PSI - Issue 15

Volume 15 • 201 9

ISSN 2452-3216

ELSEVIER

International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019

Guest Editors: L iguo Zhao Vadim V . Sil b erschmidt

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Editorial Liguo Zhao Vadim V Silberschmidt Editorial Liguo Zhao Vadim V Silberschmidt Editorial Liguo Zhao Vadim V Silberschmidt Editorial Liguo Zhao Vadim V Silberschmidt Editorial Liguo Zhao Vadim V Silberschmidt Editorial Liguo Zhao Vadim V Silberschmidt

Procedia Structural Integrity 15 (2019) 1

2452-3216  2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. 10.1016/j.prostr.2019.07.001 This issue presents a selection of research papers presented at the International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. The Conference was organised by Technical Committee 14 "Integrity of Biomedical and Biological Materials" of the European Structural Integrity Society (ESIS). The Conference Organisers would like to acknowledge its sponsors: European Structural Integrity Society (ESIS); Engineering and Physical Sciences Research Council (EPSRC), the main funding body for engineering and physical sciences research in the UK; and Loughborough University, UK. Wit in the framework of he Conference, a Special Session “Design, Manufacturing and Evaluation of Shape-memory-alloy Sten s” was o ganis d b partners of the EPSRC UK project (2018-2020): "Smart Peripheral Stents for the Lower Extremity - Design, Manufacturing and Evaluation.” The Session focused on the top s, directly relat d to the proj ct: le on-specific design; additive manufacturing; biomechanical testing; modelling of self-expansion; biocompatibility study; in-v tro haemodynamics; in-vivo evaluation; modelling of deployment; deformations due to severe twisting and bending. This issue presents a selection o research papers presented at the International Conf rence on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. The Conferenc was organised by Technical Committee 14 "Integrity of Biomedical and Bi logical Materials" of the European Structural Integrity ocie y (ESIS). The Conference Organisers would like to acknowledge its sponsors: European Structural I tegrity Society (ESIS); Engi eering and Physical Sciences Res arch Council (EPSRC), the main funding body for engineering and physical sciences research in the UK; and Loughborough University, UK. manufacturing; stent failure and fracture; i -vitro and in-vivo studies; biocompatibility of stents; stent vessel interaction; fluid-solid interaction; in-stent restenosis; biological and clinical issues related to stents; stent deployment and delivery; medical-imaging-based assessment. Within the framework of the Conference, a Special Session “Design, Manufacturing and Evaluation of Shape-memory-alloy Stents” was organis d b partners of the EPSRC UK project (2018-2020): "Smart Peripheral Stents for the Lower Extremity - Design, Manufacturing and Evaluation.” The Session focused on the topics, directly related to the project: lesion-specific design; additive manufacturing; biomechanical testing; modelling of self-expansion; biocompatibility study; in-vitro haemodynamics; in-vivo evaluation; modelling of deployment; deformations due to severe twisting and bending. This issue presents a selection of research papers presented at the International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. The Conferenc was organised by Technical Committee 14 "Integrity of Biomedical and Biological Materials" of the European Structural Integrity ociety (ESIS). The Conference Organisers would like to acknowledge its sponsors: European Structural I tegrity Society (ESIS); Engi eering and Physical Sciences Research Council (EPSRC), the main funding body for engineering and physical sciences research in the UK; and Loughborough University, UK. materials science, experimental mechanics, modelling and various aspects of processing and manufacturing as well as medical practitioners to discuss advances in stent technologies. Over 30 papers presented at the Conference by researchers from 10 countries covered various topics including: metallic and polymeric materials for stents; mechanical properties of stents; development of biodegradable stents; modelling and simulations of stent deformation; stent design; stent manufacturing; stent failure and fracture; in-vitro and in-vivo studies; biocompatibility of stents; stent vessel interaction; fluid-solid interaction; in-stent restenosis; biological and clinical issues related to stents; stent deployment and delivery; medical-imaging-based assessment. Within the framework of the Conference, a Special Session “Design, Manufacturing and Evaluation of Shape-memory-alloy Stents” was organised by partners of the EPSRC UK project (2018-2020): "Smart Peripheral Stents for the Lower Extremity - Design, Manufacturing and Evaluation.” The Session focused on the topics, directly related to the project: lesion-specific design; additive manufacturing; biomechanical testing; modelling of self-expansion; biocompatibility study; in-vitro haemodynamics; in-vivo evaluation; modelling