冠状动脉支架力学性能数值研究与优化设计
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摘要
心血管病是威胁居民健康的重大疾病。据统计,国内每年死于心血管病的人数约为三百万,占总死亡人数的45%左右,每年用于心血管病的医疗费用超过1300亿元人民币。冠状动脉内支架植入术是治疗冠心病的一种有效手段,近年来越来越多地得到了广泛应用。冠脉支架的力学性能,是关系到支架术效果的关键因素之一。许多医务工作者和工程界的学者都在努力研究这一课题。本文利用有限元方法来研究冠脉支架的力学性能。
论文的主要工作包括：
针对冠脉裸支架结构,研究了有限元模型所采用的单元类型(高阶实体单元、低阶实体单元、壳单元、梁单元)和网格剖分密度对计算效率和精度的影响,模拟了冠脉裸支架全寿命内的变形过程所涉及到的力学性能。通过模拟支架生产过程中的压握变形、手术过程中的膨胀变形以及在冠状动脉内长期工作时的压缩变形,本文发现：压握过程对膨胀性能的影响较小,而膨胀程度对支架在工作状态下抵抗压缩载荷的径向支撑力具有较大的影响。另外,根据支架的膨胀性能曲线进行深入分析后得到了膨胀速度曲线,发现了膨胀速度曲线与支架的最佳膨胀范围的内在联系。
本文对冠脉支架与球囊的接触问题进行了模拟,得到了比较准确的变形结果。在此基础上,提出了利用应变能来计算真实接触压力的方法。一般来说,通过接触分析所得到的球囊与支架间的接触压力,与实际情况下均匀一致的压力相比,误差往往比较大,这是由于支架金属丝比较细而只能在接触面上采用较粗的网格单元所导致的。根据功能原理,并且考虑到接触压力是驱动支架膨胀而产生应变能的唯一直接原因,本文利用支架应变能占全部应变能的百分比对膨胀载荷进行了修正,得到了支架与球囊之间真实而且均匀的接触压力,其结果与裸支架的膨胀曲线相互一致。这个方法可以作为验证接触分析结果正确性的依据。
针对冠脉支架的纵向柔顺性,建立的悬臂梁弯曲模型,克服了三点载荷法和简支梁模型的缺陷,能够更准确、更全面地描述支架整体弯曲性能。以该模型为基础,本文详细研究了目标支架在较大弯曲曲率范围内的瞬时抗弯刚度情况,结果表明：在弯曲曲率较小的情况下,支架瞬时抗弯刚度一般表现为各向同性；而当弯曲曲率较大时,则出现非常明显的各向异性。此外,利用悬臂梁模型还发现,支架弯曲时还伴随发生了在弯曲平面外的侧向偏转以及绕支架中心轴的扭转变形。这两种附带变形是由支架弯曲变形而引起的,在一定程度上改变了支架的实际弯曲方向和曲率。这两种附带变形也正是瞬时弯曲刚度存在各向异性的证据。
在优化设计工作中,利用ANSYS的APDL语言开发了适用于冠脉血管支架有限元分析的计算程序,该程序具有自动化运行、参数化建模、仝过程分析、鲁棒性计算及优化等特点,将此程序进一步加以完善后,即可作为专门用于血管支架力学性能模拟的软件。以此程序为基础,本文分别建立了描述支架膨胀综合性能和柔顺性能的数学模型,对目标支架的几何形状及尺寸进行了优化,改善了目标支架各项力学性能。以往在血管支架设计领域里采用的传统模式是对有限数量的设计方案分别进行数值模拟或实验分析,然后比较支架的力学性能结果并进行人工选优。本文的优化工作则将最优化理论拓展到血管支架的设计工作,有效地提高了血管支架优化设计工作的效率。
Coronary artery heart disease (CHD) has become the most dangerous reason which threatens human health. It is reported by national authority that three million people die of CHD every year and the number reaches 45% of total death. Annually, it costs more than 130 billion RMB in this field. Coronary artery stent implantation is the latest effective therapy. As stent technology develops rapidly, stent is used in more heart surgery instead of CABG (coronary artery bypass graft surgery). The mechanical properties of stent are important. Cardiologists from hospitals, engineers who design the products and scientists of mechanics community share the same interest on this subject. This dissertation studies the mechanical properties of stent utilizing finite element method.
At the beginning of this dissertation, a bare stent is studied. Firstly, attention is paid to how element type and mesh density influence the simulation results of deformation. Secondly, the expansion speed curve is derived from the expansion curve, and an instinct relationship between the expansion speed and the recommended expansion range is obtained. Thirdly, the deformation during crimp stage to assemble stent and balloon together is simulated and the results show that it does not affect expansion and compression. However, the expanding process will change the resistance to external pressure of stent greatly. At last, beam element is employed to construct the finite element model. In terms of computational accuracy and effectiveness, beam element model is compared with those of shell and solid element.
