骨骼有限元精确建模方法及骨水泥断裂和疲劳损伤研究
|
摘要
生物力学是运用力学的原理和方法对生物体中的力学问题进行定量研究。其广泛的研究和应用兴起于上个世纪60年代,发展至今已成为一门独立的交叉类学科。在生物力学研究的众多分支中,临床骨科生物力学的研究和应用是非常活跃的领域。骨科中的常见病和多发病严重威胁人们的健康,影响着人们的生活质量,临床上迫切需要在诊断、治疗和预防上对此能有更准确以及定量的认识。
试验测试和数值分析是生物力学研究的两大主要手段。采用体外(也称离体,invitro)生物力学试验可以直观地获得生物力学性能信息,得到的结果和结论具有通用的参考价值,但对病人个体缺乏全面、客观的信息支持。与生物力学试验相比,有限元法用于形状、结构、材料和载荷情况极其复杂的在体(in vivo)骨骼的分析具有独特的优势,其模拟成本低,无试验误差,力学性能测试全面,“非破坏性”的试验使“样本”可无限次重复使用,更重要的是可以建立具有生物力学复杂材料特性的逼真的在体骨骼模型,可以施加符合实际生理环境的边界和载荷条件,个性化分析结果可以直接用于辅助临床诊断、手术预案分析、术后评估、外科整形、假体设计与制造等。
自1972年Brekelmans和Rybicki分别率先将有限元方法应用于椎骨和股骨的生物力学研究以来,该技术的应用陆续覆盖了人体所有骨骼。早期的数值分析方法在骨科的应用上仅局限于二维模型、简单载荷和边界条件的线性问题分析,分析结果与实际情况相去甚远。随着计算机技术的提高和数值分析理论的完善,其应用有了质的飞跃,对骨科生物力学中存在的复杂非线性和多介质耦合等问题都有了较为成熟的应用。实践证明,只要模拟条件与实际情况的近似度越高,获得的分析结果就越真实、可靠。
目前,常用的骨骼组织几何建模方法是基于CT图像的Marching Cube法(MC),该方法对复杂三维骨骼结构的解析常存在几何上的歧义,容易导致后续有限元网格划分的困难或失败；试验表明骨骼材料表现为非均质和各向异性的特点,而非简单的密质骨和松质骨之分,如何获取精确骨骼的几何和材料信息,构建精确的骨骼有限元模型生成系统依然非常重要。
临床骨外科假体置换术中还有一类问题如：强度、稳定性和疲劳损伤及寿命的定量分析迫切需要相关的理论指导。置换术中的界面是置换系统中薄弱环节,是系统断裂破坏主要的萌生地,由此容易诱发假体下沉、松动甚至断裂等术后并发症,其断裂分析可以借助界面断裂力学方法。人体骨骼的蜂窝状结构、骨水泥气泡的陷入、假体微缺陷的存在等诸多因素也是影响未来系统长期稳定性的主要因素,这些内部的微缺陷和微裂纹在生产、制造和使用过程中是不可避免的,因为它们的产生存在着很大的随机性和差异性,在数值分析建模时,骨骼、骨水泥和假体通常作为连续介质来对待；但是,研究连续介质的断裂时,由于裂纹源未知,裂纹扩展方向未知,不能采用基于经典断裂力学的数值分析方法；因此,非常有必要研究一种在裂纹源未知的构件内确定断裂可能发生的地点、估算构件强度和使用寿命的方法。粘聚元耦合有限元技术在复合材料界面断裂分析中已得到广泛应用,基于这一思路,在连续介质力学的研究框架下,引入损伤力学的损伤变量概念,在连续介质中插入反映潜在的裂纹路径的粘聚元,通过粘聚元上、下表面的分离表示连续介质断裂产生的不连续位移场,可以实现断裂分析的模拟。基于强度弱化和刚度劣化理论,还可以进一步实现连续介质从累积损伤到断裂整个疲劳过程的模拟。
针对以上问题,本文主要研究了如下内容：
(1)构建了骨骼有限元精确模型生成框架
针对面绘制MC法处理复杂骨组织时容易产生几何上的歧义问题,本文采取了图像预处理的方法,制定了首先分割得到感兴趣区域(region of interest, ROI),将分割得到的ROI叠砌为VOI (volume of interest),然后将VOI进行表面化处理、顺滑,获得三维模型闭合面域的策略；进一步研究了将VOI直接转换为有限元网格模型的方法(voxel-based-mesh model);编制了质心、节点、栅格中心多种材料性能映射方法程序；因某些骨骼试样难以采集导致现有的骨骼材料模型大多呈现非连续性,针对该问题,本文研究了采用顺滑算子的方法减少材料性能大的梯度跳跃；鉴于平均分组方法会低估或高估某些材料的性能,本文提出了基于单元体积的Kmean聚类材料分组算法；最后,根据商用Abaqus软件的数据格式,研究组装分析模型的方法并编制了相应程序。对比商用软件,该框架避免了复杂骨结构建模时常出现的网格划分困难,增加了材料映射、顺滑和聚类方法,可以赋予骨模型非均质和各向异性特性。整个框架提供了开放式平台,用户根据需要方便自行扩充。
(2)基于上述框架,采用有限元方法分析
①优化设计了定制型大块股骨缺损假体