of deployment; deformations due to severe twisting and bending. This issue presents a selection of research papers presented at the International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. The Conference was organised by Technical Committee 14 "Integrity of Biomedical and Biological Materials" of the European Structural Integrity Society (ESIS). The Conference Organisers would like to acknowledge its sponsors: European Structural Integrity Society (ESIS); Engineering and Physical Sciences Research Council (EPSRC), the main funding body for engineering and physical sciences research in the UK; and Loughborough University, UK. Stenosis refers to a partial or total blockage of arteries caused by accumulation of fatty deposits on the vessel wall. The disease results in a progressive damage to patients’ health and wellbeing due to the restriction of blood supply to muscles and organs. For instance, coronary-artery stenosis is a leading reason of heart attack, while peripheral-artery stenosis causes pain when walking and tissue death of a leg. The disease can be effectively treated with vascular stents, which are essentially meshes of synthetic materials used to reopen the blocked blood vessels. However, stenting in arteries proved problematic and challenging, given the complexity of the arterial disease and constant exposure of stents to biomechanical forces and physiological environment. Consequently, it requires continuous research and development, in terms f material, design and manufacturing technologies, in order to improve patency times and reduce complications in interventional therapy. To address these challenges, an International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019 was held on 15-17 July 2019 at Loughborough University London, UK. The aim of this Conference was to bring together specialists in biomedical engineering, biomechanics, aterials science, experimental mechanics, odelling and various aspects of processing and manufacturing as well as medical practitioners to discuss advances in stent technologies. Over 30 papers presented at the Conference by researchers from 10 countries covered various topics including: metallic and polymeric materials for stents; mechanical properties of stents; development of biodegradable stents; modelling and si ulations of stent deformation; stent design; stent manufacturing; stent failure and fracture; i -vitro and i -vivo studies; biocompatibility of stents; stent vessel interaction; fluid-solid interaction; in-stent restenosis; biological and clinical issues related to stents; stent deployment and delivery; medical-imaging-based assessment. Within the framework of the Conference, a Special Session “Design, Manufacturing and Evaluation of Shape-memory-alloy Stents” was organised b partners of the EPSRC UK project (2018-2020): "Smart Peripheral Stents for the Lower Extremity - Design, Manufacturing and Evaluation.” The Session focused on the topics, directly related to the project: lesion-specific design; additive manufacturing; biomechanical testing; modelling of self-expansion; biocompatibility study; in-vitro haemodynamics; in-vivo evaluation; modelling of deployment; deformations due to severe twisting and bending. This issue presents a selection of research papers presented at the International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. The Conference was organised by Technical Committee 14 "Integrity of Biomedical and Biological Materials" of the European Structural Integrity Society (ESIS). The Conference Organisers would like to acknowledge its sponsors: European Structural Integrity Society (ESIS); Engineering and Physical Sciences Research Council (EPSRC), the main funding body for engineering and physical sciences research in t e UK; and Loughborough University, UK. Stenosis ref rs to a p rtial or total blockage of arteries caused by accumulation of fatty deposits on the vessel wall. The disease results in a progressive damage to patients’ health and wellbeing due to the stricti n of blood supply to muscl s and o gans. For instance, coronary-artery ste os is a le ding r ason of heart attack, while peripheral-artery stenosis causes pain when walking and tissue death of a l g. The disease can be effectively tr ated with vascular stents, whi h are essentially meshes of synth tic materials us d to reopen the blocked blood vessels. However, stenting in arteries proved problemat c and challenging, given t e c mplexity of the arterial disease and constant exp sure f stents to biomechanical forces and physi logical nvironment. Consequently, it requires continuous research and developme t, in terms f material, design and ma ufacturing technologies, in order to improve patency times and reduce complications in interventional therapy. To address these challenges, an Int rnational Conference on Stents: Materials, M chanics and Manufacturi g ICS3M 2019 was held on 15-17 July 2019 at Loughborough Univ rsity London, UK. The aim of this Conferenc w s to bring together specialists in biomedical engineering, bi mechanics, teri ls science, experimental mechanics, odelling