Contact analysis involving stent and balloon structures is accomplished. The results are in accordance with the actual deformation. The contact pressure obtained from contact elements, which should have been average, varies greatly due to the coarse meshes. In order to validate the simulation, strain energies of all elements are collected from results when the non-linear iteration converges every time. By re-calculating the expanding load according to strain energy distribution, real contact pressure is obtained and the results match the expanding force used for bare stent very well.
A cantilever model is proposed to mimic stent's flexibility, which has some advantages over 3-point load method and the simple beam model. The IBS (Instant Bending Stiffness) of stent is studied and it is found that IBS maybe anisotropic when curvature grows large enough. In addition, a deflection and a rotation angle occur to the stent because of the anisotropic IBS.
Design optimization is the most important content of this research. Optimization theory is applied to improve the mechanical properties of the stent. A program which is automatic, parametric, integrated and robust is developed using ANSYS parametric design language. According to the findings that obtained respectively from the simulations about expansion and flexibility of chapter 2 and 4, objective functions to improve the expansion properties and flexibility are proposed. And then, the proper design variables are chosen and the entire optimization models are built in mathematical formulation. Finally, the optimization tasks are performed and the optimal designs are obtained successfully. This research introduces the optimization theory to the design of coronary stent, which improves the design efficiency in this field.
论文的主要工作包括：
针对冠脉裸支架结构,研究了有限元模型所采用的单元类型(高阶实体单元、低阶实体单元、壳单元、梁单元)和网格剖分密度对计算效率和精度的影响,模拟了冠脉裸支架全寿命内的变形过程所涉及到的力学性能。通过模拟支架生产过程中的压握变形、手术过程中的膨胀变形以及在冠状动脉内长期工作时的压缩变形,本文发现：压握过程对膨胀性能的影响较小,而膨胀程度对支架在工作状态下抵抗压缩载荷的径向支撑力具有较大的影响。另外,根据支架的膨胀性能曲线进行深入分析后得到了膨胀速度曲线,发现了膨胀速度曲线与支架的最佳膨胀范围的内在联系。
本文对冠脉支架与球囊的接触问题进行了模拟,得到了比较准确的变形结果。在此基础上,提出了利用应变能来计算真实接触压力的方法。一般来说,通过接触分析所得到的球囊与支架间的接触压力,与实际情况下均匀一致的压力相比,误差往往比较大,这是由于支架金属丝比较细而只能在接触面上采用较粗的网格单元所导致的。根据功能原理,并且考虑到接触压力是驱动支架膨胀而产生应变能的唯一直接原因,本文利用支架应变能占全部应变能的百分比对膨胀载荷进行了修正,得到了支架与球囊之间真实而且均匀的接触压力,其结果与裸支架的膨胀曲线相互一致。这个方法可以作为验证接触分析结果正确性的依据。
针对冠脉支架的纵向柔顺性,建立的悬臂梁弯曲模型,克服了三点载荷法和简支梁模型的缺陷,能够更准确、更全面地描述支架整体弯曲性能。以该模型为基础,本文详细研究了目标支架在较大弯曲曲率范围内的瞬时抗弯刚度情况,结果表明：在弯曲曲率较小的情况下,支架瞬时抗弯刚度一般表现为各向同性；而当弯曲曲率较大时,则出现非常明显的各向异性。此外,利用悬臂梁模型还发现,支架弯曲时还伴随发生了在弯曲平面外的侧向偏转以及绕支架中心轴的扭转变形。这两种附带变形是由支架弯曲变形而引起的,在一定程度上改变了支架的实际弯曲方向和曲率。这两种附带变形也正是瞬时弯曲刚度存在各向异性的证据。
在优化设计工作中,利用ANSYS的APDL语言开发了适用于冠脉血管支架有限元分析的计算程序,该程序具有自动化运行、参数化建模、仝过程分析、鲁棒性计算及优化等特点,将此程序进一步加以完善后,即可作为专门用于血管支架力学性能模拟的软件。以此程序为基础,本文分别建立了描述支架膨胀综合性能和柔顺性能的数学模型,对目标支架的几何形状及尺寸进行了优化,改善了目标支架各项力学性能。以往在血管支架设计领域里采用的传统模式是对有限数量的设计方案分别进行数值模拟或实验分析,然后比较支架的力学性能结果并进行人工选优。本文的优化工作则将最优化理论拓展到血管支架的设计工作,有效地提高了血管支架优化设计工作的效率。
Coronary artery heart disease (CHD) has become the most dangerous reason which threatens human health. It is reported by national authority that three million people die of CHD every year and the number reaches 45% of total death. Annually, it costs more than 130 billion RMB in this field. Coronary artery stent implantation is the latest effective therapy. As stent technology develops rapidly, stent is used in more heart surgery instead of CABG (coronary artery bypass graft surgery). The mechanical properties of stent are important. Cardiologists from hospitals, engineers who design the products and scientists of mechanics community share the same interest on this subject. This dissertation studies the mechanical properties of stent utilizing finite element method.