本案例分析中首次提出了基于个体股骨质量和有限元分析的骨水泥型假体设计理念；建立股骨大块缺损置换前、后有限元分析模型,为使分析结果对比更加全面和客观,置换前、后股骨模型采用了一致网格技术,本文详细阐述了该技术具体的实施方法。分析了有、无肌肉力两种情况下正常行走、爬楼两个日常动作；修正应力屏蔽信号为应变能偏移率,分析了骨组织的应力屏蔽效应及其未来破裂的风险；综合考察分析结果,最终确定了优化设计方案。
②比较了治疗颈椎不稳寰椎侧块-枢椎椎弓根(C1LM-C2P)(?)口寰椎侧块-枢椎椎板(C1LM-C2L)两种后路固定术
本案例首先解剖量化了个体寰枢锥结构,确定实施两种手术具有足够的空间,并首次建立了包含寰齿前车轴关节和寰枢摩动关节的C1LM-C2P和C1LM-C2L固定术的精细有限元分析模型,两种固定术中寰枢锥采用了一致网格技术；分析模拟了人体寰枢椎的七个日常动作：前移,后伸/前屈,侧弯(左、右)和旋转(左、右)；考察钉棒结构的应力分布和表征系统稳定性的位移、刚度和主应变等参量,与相关生物力学试验结果进行了对比,得出了一致性的结论。(3)分析评估了大块股骨缺损的骨水泥型假体置换系统的稳定性
首先应用三明治试验方法测试了骨水泥/假体界面的剪切强度,首次采用端边切口试验(End-notched flexure test, ENF)结合柔度标定法测量了骨水泥/假体界面的剪切断裂韧性,避开了测量闭合裂纹扩展长度变化的难题,求解获得了界面剪切断裂韧性解析解；建立了粘聚元耦合有限元ENF试验模型,分析获得了界面剪切断裂韧性数值解,并将两种解与相关试验进行了比较。在以上工作的基础之上,引入粘聚元耦合有限元技术,定量分析了假体表面质量对大块股骨缺损骨水泥型假体置换系统稳定性的影响,为临床预案和术后评估提供了理论指导。
(4)利用粘聚元耦合有限元技术,分析了骨水泥断裂过程及断裂性能
根据作用载荷的性质,本文研究了一种在连续介质中设置通用潜在裂纹路径的方法,并开发了基于该法和商用软件Abaqus四面体单元的断裂分析模型自动生成程序。建立了骨水泥材料断裂分析模型,模拟了在拉载荷作用下骨水泥的断裂过程。分析了该断裂过程中应力场和损伤场的变化规律,深入探究了潜在裂纹路径的数量以及含裂纹构件中不同裂纹形态对断裂机理和断裂性能的影响。对比相关试验,验证了粘聚元耦合有限元技术分析连续脆性介质的断裂过程的可行性。为了提高计算效率,本文利用了危险区概念。将容易发生断裂的区域采用粘聚元耦合有限元技术建模,其他区域采用传统有限元技术建模。
(5)利用粘聚元耦合有限元技术,建立了骨水泥疲劳损伤模型,研究其疲劳损伤过程
以准脆性材料骨水泥拉伸疲劳为例,基于强度弱化理论,将粘聚元引入了连续介质(骨水泥)的疲劳累积损伤分析中。将疲劳损伤过程分为无疲劳裂纹萌生、疲劳裂纹萌生、裂纹扩展三个阶段,研究了不同阶段中材料性能的变化和损伤程度的变化,首次提出了一种疲劳累积损伤及破坏模型。利用Visual C编写了调用Abaqus求解器的控制程序,实现了连续脆性介质(骨水泥)疲劳循环全过程损伤分析。对比线性和对数型两种强度弱化模式,研究了构件损伤和破坏机制的差异及其特点,计算了疲劳裂纹萌生、疲劳裂纹扩展和断裂扩展各阶段的寿命。对比有关试验研究,验证了粘聚元耦合有限元方法在疲劳损伤分析中的可行性和三段式疲劳累积损伤及破坏模型的合理性。
Biomechanics is the application of mechanical engineering theory and practice to biological materials and systems. It has been widely studied and applied since the1960's. It encompasses many disciplines including material science, mechanics, anatomy, physiology, computer science. It develops rapidly and emerges as an independent cross-discipline subject now. Among many branches of biomechanical research, its application in orthopedics is becoming more and more important because of urgent needs for accurate quantitative assessment in diagnosis, treatment and prevention of the common and frequently-occurring disease which are harmful to people's health and the quality of life.