and various aspects of processing and manufacturing as well as medical practitioners to discuss advances in stent technologies. Over 30 papers presented at the C nference by researchers from 10 countries covered various topics including: metallic a d polymeric materials for tents; mechanical prope ties f stents; development of biodegradable stents; modelli g and si ulations of stent def rmation; stent design; stent manufactu ing; stent failure and f ure vitro and i -v vo studies; biocompatibil ty of st nts; stent vessel interacti n; fluid-solid interaction; in-stent restenosis; biological and clinical issues related to stents; stent deployment and delivery; medical-imaging-based assessment. Wit in the framework of the Conference, a Special Session “Design, Manufacturing and Evaluation of Shape-memory-alloy Sten s” was o ganised by partners of the EPSRC UK project (2018-2020): "Smart Peripheral S ents for the Lower Extremity - Design, Manufacturing and Evaluation.” The Session focused on the topics, directly relat d to the proj ct: lesi n-specific design; additive manufacturing; biomechanical testing; modelling of self-expansion; bioc mpatibility study; in-vitro haemodynami s; in-vivo evaluation; modelling of deploym nt; deformations due to severe twisting and bending. This issue pr sents a selection o research papers presented t the Int rnational Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. Th Conferenc was organised by Technical Committee 14 "Integrity of Biomedical and Bi logical Materials" of the European Structural Integrity ociety (ESIS). The Conference Organisers would like to acknowledge its sponsors: European Structural I tegrity Society (ESIS); Engi eering and Physical Sciences Res arch Council (EPSRC), the main funding body for engineering and physical sciences research in the UK; and Loughborough University, UK. Stenosis refers to a partial or total blockage of arteries caused by accumulation of fatty deposits on the vessel wall. The disease results in a progressive damage to patients’ health and wellbeing due to the restriction of blood supply to muscles and organs. For instance, coronary-artery stenosis is a leading reason of heart attack, while peripheral-artery stenosis causes pain when walking and tissue death of a leg. The disease can be effectively treated with vascular stents, which are essentially meshes of synthetic materials used to reopen the blocked blood vessels. However, stenting in arteries proved problematic and challenging, given the complexity of the arterial disease and constant exposure of stents to biomechanical forces and physiological environment. Consequently, it requires continuous research and development, in terms of material, design and manufacturing technologies, in order to improve patency times and reduce complications in interventional therapy. To address these challenges, an International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019 was held on 15-17 July 2019 at Loughborough University London, UK. The aim of this Conference was to bring together specialists in biomedical engineering, biomechanics, materials science, experimental mechanics, modelling and various aspects of processing and manufacturing as well as medical practitioners to discuss advances in stent technologies. Over 30 papers presented at the Conference by researchers from 10 countries covered various topics including: metallic and polymeric materials for stents; mechanical properties of stents; development of biodegradable stents; modelling and simulations of stent deformation; stent design; stent manufacturing; stent failure and fracture; in-vitro and in-vivo studies; biocompatibility of stents; stent vessel interaction; fluid-solid interaction; in-stent restenosis; biological and clinical issues related to stents; stent deployment and delivery; medical-imaging-based assessment. Within the framework of the Conference, a Special Session “Design, Manufacturing and Evaluation of Shape-memory-alloy Stents” was organised by partners of the EPSRC UK project (2018-2020): "Smart Peripheral Stents for the Lower Extremity - Design, Manufacturing and Evaluation.” The Session focused on the topics, directly related to the project: lesion-specific design; additive manufacturing; biomechanical testing; modelling of self-expansion; biocompatibility study; in-vitro haemodynamics; in-vivo evaluation; modelling of deployment; deformations due to severe twisting and bending. Stenosis refers to a p rtial or otal blockage of arteries caused by accumulation of fatty deposits on the v ssel wall. The disease results in a progressive damage to patients’ health and wellbeing due to the striction of blood supply to muscles and organs. For instance, coronary-artery stenos is a l ding r ason of heart attack, while peripheral-artery stenosis causes pain when walking and tissue death of a leg. The disease can be effectively tr ated with vascular stents, which are essentially meshes f synth tic materials us d to reopen the bl cked blood vessels. Howev r, ste ting in r eries proved problemat c and challenging, given the complexity of