and then compressed into a delivery system. These stents spring back to substantially original geometry when releasing at the target places [1]. Materials with low elastic modulus and high yield stress that give large elastic range are preferred for self-expandable stents [1]. Stainless steel, tantalum, martensitic nitinol, platinum iridium, polymers, niobium alloy, and cobalt alloy are common materials of balloon-expanding stents while materials of selfexpandable stents usually include nitinol (nickel-titanium), cobalt alloy, and stainless steel [3]. Stainless steel 316L, the most popular material in the stent industry, is a typical corrosionresistant material [6]. Stainless steel 316L is often considered as gold standard for biomaterials in stent applications [7]. A fully annealed stainless steel provides great deformation performance in the stent expansion and crimping. Alternative balloon-expanding stent materials with high strength, large corrosion resistance and radiopacity like tantalum, platinum alloys, niobium alloys, and cobalt alloys allow a smaller size and delivery system [3]. Figure 1.1 is a tantalum made stent [8]. Figure 1.1: The Cordis Crossflex stent made from tantalum (figure provided by Medical Product, Still Life & Catalog - Product & Catalog - Geoff Reed Phoenix Arizona portrait photography. (n.d.). Retrieved July 14, 2015, from 2

20 Large elastic strain range is essential for materials for self-expandable stent manufacturing. Nitinol, a type of alloy made from nickel and titanium, is the most popular material used in selfexpandable stents [3]. Nitinol has elastic deformation up to 10% [3]. Figure 1.2 is a nitinol stent made by InSitu Technology Inc [9]. The large elastic range (commonly known as super elasticity) of nitinol is the result of thermo-elastic martensitic transformation [3]. Other ordinary materials like stainless steel (e.g. Cook Medical s Zilver Biliary Stent) and cobalt based alloys (e.g. Boston Scienific s Wallstent [10], Figure 1.3) have limited elastic range which needs to be considered in stent geometric design [3]. Figure 1.2: A stent made from nitinol (figure provided by Peripheral stent/nitinol/self-expanding - XOLO&trade - InSitu Technologies. (n.d.). Retrieved July 14, 2015, from Figure 1.3: The Wallstent (figure provided by WALLSTENT TM Endoprosthesis Boston Scientific. (n.d.). Retrieved July 14, 2015, from US/products/stents--vascular/wallstentendoprosthesis.html) A stent can be made from tube, wire, sheet, and ribbon [3]. Tube and wire with either round or flat cross sections are the majority [3]. Stents made from pieces of metal sheets need to be rolled to be a tubular configuration for welding or mechanical locking feature later on [3]. Figure 1.4 is an example of Medinol s NIR stent [11]. 3

21 Figure 1.4: Medinol s NIR stent (figure provided by OLYMPUS: The collaboration with Medinol, the release announcement of the biliary metallic stent, X-Suit NIR (n.d.). Retrieved July 14, 2015, from Geometry Classification Early stents designs were either coils or slotted tubes [3]. Slotted tubes have excellent radial strength but lack of flexibility while coil designs are the other way around [3]. For years, a variety of complex designs competed for the crowded market, all of them seeking a balance between strength and flexibility. Based on the design geometries, Stoeckel et al categorized stents into 5 classes (Figure 1.5), coil, helical spiral, woven, individual rings, and sequential rings which are divided into categories of closed and open cell design [3]. 4

22 Coil Helical Spiral Woven Individual Rings Sequential Rings Closed Cell Open Cell Flex Connection Non-flex Connection Combined Peak-to- Peak Peak-to- Valley Midstrut-to- Midstrut Figure 1.5: Stent structure classifications i. Coil Coil designs are commonly used in applications of non-vascular field [3]. A coil stent is retrievable after the placement. Coil stents are very flexible with low strength and expansion ratio. Figure 1.6 shows a typical structure of a coil stent. Figure 1.6: A typical example of coil stent 5

23 ii. Helical Spiral Helical designs have great flexibility while having minimal internal connections [3]. Low longitudinal strength is the shortcoming of the helical structures. These stents with irregular cell geometries yield to elongation or compression during delivery and deployment [3]. The flexibility and longitudinal strength are in inverse proportion. With the internal connections increasing, the flexibility is decreased [3]. Figures 1.7 is an example of a regular helical stent [12]. Figure 1.7: A typical helical stent design (figure provided by Micro and Nano Structuring with Lasers - Fraunhofer ILT. (n.d.). Retrieved July 14, 2015, from iii. Woven Woven stents contain a large design family with multiple wires. Self-expandable structures often use woven designs, such as the Boston Scientific WallStent, as shown in Figure 1.3. Stent length shrink during expansion is one of the main drawbacks. Radial strength is also dependent on the designs [3]. The following Figure 1.8 shows a Cook ZA self-expandable stent made from knitted nitinol wire [13]. 6

24 Figure 1.8: Cook ZA self-expandable stent (figure provided by Colonic Z-Stent. (n.d.). Retrieved July 14, 2015, from iv. Individual Rings Similar to coil stents, stents with individual-rings design are also not commonly used in vascular field. Supporting grafts is a typical application for a Z-shaped wave ring stent [3]. These stents can be either sutured or attached to a graft [3]. v. Sequential Rings Sequential-ring designs own the largest commercial stent market share. These stents are usually comprised of multiple wave-shaped struts and connecting bridges among struts. According to the connection manners of struts and bridges, there are three types Regular Connection: bridges connect to every inflection point on the struts [3] Periodic Connection: bridges connect to inflection points in each group set [3] Peak-to-Peak or Peak-to-Valley Connection: bridges connect to two corresponding inflection points, each from the wave or Z shaped adjacent struts outer peak curve or from the wave or Z shaped adjacent struts outer peak curve and inner valley curve [3] Based on stent cell structure, sequential-ring stents are generally divided into 2 categories, closed cell and open cell structures. 7

25 A. Closed Cell A closed cell structure is that all internal points of changing direction are connected by bridges (Figure 1.9). It is introduced in 1995 for a carotid artery application [2]. Peak-to-peak bridge connection design is a typical form. Strength and flexibility are dependent on the specific structures. Slotted-tube designs with straight bridges like Palmaz Stent [14] (Figure 1.10) are strong but not flexible; the U and S -shaped bridge types [15] (Figure 1.11) allow better plastic deforming performance on the relative movements of adjacent parts during expansion and bending. One significant advantage of a closed-cell stent is the strength, which on the other hand results in inflexibility, a drawback of closed-cell structure [3]. Figure 1.9: A typical structure of closed-cell designs Figure 1.10: The appearance of Palmaz Stent (figure provided by PALMAZSCHATZ Balloon-Expandable Stent. (n.d.). Retrieved July 14, 2015, from 8

26 Figure 1.11: Abbott's self-expandable Xact Stent (figure provided by Carotid Artery Stent Reduces Plaque Release. (n.d.). Retrieved July 14, 2015, from B. Open Cell An open cell structure is that part or all of the internal points of changing direction are not connected by any bridges (Figure 1.12). Peak-to-peak, peak-to-valley, and mid-strut to midstrut connections or combination of the three are the conventional forms of open-cell designs [3]. The shift-free segments are the reason of that an open-cell structure has better longitudinal flexibility than any closed-cell stent. The self-expandable IntraStent in Figure 1.13 is a peak-to-peak design with periodical connections [16]. In addition, a peak-to-valley pattern (Figure 1.14), such as the Premier Stent, reduces the length shrink and insures the alignments of the adjacent peaks in longitudinal direction [17]. The peak-to-valley types, however, occupy material that could be used for struts, major body of a stent. The sequential outcome is that a peak-to-valley structure is not as strong as the similar structured peak-topeak design [3]. Figure 1.12: A typical structure of open-cell designs 9

27 Figure 1.13: The self-expandable peak-to-peak IntraStent (figure provided by International Peripheral Products, IntraStent LD Family of Unmounted Stents. (n.d.). Retrieved July 14, 2015, from Figure 1.14: The peak-to-valley Premier Stent (figure provided by First Worldwide Implants of the Next-generation Promus PREMIERTM Everolimus-Eluting PtCr Coronary Stent System. (n.d.). Retrieved July 14, 2015, from 10

28 1.2. Biodegradable Stent Angioplasty is a surgical procedure originally created by Dr. Andreas Gruentzig in the 1977 [5, 18]. An inflatable small balloon was used to dilate the blood vessel blockage [5]. The method is called Percutaneous Transluminal Coronary Angioplasty (PTCA), which was a major breakthrough but lead to restenosis [7]. Restenosis is defined as blood vessel healing response after injury and caused by a local vessel s biologic response to the injury [7]. Ultrasound indicates that recoiling is a main reason for restenosis after PTCA [19]. In 1988, Dr. Julio Palmaz introduced the concept of stent to improve the angioplasty [5]. The mechanical scaffolding from stents alleviates the vessel recoil and reduced restenosis [7]. At the same time, due to the long-term pressure from the vessel wall to the stent, neointimal hyperplasia has become a newly created problem resulting in luminal narrowing, i.e. in-stent restenosis. The common solution for in-stent restenosis is using stents eluted with drugs. However, the shortcoming of the drug coated stents, high rate of late thrombosis and restenosis comparing to bare metal stents, is also remarkable [20]. Since the function of stents is not a long-term sustained requirement in many situations, a temporary stent that can last until the healing is considerable. Biodegradable stents made from polymer, iron, and magnesium alloys have been tested as alternative stents materials [7] Advantages of Biodegradable Stent Metal biodegradable stents combine advantages of degradation potentiality, strength, and flexibility from both stainless steel stents and biodegradable polymer stents. Biodegradable materials and biodegradable stents are an emerging field since the first patent metallic stent which is degradable in vivo in 2002 by Heublein [21]. Iron-based and magnesium-based alloys 11