There are two main methods used in biomechanical research:biomechanical testing and numerical simulation analysis. Biomechanical testing, in vitro, can directly obtain the information about the mechanical properties of measured object. The results and conclusions from the testing depend on test condition and method. Therefore, it only provides some heuristic guidelines in qualitative researches, but neglect the differences of individuals. Compared with biomechanical testing, Finite Element (FE) method, an important method of numerical simulation analysis, has many advantages: the cost of simulation is low, test finish without errors, non-invasive and non-destructive model can be repeatedly used and the complicated boundary condition can be added conveniently, etc. It is more important that FE method can built the complicated models of bone tissue of individuals, special in vivo, with very realistic geometry and material property. Thus, the analysis results can serve as references for clinical diagnosis, operation plan evaluation, plastic surgery, prosthetic design and manufacturing, etc.
In1972, Brekelmans and Rybicki took the lead in the application of FE techniques in the biomechanical studies on vertebrae and femur. From then on, the technique came into widespread use which covered almost all human bones. The early efforts of the technology were limited in the analysis of two-dimensional linear problem with simplified loads and boundary conditions. The analysis results were far from the actual fact. With the development of computer technology and numerical analysis theory, there are many mature examples of FE application in complicated nonlinear and multi-medium coupling problems. It has been proved that the more accurate model get and more realistic conditions imposed, the more accurate results acquired. In existing commercial software, there is no better solution for the presence of face ambiguity for the complicated bone tissue model. Difficulties may arise when one attempts to generate the FE meshes from the geometrical model with face ambiguity. Thus, to build a frame which generates bone FE model effectively and accurately is still necessary.
In clinic, the quantitative assessments about strength, stability, damage and fatigue life, are urgent needs for theoretical guidance. All those problems are involved with fracture and damage theory. The interfaces of bone-cement/bone, bone-cement/metal and bone/metal are weak links in replacement surgery. Fracture initiation and propagate may occur easily along weak interfaces. Thus, the weak interfaces are easy to induce postoperative complications such as prosthetic loosening, subsidence and rupture. Interface fracture mechanics can solve and explain the crack of the interfaces. However, honeycomb structure in human bone tissue, bubbles trapped in bone-cement and micro defects in prosthesis also contribute to the causes of postoperative complications. The occurrences of micro cracks and micro defects in bone tissue, bone-cement and prosthesis are inevitable, and the generation and distribution of them are at random. In FE modeling, micro cracks and micro defects are very hard to represent, thereby, bone, bone-cement and prosthesis are actually regarded as continuum media. Classical fracture mechanics take the model with crack as their research object. Numerical analysis method based on classical fracture mechanics seems incapable of solving the fracture problem of continuum media because the initial crack position and crack propagation direction are unknown. To explore a new method to determine crack position, estimate the fracture strength and fatigue life of continuum media has a very important practical significance. The coupling technology of cohesive zone model (CZM) and finite element has been widely used in the analysis of composite materials interface crack. This is beneficial attempt to introduce this technology for the assessment of interface damage and fracture in replacement surgery. Material damage is the gradual process of mechanical property deterioration. The concept of damage variable, which represents the change in material stiffness, is introduced to continuum mechanics. Cohesive elements are inserted into continuum media to represent potential crack paths. The separation of the upper and lower surfaces of cohesive element can be expressed as the discontinuous displacement during the deformation and fracture of continuum media. Additionally, it is desired to further implement the computer simulation of fatigue and fracture process based on strength deterioration theory.