the arterial di ease and constant exp sure f stents to biom chanical forces and physiological nvironment. Consequently, it requ res continuous research and developme t, in terms f mater al, design and ma ufacturing technologies, in order to improve patency times and reduce complications in interventional therapy. To address these challenges, an Int rnational Conference on Stents: Materials, M chanics and Manufacturing I S3M 2019 was held on 15-17 July 2019 at Loughborough Univ sity London, UK. The a m of this Conferenc w s to bring together specialists in biomedi al engineering, biomechanics, teri ls science, experimental mechanics, modell ng and various aspects of processing and manufacturing as well as medical practitioners to discuss advances in stent technologies. Over 30 papers presented at the Conference by researchers from 10 countries covered various topics including: metallic and polymeric materials for stents; mechanical properties f stents; development of biodegradable stents; mod lli g and simulations of stent def rmation; stent design; s ent manufac u ing; stent failure and fra ure i vitro and in-v vo studies; biocompatibility of st nts; s ent vessel interaction; fluid-solid interaction; in-stent restenosis; biological and clinical issues related to stents; stent deployment and delivery; medical-imaging-based assessment. Stenosis refers to a p rtial or total blockage of arteries caused by accumulation of fatty deposits on the vessel wall. The disease results in a progressive damage to patients’ health and wellbeing due to the restriction of blood supply to muscles an organs. For instance, coronary-artery stenosi is a l ding r ason of heart attack, while peripheral-artery stenosis causes pain when walking and tissue death of a leg. The disease can be effectively treated with vascular tents, which are ssentially meshes f synthetic materials us d to reopen the blocked blood vessels. However, stenting in rteries proved problematic and challenging, given t e complexity of the arterial disease and constant exp sure f stents to biomechanical forces and physiological environment. Consequently, it requires continuous research and development, in terms of material, design and manufacturing technologies, in order to improve patency times and reduce complications in interventional therapy. o address these challenges, an Int rnational Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019 was held on 15-17 July 2019 at Loughborough Univ rsity London, UK. The aim of this Conference was to bring together specialists in biomedical engineering, biomechanics, teri ls science, experimental mechanics, modelling and various aspects of processing and anufacturing as well as medical practitioners to discuss advances in stent technologies. Over 30 papers presented at the Conference by researchers from 10 countries covered various topics including: metallic and polymeric materials for stents; mechanical properties of stents; development of biodegradable stents; modelli g and simulations of stent deformation; stent design; stent Stenosis refers to a partial or total blockage of arteries caused by accumulation of fatty deposits on the vessel wall. The disease results in a progressive damage to patients’ health and wellbeing due to the restriction of blood supply to muscles and organs. For instance, coronary-artery stenosis is a leading reason of heart attack, while peripheral-artery stenosis causes pain when walking and tissue death of a leg. The disease can be effectively treated with vascular stents, which are essentially meshes of synthetic materials used to reopen the blocked blood vessels. However, stenting in arteries proved problematic and challenging, given the complexity of the arterial disease and constant exposure of stents to biomechanical forces and physiological environment. Consequently, it requires continuous research and development, in terms of material, design and manufacturing technologies, in order to improve patency times and reduce complications in interventional therapy. To address these challenges, an International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019 was held on 15-17 July 2019 at Loughborough University London, UK. The aim of this Conference was to bring together specialists in biomedical engineering, biomechanics, Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK E-mail: L.Zhao@Lboro.ac.uk; V.Silberschmidt@Lboro.ac.uk Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough Unive sity, Loughborough, Leicestershire, LE11 3TU, UK E-mail: L.Zhao@Lboro.ac.uk; V.Silberschmidt@Lboro.ac.uk Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK E-mail: L.Zhao@Lboro.ac.uk; V.Silberschmidt@Lboro.ac.uk Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK E-mail: L.Zhao@Lboro.ac.uk; V.Silberschmidt@Lboro.ac.uk Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK E-mail: L.Zhao@Lboro.ac.uk; V.Silberschmidt@Lboro.ac.uk Wolfson School of Mechanical, Electrical and Manufa turing Engineering, Loughborough Unive sity, Loughborough, Leicestershire, LE11 3TU, UK E-mail: L.Zhao@Lboro.ac.uk; V.Silberschmidt@Lboro.ac.uk