29 have been the only two varieties being proposed and tested so far [21 24]. There are several advantages of biodegradable stents. Similar to conventional stents that remain in bodies permanently, degradable stents could provide the early stage scaffolding in the target blood vessel to increase its diameter for better blood flow. Biodegradable stents could act as a conduit for the temporary blood vessel remodeling and inhibiting neointimal hyperplasia, which lowers patients anxiety for the late thrombosis from conventional stents [7]. In addition, this kind of stents will dissolve and disappear in certain period of time so that can have higher loading of drug capacity and avoid long-term usage of anti-platelet agents [7] Material Type i. Iron Based Stent Iron is a proper biodegradable material candidate for stents due to its mechanical features. It has a high Young s modulus, which can translate to large radial strength when made into stents [6]. Iron also has a high ductility that supports plastic deformation of a stent [25]. ARMCO is the first company who built the biodegradable stents with high purity of iron, which was tested in the arteries of white rabbits for 18 months in New Zealand, 2001 [6, 22]. Irons, ferric and ferrous are essential elements for human bodies, but the excess of quantity could be toxic [26]. The results of the first iron stent implantation didn t show significant inflammatory issues and neointimal hyperplasia [6]. The examination of organs indicated non-toxicity [6]. However, the ARMCO stents did not dissolve completely during the degradation period; therefore, faster degradation rate is needed [6, 22]. One experiment for safety study lasting 360 days was performed in 2006 with a corrodible iron made peripheral stent, which was inserted into a mini-pig s artery [6, 27]. A SS 316L made stent was also implanted as reference. Regarding to the neointimal hyperplasia, there is no big difference of 12

30 these two stents. Another trial was performed with an iron stent implanted into the coronary artery of a pig [23]. The iron stent began to show the sign degradation without big stent particles and causing inflammation [6]. Stent particles or pieces are critical during degradation time. Because of the short experiment period limitation, there was no conclusion about the degradation rate [6]. ii. Magnesium Based Stent Magnesium which has low thrombogenicity and outstanding biocompatibility is another wellknown material [6]. Magnesium has lots of attractive facts as for a stent material choice. Magnesium is a basic element of tissue and organism. Magnesium ions are involved in over 300 bio-reactions in bodies [6, 28]. Magnesium is a biological trace element with a high toxic tolerance of 7 10 mmol in every liter of serum [6]. Magnesium is considered as an anti-carcinogenic element [6, 29]. On the other hand, High degradation rate of magnesium materials could be a disadvantage. Rapids dissolving rate with the overload degradation products could cause neointimal formation [6]. Also, the mechanical property of stent is related to the degradation rate. Large amount of mass loss in short period influences the stent strength. In order to reduce the degradation rate and increase strength, magnesium is usually alloyed with aluminum, manganese, and rear earth [6, 30]. However, the accumulation of aluminum and manganese in cells are the possible cause of the Parkinson's disease. In the history, the first magnesium material application was used as Mg wire to stop bleeding vessels by Huse in 1878 [6, 28]. In 20th century, magnesium as a biodegradable material was utilized in connections of vessel anastomosis [6, 31]. Magnesium based cardiovascular stents made by AE21 was firstly imported by Heublein et al for animal 13

31 study [21, 32]. Numbers of pigs were tested for 10, 35, and 56 days [6]. Histology results indicated that AE21 magnesium stents induced neointimal response [6]. The stents also degraded faster than expected and started to lose mechanical strength after 35 days [6]. All the investigation and experiments in the past resulted in a new generation of biodegradable stent from Biotronik, called Lekton Magic stent [6, 21]. The 33 mini-pigs experiments inserted WE43 made magnesium biodegradable stents were reported by Di Mario et al [6, 33]. Also, Peeters et al made report about the first 20 patients clinical trials of the Lekton Magic stents on treatment of low limb ischemia [6, 24]. No toxic issues and other allergic response were shown in the results [6]. However, these stents didn t retain their efficacy in long-term testing. Zartner et al successfully implanted the first biodegradable stent in human bodies [6, 34]. In the next 5 months degradation period, the stent disappeared completely without neoinitimal growth [6]. Waksman et al in 2006 did more tests in pigs for period 3 months [35]. Results like no evidence of stent particles, thrombosis, and less neointima were obtained [6]. In 2007, 71 WE43 made magnesium stents implanted into 63 patients [36]. Angiography showed an increased diameter stenosis of 17% [6]. Neointimal hyperplasia and negative remodeling were the major factors of restenosis [6]. In summary, bioabsorbable magnesium stents can achieve an angiographic result immediately, reduce neointima, and degrade safely in limited time [6]. 14

32 1.3. Stent Computational Analysis In general, two basic approaches are used to determine the theoretical mechanical properties of a stent. The first one is the routine method, structural mechanics. Bernoulli-Euler beam theory, Hook s Law, and Coulomb torsion theory could be applied in simple structured stent, such as woven wire stents that have easy and repeated structures [1, 37]. Numerical method is the second solution. Finite Element Method/Analysis (FEM/FEA) is the most popular choice. FEM can identify both linear and nonlinear mechanical properties of stents during expansion, blood vessels, blood flow, and the interactions (balloon-stent, stent-vessel, balloon-vessel), which routine methods cannot predict [1, 38]. The popularity and importance of FEM is increasing due to the growth of processing capacity and software. FEM has become a useful method in the designs of new stents. FEM stent analysis studies have been published recently. Kwek, Gervaso, and Raamachandran reported balloon-stent analysis [38, 39]. For example, Figure 1.15 shows Von Mises stress distributions of a Codix BX-Velocity stent under alternative situations by Gervaso [40, 41]. These are partial expansion tests. Strain and stress have uneven distribution. Figure 1.15: The Von Mises stress distributions of a Codix BX-Velocity stent (figure provided by Computational Modeling of Stents in Arteries. (n.d.). Retrieved July 14, 2015, from 15

33 Raamachandran used Abaqus to study six different stent designs, as shown in Figure 1.16 [41]. Stent material was stainless steel 316L whose elastic modulus is 201 GPa, Poison s ratio 0.3, and yield stress 170 MPa [41]. A balloon-stent system expansion procedure was simulated by FEA. According to the figure, the balloon was being focused. The balloon was modified as a cylinder which diameter was 1.24 mm with the thickness of 0.02 mm [41]. In the process, the internal balloon pressure increased from 0 to 0.16 MPa in 30 ms; and remained constant from 30 ms to 50 ms [41]. Also, the contact between the stent and balloon was made using the finite sliding surface-to-surface contact [41]. Figure 1.16: Six different stents expanding simulations by Abaqus (figure provided by Computational Modeling of Stents in Arteries. (n.d.). Retrieved July 14, 2015, from Berry and Liang reported stent-artery analysis [38, 42]. The FEA simulated 2 steps of the stent implantation, balloon inflation and deflation. The results showed that the distal end of the stent could tilt and may damage the vessel wall [38]. Figure 1.17 shows the entire system of the stent implantation in artery [38]. 16

34 Figure 1.17: The entire system layout of the stent implantation in artery (figure provided by Liang DK, Yang DZ, Qi M, Wang WQ. Finite element analysis of the implantation of a balloon-expandable stent in a stenosed artery. International Journal of Cardiology 2005; 104: ) The stent was also made from SS 316L. The simulation was analyzed by Ansys. In the mesh, four types of elements were applied to four objects with different meshing thickness [38]. The mechanical properties of the plaque, artery, and balloon were also known. Figure 1.18 displays the strain-stress curves [38]. ( a ) ( b ) Figure 1.18: (a) the strain-stress curves of the artery and plaque, (b) the strainstress curve of the balloon (figure provided by Liang DK, Yang DZ, Qi M, Wang WQ. Finite element analysis of the implantation of a balloon-expandable stent in a stenosed artery. International Journal of Cardiology 2005; 104: ) In the analysis, the balloon was applied a pressure at 15 atm and the lumen of artery opened from 1.5 mm to 3.5 mm [38]. The stent cross-sectional diameter recoiled from 3.5 mm to 3.07 mm 17

35 [38]. The results are shown in Figure Because the stent was longer than the plaque, the distal end of the stent tilted after expansion as shown in Figure 1.19a [38]. The stress of the end of the stent contacted the artery wall was MPa while the surroundings had only MPa which indicated the stent pinch the wall as shown in Figure 1.19b [38]. (a) (b) Figure 1.19: (a) the tilted stent after expansion by balloon, (b) the stress on the contact of the distal-end stent and artery (figure provided by Liang DK, Yang DZ, Qi M, Wang WQ. Finite element analysis of the implantation of a balloon-expandable stent in a stenosed artery. International Journal of Cardiology 2005; 104: ) Besides, FEM simplifies the process of stent structure optimization. Stent geometry optimization is a difficult task in the following respects i. A series of same geometric models are needed for repeated meshing and modeling process [43, 44] ii. Parametric model optimization process transports among different software causing interactions on data [43, 44] iii. Convergence failure needs to be avoided [43, 44] According to Wu et al, different shapes of possible optimized designs were simulated by applying the morphing procedure in FEA [44]. Multiple times of minor geometry shifts lead to heavy calculations if using structural mechanics by equations. The FEM software shortens the time and simplifies the difficulty. The original stent structure is shown in Figure 1.20 [44]. 18

36 Figure 1.20: The original stent structure design by Wu et al (figure provided by Wu W, Petrini L, Gastaldi D, Villa T, Vedani M. Finite element shape optimization for biodegradable magnesium alloy stents. Ann. Biomed. Eng. 2010; 38(9): ) The morphing procedure is the process that nodes at the edges were commanded to have minor shifts to change the shape [44]. Figure 1.21 demonstrates four different types of shape changing [44]. Figure 1.21: The morphing procedure of shape changing (figure provided by Wu W, Petrini L, Gastaldi D, Villa T, Vedani M. Finite element shape optimization for biodegradable magnesium alloy stents. Ann. Biomed. Eng. 2010; 38(9): ) 19