In view of the above, the main research contents and results in this paper are described as follows:
(1) To establish a framework for precision bone FE model
Considering that the face ambiguity of the model which generate by3D surface reconstruction using Marching Cube (MC) algorithm, is likely to lead to the difficult of mesh generation, a strategy is formulated:preprocessing of medical images for ROI (region of interest), stacking VOI (volume of interest) with ROI, smoothing the VOI for a closed surface domain of3D model. According to the characteristics of medical images, the voxels in medical image data can convert to the hexahedral meshes of FE bone model (voxel-based mesh model) directly by home-made program. The framework provides different mapping methods, such as centroid-based, node-based, grid-based, etc, and assigns inhomogeneous anisotropic properties for bone tissue. Due to little amount of the bone tissue with CT grey value～800Hu in human body, it is very hard to make suitable sample for testing material property. In the result, the material model represents a discontinuous leap. A smooth template is proposed to smooth the leap. Some researches show that the average method to group the material properties may overestimate or underestimate the material properties of bone. Thus, K-mean algorithm based on the volume of element is proposed to cluster the groups of material properties. Finally, the information about nodes, elements and material properties of model could be arranged automatically in accordance with different FE software packages. In contrast to the other commercial software, the framework avoids mesh generation bottleneck for complicated bone model, increases the mapping, smoothing, and clustering methods for the assignment of material properties, and also can describe the anisotropic property of bone tissue. The frame could be expanded to meet the users' requirements.
(2) Based on the above framework, two cases in orthopedic are analyzed.
①Case one:To design custom prosthesis for patients with massive bone loss in proximal femur.
In this case, a new concept of design based on investigating individual femur shape and femoral bone quality is proposed before custom prosthesis design. Then, the FE models including before and after the prosthesis replacement are built. The mesh models of femoral bone before and after the prosthesis replacement have the same structure. The technique of consistent meshes may make analysis results more comprehensive and objective. Two activities of daily living, normal walking and stair climbing, are simulated and muscle force is/is not simultaneously exerted. The change rate of strain energy is revised to replace stress shield signal to assess not only stress shield effect but fracture risk of bone tissue. Finally, an optimum scheme of custom prosthesis is determined after the comparison among simulation results.
②Case two:To compare and evaluate two posterior atlantoaxial fixations including C1lateral mass to C2pedicle fixation (C1LM-C2P) and C1lateral mass to C2laminar fixation (C1LM-C2L).
In this case, first analyze the anatomy structure of individual atlantoaxial and validate the feasible of C1LM-C2P and C1LM-C2L, then build fine FE models of C1LM-C2P and C1LM-C2L containing atlanto-odontoid and arthrodial. Seven loads to simulate different head postures:anterior-posterior (AP), translation (forward), extension, flexion, lateral bending (left/right), and torsion (left/right) are exerted for simulations. The FE analysis results are shown to be in good agreement with the published experimental data. To draw a conclusion is stating that C1LM-C2L is an alternative for some patients with congenital anomalies who are not suitable for other fixation treatment. It is worth to point out that the stability of C1LM-C2L is worse than the one of C1LM-C2P.
(3) To analysis and assess the stability of cemented fixation for patients with massive bone loss in proximal femur using the technique of Cohesive Zone Model (CZM).
In this research, shear strength and shear fracture toughness of cement/metal interface are measured by, respectively, sandwich shear and End Notched Flexure (ENF) testing. To avoid the measurements of the crack length during the crack growth, compliance calibration method is applied to determine the critical strain energy release (GIIC), a kind of fracture toughness, in ENF test. The coupling of CZM and FE method is employed to simulate the process of ENF test for the analytical solution of GIIC. The two solutions are compared with published experiment data. Furthermore, the stability of cemented fixation for patients with massive bone loss in proximal femur and the influences of the surfaces of prosthesis are investigated with the coupled method. The analysis results provide valuable insights into relevant clinical phenomena and quantitative guides to clinical therapy.
(4) To investigate the fracture process and fracture property of bone-cement with the technique of coupling of cohesive element and FE.
This research presents the different methods to set up potential crack paths corresponding to different load cases. A general method to set up potential crack paths is proposed. The model for fracture analysis based on this method could generate automatically by virtue of home-made program. The program is suitable for the tetrahedron element in commercial software ABAQUS. It can be expanded to other software. The uniaxial tensile test of bone-cement is taken as an example. The fracture process of this model is tracked. The results display the changes of stress field and damage field in the whole fracture process. The other focus of this study is to explore the influences of the numbers of potential crack path and crack morphology upon fracture mechanism and fracture property. That the findings agree well with other published experiment data validates the feasibility of application of the coupled method as mentioned above in solving the fracture problem of quasi-brittle or brittle material. In order to improve computational efficiency, components should be divided into two zones. One is the fracture risk zone. Fractures commonly occur in the zone and the model of the zone is built by the coupled method, whereas, another zone is only built by FE method.