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000–000 ScienceDirect

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Procedia Structural Integrity 15 (2019) 67–74

© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. Abstract In order t address new challe ges th t arise in the d gradation behavi r of absorbable me al ste ts (AMSs) i vivo , new m delling and simulation re presented in this study. A dynamic corrosion mod l (Model 1) considering uniform corrosion, stress corrosion me hanisms and dynamic cyclic puls loading was proposed to imul te the stent degradation based on Con inuum Damage Mechanics (CDM). A control group (Model 2) was stablished which only considered the mechanisms of uniform nd str ss corrosion. The time of stent d graded compl tely in Model 1 was set as a normalized time unit (100t) to illustrate the results. Wi h the increase of tim , the mass and supporting performance of the stent decreased, especially at 10t to 20t. The verage von Mises Stress of th stent in the Model 1 decrea es from 86.19 MPa to 48.65 MPa rough y at 5t to15 , whil the average von Mises S ress in Model 2 decreases from 87.12 MPa to 50 MPa. The mass l ss ratio of stents in Model 1 is always higher than that in Model 2, and the relative error of the mass ratio reac ed 14.3% at 20t. The results showed that the corrosio occurs a first in the stent struts with the highest von Mises stress. In addition, the dynamic cyclic pulse loading accelerated the degradation rate and the supporting performance loss of stent. These modelling and simulation techniques may provide new insight to in vivo AMS p rfo mance. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019 A Computational Modelling of the Mechanical Performance of a Bioabsorbable Stent Undergoing Cyclic Loading Xinyang Cui a , Kun Peng a , Sicong Liu a , Qingshuai Ren a,b , Gaoyang Li a,c , Zhaoyong Gu a , Aike Qiao a, 0F * a College of Life Science and Bioengineering, Beijing University of Technology, No.100, Pingleyuan, Chaoyang District, Beijing, 100022,China. Abstract In order to address new challenges that arise in the degradation behavior of absorbable metal stents (AMSs) in vivo , new modelling and simulation are presented in this study. A dynamic corrosion model (Model 1) considering uniform corrosion, stress corrosion mechanisms and dynamic cyclic pulse loading was proposed to simulate the stent degradation based on Continuum Damage Mechanics (CDM). A control group (Model 2) was established which only considered the mechanisms of uniform and stress corrosion. The time of stent degraded completely in Model 1 was set as a normalized time unit (100t) to illustrate the results. With the increase of time, the mass and supporting performance of the stent decreased, especially at 10t to 20t. The average von Mises Stress of the stent in the Model 1 decreases from 86.19 MPa to 48.65 MPa roughly at 5t to15t, while the average von Mises Stress in Model 2 decreases from 87.12 MPa to 50 MPa. The mass loss ratio of stents in Model 1 is always higher than that in Model 2, and the relative error of the mass loss ratio reached 14.3% at 20t. The results showed that the corrosion occurs at first in the stent struts with the highest von Mises stress. In addition, the dynamic cyclic pulse loading accelerated the degradation rate and the supporting performance loss of stent. These modelling and simulation techniques may provide new insights to in vivo AMS performance. International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019 A Computational Modelli g of the Mechani al Performance of a Bioabsorbable Stent Undergoing Cyclic Loading Xinyang Cui a , Kun Peng a , Sicong Liu a , Qingshuai Ren a,b , Gaoyang Li a,c , Zhaoyong Gu a , Aike Qiao a, 0F * a College of Life Science and Bioengineering, Beijing University of Technology, No.100, Pingleyuan, Chaoyang District, Beijing, 100022,China. b Institute of Mechanics, Chinese Academy of Science, No.15, BeiSiHuanWest Road, Beijing, 100190, China. c Graduate School of Biomedical Engineering, Tohoku University, Sendai, Miyagi, 980-8577, Japan b Institute of Mechanics, Chinese Academy of Science, No.15, BeiSiHuanWest Road, Beijing, 100190, China. c Graduate School of Biomedical Engineering, Tohoku University, Sendai, Miyagi, 980-8577, Japan

* Corresponding author. Tel.: +81-10-67396657; fax: +81-10-67396657. E-mail address: qak@bjut.edu.cn

2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. 2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. * Corresponding author. Tel.: +81-10-67396657; fax: +81-10-67396657. E mail address: qak@bjut.edu.cn

2452-3216  2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of International Conference on Stents: Materials, Mechanics and Manufacturing ICS3M 2019. 10.1016/j.prostr.2019.07.013

Xinyang Cui et al. / Procedia Structural Integrity 15 (2019) 67–74 Cui et al. / Structural Integrity Procedia 00 (2019) 000–000

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Keywords: Finite element analysis; Absorbable stent; Corrosion modelling; Biomechanics