37 Each of the shape change needed the FEA validation. In the end, the best one became the optimization design. Figure 1.22 shows the finalized detail design and Figure 1.23 shows the FEA validation result [44]. After the optimization, the highest strain of a AZ31 stent dropped from to 0.116; the highest strain of a AZ80 made stents dropped from to 0.104; and the highest strain of a AM21 made stent dropped from to [44]. Figure 1.22: The optimized geometry design (figure provided by Wu W, Petrini L, Gastaldi D, Villa T, Vedani M. Finite element shape optimization for biodegradable magnesium alloy stents. Ann. Biomed. Eng. 2010; 38(9): ) Figure 1.23: The comparisons between (a) original and (b) optimized designs (figure provided by Wu W, Petrini L, Gastaldi D, Villa T, Vedani M. Finite element shape optimization for biodegradable magnesium alloy stents. Ann. Biomed. Eng. 2010; 38(9): ) 20

38 1.4. Stent Manufacturing In the current market, most implant metallic stents are manufactured by casting and thermomechanical treatment [45]. In general, the stents fabrication process follows these steps, casting of metallic ingot, thermo-mechanical treatment, mini-tube drawing, laser cutting, annealing and acid pickling, and electropolishing [6]. The metal ingot can be cast directly into either the target shape or an intermediate geometry for other subsequent forming processes. Casting is usually a preferred method by factories to form metal components because subsequent procedures including forming, extruding, annealing, and joining can add to the cost [6]. Thus, casting is considered as the primary fabrication process, other forming and thermo-mechanical processes are usually preferred to achieve a desire shape and mechanical properties [46]. Tubing manufacturing such as welded-redrawn and seamless form is the next step. The seamless technology is preferred because the welding method cannot guarantee avoiding localized microcontamination and segregation even though the modern welding equipment has improved [6]. The third step is the drawing process, which is required to guarantee repeatable properties for the tube [6]. Different materials have different sensitivity to parameters. Laser cutting as the continuous step provides a digitally controlled precise cutting procedure which allows larger stent structure flexibility [6]. Annealing after laser cutting is able to improve mechanical properties. During annealing temperature is raised slowly and remains for certain amount of time. The metal then cools down at an appropriate rate. It can reduce the hardness and refine the grain size on the metal surface. Electropolishing is the last step. Electropolishing removes burrs and mechanical defects from all of the previous procedures [47]. Geometry readjustment can also be achieved by electropolishing. 21

39 1.5. Application and Project Goal Problem Statement In the United States, about 350,000 patients receive the hemodialysis treatment each year. Hemodialysis is a procedure of purifying the blood in patients who have kidney failure [48]. Patients undergo hemodialysis 3 times per week which involves vascular access by using a needle and tube temporarily passing their blood through a dialysis machine for purifying and then back into the patients. There are 3 major dialysis forms, the arteriovenous (AV) fistula, polytetrafluoroethylene (PTFE) dialysis access graft, and tunneled dialysis catheter. Unfortunately, complications accompany with all these 3 methods. Specially, both PTFE grafts and catheters have high rates of infection and thrombosis [49, 50]. Only fistula is usually considered the best type of vascular access because of its relatively low rate of stenosis, thrombosis and infection [51 53]. However, a newly created fistula s maturation period is about 6-12 weeks before the hemodialysis. During the maturation, the connected artery and vein dilate and remodel to increase blood volume flow, which is the result of creating the AV anastomosis [54 57]. A fully matured AV fistula (AVF) is also the best dialysis type so far with the consideration of the cost and patient survival rate [58]. While AV fistula is the primary choice of dialysis, its non-maturation situation remains as a non-ignorable problem. Data from a NIH funded multi-center clinical trial claims that more than 60% of AVF are not suitable for dialysis between 4-5 months after surgery [59, 60]. The combination of the increased dependence on catheters during fistula maturation and surgical interventions for non-matured fistula have all ended with hemodialysis vascular access dysfunction, perhaps the most important factor of morbidity and hospitalization in the hemodialysis population with an annual cost of over 1 billion dollars [61, 62]. 22

40 Project Goal Although the arteriovenous (AV) fistula is the best vascular access form of hemodialysis, about half of AV fistulas fail to mature later on, which even becomes the weak link of the hemodialysis. However, currently there are no effective therapeutic interventions for AVF maturation failure. Conventional stents last in blood vessels permanently and very possibly excite aggressive instent restenosis leading to the situation of blood flow limitation that reduces the maturation rate. A magnesium based biodegradable stent could improve hemodynamics optimization and provide the early stage scaffolding at the targeted blood vessel to increase its diameter for large amount of blood flow in the first 4 to 8 weeks, the critical maturation period. The biodegradable material is able to protect against the downsides of the long-term presence of a foreign body, such as instent stenosis [63]. In the end, the stent will disappear after the AVF matures. One possible approach to raise the AVF maturation success rate is that implanting a biodegradable stent during the AV fistula surgery will maintain the fistula open and enhance the maturation. In addition, this approach could also be applied for enlarging small arteries and veins for ease of AV fistula creations. However, lower mechanical performance is a major disadvantage of magnesium-based materials. Unlike stainless steel 316L, a typical and gold standard conventional-stent material, magnesium alloy AZ31 has low yield point, ultimate tensile strength, and ductility [6], which only allows minor deformation in each stent segment during the expansion process. Stents made from stainless steel undergo large local strain about during the expansion [64], while AZ31 s elongation is below 0.2 [44]. In order to expand to a similar diameter range, AZ31 made stents require a lot more components to deform while SS316L based stents only count on a few large local deformations. The elastic modulus of AZ31 is about ¼ of the stainless steel, which requires 23

41 more material for providing adequate scaffolding. On the other hand, more material sometimes increases the strain during expansion. Overall, an appropriate stent design is the foundation of the entire project. Due to the material limitations on mechanical properties, finite element method (FEM) is an essential tool to study and guide the stent design [40, 65]. Dumoulin and Cochelin firstly used FEM to study the mechanical behavior of stents during and after implantation [66]. Results of expansion, recoil, and fatigue life of balloon-expanding stents are reported [5]. Etave et al performed finite element analysis (FEA) studies that illustrate the main mechanical characteristics of stents [5, 67]. In the study, two stent designs were analyzed by FEM and the FEA concentrates on both designs expansions and recoiling processes. The simulation results demonstrate the strengths and weakness of both designs. According to the simulation and the specific stent application, one of the designs has been fabricated and tested in vivo experiment. The procedures of the stent manufacture include 3 major steps: tube manufacturing, laser cutting, and post processing. The AVF maturation and stent degradation were studied by CT scan, ultra sound, and micro CT during in vivo experiment in which experimental subject was pig. The AV fistula was created at the femoral artery and vein (Figure 1.24) and the arteriovenous (AV) anastomosis was the intersection of the femoral artery and vein [68]. In Figure 1.24, the two identical femoral artery and vein systems located on two sides of the pig were used for comparative experiments. The pig s right side was implanted a biodegradable stent while the left was the control side without a stent. The long-term experiment has been tested for 63 days. CT scan and ultrasound were used to observe the artery and vein geometries and blood flow amount weekly. In the end of the experiments (after pig sacrifice), micro CT and SEM have also been processed for studying stent degradation. 24

42 Figure 1.24: The location of the femoral artery and vein (figure provided by Ultimate Fetal Pig Anatomy Review. (n.d.). Retrieved March 14, 2015, from 25

43 2.1. Design Requirement 2. Stent Structure Design There are many factors influencing the stent design, such as stent application, material, operation method, structure, and expansion ratio. The AV fistula application requires the stent placed in the outflow vein. Due to the brittleness of magnesium alloys, features of low yield stress and small elastic region are the characteristics of balloon-expanding stents. Besides, veins have thinner vessel walls and larger lumen diameter than arteries. The less elasticity caused by the thinner walls provide less capacity for expanding. The larger lumen diameter allows inserting a bigger stent. As a result, the AVF stent shall have small expanding ratio. Furthermore, the stent structure is the most important design factor. According to the features of different stent classifications, the sequential-ring design provides the most balanced characteristics to meet the requirement of AVF stent. Open-cell structure has been further selected because the open-cell structure has better longitudinal flexibility, larger design freedom for details such as peak-topeak or peak-to-valley structure, and smaller length shrink than closed-cell stents. The radial strength could be the only shortcoming. Ideally, the stent remains the expansion state for at least 2-4 weeks while degrading and then dissolves quickly without breaking off leaving big particles in the blood flow. The degradation rate mainly depends on the material. The AVF stents are made of magnesium based AZ31 alloys at present. For a degradable stent, a perfect degradation process is always preferred. A perfect degradation is the process that each segment of the stent degrades at the same rate from the implantation to the fully disappearance. In practice, it is difficult avoiding large material particles during the degradation process. Blood circulation continues in human bodies. Blood with oxygen after pulmonary exchange is pumped by heart to flow through arteries to capillaries. Blood after 26

44 metabolism flows back to the heart through veins and then is pumped again into lungs. If a stent were fractured, metal pieces could access to the heart and lungs, which might cause other huge adverse effects. That s why a perfect degradation process is expected. Mechanical property is the key feature of any stent. Conventional stents usually undergo uneven strain distribution because material such as stainless steel 316L allows large local deformation. The peak strain value can reach 0.5 [44]. In order to expand to the targeted value, cardiovascular stents are able to rely on deformations from only a few periodic structures. On the contrary, biodegradable stents need to form a low concentration ratio of strain distribution as the primary goal due to the low ductility of AZ31. From the design perspective, each portion of the stent would better share the deformation to reduce the stress concentration level so that the stent can enable large geometry change with acceptable strain value at each partial unit. Two designs were proposed in the past, named here Design #1 and Design #2. Design #1 was made for the typical femoral vein AVF access and Design #2 was designed for jugular vein with large diameter Structure of the Design #1 Stent The CAD model of the Design #1 biodegradable stent shown in Figure 2.1 was completed in Soildworks. The major structure is a peak-to-valley type, which has smaller cell size than that of a peak-to-peak type. Based on the opinion of the clinician (Dr. Yang Wang), a relative small cell size is preferred in clinical setting for preventing thrombosis tissue. 27