(5) To establish fatigue cumulative damage model with the technique of coupling of CZM and FE and to investigate the fatigue damage process of bone-cement.
Based on strength degradation theory, the technique of coupling of CZM and FE is introduced in the analysis of fatigue cumulative damage. The tensile fatigue test of bone-cement is taken as an example. A new fatigue cumulative damage model with three stages is proposed. The three stages correspond to before crack initiation (I), fatigue crack initiation (II) and fatigue crack propagation (III). This research investigates the changes of material properties in damage evolution process. A program is written in Visual C language to control Abaqus solver for the analysis of fatigue damage evolution process. The mechanism of damage is investigated and fatigue life in different stages can be predicted under linear and logarithmic strength degradation modes. Compared with published experiment data, this research confirmed the feasibility of the coupled method in the application of fatigue damage and the validation of the fatigue cumulative damage model with three stages proposed in this study.
试验测试和数值分析是生物力学研究的两大主要手段。采用体外(也称离体,invitro)生物力学试验可以直观地获得生物力学性能信息,得到的结果和结论具有通用的参考价值,但对病人个体缺乏全面、客观的信息支持。与生物力学试验相比,有限元法用于形状、结构、材料和载荷情况极其复杂的在体(in vivo)骨骼的分析具有独特的优势,其模拟成本低,无试验误差,力学性能测试全面,“非破坏性”的试验使“样本”可无限次重复使用,更重要的是可以建立具有生物力学复杂材料特性的逼真的在体骨骼模型,可以施加符合实际生理环境的边界和载荷条件,个性化分析结果可以直接用于辅助临床诊断、手术预案分析、术后评估、外科整形、假体设计与制造等。
自1972年Brekelmans和Rybicki分别率先将有限元方法应用于椎骨和股骨的生物力学研究以来,该技术的应用陆续覆盖了人体所有骨骼。早期的数值分析方法在骨科的应用上仅局限于二维模型、简单载荷和边界条件的线性问题分析,分析结果与实际情况相去甚远。随着计算机技术的提高和数值分析理论的完善,其应用有了质的飞跃,对骨科生物力学中存在的复杂非线性和多介质耦合等问题都有了较为成熟的应用。实践证明,只要模拟条件与实际情况的近似度越高,获得的分析结果就越真实、可靠。
目前,常用的骨骼组织几何建模方法是基于CT图像的Marching Cube法(MC),该方法对复杂三维骨骼结构的解析常存在几何上的歧义,容易导致后续有限元网格划分的困难或失败；试验表明骨骼材料表现为非均质和各向异性的特点,而非简单的密质骨和松质骨之分,如何获取精确骨骼的几何和材料信息,构建精确的骨骼有限元模型生成系统依然非常重要。
临床骨外科假体置换术中还有一类问题如：强度、稳定性和疲劳损伤及寿命的定量分析迫切需要相关的理论指导。置换术中的界面是置换系统中薄弱环节,是系统断裂破坏主要的萌生地,由此容易诱发假体下沉、松动甚至断裂等术后并发症,其断裂分析可以借助界面断裂力学方法。人体骨骼的蜂窝状结构、骨水泥气泡的陷入、假体微缺陷的存在等诸多因素也是影响未来系统长期稳定性的主要因素,这些内部的微缺陷和微裂纹在生产、制造和使用过程中是不可避免的,因为它们的产生存在着很大的随机性和差异性,在数值分析建模时,骨骼、骨水泥和假体通常作为连续介质来对待；但是,研究连续介质的断裂时,由于裂纹源未知,裂纹扩展方向未知,不能采用基于经典断裂力学的数值分析方法；因此,非常有必要研究一种在裂纹源未知的构件内确定断裂可能发生的地点、估算构件强度和使用寿命的方法。粘聚元耦合有限元技术在复合材料界面断裂分析中已得到广泛应用,基于这一思路,在连续介质力学的研究框架下,引入损伤力学的损伤变量概念,在连续介质中插入反映潜在的裂纹路径的粘聚元,通过粘聚元上、下表面的分离表示连续介质断裂产生的不连续位移场,可以实现断裂分析的模拟。基于强度弱化和刚度劣化理论,还可以进一步实现连续介质从累积损伤到断裂整个疲劳过程的模拟。
针对以上问题,本文主要研究了如下内容：
(1)构建了骨骼有限元精确模型生成框架