At the beginning of this dissertation, a bare stent is studied. Firstly, attention is paid to how element type and mesh density influence the simulation results of deformation. Secondly, the expansion speed curve is derived from the expansion curve, and an instinct relationship between the expansion speed and the recommended expansion range is obtained. Thirdly, the deformation during crimp stage to assemble stent and balloon together is simulated and the results show that it does not affect expansion and compression. However, the expanding process will change the resistance to external pressure of stent greatly. At last, beam element is employed to construct the finite element model. In terms of computational accuracy and effectiveness, beam element model is compared with those of shell and solid element.
Contact analysis involving stent and balloon structures is accomplished. The results are in accordance with the actual deformation. The contact pressure obtained from contact elements, which should have been average, varies greatly due to the coarse meshes. In order to validate the simulation, strain energies of all elements are collected from results when the non-linear iteration converges every time. By re-calculating the expanding load according to strain energy distribution, real contact pressure is obtained and the results match the expanding force used for bare stent very well.
A cantilever model is proposed to mimic stent's flexibility, which has some advantages over 3-point load method and the simple beam model. The IBS (Instant Bending Stiffness) of stent is studied and it is found that IBS maybe anisotropic when curvature grows large enough. In addition, a deflection and a rotation angle occur to the stent because of the anisotropic IBS.
Design optimization is the most important content of this research. Optimization theory is applied to improve the mechanical properties of the stent. A program which is automatic, parametric, integrated and robust is developed using ANSYS parametric design language. According to the findings that obtained respectively from the simulations about expansion and flexibility of chapter 2 and 4, objective functions to improve the expansion properties and flexibility are proposed. And then, the proper design variables are chosen and the entire optimization models are built in mathematical formulation. Finally, the optimization tasks are performed and the optimal designs are obtained successfully. This research introduces the optimization theory to the design of coronary stent, which improves the design efficiency in this field.
引文
[1]戴汝平,高建华.冠状动脉多排螺旋CT成像[M].科学出版社,2007.
[2]主编汪丽蕙,吴树燕.现代心血管疾病诊疗手册[M].1.北京：北京医科大学、中国协和医科大学联合出版社,1998：521.
[3]李国彰.冠状循环与冠心病[J].中国医刊.1987(06)：7-10.
[4]袁荣玺.冠心病心绞痛的诊断与治疗[J].辽宁医学杂志.1994,8(02)：58-69.
[5]陈文广.3种抗冠心病药物治疗稳定型心绞痛的临床评价[J].云南中医中药杂志.2008,29(03)：17.
[6]王绿娅,许金鹏,赵全明.斑块稳定-冠心病药物治疗的起点与终点[J].中国药物应用与监测.2004(04)：11-15.
[7]孙福成.冠心病药物治疗的进展[J].中国医刊.1999,34(03)：9-11.
[8]蔡立英.冠心病药物治疗的进展[J].中国初级卫生保健.1988(12)：26-27.
[9]胡大一,孙艺红.冠心病药物治疗的最新进展和展望[J].中国实用内科杂志.2006,26(02)：88-91.
[10]刘登智.冠心病药物治疗近况[J].西南民族学院学报(自然科学版).2000,26(01)：91-94.
[11]吕树铮.冠心病药物治疗新进展[J].中国处方药.2008(05)：74-75.
[12]陈艰,刘志芳.自体血管在冠状动脉搭桥术中的应用[J].江西医药.2008,43(06)：611-613.
[13]陈鑫.冠状动脉搭桥治疗冠心病的现状和进展[J].实用临床医药杂志.2005,9(03)：3-8.
[14]陈铮.天堑变通途——探秘心脏搭桥手术[J].首都医药.2008(05)：50-51.
[15]高成杰,宁吉顺,王惠霞等.急诊冠脉搭桥术适应证探讨[J].临床急诊杂志.2007,8(02)：93-94.
[16]欧阳墉.我国血管狭窄和(或)闭塞性病变介入治疗的发展历程[J].中华放射学杂志.2005,39(09)：7-10.
[17]刘冰,高润霖.经皮冠状动脉介入治疗指南[J].现代实用医学.2004,16(01)：55-64.
[18]欧阳墉.管腔内支架：I.作用机制和性能[J].国外医学.临床放射学分册.1997(04)：20-23.
[19]高惠荣.冠状动脉成形术和冠状动脉搭桥手术的比较[J].浙江医学情报.1994(02)：9-16.
[20]王强,姜楠,王联群等.急诊冠状动脉搭桥术的临床应用[J].天津医药.2007,35(10)：792-793.
[21]罗坤.血管成形术对搭桥手术：棋逢敌手[J].心血管病防治知识.2007(12)：29.