45 ( a ) ( b ) Figure 2.1: The 3-dimentional Design #1 stent model made in Solidworks, (a) the standard version of 6 peak-to-valley wavy units with 8 struts, (b) the alternative version of 4 peak-to-valley wavy units with 6 struts The Design #1 stent has 8 transverse struts connected by vertical straight bridges. In each strut, there are 6 peak-to-valley units in circular directions (Figure 2.2). The outer and inner manufacture diameters of the stent are 6.0 mm and 5.2 mm, which give the strut thickness of 0.4 mm. Design #1 has the length of 26.7 mm and its strut surface width is 0.3 mm. The preferred expansion geometry is 10.0 mm. Based on the experiment requirements and clinician preference, the stents can also customize to alternative length and diameter. For example, 20 mm long stents with 6 struts and 4 peak-to-valley units are the most commonly used in pig in vivo surgeries (Figure 2.1b). 28

46 Figure 2.2: The complete 2-dimensional drawing of the Design #1 stent Experience from literature surveys and experiment data indicate that sharp curves and/or corners are not recommended in the biodegradable-material stent because extreme stress and strain always gather at these positions. On the other hand, sharp curves/corners indeed bring benefits on geometry size. Sharp-curve design could save space on circumferential surface which is directly related on stent s original diameter and ease of implantation. Coincidentally, veins have larger lumen volume than arties. Stents with low curvature struts design can be established. 29

47 (a) (b) Figure 2.3: The Design #1 stent detailed drawing in 2dimension (a) the major components of the stent structure, (b) the design details Table 2.1: Components Design Details in the Design #1 Stent Strut Crown Height Width Doublearc radius Singlearc radius 3.4 mm 0.3 mm 0.8 mm π/8 arc 1.5 mm 0.13π arc Bar arm Length of Arc straight radius bar 1.1 mm 0.94 mm π/8 arc Bridge Height Width 3.0 mm 0.3 mm Figure 2.3a is a zoomed in picture showing details of the peak-to-valley unit. The Design #1 stent consists of 3 elements, crown, bar arm, and bridge. Crowns and bar arms are the elements of periodical peak-to-valley unit. Figure 2.3b provides detailed design parameters which are listed in Table 2.1 as well. The peak-to-valley unit is about 2.5 mm in height and 3.14 mm in length. The space of adjacent struts is 3.4 mm away from each other. All bridges have the length of 3 mm and the same width of 0.3 mm as the struts. Most conventional stents simulation results show that extreme stress and strain accumulate at the crown. Instead of sharp corners that are used in permanent stents, low curvature struts with large 30

48 radius at the crowns are applied in the Design #1 stent. Low curvature struts usually occupy more space on stent s 2D expansion drawing. Besides, in the case of multiple-curve combinations, the common tangent connection would require extra space on circumferential surface. Both situations will be resulted in exceeded diameter value of a crimped stent. A nontangent connection type between the crown and the bar arms are utilized. Though a non-tangent connection is considered as a sharp corner, this kind of connection located near edge of the crown and promoting circumferential space saving is a win-win situation. In order to improve the corner edge and reduce the sharpness as much as possible, the fillet transitions with outer radius of 0.5 mm and inner radius of 0.2 mm are introduced. In addition, as shown in Figure 2.3b, there are two geometry designs at the crown. The double-arc design has a radian of π/8 with a radius of 0.8 mm. The single-arc has the radian of 0.13 with 1.5 mm radius. Two reasons were made for alternative crown designs: The double-arc crown on the top of the bridge and the single-arc crown at the bottom of the bridge form a Y structure which could strengthen the structure. Simulation result can help evaluate these two alternative crown designs and result can be used as future reference. Each bar arm contains 2 identical arcs and one straight bar. The arc is an eighth round and has the radius of 1.1 mm. The straight bar s length is 0.94 mm. Bridges usually do not play important roles during the entire stent operation period but the design layout directly influence the mechanical properties. Before finalizing the design, there were four bridge design drafts (Figure ). 31

49 Figure 2.4: The bridge layout design, draft #A Figure 2.5: The bridge layout design, draft #B Figure 2.6: The bridge layout design, draft #C 32

50 Figure 2.7: The bridge layout design, draft #D Draft A (Figure 2.4) is a closed-cell design which has been abandoned. It is a strong structure just by visual sense. The high dense structure will apparently decrease the degradation process. Draft B (Figure 2.5), an open-cell structure, has the least dense bridges and the largest cell size among the three drafts. The low dense bridges may cause over flexibility on the circumferential direction during expansion. Draft C (Figure 2.6), an open-cell structure, has the median dense bridges. Its structure is likely a transition between Draft B and D. The major issue of this design is the uneven distribution of bridges. This type of bridge layout can only last for three struts. Stents with more than three struts would have different radial strengths at different segments. Draft D (Figure 2.7), an open-cell structure, utilizes the bridge layout of the Lekton Magic stent from Biotronik, Berlin, Germany shown in Figure 2.8 [69]. The bridges are divided into two as a group and inserted between every two peak-to-valley periodical struts. This type of layout provides a balance among bridge density, flexibility, and cell size. 33

51 Figure 2.8: The Lekton Magic stent (figure provided by Biotronik, Berlin, Germany. Retrieved July 14, 2015, from Due to the uneven bridge layout, Draft C was eliminated first. Although Draft B and D are very close on the structure, Draft D was further selected due to the balance on bridge density and cell size. Compare to Draft D, Draft B has relatively larger cell size and lower bridge density than Draft D. Most importantly, Draft B has free crowns. Crowns usually are the major segments during expansions. Crowns with capacity of free movement would possibly cause uneven deformation, which is against the design primary goal. As shown in Figure 2.3, the bridges with height of 3.0 mm connect the neighboring struts. 0.1 mm radius fillets are used at the intersection with the stent struts. In Solidworks, a 2D circumferential surface drawing was made at first (Figure 2.2) and the 3D model (Figure 2.1) was then made from the 2D drawing. The plane drawing was wrapped onto the inner face of a temporary tube whose inner circumference was almost equivalent to the width of the 2D model (Figure 2.9). Unfortunately, a closure error of the 0.01 mm gap cannot be avoided during the wrapping (Figure 2.10). Compare to the circumference of 18.7 mm, 0.01 mm is a negligible value, which error percentage is only 0.05%. As a preparation work for the simulation, either surface knit or extrude tool in SolidWorks can be used to close the gap. 34

52 Figure 2.9: The stent model after wrapping into a tube in Solidworks Figure 2.10: The gap at the closure after wrapping in Solidworks 2.3. Structure of the Design #2 Stent Figure 2.11 shows the Design #2 stent. It is an open-cell peak-to-peak structure and was designed for AV fistula created at pig s jugular veins. The 3D and 2D figures are displayed in Figure 2.11 and Figure 2.13 provides the design details. The Design #2 stent is about 2 cm long and 8 mm in diameter. It consists of 4 struts and each strut has 10 periodical wavy units. Bridges link the adjacent struts by every other wavy unit. Contrast to Design #1, the crowns have smaller radius but smooth tangent transitions, which brings larger intersecting surface of the stent. The jugular veins are major vessels in the blood circulation system. The larger size of the vein requires a bigger stent. Instead of the straight bridge in Design #1, the Design #2 uses an S 35

53 shaped connection. This type of bridge is expected to have better flexibility. On the other hand, the radial strength level is decreased. Figure 2.11: The 3-dimentional Design #2 stent model made in Solidworks Figure 2.12: The complete 2-dimensional drawing of the Design #2 stent 36

54 Figure 2.13: The design details of the Design #2 stent Table 2.2: Details of Design #2 Stent (unit: mm) Strut Crown Height Width Radius Bar arm Straight Arc(s) bar radius length Strut width 0.15 Bridge SemiConnection circle(s) arc(s) radius Short bar(s) length 0.3 Long bar length 0.6 The smooth tangent segment connection is affirmative. The defective side is arcs and curves with small radius. In addition, the difference of strut and bridge widths may cause structure instability during degradation. 37

55 3. Design Simulation and Evaluation Computer-aided simulation assists design process. Creating and validating physical prototypes is an expensive and time-consuming task and it usually doesn t afford sufficient feedback [5]. Numerical analysis like FEA can provide less costly option and be more efficient for validating complex geometries. In the stent design situation, understanding the difference between conventional stent material like stainless steel and the biodegradable stent material, magnesium alloy, is essential during the designing and manufacturing. A stent model simulation can predict the strain and stress magnitude, distribution and possible fracture area during the expansion. Abaqus was used as the FEA tool in the stent analysis. In order to increase the simulation accuracy, a segmented model of 2 peak-to-valley struts that include entire elements of the stent was used in the following analysis Mathematical Mechanics Before performing computational analysis of the stent, it is necessary to understand the basic mechanics. The governing equation which applies to the stent is the conservation of linear momentum [41]. Ə 𝜎𝜎𝑖𝑖𝑖𝑖 Ə 𝑥𝑥𝑗𝑗 + 𝑓𝑓𝑖𝑖 = 𝜌𝜌𝑎𝑎𝑖𝑖 [41] Equation 1 (i, j = 1, 2, 3) Where σ is the stress tensor during expansion; x indicates the coordinates variation; f is the vector of applied force on stent; ρ is the density of the material; and a represents the acceleration vector. The equation of a i is the derivative of ν i as the velocity of a piece of material or an element in the stent; and the velocity ν i is the derivative of u i as the displacement of an element. 38