1. I ntroduction Bioabsorbable intravascular stents have gained attention to treat the artery disease in recent years since they can perform a mechanical support to the artery for a scaffolding period (6-12 months) and then be absorbed by the body. This characteristic is not only suitable for adult patients but also benefit for the growing vessels of paediatric patients (Zartner et al., 2005; Schranz et al., 2006; Wykrzykowska et al., 2009), and can avoid long-term complications (Köster et al., 2000; Virmani et al., 2004), reduce risk of in-stent restenosis [Mitra, 2006; Hoffmann et al., 1996] and late stent thrombosis (Morlacchi et al., 2014). A bioabsorbable stent is supposed to disappear completely after the scaffolding time is complete and the arterial wall has remodelled. In this certain scaffolding period, the bioabsorbable materials, such as metallic alloys (ferroalloy, magnesium alloy, zinc alloy, etc.) have many chemical and physical reactions. As reviewed by Boland et.al, the description of corrosion mechanism of metal alloys generally includes but not limited to micro-galvanic corrosion, pitting corrosion and intergranular corrosion, stress corrosion cracking (SCC) and corrosion fatigue. Taking a zinc alloy stent as an example, firstly, the zinc alloy is highly susceptible to micro-galvanic corrosion. In in vivo corrosion environment, the metal zinc acts as anode, alloy element or impurity acts cathode, and localized pitting corrosion occurs at the cathode. After the crimped stent expanded the stenotic vessel to a healthy diameter, the interaction between the residual stress and the blood environment can lead to SCC. More attention should be paid to SCC because it can lead to stent fast fracture (Morlacchi et al., 2014; Auricchio et al., 2015), eventually cause an in-stent restenosis (Shaikh et al., 2008; Adlakha et al., 2010). During the stent service period, the blood flow induced pulsatile pressure acts on the inner surface of the blood vessel. The corrosion fatigue of stent is caused by the combined action of an alternating stress or the pulsatile stress and the blood aggressive environment. In the degradation process, the stent structure damages and the material mechanical properties weakening occur simultaneously and interact with each other. In the meanwhile, the interaction between the stent and the blood vessels also keeps changing until the stent degrades completely (Grogan et al., 2013). Finite element analysis (FEA) has been a valuable tool for accounting for corrosion modelling. Based on Continuum Damage Mechanics (CDM), a number of numerical models for micro-galvanic and pitting corrosion have been proposed (Wu et al., 2011; Grogan et al., 2014) to predict the corrosion rate. Wu et al. developed the coupled formulation of uniform micro-galvanic corrosion and stress corrosion to optimize the mechanical performances of the absorbable stent. The influence of aggressive environment and a cyclic pulse stress on the corrosion fatigue was studied by tests under different corrosive environments (Bhuiyan et al., 2008; Nan et al., 2008; Boland et al., 2016). The corrosion fatigue behavior under in vivo condition is still a hard challenge, especially capturing the effects of the in vivo environment (cyclic pulsatile loading) on the rates of corrosion with computation technique (Winzer et al., 2005). 2. Methodology 2.1. Geometry models and material properties Bioabsorbable zinc alloy was selected as the stent material due to its combination of mechanical properties and biocompatibility. The zinc alloy in this paper was consisted of Zn, Mg, Al, and the true strain-stress curves of this zinc alloy was shown in Fig.1. The zinc alloy has a modulus of 98 GPa, Poisson’s ratio of 0.30, density of 6.7 g/mm 3 , a yield stress of 220 MPa, and ultimate tensile strength of 325 MPa, and it was modelled as a homogeneous, isotropic, elastoplastic material. To save the simulation time, only one stent ring consisted of 10 crowns was chosen for the degradation model. The dimension details were shown in Fig. 2. The artery vessel property used in this paper is identical to that used in our previous studies (Cui et al., 2018a; Cui et al., 2018b). The combination of the stent and the artery were meshed with the C3D8R using the software Hypermesh 11.0. To investigate the influence of cyclic pulsatile loading on the stent degradation behavior, a dynamic corrosion model (named Model 1) was established where not only two corrosion mechanisms was considered, but also the

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influence of dynamic cyclic pulsatile loading on corrosion behaviour was taken into account. In addition, a control group (named Model 2) considering only two corrosion mechanisms was established.

Fig. 1. True strain-stress curves of the zinc alloy.

Fig. 2. Geometrical dimensions of the stent and artery.