[22]卿清.冠脉多支阻塞,搭桥或许优于血管成形术[J].心血管病防治知识.2008(03)：41.
[23]邱杏霖.选择血管成形术还是搭桥手术?[J].心血管病防治知识.2008(05)：34-35.
[24]徐在品.抑制血管内膜增生的血流动力学和血液流变学机理研究[D].重庆大学,2005.
[25]乔树宾.冠心病介入治疗进展-(7)冠状动脉内支架的设计和临床应用进展[J].中国循环杂志.2003,18(02)：5-8.
[26]周永恒,蒙红云,曾常春等.血管内支架的技术与性能[J].生物医学工程学杂志.2007,24(6)：225-229.
[27]高振宇.医用镍钛合金支架结构的优化设计[D].大连理工大学,2006.
[28]高振宇,粱栋科,齐民等.镍钛合金超弹性支架抗压缩性能的实验与分析[J].功能材料与器件学报.2006,12(01)：51-55.
[29]徐强,刘玉岚,王彪等.形状记忆合金心血管支架自扩张过程的数值模拟与支架的“最优化网格”[J].生物医学工程学杂志.2008,25(5)：125-130.
[30]赵振心,刘道志,孙康等.镍钛合金血管支架的有限元分析及疲劳测试[J].中国医疗器械杂志.2008,32(5)：69-72.
[31]Thierry B, Merhi Y, Bilodeau L, et al. Nitinol versus stainless steel stents:acute thrombogenicity study in an ex vivo porcine model[J]. Biomaterials.2002,23(14): 2997-3005.
[32]贾楠,肖越勇,张金山.生物可降解性血管内支架及药物释放支架的研制[J].中国医学影像技术.2007,23(01)：120-124.
[33]肖越勇,张金山,崔福斋等.生物可降解性血管内支架的制备及其性能研究[J].中华放射学杂志.2003,37(11)：76-82.
[34]唐剑飞.生物可降解性血管内支架的研究进展[J].国外医学(骨科学分册).2002,23(04)：233-235.
[35]Rieu R, Barragan P, Garitey V, et al. Assessment of the trackability, flexibility, and conformability of coronary stents:a comparative analysis[J]. Catheterization and Cardiovascular Interventions.2003,59(4):496-503.
[36]Petrini L, Migliavacca F, Auricchio F, et al. Numerical investigation of the intravascular coronary stent flexibility[J]. Journal of Biomechanics.2004,37(4): 495-501.
[37]刘明.冠状动脉支架的生物力学行为分析[D].哈尔滨工程大学,2007.
[38]周承倜,董何彦.冠状动脉支架力学性能的理论和实验研究[J].应用力学学报.2008,25(04)：26-31.
[39]高振宇,梁栋科,齐民等.镍钛合金超弹性支架纵向柔顺性分析[J].功能材料.2007,38(01)：117-118.
[40]周承倜,董何彦.微型网状结构支架的力学性能研究[J].应用力学学报.2004,21(03)：4-11.
[41]David Chua S N, Mac Donald B J, Hashmi M S J. Finite-element simulation of stent expansion[J]. Journal of Materials Processing Tech.2002,120(1-3):335-340.
[42]Migliavacca F, Petrini L, Montanari V, et al. A predictive study of the mechanical behaviour of coronary stents by computer modelling [J]. Medical Engineering and Physics. 2005,27(1):13-18.
[43]Tan L B, Webb D C, Kormi K, et al. A method for investigating the mechanical properties of intracoronary stents using finite element numerical simulation[J]. International Journal of Cardiology.2001,78(1):51-67.
[44]Etave F, Finet G, Boivin M, et al. Mechanical properties of coronary stents determined by using finite element analysis[J]. Journal of Biomechanics.2001,34(8):1065-1075.
[45]倪中华,王跃轩,程洁.球囊扩张式冠脉支架扩张变形机理数值模拟方法[J].机械工程学报.2008,44(01)：102-108.
[46]王勖成,邵敏.有限单元元基本原理和数值方法[M].清华大学出版社,1997.
[47]机械工程材料性能数据手册编委会.机械工程材料性能数据手册[M].北京：机械工业出版社,1995：433.
[48]戴雅康.金属力学性能实验[M].北京：机械工业出版社,1991.
[49]张庆宝,王伟强,齐民等.不同材料冠状动脉支架膨胀行为分析[J].功能材料.2007,38(01)：130-134.
[50]黄远,李林安,刘文西.医用心血管支架的非线性有限元分析[J].中国生物医学工程学报.2003,22(02)：139-148.
[51]王跃轩,易红,倪中华等.医用血管支架生物力学性能分析方法研究[J].东南大学学报(自然科学版).2005,35(02)：216-221.
[52]Wu W, Yang D Z, Qi M, et al. An FEA method to study flexibility of expanded coronary stents[J]. Journal of Materials Processing Tech.2007,184(1-3):447-450.