56 aa ii = dν i = Əν i + νν Əν i dt Ət jj [41] Equation 2 Əx j ν i = du i = Əu i + νν Əu i dt Ət jj [41] Equation 3 Əx j With the large geometric deformation during stent expansion, it is very necessary to consider the nonlinear mechanics theory. The finite element method (FEM) is the most widely used technique for solid s large deformation. The term finite delegates the large deformation where nonlinear behavior happens [41]. The deformation gradient tensor and Cauchy-Green tensor are often used in material with large deformation [41]. The equation of the deformation gradient tensor F ij is F ij = Əx i ƏX j = Əu i ƏX j + δ ij [41] Equation 4 (i, j = 1, 2, 3) Where x i and X i respectively represent the deformed and un-deformed element s coordinates; u i refers to the displacement. δ ij = 0 if i j, and δ ij = 1 if i = j. The Cauchy-Green tensor then is defined in terms of F ij, B ij = F ik F jk = Əx i ƏX k Əx jj ƏX k [71] Equation 5 In nonlinear deformation, strain tensor is often a convenient access to describe displacement [41]. The Green s strain tensor, for example, is expressed as E ij = 1 2 (F kif kj δ ij ) = 1 2 (Əu i ƏX j + Əu jj ƏX i + Əu k ƏX ii Əu kk ƏX j ) [41, 71] Equation 6 In addition, the Piola-Kirchoff stress tensor formula sometimes could be even easier method than the stress tensor [41]. These two stress tensors are related by σσ iiii = 1 det (F) F ikss kkkk FF jjjj [41, 71] Equation 7 Where S ij is the Piola-Kirchoff stress tensor; σ ij is the stress tensor. 39

57 In order to solve the stress, strain, and displacement of a solid, a constitutive equation has to be determined [41]. The governing equation with specific boundary conditions then can be solved by FEM. Due to the nonlinearity, it is usually difficult exploring the constitutive equation [41]. For the stent material that behaves in the nonlinear region, strain energy W is a relative simple method to determine the constitutive function [41]. The Piola-Kirchoff stress tensor is the derivative of strain energy W with respect to Green s strain tensor SS iiii = ƏW ƏE ij [41] Equation 8 Stents are made of metal alloys. Similar to the Hooke s Law, the neo-hookean solid model can be used for predicting nonlinear stress-strain behavior of materials undergoing large deformation [41]. The strain energy function is W = C (I 3) + DD ( JJ 1) Equation 9 I = λλ λλ λλ Equation 10 J = dddddd(ff) = λλ 1 λλ 2 λλ Equation 11 Where I is the first invariant of Cauchy-Green tensor; λ is the principle stretches; F is the deformation gradient tensor; C and D are material constants that are related to elastic modulus and Poisson s ratio Material Properties Conventional stents are usually made from Stainless steel, Titanium, or polymers. The AZ31 alloy is considered as a biodegradable material for the biodegradable stent. AZ31 alloys have variety due to different thermal treatment. The AZ31B-TP is the specific material used in stent fabrication. It is wrought magnesium tooling plate alloy. This kind of alloy usually contains 2.5% 3.5% of aluminum, 0.7% 1.3% of Zinc, and a small number of Manganese. Tooling plate is 40

58 non-magnetic with high electrical and thermal conductivity. The following table lists the mechanical properties of AZ31B-TP alloy [44, 70]. Table 3.1: Mechanical Properties of AZ31B-TP Alloy Young s Ultimate Poisson s Yield Stress Elongation Density Modulus Tensile Stress Ratio 45 GPa 174 MPa MPa g/mm 3 In the Abaqus analysis, true strain and stress data is needed. Based on the engineering strain and stress data, the true strain and stress data can be obtained from Equation 12 and 13. εε tttttt = ln 1 + εε eeeeee Equation 12 σσ tttttt = σσ eeeeee (1 + εε eng ) Equation 13 The maximum stress then is 322 MPa. Magnesium alloy true strain-stress graph is shown in Figure 3.1 [44, 70]. Figure 3.1: The true strain-true stress curve of AZ 31 alloy and other common stent materials (Wu W, Petrini L, Gastald D, Villa T, Vedani M. Finite element shape optimization for biodegradable magnesium alloy stents. Ann. Biomed. Eng. 2010; 38(9): ) 41

59 3.3. Evaluation of the Design #1 Stent Expansion Analysis of the Design #1 Stent The 2 peak-to-valley struts model was initially created in Solidworks (Figure 3.2) and then Abaqus imported the model from Solidworks (Figure 3.3). Figure 3.2: The 2-struts stent model created in Solidworks Figure 3.3: The original stent model in Abaqus after importing from Solidworks The first step is the inputting of material properties. It is necessary to have the typical characteristics data of density, elastic modulus, yield stress, strain-stress coordinates in plastic region, fracture strain, and Poisson s ratio. The second step is meshing. In general, meshing divides the model into lots of pieces of elements. Each of the elements has a certain amount of nodes. Quality of meshing is directly related to the accuracy of simulation results. The meshing size, shape control, and element type are the typical factors. Keeping the meshing size as small as possible has always been the target. Tetrahedron and hexahedron are the common 3D solid meshing element shape. Tetrahedron fits any geometry while hexahedron has limitations and requirements for the model geometry. Hexahedron 42

60 elements with a better accuracy reduce the number of nodes and computational expense. It s usually a preferred element shape. A stent is usually considered as a complicated model. If meshing without any model correcting, meshing is then restricted to the tetrahedron element and Figure 3.4 demonstrates the existing problems. Figure 3.4: The meshed stent model with tetrahedron element Due to the importance of each segment of the stent, the mesh density is expected to be the same everywhere. From Figure 3.4, elements are not in similar size. Some elements at the top of the crown have very narrow edges which will often be resulted in error in the computational process. In order to improve the meshing, preparation work is needed. There are two methods, partition and virtual topology. Partition divides the stent model into regular shapes and provides the possibility for different mesh density. For example, the Design #1 stent can be segmented into the straight bridge cuboid, the crown, the straight short cuboid in bar arm, and two identical curves in bar arm. All these parts then can be used to mesh specifically, which takes a lot of time and effort. The virtual topology is a tool that can integrate irregular boundaries or faces into a suitable condition for better quality meshing (Figure 3.5). 43

61 Figure 3.5: An example of the function of virtual topology, combining unexpected boundaries In the figure 3.5, circles point out the closure gap after wrapping in Solidworks and unexpected edges during the model importing from Solidworks to Abaqus. Virtual topology combines all of these unnecessary boundaries and faces as much as possible to improve meshing condition. The color of model indicates whether the further partition is needed or not. Orange as shown in Figure 3.5 means further preparation work is needed while yellow in Figure 3.6 implies the accomplishment of the model. Figure 3.6: Stent model appearance after virtual topology and partition 44

62 Element type is another factor. Linear and quadratic geometry orders are the major two options. By using the hexahedron shape as an example, a linear first-order element has 2 integral points in one direction while the quadratic second-order element has 3 integral points. Due to the extra point, quadratic element can have curved boundaries and sometimes have more accurate results. However, problems with large strain change or buckling often leads to distorted mesh, which was often appeared in Abaqus warning section. A stent expansion process is similar to this situation. In this case, a linear high density mesh with reduced integration is needed. The C3D8R element was selected for the stent model. Figure 3.7 shows the model of meshing with a control size of 0.06 mm. Figure 3.7: The stent model after complete meshing Boundary condition and load setup is the third step that directly impacts the expansion procedure. Two approaches have been considered, expansion by radial displacement and expansion by pressure load. Expansion by radial displacement (Figure 3.8) usually seems a very acceptable method. Each node expands at the same rate through the radial axis until the pre-established position. In other words, it may simulate a perfect expansion process. However, the longitudinal displacement is omitted. During the expansion, a longitudinal length shrinks more or less on 45

63 stents based on specific structure. The method of expansion by radial displacement forces each node to only move in radial direction instead of both radial and longitudinal directions. Figure 3.8: Stent expansion by radial displacement The approach of expansion by pressure load solves the problem. The data of real-time exterior pressure acting on the inner surface was obtained while stents was expanded by high-pressure balloon during animal surgeries in the past. Diameter of vein (mm) Pressure (mm H 2 O) Figure 3.9: The real-time pressure data between the high-pressure balloon and the Design #1 stent. Data provided by Dr. Zhangzhang Yin 46

64 Figure 3.10: The stent model after the load setting After inputting the loading data, the stent model is fully prepared for computational analysis (Figure 3.10). The last step is to decide analysis method. A static analysis uses a simple linear matrix equation, such as CC xx = DD. A dynamic analysis follows an governing equation such as AA xx + BB xx + CC xx = D. Implicit and explicit methods are two nonlinear algorithms in FEA. ReBelo et al has reported the comparison of implicit and explicit method [72]. Both methods simulate that an object changes on geometry by incremental load or displacement steps. The geometry and mechanics of each increment base on the previous increment state. The implicit algorithm is an unconditionally stable method [72]. It finds a solution by solving equations involving the current and the next increment step. The algorithm requires calculating the inverse of the stiffness matrix at each step. Especially in a complicated three-dimensional model, stiffness matrix costs intensive computational work [72]. In addition, the implicit analysis enforces the equilibrium of the internal and external forces. However, local instabilities in 3D model often cause the equilibrium to be difficult to achieve [72]. The explicit algorithm is introduced to overcome the disadvantages of the implicit method [72]. It calculates the state of 47

65 the object at the next time step from the state at the current step. In the other words, it solves for 𝑥𝑥 instead of 𝑥𝑥, which avoids the stiffness matrix. This type of method is conditionally stable. It requires the time increment must be less than a critical value for allowing the dilatational wave to cross the meshing element [72]. The final result accuracy depends on the size of increment. If the number of increments is not sufficient, the result tends to shift from the accuracy. Besides, the explicit method is used for quasi-static problems, the inertia effect have to be negligible [72]. The dynamic explicit algorithm was then chosen to apply to the expansion procedure. The Design #1 stent expanded from 6.0 mm to 10.0 mm in radial direction. The process running time was set to 10 seconds, which was long enough to reduce inertia effect. The total time increments were 200. After running the analysis (detailed data output see Appendix), the final simulation results at diameter of 10 mm are shown in the following (Figure 3.11). (a) (b) Figure 3.11: The expansion results of the Design #1 stent, (a) the strain distribution and (b) the stress distribution at diameter of 10.0 mm 48