Two simulation steps were executed for the whole simulation. Step 1: stent crimping-expansion. In order to simulate crimping of the stent on a balloon catheter, a displacement load corresponding to a diameter of 15% was assigned. Subsequently, the stent was delivered to the stenotic lesion. A uniform radial deformation, up to a diameter of 1.1 times of the healthy vessel inner diameter, was imposed on the inner surface of the carotid stent along the longitudinal axis (Dordoni et al., 2014). At the end of this step, the stent was deflated and the vessel wall elastically recoiled. In this step, the corrosion procedure was not taken into account, and this process was simulated using ABAQUS/Standard solver. Step 2: the whole model and its mechanical results after the step 1 were imported into the corrosive environment. This approach was implemented in ABAQUS/Explicit through user subroutines VUSDFLD. A flowchart outlining the operation of the corrosion model was shown in Fig. 3. After subjecting the stent to a large deformation in step 1, the stent underwent pulsatile loading produced from the oscillation of the internal blood pressure. To simulate the blood cyclic pulsatile loading effects on the stent degradation, the pulsatile pressure that changes over time was applied to the inner surface of the vessel. The stent began to degrade in corrosive environment similar to in vivo situation. 2.2. Establishment of corrosion degradation model Based on continuous damage mechanics, a corrosion model of zinc alloy was established where the uniform

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current corrosion and stress corrosion cracking (SCC)) were taken into account. With regards to the isotropic damage hypothesis, the continuous damage model sets the damage field D by defining a continuous function related to time and boundary conditions, so as to simulate the reduction of macroscopic mechanical properties (such as stiffness, yield stress, etc.) of the material. The effective stress during the damage process can be calculated as shown in Equation (1), σ = （ 1 − D ） (1) where σ means the effective stress, is the undamaged stress, D is a damage variable which increases monotonously from 0 to 1. There is not any damage in the material if D is equal to 0, while D= 1 means the material completely lost its capability. Considering the uniform micro-current corrosion and stress corrosion which caused the overall degradation of the stent, D is assumed to be linear superposition of the uniform corrosion damage and the stress corrosion damage , as shown in Equation (2), D = + (2)

Fig. 3. Simplified flowchart of the corrosion model process. The uniform corrosion damage is defined to describe the mass loss of material when the material is exposed in aggressive environment. The damage evolution law of uniform corrosion process is supposed to be functions of U δ , U k and e L with the following form of equation (3).

(3)

U D δ = 

k

U

U

L

e

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where U k is a parameter related to the kinetics of the uniform corrosion process, U δ is a characteristic dimension of the uniform corrosion process, and e L is the characteristic length of a finite element. In Gastaldi’s research, the value of U k is between 0.01/h and 0.1/h (Gastaldi et al., 2011). Based on the immersion test completed in our research, the details of uniform corrosion dynamic parameters are listed in Table 1. The D SC represents the damage associated with stress corrosion cracking (SCC) processes . Stress corrosion cracking model can be established, as shown in equation (4) and equation (5).

(4)

eq σ < *

σ

0 = SC D 

th

*

σ

L S

(5)

* ≥ > th eq σ

0

σ

eq R

D 

(

)

e

=

SC

1

D

δ

−

sc

where * e L is Element feature size in finite element analysis, m. SC δ means the characteristic size of the stress corrosion process, m. th σ is the stress threshold, closely related (Winzer et al., 2005) to the combination of material composition, metallurgical conditions and corrosive environment, and is set to 50% of the yield stress of zinc alloy, 110 MPa. S and R relate to the kinetics of the stress corrosion process, are a function of the corrosive environment. Based on the Costa-Mattos’ research (Costa-Mattos et al., 2008), S and R are kept constant because a constant pH is adopted for the corrosive environment, the details of these relevant parameters are listed in Table 1. eq σ is the equivalent Mises stress causing the stress corrosion of the stent,

Table 1 Parameters for the material degradation model. Parameters U δ U k SC δ

th σ

R

S

value

0.1mm

0.05/h

0.07mm

110MPa

0.005mm 2 h /N

2

The material degradation model is implemented into a finite element framework using the commercial code ABAQUS/Explicit 6.13 (ABAQUS Inc., USA) by means of a user subroutine (VUSDFLD). For beginning and evolution of the corrosion, the stress state is calculated and updated in the explicit time integration. In addition, the s implified flowchart of the corrosion model process is shown in Fig. 3. The corrosion model considering the influence of the dynamic load of the blood flow pulsatile pressure is set to Model 1, in which the stent is implanted into the blood environment and which is set as the start time of 0, and the time for the complete degradation of the stent is set as 100 Time Unit (100t). The degradation of the stents in the two models was compared. 3. Results and discussion The influence of pulsatile pressure on the degradation rate of stent will be discussed as follows. (1) The mass loss ratio was selected as an evaluation index to compare the degradation rates in these two models. The volume of the stents at the time t ( ) during the degradation process can been extracted from the finite element simulation results, and the material density ( ρ ) was assumed to be constant. Based on these, the approximate mess of the stent during the degradation process at the time t can be calculated as t M = . The calculation formula of mass loss ratios of stents was shown in equation (6) and the results were shown in Fig. 4.

initial t initial -M M

M = γ

(6)

where M initial means the initial mess of the stent when it was not degraded;

t M means the approximate mess of the

stent at the time t.