[53]Gu L, Santra S, Mericle R A, et al. Finite element analysis of covered microstents[J]. Journal of Biomechanics.2005,38(6):1221-1227.
[54]Mcgarry J P, O'Donnell B P, Mchugh P E, et al. Analysis of the mechanical performance of a cardiovascular stent design based on micromechanical modelling [J]. Computational Materials Science.2004,31(3-4):421-438.
[55]Walke W, Paszenda Z, Filipiak J. Experimental and numerical biomechanical analysis of vascular stent[J]. Journal of Materials Processing Tech.2005,164:1263-1268.
[56]Poncin P, Proft. J. Stent Tubing:Understanding the Desired Attributes. [C].2003.
[57]唐纳德.不锈钢手册[M].北京：机械工业出版社,1987：713-767.
[58]冶金工业部.合金钢钢种手册第一册[M].北京：冶金工业出版社,1983：75.
[59]周永恒.血管内支架结构的设计优化[J].中国医疗器械杂志.2007,31(02)：30-32.
[60]周永恒,廖健宏,蒙红云等.血管内支架扩张行为的有限元分析[J].应用力学学报.2007,24(04)：125-127.
[61]张庆宝.冠状动脉支架设计及力学行为分析[D].大连理工大学,2006.
[62]张庆宝,王伟强,齐民等.冠状动脉支架紧缩反弹行为有限元分析[J].北京生物医学工程.2006,25(04)：366-370.
[63]Xia Z, Ju F, Sasaki K. A general finite element analysis method for balloon expandable stents based on repeated unit cell (RUC) model [J]. Finite Elements in Analysis & Design. 2007,43(8):649-658.
[64]Migliavacca F, Petrini L, Colombo M, et al. Mechanical behavior of coronary stents investigated through the finite element method [J]. Journal of Biomechanics.2002,35(6): 803-811.
[65]Rieu R, Barragan P, Masson C, et al. Radial force of coronary stents:a comparative analysis[J]. Catheterization and Cardiovascular Interventions.1999,46(3):380-391.
[66]王伟强.冠状动脉支架力学行为有限元分析及其结构优化[D].大连理工大学,2005.
[67]梁栋科.血管内支架的加工及其力学性能的分析与评价[D].大连理工大学,2005.
[68]Bjarnason H, Hunter D W, Crain M R, et al. Collapse of a Palmaz stent in the subclavian vein[J]. American Journal of Roentgenology.1993,160(5):1123-1124.
[69]Hautmann H, Huber R M. Stent flexibility:an essential feature in the treatment of dynamic airway collapse[J]. European Respiratory Journal.1996,9(3):609-611.
[70]王伟强,梁栋科,杨大智等.冠脉支架系统瞬时膨胀过程的有限元分析及其优化设计[J].中国生物医学工程学报.2005,24(03)：59-64.
[71]王伟强,王丽,杨大智等.血管支架有限元优化设计[J].生物医学工程学杂志.2008,25(02)：372-377.
[72]王伟强,杨大智,齐民.冠状动脉支架膨胀行为的有限元分析[J].生物医学工程学杂志.2006,23(06)：1258-1262.
[73]David Chua S N, Macdonald B J, Hashmi M. Finite element simulation of slotted tube (stent) with the presence of plaque and artery by balloon expansion [J]. Journal of Materials Processing technology.2004,156:1772-1779.
[74]David Chua S N, Macdonald B J, Hashmi M. Effects of varying slotted tube (stent) geometry on its expansion behaviour using finite element method[J]. Journal of materials processing technology.2004,155:1764-1771.
[75]左亮,肖绯雄.橡胶Mooney-Rivlin模型材料系数的一种确定方法[J].机械制造.2008,46(7)：38-40.
[76]郑明军,王文静,陈政南等.橡胶Mooney-Rivlin模型力学性能常数的确定[J].橡胶工业.2003,50(8)：462-465.
[77]王伟,邓涛,赵树高.橡胶Mooney-Rivlin模型中材料常数的确定[J].特种橡胶制品.2004,25(4)：8-10.
[78]任全彬,蔡体敏,安春利等.硅橡胶“0”形密封圈Mooney-Rivlin模型常数的确定[J].固体火箭技术.2006,29(2)：130-134.
[79]黄庆专.橡胶Mooney-Rivlin模型及其系数最小二乘解法[J].热带农业科学.2009,29(5)：20-24.
[80]David Chua S N, Mac Donald B J, Hashmi M. Finite element simulation of stent and balloon interaction[J]. Journal of Materials Processing Tech.2003,143-144:591-597.
[81]Ormiston J A, Dixon S R, Webster M, et al. Stent longitudinal flexibility:a comparison of 13 stent designs before and after balloon expansion[J]. Catheterization and Cardiovascular Interventions.2000,50(1):120-124.
[82]Mori K, Saito T. Effects of stent structure on stent flexibility measurements[J]. Annals of biomedical engineering.2005,33(6):733-742.