66 Table 3.2: Design #1 Stent, the Highest Local Strain and Stress during the Expansion Diameter (mm) Plastic Strain E-03 E-02 E-02 E-02 E-02 E-02 E-02 E-01 Crown Stress (MPa) Plastic Bar Strain E-03 E-02 E-02 E-02 E-02 E-02 E-02 arm Stress (MPa) Plastic Strain Bridge Stress (MPa) Abaqus outputs the equivalent plastic strain and stress intensity (Eq. 14), which is also called Von Mises. σσ 2 vv = 1 [ σσ 2 11 σσ σσ 22 σσ σσ 33 σσ σσ σσ σσ 2 31 ] --- Equation 14 In Figure 3.11, colors from blue to green to yellow to orange to red represent the growth of the corresponding values. The largest local equivalent plastic strain is (Table 3.2 and Figure 3.11a) and the maximum principle strain is The highest local stress intensity is MPa (Table 3.2 and Figure 3.11b). The percentage of the peak strain over the ultimate tensile strain is 79%. According to Wu et al [44], the plastic strain of elongation percentage under 80% is a safe region. The simulation result (Table 3.2) confirms that the magnesium alloy AZ31 is a brittle material. The stress intensity and plastic strain have significantly increase at the very beginning of the expansion. After the material deformation accesses into the plastic region, the variation tends to be gentle, which matches the strain-stress diagram of AZ31 alloy. The bridge material stayed under the yield stress in the entire process. In general, the final strain and stress distributions are similar as the prediction. The strain and stress concentration are located at and near the crown while all bridges has the least applied force. The arcs of bar arms have relatively 49

67 higher strain and stress concentration than the straight bar area. Figure 3.11a and b also point the peak value of strain and stress. In order to learn the strain and stress change during the expansion, those elements near the peak strain and stress value were selected (Figure 3.12). The red-color elements are located exactly at the non-tangent connection between the crown and bar arm, which maybe indicate a design flaw. Figure 3.13 and Figure 3.14 respectively show the strain and stress growth along the time increment from 0 to 10 second. Figure 3.12: The selected region of the highest strain & stress of the Design #1 stent during expansion Figure 3.13: The growth of the equivalent plastic strain during the expansion in the selected region of the Design #1 stent 50

68 Figure 3.14: The growth of the stress intensity during the expansion in the selected region of the Design #1 stent At 4 second, the deformation of the stent structure started to approach the plastic region. Because the pressure in the balloon was increasing, the expansion was not at a constant rate. It took 4 seconds for the load to grow inside the balloon against the elastic region to start the expansion process. After entering the plastic region, stress increase tended to be stable. This is the area (Figure 3.12) which geometry optimization can be aimed on in order to reduce the highest strain and stress. Figure 3.15 demonstrates a common mechanical failure in vitro test by over expanding the stent. An 18 mm diameter balloon was used in this experiment and the stent in picture had been crimped to normal size. In the graph, the two fractures are located at the identical structure region as shown in Figure 3.12, which can be considered as a validation of the FEA analysis accuracy. 51

69 As mentioned in the stent design requirement (Section 2.1), a biodegradable stent prefer to share the deformation along its strut to reduce the strain and stress concentration ratio. Figure 3.16 shows the strain distribution of the selected continuous elements along the strut at the expanded state. From crown to bar arm, strain value decreases. Conversely, strain increases. Base on the nodes-strain graph, there are about 100 nodes along the strut in one wavy period. About 60% of the nodes (node #1 #24, #41 45/51 #61, and #81 #100) contributed to the expanding activity. About one third out of these 60% nodes (node #1 #10 and #91 #100) experienced major deformation. The higher percentage number and the higher ratio of the major and total deformed nodes suggests the low concentration level of strain and stress and better accomplishment of the stent design. Figure 3.15: The design #1 stent failure test after over expansion 52

70 Figure 3.16: The Design #1 stent plastic strain distribution at the diameter of 10 mm along the strut In addition, arrow 1 and 4 point the nodes on the inner strut curve while arrow 2 and 3 point the nodes on the outer strut curve. From the plastic-strain graph, nodes located at inner and outer strut curve have significant difference on strain value. This is because the inner strut curve bore tension to increase the angle between the crown and bar arm. As mentioned in section 2.2, there are two crown designs, the single-arc crown and the doublearc crown. The simulation result can evaluate the alternative designs. The stress distribution on both crowns inner and outer strut curve is shown in Figure Although the outer strut curves have almost the equivalent outcome, the single-arc design has a better stress distribution than that of the double-arc design at the inner strut curve. The peak stress value appears less in the single-arc crown. Moreover, according to Figure 3.16, the left side of the selected elements is located near the single-arc crown and the selected elements at right are located near the double- 53

71 arc crown. The single-arc design has a better organization on the strain value dropping region (node #1 #20). Figure 3.17: The stress comparisons of the single-arc and double-arc crown designs Recoiling Analysis of the Design #1 Stent A complete stent expansion procedure by pressurized balloon consists of two steps, expansion and recoiling. Recoiling happens after the deflation of the balloon. A stent tends to recoil due to the elastic deformation and compression by vessels. Studies from Joseph et al claim that commercial coronary stents often fail to achieve the recoiling ratio of 11% 23% [73]. Slottedtube stent (closed-cell design) usually have good performance with recoiling ratio of 8% 9% [73]. The Design #1 stent was analyzed on free recoiling situation. Due to the non-external force, the analysis was run under static process. The initial state was the end state of the expansion process. Except the material properties and the meshing, the entire previous step s settings were needed to eliminate. A segmentation of the stent must be fixed in this step for allowing the recoiling. In 54

72 Figure 3.18, a bridge has been locked at all 3 directions in both Cartesian coordinates and spherical coordinates so that the rest of the stent can recoil freely. The recoiling results and the comparisons with the initial state are listed Figures Figure 3.18: A fixed segmentation of the Design #1 stent before the recoiling analysis (a) (b) Figure 3.19: The recoiling results of the Design #1 stent, the radial displacement (a) before and (b) after the recoiling 55

73 (a) (b) Figure 3.20: The recoiling results of the Design #1 stent, the plastic strain distribution (a) before and (b) after the recoiling (a) (b) Figure 3.21: The recoiling results of the Design #1 stent, the stress distribution (a) before and (b) after the recoiling Figures respectively exhibit the comparisons of displacement, plastic strain, and stress intensity before and after recoiling. In Figure 3.19b, the color turning from blue, green, yellow, orange to red represents the displacement increasing from low to high. The blue-color bridge is the fixed segment (Figure 3.18), whose displacement is 0 mm. The red segment has a displacement about 3.43 mm. With the consideration that the stent cross-sectional radius is 3 mm 56

74 at original state, the actual diameter of the stent after recoiling is 9.43 mm. According to the recoiling ratio equation [38]: 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 Where 𝑑𝑑 is diameter of the stent 100% Equation 15 The Design #1 stent s recoiling ratio is 5.7% and has the radial strength of 128 MPa (Figure 3.22). The maximum stress intensity drops to 225 MPa after the recoiling. The stress distributions of the crowns, bar arms, and bridges remain at the similar concentration ratio but with decreased magnitudes. The plastic strain remains the same. Figure 3.22: The recoiling results of the Design #1 stent, the radial stress The two crown designs have the different results after recoiling as well. As shown in Figure 3.21b, though blue and green are the major colors, which corresponding stress values are under 150 MPa, the peak value is over 200 MPa. All of the peak value in red appears at the double-arc crowns (Figure 3.23), which provide another reason in the comparison of both designs. 57

75 Figure 3.23: The recoiling results of the Design #1 stent, stress comparisons of both crowns after recoiling 3.4. Evaluation of the Design #2 Stent The Design #2 stent model has also been analyzed with the same procedure as Design #1 stent. Because of the different design purposes and applications, both stents cannot be compared at the same expansion range. Instead, the ratio of the strut perimeter and the expansion diameter was measured. The strut perimeter of Design #1 stent is 46.8 mm while the Design #2 stent has the perimeter of 84.9 mm. The Design #1 stent s ratio of the strut perimeter and lumen diameter is 46.8 mm / 10 mm = According to this ratio, Design #2 would be expected to reach the diameter of 18.1 mm. The Design #2 meshing thickness also changed. With the number of nodes limitations in Abaqus, meshing control size was increased due to the larger geometry. However, the expansion target exceeded the capacity of Design #2 stent in the FEA. Stent structure failed in the analysis process. The newly adjusted target was to expand the Design #2 stent until its peak stress intensity reaching the final value of Design #1 stent. Figure 3.24 displays the strain and stress distributions of the Design #2 stent during the new expansion trial. 58

76 ( a ) ( b ) Figure 3.24: The expansion results of the Design #2 stent, (a) the strain distribution and (b) the stress distribution at diameter of 13.8 mm Table 3.3: Design #2 Stent, the Highest Strain and Stress during the Expansion Diameter (mm) Plastic Design Strain E-02 E-02 E-02 E-02 E-02 E-02 E-01 E-01 #2 Stress (MPa) When the peak stress intensity reaches the value of 318 MPa, the lumen diameter is 13.8 mm. By calculating the strut perimeter to the lumen diameter ratio, it is 84.9 mm / 13.6 mm = 6.15, which is 1.3 times of the ratio of Design #1 stent. The Design #2 stent was supposed to expand to 18 mm to be equivalent with the ratio of Design #1. As the result, the Design #2 expanding capacity is only 76% of the Design #1 stent s. Design #1 is a better structure. The strain and stress concentration field is located at the crown s inner strut curve (Figure 3.25). Figure 3.26 and 3.27 respectively display the plastic strain and stress growth for the selected nodes (Figure 3.25) during the expansion. Both the strain and stress increase have the close behavior as Design #1 stent s. 59

77 Figure 3.25: The selected region of the highest strain & stress of the Design #2 stent during expansion Figure 3.26: The growth of the equivalent plastic strain during the expansion in the selected region of the Design #2 stent 60