针对面绘制MC法处理复杂骨组织时容易产生几何上的歧义问题,本文采取了图像预处理的方法,制定了首先分割得到感兴趣区域(region of interest, ROI),将分割得到的ROI叠砌为VOI (volume of interest),然后将VOI进行表面化处理、顺滑,获得三维模型闭合面域的策略；进一步研究了将VOI直接转换为有限元网格模型的方法(voxel-based-mesh model);编制了质心、节点、栅格中心多种材料性能映射方法程序；因某些骨骼试样难以采集导致现有的骨骼材料模型大多呈现非连续性,针对该问题,本文研究了采用顺滑算子的方法减少材料性能大的梯度跳跃；鉴于平均分组方法会低估或高估某些材料的性能,本文提出了基于单元体积的Kmean聚类材料分组算法；最后,根据商用Abaqus软件的数据格式,研究组装分析模型的方法并编制了相应程序。对比商用软件,该框架避免了复杂骨结构建模时常出现的网格划分困难,增加了材料映射、顺滑和聚类方法,可以赋予骨模型非均质和各向异性特性。整个框架提供了开放式平台,用户根据需要方便自行扩充。
(2)基于上述框架,采用有限元方法分析
①优化设计了定制型大块股骨缺损假体
本案例分析中首次提出了基于个体股骨质量和有限元分析的骨水泥型假体设计理念；建立股骨大块缺损置换前、后有限元分析模型,为使分析结果对比更加全面和客观,置换前、后股骨模型采用了一致网格技术,本文详细阐述了该技术具体的实施方法。分析了有、无肌肉力两种情况下正常行走、爬楼两个日常动作；修正应力屏蔽信号为应变能偏移率,分析了骨组织的应力屏蔽效应及其未来破裂的风险；综合考察分析结果,最终确定了优化设计方案。
②比较了治疗颈椎不稳寰椎侧块-枢椎椎弓根(C1LM-C2P)(?)口寰椎侧块-枢椎椎板(C1LM-C2L)两种后路固定术
本案例首先解剖量化了个体寰枢锥结构,确定实施两种手术具有足够的空间,并首次建立了包含寰齿前车轴关节和寰枢摩动关节的C1LM-C2P和C1LM-C2L固定术的精细有限元分析模型,两种固定术中寰枢锥采用了一致网格技术；分析模拟了人体寰枢椎的七个日常动作：前移,后伸/前屈,侧弯(左、右)和旋转(左、右)；考察钉棒结构的应力分布和表征系统稳定性的位移、刚度和主应变等参量,与相关生物力学试验结果进行了对比,得出了一致性的结论。(3)分析评估了大块股骨缺损的骨水泥型假体置换系统的稳定性
首先应用三明治试验方法测试了骨水泥/假体界面的剪切强度,首次采用端边切口试验(End-notched flexure test, ENF)结合柔度标定法测量了骨水泥/假体界面的剪切断裂韧性,避开了测量闭合裂纹扩展长度变化的难题,求解获得了界面剪切断裂韧性解析解；建立了粘聚元耦合有限元ENF试验模型,分析获得了界面剪切断裂韧性数值解,并将两种解与相关试验进行了比较。在以上工作的基础之上,引入粘聚元耦合有限元技术,定量分析了假体表面质量对大块股骨缺损骨水泥型假体置换系统稳定性的影响,为临床预案和术后评估提供了理论指导。
(4)利用粘聚元耦合有限元技术,分析了骨水泥断裂过程及断裂性能
根据作用载荷的性质,本文研究了一种在连续介质中设置通用潜在裂纹路径的方法,并开发了基于该法和商用软件Abaqus四面体单元的断裂分析模型自动生成程序。建立了骨水泥材料断裂分析模型,模拟了在拉载荷作用下骨水泥的断裂过程。分析了该断裂过程中应力场和损伤场的变化规律,深入探究了潜在裂纹路径的数量以及含裂纹构件中不同裂纹形态对断裂机理和断裂性能的影响。对比相关试验,验证了粘聚元耦合有限元技术分析连续脆性介质的断裂过程的可行性。为了提高计算效率,本文利用了危险区概念。将容易发生断裂的区域采用粘聚元耦合有限元技术建模,其他区域采用传统有限元技术建模。
(5)利用粘聚元耦合有限元技术,建立了骨水泥疲劳损伤模型,研究其疲劳损伤过程
以准脆性材料骨水泥拉伸疲劳为例,基于强度弱化理论,将粘聚元引入了连续介质(骨水泥)的疲劳累积损伤分析中。将疲劳损伤过程分为无疲劳裂纹萌生、疲劳裂纹萌生、裂纹扩展三个阶段,研究了不同阶段中材料性能的变化和损伤程度的变化,首次提出了一种疲劳累积损伤及破坏模型。利用Visual C编写了调用Abaqus求解器的控制程序,实现了连续脆性介质(骨水泥)疲劳循环全过程损伤分析。对比线性和对数型两种强度弱化模式,研究了构件损伤和破坏机制的差异及其特点,计算了疲劳裂纹萌生、疲劳裂纹扩展和断裂扩展各阶段的寿命。对比有关试验研究,验证了粘聚元耦合有限元方法在疲劳损伤分析中的可行性和三段式疲劳累积损伤及破坏模型的合理性。
Biomechanics is the application of mechanical engineering theory and practice to biological materials and systems. It has been widely studied and applied since the1960's. It encompasses many disciplines including material science, mechanics, anatomy, physiology, computer science. It develops rapidly and emerges as an independent cross-discipline subject now. Among many branches of biomechanical research, its application in orthopedics is becoming more and more important because of urgent needs for accurate quantitative assessment in diagnosis, treatment and prevention of the common and frequently-occurring disease which are harmful to people's health and the quality of life.