[83]白雪.TiNi形状记忆合金医用内支架力学性能研究[D].北方工业大学,2003.
[84]徐强,刘玉岚,王彪.形状记忆合金超弹性自扩张血管支架的优化设计[J].上海生物医学工程.2006,27(4)：195-199.
[85]劳永华,支晓兴,林泽枫等.基于生物力学性能的血管内支架弧梁单元结构优化设计[J].中国组织工程研究与临床康复.2010,14(30)：5581-5585.
[86]Li N, Zhang H, Ouyang H. Shape optimization of coronary artery stent based on a parametric model[J]. Finite Elements in Analysis and Design.2009,45(6-7):468-475.
[87]Guimar Es T A, Oliveira S, Duarte M A. Application of the topological optimization technique to the stents cells design for angioplasty[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering.2008,30(3):261-268.
[88]Guimar Es T A, Duarte M, Oliveira S. Topology Optimization of the Stent Cells Plane Model With Maximum Hardening and Flexibility[C].2004.
[2]主编汪丽蕙,吴树燕.现代心血管疾病诊疗手册[M].1.北京：北京医科大学、中国协和医科大学联合出版社,1998：521.
[3]李国彰.冠状循环与冠心病[J].中国医刊.1987(06)：7-10.
[4]袁荣玺.冠心病心绞痛的诊断与治疗[J].辽宁医学杂志.1994,8(02)：58-69.
[5]陈文广.3种抗冠心病药物治疗稳定型心绞痛的临床评价[J].云南中医中药杂志.2008,29(03)：17.
[6]王绿娅,许金鹏,赵全明.斑块稳定-冠心病药物治疗的起点与终点[J].中国药物应用与监测.2004(04)：11-15.
[7]孙福成.冠心病药物治疗的进展[J].中国医刊.1999,34(03)：9-11.
[8]蔡立英.冠心病药物治疗的进展[J].中国初级卫生保健.1988(12)：26-27.
[9]胡大一,孙艺红.冠心病药物治疗的最新进展和展望[J].中国实用内科杂志.2006,26(02)：88-91.
[10]刘登智.冠心病药物治疗近况[J].西南民族学院学报(自然科学版).2000,26(01)：91-94.
[11]吕树铮.冠心病药物治疗新进展[J].中国处方药.2008(05)：74-75.
[12]陈艰,刘志芳.自体血管在冠状动脉搭桥术中的应用[J].江西医药.2008,43(06)：611-613.
[13]陈鑫.冠状动脉搭桥治疗冠心病的现状和进展[J].实用临床医药杂志.2005,9(03)：3-8.
[14]陈铮.天堑变通途——探秘心脏搭桥手术[J].首都医药.2008(05)：50-51.
[15]高成杰,宁吉顺,王惠霞等.急诊冠脉搭桥术适应证探讨[J].临床急诊杂志.2007,8(02)：93-94.
[16]欧阳墉.我国血管狭窄和(或)闭塞性病变介入治疗的发展历程[J].中华放射学杂志.2005,39(09)：7-10.
[17]刘冰,高润霖.经皮冠状动脉介入治疗指南[J].现代实用医学.2004,16(01)：55-64.
[18]欧阳墉.管腔内支架：I.作用机制和性能[J].国外医学.临床放射学分册.1997(04)：20-23.
[19]高惠荣.冠状动脉成形术和冠状动脉搭桥手术的比较[J].浙江医学情报.1994(02)：9-16.
[20]王强,姜楠,王联群等.急诊冠状动脉搭桥术的临床应用[J].天津医药.2007,35(10)：792-793.
[21]罗坤.血管成形术对搭桥手术：棋逢敌手[J].心血管病防治知识.2007(12)：29.
[22]卿清.冠脉多支阻塞,搭桥或许优于血管成形术[J].心血管病防治知识.2008(03)：41.
[23]邱杏霖.选择血管成形术还是搭桥手术?[J].心血管病防治知识.2008(05)：34-35.
[24]徐在品.抑制血管内膜增生的血流动力学和血液流变学机理研究[D].重庆大学,2005.
[25]乔树宾.冠心病介入治疗进展-(7)冠状动脉内支架的设计和临床应用进展[J].中国循环杂志.2003,18(02)：5-8.
[26]周永恒,蒙红云,曾常春等.血管内支架的技术与性能[J].生物医学工程学杂志.2007,24(6)：225-229.
[27]高振宇.医用镍钛合金支架结构的优化设计[D].大连理工大学,2006.
[28]高振宇,粱栋科,齐民等.镍钛合金超弹性支架抗压缩性能的实验与分析[J].功能材料与器件学报.2006,12(01)：51-55.
[29]徐强,刘玉岚,王彪等.形状记忆合金心血管支架自扩张过程的数值模拟与支架的“最优化网格”[J].生物医学工程学杂志.2008,25(5)：125-130.