78 In summary, Design #1 is obvious a better structure than Design #2. The material usage (Table 3.4) of Design #1 stent is only 75% of the Design #2 design while it still can expand 4/3 times larger. Figure 3.27: The growth of the stress intensity during the expansion in the selected region of the Design #2 stent Table 3.4: Comparisons of Both Designs Design #1 Stent Design #2 Stent Material usage by volume mm mm 3 Strut perimeter 46.8 mm 84.9 mm Cross-sectional diameter 10.0 mm 13.8 mm However, the best balance point between the non-tangent connections and circumferential length of Design #1 design still needs improvement because the peak strain and stress values appear at the non-tangent connection. One advantage of Design #2 stent is the bridge design. The S shape provides enough offset shifting space during expansion. On the other hand, the bridges between the peak and valley in Design #1 lock each periodical wavy unit so that struts hardly have displacement on hoop direction. 61

79 4. Stent Manufacturing After selecting the structure design, manufacture is the next step. Quality of manufacture directly impacts the accomplishment of design requirements. It is an important link between the design and applications. The fabrication procedures of Design #1 stents were followed by stent design, tubing machining, laser cutting, and post-process. The stent CAD design has been established and was required to transfer to AutoCAD file. The laser cutting engraved the stent according to the AutoCAD file on the metallic tube made from tubing machining. The post-process as the final step removed burrs, polished the stents surface, and readjusted the stent geometry Tubing Machining and Laser-cutting The tubing machining started from a commercial AZ31B-TP alloy (Figure 4.1). The outer diameter of the stent is 6 mm, which also has to be the external diameter of the tube. The peakto-valley strut thickness is 0.4 mm which gives the internal diameter of the tube is 5.2 mm. Tubing for stent manufacturing can be made by extrusion or machining. Mg materials are generally difficult to extrude due to its hexagonal microstructure. Figure 4.2 shows the end product of the tubing for stent manufacturing. Figure 4.1: The AZ31B-TP ingot 62

80 (a) (b) Figure 4.2: The manufactured AZ31 tubes, (a) the top view, (b) the front Laser cutting then engraved the stent followed by the drawing onto tubes. Laser cutting utilizes the highly powered laser beam as a knife to cut material. Material irradiated by the laser is vaporized due to the high temperature. The cutting on material follows the laser beam s movement. The laser beam moves based on the input AutoCAD file. Laser cutting is very precise because the thickness of a laser beam could only be 10 µm. The most common laser is the CO 2 (carbon dioxide) laser beam. It is suitable for cutting, boring, and engraving. CO 2 lasers have widely applications on materials such as stainless steel, titanium, aluminum, magnesium, wood, plastic, and paper. There are three major types of cutting methods. Vaporization cutting Laser beam heats the material surface to its boiling point. With the material vaporization, a kerf on material is formed. The vaporization cutting usually requires enormous power to generate. Nonmetal materials are often used by this method. Fusion cutting It s also called melt and blow. Laser beam heats the material surface only to the melting point. Another beam of stable gas (nitrogen, helium, argon) blows the melted material away. This method does not need to vaporize material, which saves a lot of energy. Crystalline materials like metal are suitable for this method. 63

81 Thermal stress cracking It uses the characteristic of brittle material s sensitivity to fracture to form cut. Laser beam focuses on the material and forms a crack on the surface. These cracks expands in orders to finish the cutting. Design #1 s laser cutting process was done by InoTech Laser Corp. Stent samples are displayed in Figure 4.3. Figure 4.3: The manufactured Design #1 stents 4.2. Electrolytic Polishing Electrolytic polishing also known as electropolishing is an electrochemical process that removes burrs and increase surface brightness from a metallic work pieces. It was the post process of the Design #1 stents. Electropolishing (Figure 4.4) uses the polishing object as the anode and the insoluble material as the cathode. Electrolyte is the media of both electrodes. After turning on the circuit, metal ions from anode form a membrane of phosphate with the phosphoric acid in the electrolyte. This type of phosphate membrane is thinner at the convex and thicker at the concave. Because the current density is higher at the thinner membrane, electrolytic polishing then can remove burrs and increase surface brightness (Figure 4.5). 64

82 Figure 4.4: The schematic diagram of electropolishing Figure 4.5: The operating principle introduction of electropolishing Electropolishing process causes non-qualitative change and it is very efficient. The polished surface maintains the brightness in long term. However, work piece material, quality and temperature of electrolyte, and control of current and voltage are all factors impact the surface finishing. It is difficult finding the correct parameters for performing the best polishing. 65

83 In the case of electropolishing for magnesium alloy, the Design #1 stent was the anode and the cathode was a carbon rod. The following equation is the chemical reaction at the anode, Mg = Mg2+ + 2eThe voltage stabilizer provided the voltage at 10V. After the polishing, chromic acid was used to clean the stent surface if necessary. Figure 4.6 shows a finalized Design #1 stent. The strut crosssection geometry changed from 300 µm x 400 µm to 250 µm x 350 µm. Figure 4.6: A final processed Design #1 biodegradable stent 4.3. SEM (Scanning Electron Microscope) Scanning Electron Microscope is positioned between Optical Microscope and Transmission Electron Microscope. It is good at observing uneven surface of microscopic structure. The Hitachi branded SEM (Figure 4.7) was used to observe the surface flatness and cracks of the stents before and after the electrolytic polishing. Figure shows the stage before electropolishing while Figure displays the stage after electropolishing. 66

84 Figure 4.7: Hitachi SEM (Scanning Electron Microscope) Figure 4.8: 50 times zoomed in Design #1 stent before electropolishing 67

85 (a) (b) Figure 4.9: (a) 200 times zoomed in (b) 150 time zoomed in Design #1 stent before electropolishing Figure 4.10: 40 times zoomed in Design #1 stent after electropolishing 68

86 (a) (b) Figure 4.11: (a) 200 times zoomed in (b) 120 time zoomed in Design #1 stent after electropolishing 6 photos obviously state the surface difference before and after the electrolytic polishing. Before polishing, the burrs on edge of the strut and bridge can be clearly seen; and the stent surface is very rough. After polishing, all of the obvious burrs have been removed and stent surface much smoother than before. 69

87 5. In Vivo Experiment and Validation Pigs were used as the experiment carrier for AV fistula. In vivo experiment is very different from other laboratorial experiment. Experimental situations often remain changing. For example, the diameter and length of the blood vessels are related to of blood flow volume and stent expanded size. Unfortunately, the diameter and length shift every time. Healthy level of a pig impacts every aspect of experiment. Unfortunately, it cannot be controlled. Moreover, personnel mistake and pig s post-surgery life can also make difference. However, animal tests are probably the best form to discover problems and collect useful data. In vivo experiments were performed by Dr. Prabir Roy-Chaudhury team. The surgeries described in this study were done by Yang Wang (MD) Surgery Surgery is essential and the first step for creating a successful AV fistula. Normally, blood in arteries flows to capillaries; then flows back to veins. In AV fistula, blood comes from the proximal artery and flow into both the distal artery and the outflow vein. Left and right (origination from pig s direction) femoral veins were established to create AV fistulas. The left one was the control side without a stent while the right stent side vein was implanted a Design #1 stent. Pig #3 s surgery was done on Aug.19, 2013 and the experiment ran for 63 days. In general, there are 3 steps in the surgery. First, create an AV fistula without a stent; then, implant a stent at the outflow vein near the anastomosis (the connection of artery and vein); last, expand the stent. Figure 5.1 shows a comparison photo of right and left AV fistula in a surgery. 70

88 Figure 5.1: The comparisons of two AVFs with and without a stent 5.2. CT scan Computerized Tomography scan is the full name of CT scan. CT images are basically x-ray images. It stacks computer-processed combinations of many x-ray images taken from different angles to form cross-sectional images on target area. Each x-ray image is a layer of the CT image. CT scan utilizes different tissues having different coefficients of absorptivity and transmissivity for x-ray to produce images. CT technique allows doctors and patients observe an inside object or structure without physical cutting or surgery. CT scan was performed weekly in University of Cincinnati hospital. It is able to show the blood flow geometry and stenosis conditions around the AV fistula for careful comparisons. The CT studies performed by Dr. Prabir Roy-Chaudhary team compared the fistulas with and without a stent. Overall, CT studies provide positive results of the function of the Design #1 stent Ultrasound Ultrasound as commonly known as B mode ultrasound or CDFI (Color Doppler Flow Imaging) is another good tool to observe blood flow environment in the AV fistula. Sound usually defines the acoustic wave frequency between 20 Hz to 20,000 Hz. Audio frequency over 20,000Hz is called ultrasound. Similar to normal sound, ultrasound has direction, can penetrate 71

89 objects, and reflects when encountering barrier. Objects with different densities and geometry cause different echoes. In medical application, tissues and organs are the barriers that can reflect acoustic waves. Sensors collect these echoes and process the data information to form dynamic images on screens. The CDFI utilizes the theory of Doppler Effect to measure blood flow speed and volume flow. When blood moves toward the sensor, the color is red; conversely, it is blue (Figure 5.2). Compared to CT, ultrasound has lower cost, could provide blood flow data, and is radiation free. On the other hand, ultrasound images have lower resolution than CT images. Figure 5.2: An example of ultrasound image In the in vivo experiment, ultrasound mainly used to measure blood vessels geometries and blood volume flow. The data was collected almost weekly and each checking point data was averaged from 3 trials. The following tables and diagrams show the data of Pig #3. 72

90 Table 5.1: The Ultrasound Data on the Control Side of Pig #3 Time Proximal artery Distal artery Anastomosis Outflow 3cm Flow in fistula Week Week Week Week 8 Closed Closed 0.62 No AVFS 0.7 Closed 342 No AVFS Closed 0.21 No AVFS 0.2 Closed Diameter (cm) No AVFS 0.5 Closed Volume Flow (ml/s) Closed Diameter (cm) Volume Flow (ml/s) Diameter (cm) Volume Flow (ml/s) Diameter (cm) Table 5.2: The Ultrasound Data on the Stent Side of Pig #3 Time Proximal artery Distal artery Anastomosis Outflow 3cm Flow in fistula Week Week Week Week Diameter (cm) Volume Flow (ml/s) Diameter (cm) Volume Flow (ml/s) Diameter (cm) Volume Flow (ml/s) Diameter (cm) Anastomosis Diameter (cm) Control Week 1 Stent 0.2 Week 2 0 Week 3 Week 8 Figure 5.3: Pig #3 ultrasound data, diameter of the anastomosis 73