There are two main methods used in biomechanical research:biomechanical testing and numerical simulation analysis. Biomechanical testing, in vitro, can directly obtain the information about the mechanical properties of measured object. The results and conclusions from the testing depend on test condition and method. Therefore, it only provides some heuristic guidelines in qualitative researches, but neglect the differences of individuals. Compared with biomechanical testing, Finite Element (FE) method, an important method of numerical simulation analysis, has many advantages: the cost of simulation is low, test finish without errors, non-invasive and non-destructive model can be repeatedly used and the complicated boundary condition can be added conveniently, etc. It is more important that FE method can built the complicated models of bone tissue of individuals, special in vivo, with very realistic geometry and material property. Thus, the analysis results can serve as references for clinical diagnosis, operation plan evaluation, plastic surgery, prosthetic design and manufacturing, etc.
In1972, Brekelmans and Rybicki took the lead in the application of FE techniques in the biomechanical studies on vertebrae and femur. From then on, the technique came into widespread use which covered almost all human bones. The early efforts of the technology were limited in the analysis of two-dimensional linear problem with simplified loads and boundary conditions. The analysis results were far from the actual fact. With the development of computer technology and numerical analysis theory, there are many mature examples of FE application in complicated nonlinear and multi-medium coupling problems. It has been proved that the more accurate model get and more realistic conditions imposed, the more accurate results acquired. In existing commercial software, there is no better solution for the presence of face ambiguity for the complicated bone tissue model. Difficulties may arise when one attempts to generate the FE meshes from the geometrical model with face ambiguity. Thus, to build a frame which generates bone FE model effectively and accurately is still necessary.
In clinic, the quantitative assessments about strength, stability, damage and fatigue life, are urgent needs for theoretical guidance. All those problems are involved with fracture and damage theory. The interfaces of bone-cement/bone, bone-cement/metal and bone/metal are weak links in replacement surgery. Fracture initiation and propagate may occur easily along weak interfaces. Thus, the weak interfaces are easy to induce postoperative complications such as prosthetic loosening, subsidence and rupture. Interface fracture mechanics can solve and explain the crack of the interfaces. However, honeycomb structure in human bone tissue, bubbles trapped in bone-cement and micro defects in prosthesis also contribute to the causes of postoperative complications. The occurrences of micro cracks and micro defects in bone tissue, bone-cement and prosthesis are inevitable, and the generation and distribution of them are at random. In FE modeling, micro cracks and micro defects are very hard to represent, thereby, bone, bone-cement and prosthesis are actually regarded as continuum media. Classical fracture mechanics take the model with crack as their research object. Numerical analysis method based on classical fracture mechanics seems incapable of solving the fracture problem of continuum media because the initial crack position and crack propagation direction are unknown. To explore a new method to determine crack position, estimate the fracture strength and fatigue life of continuum media has a very important practical significance. The coupling technology of cohesive zone model (CZM) and finite element has been widely used in the analysis of composite materials interface crack. This is beneficial attempt to introduce this technology for the assessment of interface damage and fracture in replacement surgery. Material damage is the gradual process of mechanical property deterioration. The concept of damage variable, which represents the change in material stiffness, is introduced to continuum mechanics. Cohesive elements are inserted into continuum media to represent potential crack paths. The separation of the upper and lower surfaces of cohesive element can be expressed as the discontinuous displacement during the deformation and fracture of continuum media. Additionally, it is desired to further implement the computer simulation of fatigue and fracture process based on strength deterioration theory.