[30]赵振心,刘道志,孙康等.镍钛合金血管支架的有限元分析及疲劳测试[J].中国医疗器械杂志.2008,32(5)：69-72.
[31]Thierry B, Merhi Y, Bilodeau L, et al. Nitinol versus stainless steel stents:acute thrombogenicity study in an ex vivo porcine model[J]. Biomaterials.2002,23(14): 2997-3005.
[32]贾楠,肖越勇,张金山.生物可降解性血管内支架及药物释放支架的研制[J].中国医学影像技术.2007,23(01)：120-124.
[33]肖越勇,张金山,崔福斋等.生物可降解性血管内支架的制备及其性能研究[J].中华放射学杂志.2003,37(11)：76-82.
[34]唐剑飞.生物可降解性血管内支架的研究进展[J].国外医学(骨科学分册).2002,23(04)：233-235.
[35]Rieu R, Barragan P, Garitey V, et al. Assessment of the trackability, flexibility, and conformability of coronary stents:a comparative analysis[J]. Catheterization and Cardiovascular Interventions.2003,59(4):496-503.
[36]Petrini L, Migliavacca F, Auricchio F, et al. Numerical investigation of the intravascular coronary stent flexibility[J]. Journal of Biomechanics.2004,37(4): 495-501.
[37]刘明.冠状动脉支架的生物力学行为分析[D].哈尔滨工程大学,2007.
[38]周承倜,董何彦.冠状动脉支架力学性能的理论和实验研究[J].应用力学学报.2008,25(04)：26-31.
[39]高振宇,梁栋科,齐民等.镍钛合金超弹性支架纵向柔顺性分析[J].功能材料.2007,38(01)：117-118.
[40]周承倜,董何彦.微型网状结构支架的力学性能研究[J].应用力学学报.2004,21(03)：4-11.
[41]David Chua S N, Mac Donald B J, Hashmi M S J. Finite-element simulation of stent expansion[J]. Journal of Materials Processing Tech.2002,120(1-3):335-340.
[42]Migliavacca F, Petrini L, Montanari V, et al. A predictive study of the mechanical behaviour of coronary stents by computer modelling [J]. Medical Engineering and Physics. 2005,27(1):13-18.
[43]Tan L B, Webb D C, Kormi K, et al. A method for investigating the mechanical properties of intracoronary stents using finite element numerical simulation[J]. International Journal of Cardiology.2001,78(1):51-67.
[44]Etave F, Finet G, Boivin M, et al. Mechanical properties of coronary stents determined by using finite element analysis[J]. Journal of Biomechanics.2001,34(8):1065-1075.
[45]倪中华,王跃轩,程洁.球囊扩张式冠脉支架扩张变形机理数值模拟方法[J].机械工程学报.2008,44(01)：102-108.
[46]王勖成,邵敏.有限单元元基本原理和数值方法[M].清华大学出版社,1997.
[47]机械工程材料性能数据手册编委会.机械工程材料性能数据手册[M].北京：机械工业出版社,1995：433.
[48]戴雅康.金属力学性能实验[M].北京：机械工业出版社,1991.
[49]张庆宝,王伟强,齐民等.不同材料冠状动脉支架膨胀行为分析[J].功能材料.2007,38(01)：130-134.
[50]黄远,李林安,刘文西.医用心血管支架的非线性有限元分析[J].中国生物医学工程学报.2003,22(02)：139-148.
[51]王跃轩,易红,倪中华等.医用血管支架生物力学性能分析方法研究[J].东南大学学报(自然科学版).2005,35(02)：216-221.
[52]Wu W, Yang D Z, Qi M, et al. An FEA method to study flexibility of expanded coronary stents[J]. Journal of Materials Processing Tech.2007,184(1-3):447-450.
[53]Gu L, Santra S, Mericle R A, et al. Finite element analysis of covered microstents[J]. Journal of Biomechanics.2005,38(6):1221-1227.
[54]Mcgarry J P, O'Donnell B P, Mchugh P E, et al. Analysis of the mechanical performance of a cardiovascular stent design based on micromechanical modelling [J]. Computational Materials Science.2004,31(3-4):421-438.
[55]Walke W, Paszenda Z, Filipiak J. Experimental and numerical biomechanical analysis of vascular stent[J]. Journal of Materials Processing Tech.2005,164:1263-1268.
[56]Poncin P, Proft. J. Stent Tubing:Understanding the Desired Attributes. [C].2003.
[57]唐纳德.不锈钢手册[M].北京：机械工业出版社,1987：713-767.
[58]冶金工业部.合金钢钢种手册第一册[M].北京：冶金工业出版社,1983：75.
[59]周永恒.血管内支架结构的设计优化[J].中国医疗器械杂志.2007,31(02)：30-32.