91 Outflow Diameter (cm) Control Stent Week 1 0 Week 2 Week 3 Week 8 Figure 5.4: Pig #3 ultrasound data, diameter of the outflow vein at 3 cm away from the anastomosis Outflow Vein Vol. Flow (ml/min) Control Stent Week Week Week 3 0 Week 8 Figure 5.5: Pig #3 ultrasound data, volume flow in outflow vein The ultrasound data suggests the stent implantation is beneficial. In general, the right stent side has a full range of better results compare to the left control side. The diameter of anastomosis (Figure 5.3) has a lot larger value than the control side without a stent. The bigger anastomosis supports more blood flow from artery to vein, which shortens the dialysis access maturation time. The data of diameter at 1 cm away after the stent (3 cm away from the anastomosis) also shows the similar result. The right stent side maintained open while the left control side was closed 74

92 during the experiment. The left control side closed around week 4 due to bad stenosis. On the other hand, the right stent side almost remained open for the whole time. The volume flow in the fistula on the right had a much bigger value than the left side when the left control side was still open. However, the data in Figure is not corresponding to each other. The outflow vein had the largest size at week 3 but the flow was the smallest. The anastomosis reached the largest size at week 8 but the flow in vein wasn t the biggest value at the same time. There might be couple of reasons. The deepness of the fistula could impact the sensitivity of the ultrasound machine during the flow measurement. The light in-stent stenosis may cause turbulence flow at the distal-end area of the stent which disturbed the data collections Micro CT At the end of the experiment (day 63), pig #3 was sacrificed. After taking the AV fistula part out, further studying such as micro CT was used to measure the stent degradation. In micro CT, water is marked as 0. Material density that is higher than water receives positive numbers. Things lighter than water like air/gas gets negative numbers. By changing the density range of showing, certain materials in the range can be displayed. After choosing the metal range numbers, all remaining stent can be shown and measured. In Figure 5.9, the grey shadow in the background is the blood vessel tissue and the metallic looking wires are the remaining stent after degradation for 63 days. The majority of the stents have been degraded. By selecting all of the metal remaining, the volume of the Design #1 stent can be calculated, which is mm 3. During the 63 days of experiment time, the stent has been degraded for 89% of the original size (Table 5.3). Unlike most other biodegradable stents in different applications degrade too fast than what s being expected, the Design #1 stent degraded 75

93 slower than the ideal situation. The expected degradation time is about 1 month/30 days. It took twice of the time for Design #1 stent. For solving this issue, stent strut thickness should be adjusted and be validated by computational analysis. However, stent particle pieces are around the stent area. Ideally, a stent should degrade evenly; each strut dissolves at a same rate. But it could be hardly in real world, especially in vivo. Stent particles haven t been observed or sensed during the experiment by CT or ultrasound. Future study will focus on the possible metal particles and explore possible solution to improve the issue. Figure 5.6: Pig #3 micro CT image, the remaining of the Design #1 stent after 63 days of experiment Table 5.3: The Degradation Rate of the Design #1 Stent Pig #3 Volume before Degradation mm3 Volume after Degradation mm3 76 Degradation %

94 5.5. SEM Analysis The SEM analysis was also used to study the degraded stent. SEM tested the remaining element on the surface of the stent. As the result, there isn t any heavy metal element exist. The majority elements are carbon, oxygen, sodium, magnesium, and aluminum (Figure 5.10 and Table 5.4). Figure 5.7: Analysis of the degraded stent by SEM Table 5.4: The Surface Elements Analysis of the Degraded Design #1 Stent Element At% C O 5.43 Na Mg 34.3 Al 0.89

95 6. Conclusion and Future Study 6.1. Conclusion One single design of a stent can hardly have all of the ideal characteristics [5]. It is possible to find the most balanced point. Besides appearance, structure designs are expected to meet performance requirements. To be used as biodegradable stents, materials are required to satisfy the application. Through the processes of structure design, computational analysis, manufacture, and in vivo tests, Design #1 stent achieved the preliminary goals. The goal of the structure design is to achieve relatively equilibrium strain and stress distributions on the stent strut in order to overcome the low ductility of AZ31 and expand to a target value. The design principle is to avoid small radius curve on struts. The Design #1 stent uses low curvature struts but brings the side effect, non-tangent connection. While the Design #2 stent avoids non-tangent connections but ends with small radius curves. According to the computational analysis, the low curvature struts successfully spread the high strain and stress around the crown area. The ratio of the strut length and cross-sectional diameter is % of the strut length participated plastic deformation during the expansion. One third out of these 60% length had been significant deformed. On the other hand, the ratio of the strut length and crosssectional diameter of Design #2 stent is about 6.15 due to the tight turning on its strut. The expanding capacity is only 76% of the Design #1 stent. Large strain and stress gathered at the inner crown curve of the strut turnings. The analysis filtered that the Design #1 is a better choice for fabricating and in vivo tests. The fabrication used processes of tubing machining, laser cutting, and electrolytic polishing. Lasers cut the AZ31 alloy tubes based on the stent CAD design. SEM observed that the 78

96 electrolytic polishing removed rough edges and surface that caused by the laser cutting process. In vivo tests, the Design #1 stent safely expanded in the pig s femoral vein and remained wide open after the balloon deflation. CT and ultrasound as the observation methods measured the vessels and blood flow during the two-month long experiment. By comparing to the control side, the stent supported the blood vessel maintain open and helped the preparation before vascular access. In the end of the experiment, 89% of the implanted stent was degraded. However, the number of in vivo tests is not enough to fully validate functions of the stent. Due to the specific application, the degradation rate of the stent was slower than expected, which most biodegradable stents usually degrades too fast [4]. The goal of degradation time is about 1 month while the stent lasted for at least 2 months. In addition, although most of the stent seemed dissolved, no image or measurement could describe the particular procedure of the degradation, either perfectly dissolving or breaking into big particles. In summary, the Design #1 stent achieved the requirement on mechanical performance and preliminary goals on its medical application Future Study There are three aspects for further studies. Alternative stent designs and structure optimizations are the priority in the future. Unlike many other researches, structure design usually does not have theoretical basis to follow. Other designs and accumulated experience are the most useful references for new designs. Computational analysis helps accumulate experience and improving designs. Design #1 stent will be optimized on the crown, non-tangent connections between crowns and bar arms, and strut cross-sectional geometry. The single-curve crown will apply to all the crowns in Design #1 stent. The high strain and stress gathering at the inner curve of the non-tangent connection between crowns and bar arms will be optimized by minor geometry 79

97 adjustment with the computational validation. Geometry shrinks of the strut cross-section will be able to reduce the degradation time; but the new design should still have enough radial strength against blood vessels. In addition, stent analyses should extend to bending performance and fatigue life in the future. Stent fabrication methods and multiple in vivo experiments are the other two aspects. Annealing and more vitro tests should be added. Annealing promotes mechanical behavior of the stent. Vitro tests on fatigue life and even corrosion can provide more data and references about the biodegradable stents and help the structure design in return. Obviously, more animal experiments are needed for comprehensive validations about stents design, stent performance, and manufacture methods. A stent as a foreign body in blood vessels could very possibly cause neointimal hyperplasia. Different stent designs on cell size and metal density should be recorded on the neointimal hyperplasia growth during in vivo tests. Metal particles during degradations also should try to be examined in heart and lungs. In summary, Design #1 stent optimization and possible alternative structures with dynamic simulation analyses need to be further studied. Annealing that improves material mechanical properties will be added before electropolishing. Finally, more in vivo validations as feedbacks are necessary to continue. 80

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103 Appendix Expansion Process of the Design #1 Stent (a) (b) Figure A.1: Design #1, (a) the strain and (b) the stress distribution at diameter of 6.0 mm (a) (b) Figure A.2: Design #1, (a) the strain and (b) the stress distribution at diameter of 6.5 mm 86

104 (a) (b) Figure A.3: Design #1, (a) the strain and (b) the stress distribution at diameter of 7.0 mm (a) (b) Figure A.4: Design #1, (a) the strain and (b) the stress distribution at diameter of 7.5 mm (a) (b) Figure A.5: Design #1, (a) the strain and (b) the stress distribution at diameter of 8.0 mm 87

105 ( a ) ( b ) Figure A.6: Design #1, (a) the strain and (b) the stress distribution at diameter of 8.5 mm ( a ) ( b ) Figure A.7: Design #1, (a) the strain and (b) the stress distribution at diameter of 9.0 mm ( a ) ( b ) Figure A.8: Design #1, (a) the strain and (b) the stress distribution at diameter of 9.5 mm 88

106 (a) (b) Figure A.9: Design #1, (a) the strain and (b) the stress distribution at diameter of 10.0 mm Expansion Process of the Design #2 Stent (a) (b) Figure A.10: Design #2, (a) the strain and (b) the stress distribution at diameter of 8.18 mm 89

107 (a) (b) Figure A.11: Design #2, (a) the strain and (b) the stress distribution at diameter of 8.9 mm (a) (b) Figure A.12: Design #2, (a) the strain and (b) the stress distribution at diameter of 9.6 mm (a) (b) Figure A.13: Design #2, (a) the strain and (b) the stress distribution at diameter of 10.3 mm 90

108 (a) (b) Figure A.14: Design #2, (a) the strain and (b) the stress distribution at diameter of 11.0 mm (a) (b) Figure A.15: Design #2, (a) the strain and (b) the stress distribution at diameter of 11.7 mm (a) (b) Figure A.16: Design #2, (a) the strain and (b) the stress distribution at diameter of 12.4 mm 91

109 (a) (b) Figure A.17: Design #2, (a) the strain and (b) the stress distribution at diameter of 13.1 mm (a) (b) Figure A.18: Design #2, (a) the strain and (b) the stress distribution at diameter of 13.8 mm 92