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Fig. 4. Comparison of mass loss ratios of stents in degradation models.

(2) The structure of the stents changed with time during the degradation was shown in Fig. 5, and the damage condition of the stents can be compared using these damage contours. (3) The average value of the von Mises Stress during the degradation process of the stent was selected to evaluate the influence of the dynamic load of the blood flow pulsatile blood pressure on the mechanical properties during the degradation process of the stent, as shown in Fig. 6. In Fig. 4, quantitative comparison shows that the difference in mass loss ratio of the stent in the two degradation models is not obvious. Especially before 5t, the corrosion degradation of the stent hardly occurs and the mass loss ratio of the stent is small. During the degradation process, the mass loss ratio has positively correlation with time. The mass loss ratio of the stent begins to change within 5t-20t. After 10t, the stent degradation accelerates, and the growth of the mass loss ratio increases obviously. The mass loss ratios of stents in Model 1 is always higher than that in Model 2, and the relative error of the mass loss ratio reached 14.3% when t=20. Until 20t, the mass loss ratio in model 1 is larger than 0.80, which indicates that a large-area of stent structure fracture results in the rapid quality decrease. After this time, the difference of the mass loss ratios of stents in two models is obvious. This indicates that the blood flow pulsatile pressure promotes the degradation of the stent. It is necessary to pay attention on the degradation of the stent structure and the support performance of the stent during 5t to 20t.

Fig. 5. Corrosion contour and structural damage comparison of the stents in the two models.

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As shown in Fig. 5, compared to the corrosion contour and structural damage of the stents in the two models, the stents showed no damage in the two models before 5t. At this time, the corrosion factor contour is very similar. As can be seen from the corrosion contour, the element deletion occurs first at the inner surface of the bend in the stent crown, where the residual stress generated in the crimping-expansion process is much higher. The residual stress is the cause of the SCC. After 10t, the corrosion factor of in Model 1 is always higher than that in the Model 2. It indicates that the blood flow pulsation pressure has no significant effect on the initial cracking time of the stent, but once the stent cracked, the dynamic load of blood flow pulsatile pressure significantly accelerates the process from the cracking to the end of degradation. As shown in Fig.5, the changing rate of the stent damage and degradation under the effect of blood flow pulsatile pressure is higher than that without the influence of pulsatile dynamic pressure.

Fig. 6. Average von Mises stress of stents at 5t-15t.

The decrease of the average von Mises Stress represents the reduction of the support performance of the entire stent structure. The average equivalent stress of the stent during degradation from 5t to 15t is statistically calculated, as shown in Fig. 6. The average von Mises Stress of the stent in the Model 1 decreases from 86.19 MPa to 48.65 MPa roughly at 5t to15t, while the average von Mises Stress in Model 2 decreases from 87.12 MPa to 50 MPa. At 15 t, the average von Mises Stress of the stent is smaller than the threshold of stress corrosion, and the effect of stress corrosion cracking decreases over time. With the increase of degradation time, the stent degrades under the action of uniform corrosion and blood pulsatile pressure, and the degradation rate becomes slow. This is also the reason why the mass loss ratio in Fig. 4 decreases after 20t, and the support performance of the stent continues to be lost. Quantitative comparison shows that the stress distribution in Model 1 is slightly lower than that in Model 2, indicating that the support performance of the stent in Model 1 is lost faster than in Model 2 at the same time. This indicates that the blood flow pulsatile pressure dynamic load accelerates the loss of the support performance of the stent. 4. Conclusions In the degradation process, the evolution of material degradation leads to a continuous weakening of stent structure and supporting properties. At the initial period of stent degradation, the stress corrosion plays a great rule in the corrosion of stent. The main influencing factor of the initial cracking of the stent is the residual stress after the stent expanded; the corrosion cracking occurs at first in the stent struts with the highest von Mises stress. In the corrosive environment, once the stent is cracked, it would accelerate the degradation rate of the stent and the loss of the mechanical properties even the dynamic pressure of the blood flow is very small. Cyclic pulsatile loading has strong influence on the degradation behavior and the mechanical performance of stent. The established computational modelling of stent undergoing cyclic loading will contribute to a more proper mechanical analysis of bioabsorbable stents.

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