[60]周永恒,廖健宏,蒙红云等.血管内支架扩张行为的有限元分析[J].应用力学学报.2007,24(04)：125-127.
[61]张庆宝.冠状动脉支架设计及力学行为分析[D].大连理工大学,2006.
[62]张庆宝,王伟强,齐民等.冠状动脉支架紧缩反弹行为有限元分析[J].北京生物医学工程.2006,25(04)：366-370.
[63]Xia Z, Ju F, Sasaki K. A general finite element analysis method for balloon expandable stents based on repeated unit cell (RUC) model [J]. Finite Elements in Analysis & Design. 2007,43(8):649-658.
[64]Migliavacca F, Petrini L, Colombo M, et al. Mechanical behavior of coronary stents investigated through the finite element method [J]. Journal of Biomechanics.2002,35(6): 803-811.
[65]Rieu R, Barragan P, Masson C, et al. Radial force of coronary stents:a comparative analysis[J]. Catheterization and Cardiovascular Interventions.1999,46(3):380-391.
[66]王伟强.冠状动脉支架力学行为有限元分析及其结构优化[D].大连理工大学,2005.
[67]梁栋科.血管内支架的加工及其力学性能的分析与评价[D].大连理工大学,2005.
[68]Bjarnason H, Hunter D W, Crain M R, et al. Collapse of a Palmaz stent in the subclavian vein[J]. American Journal of Roentgenology.1993,160(5):1123-1124.
[69]Hautmann H, Huber R M. Stent flexibility:an essential feature in the treatment of dynamic airway collapse[J]. European Respiratory Journal.1996,9(3):609-611.
[70]王伟强,梁栋科,杨大智等.冠脉支架系统瞬时膨胀过程的有限元分析及其优化设计[J].中国生物医学工程学报.2005,24(03)：59-64.
[71]王伟强,王丽,杨大智等.血管支架有限元优化设计[J].生物医学工程学杂志.2008,25(02)：372-377.
[72]王伟强,杨大智,齐民.冠状动脉支架膨胀行为的有限元分析[J].生物医学工程学杂志.2006,23(06)：1258-1262.
[73]David Chua S N, Macdonald B J, Hashmi M. Finite element simulation of slotted tube (stent) with the presence of plaque and artery by balloon expansion [J]. Journal of Materials Processing technology.2004,156:1772-1779.
[74]David Chua S N, Macdonald B J, Hashmi M. Effects of varying slotted tube (stent) geometry on its expansion behaviour using finite element method[J]. Journal of materials processing technology.2004,155:1764-1771.
[75]左亮,肖绯雄.橡胶Mooney-Rivlin模型材料系数的一种确定方法[J].机械制造.2008,46(7)：38-40.
[76]郑明军,王文静,陈政南等.橡胶Mooney-Rivlin模型力学性能常数的确定[J].橡胶工业.2003,50(8)：462-465.
[77]王伟,邓涛,赵树高.橡胶Mooney-Rivlin模型中材料常数的确定[J].特种橡胶制品.2004,25(4)：8-10.
[78]任全彬,蔡体敏,安春利等.硅橡胶“0”形密封圈Mooney-Rivlin模型常数的确定[J].固体火箭技术.2006,29(2)：130-134.
[79]黄庆专.橡胶Mooney-Rivlin模型及其系数最小二乘解法[J].热带农业科学.2009,29(5)：20-24.
[80]David Chua S N, Mac Donald B J, Hashmi M. Finite element simulation of stent and balloon interaction[J]. Journal of Materials Processing Tech.2003,143-144:591-597.
[81]Ormiston J A, Dixon S R, Webster M, et al. Stent longitudinal flexibility:a comparison of 13 stent designs before and after balloon expansion[J]. Catheterization and Cardiovascular Interventions.2000,50(1):120-124.
[82]Mori K, Saito T. Effects of stent structure on stent flexibility measurements[J]. Annals of biomedical engineering.2005,33(6):733-742.
[83]白雪.TiNi形状记忆合金医用内支架力学性能研究[D].北方工业大学,2003.
[84]徐强,刘玉岚,王彪.形状记忆合金超弹性自扩张血管支架的优化设计[J].上海生物医学工程.2006,27(4)：195-199.
[85]劳永华,支晓兴,林泽枫等.基于生物力学性能的血管内支架弧梁单元结构优化设计[J].中国组织工程研究与临床康复.2010,14(30)：5581-5585.
[86]Li N, Zhang H, Ouyang H. Shape optimization of coronary artery stent based on a parametric model[J]. Finite Elements in Analysis and Design.2009,45(6-7):468-475.
[87]Guimar Es T A, Oliveira S, Duarte M A. Application of the topological optimization technique to the stents cells design for angioplasty[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering.2008,30(3):261-268.
[88]Guimar Es T A, Duarte M, Oliveira S. Topology Optimization of the Stent Cells Plane Model With Maximum Hardening and Flexibility[C].2004.