In view of the above, the main research contents and results in this paper are described as follows:
(1) To establish a framework for precision bone FE model
Considering that the face ambiguity of the model which generate by3D surface reconstruction using Marching Cube (MC) algorithm, is likely to lead to the difficult of mesh generation, a strategy is formulated:preprocessing of medical images for ROI (region of interest), stacking VOI (volume of interest) with ROI, smoothing the VOI for a closed surface domain of3D model. According to the characteristics of medical images, the voxels in medical image data can convert to the hexahedral meshes of FE bone model (voxel-based mesh model) directly by home-made program. The framework provides different mapping methods, such as centroid-based, node-based, grid-based, etc, and assigns inhomogeneous anisotropic properties for bone tissue. Due to little amount of the bone tissue with CT grey value～800Hu in human body, it is very hard to make suitable sample for testing material property. In the result, the material model represents a discontinuous leap. A smooth template is proposed to smooth the leap. Some researches show that the average method to group the material properties may overestimate or underestimate the material properties of bone. Thus, K-mean algorithm based on the volume of element is proposed to cluster the groups of material properties. Finally, the information about nodes, elements and material properties of model could be arranged automatically in accordance with different FE software packages. In contrast to the other commercial software, the framework avoids mesh generation bottleneck for complicated bone model, increases the mapping, smoothing, and clustering methods for the assignment of material properties, and also can describe the anisotropic property of bone tissue. The frame could be expanded to meet the users' requirements.
(2) Based on the above framework, two cases in orthopedic are analyzed.
①Case one:To design custom prosthesis for patients with massive bone loss in proximal femur.
In this case, a new concept of design based on investigating individual femur shape and femoral bone quality is proposed before custom prosthesis design. Then, the FE models including before and after the prosthesis replacement are built. The mesh models of femoral bone before and after the prosthesis replacement have the same structure. The technique of consistent meshes may make analysis results more comprehensive and objective. Two activities of daily living, normal walking and stair climbing, are simulated and muscle force is/is not simultaneously exerted. The change rate of strain energy is revised to replace stress shield signal to assess not only stress shield effect but fracture risk of bone tissue. Finally, an optimum scheme of custom prosthesis is determined after the comparison among simulation results.
②Case two:To compare and evaluate two posterior atlantoaxial fixations including C1lateral mass to C2pedicle fixation (C1LM-C2P) and C1lateral mass to C2laminar fixation (C1LM-C2L).
In this case, first analyze the anatomy structure of individual atlantoaxial and validate the feasible of C1LM-C2P and C1LM-C2L, then build fine FE models of C1LM-C2P and C1LM-C2L containing atlanto-odontoid and arthrodial. Seven loads to simulate different head postures:anterior-posterior (AP), translation (forward), extension, flexion, lateral bending (left/right), and torsion (left/right) are exerted for simulations. The FE analysis results are shown to be in good agreement with the published experimental data. To draw a conclusion is stating that C1LM-C2L is an alternative for some patients with congenital anomalies who are not suitable for other fixation treatment. It is worth to point out that the stability of C1LM-C2L is worse than the one of C1LM-C2P.
(3) To analysis and assess the stability of cemented fixation for patients with massive bone loss in proximal femur using the technique of Cohesive Zone Model (CZM).
In this research, shear strength and shear fracture toughness of cement/metal interface are measured by, respectively, sandwich shear and End Notched Flexure (ENF) testing. To avoid the measurements of the crack length during the crack growth, compliance calibration method is applied to determine the critical strain energy release (GIIC), a kind of fracture toughness, in ENF test. The coupling of CZM and FE method is employed to simulate the process of ENF test for the analytical solution of GIIC. The two solutions are compared with published experiment data. Furthermore, the stability of cemented fixation for patients with massive bone loss in proximal femur and the influences of the surfaces of prosthesis are investigated with the coupled method. The analysis results provide valuable insights into relevant clinical phenomena and quantitative guides to clinical therapy.
(4) To investigate the fracture process and fracture property of bone-cement with the technique of coupling of cohesive element and FE.
This research presents the different methods to set up potential crack paths corresponding to different load cases. A general method to set up potential crack paths is proposed. The model for fracture analysis based on this method could generate automatically by virtue of home-made program. The program is suitable for the tetrahedron element in commercial software ABAQUS. It can be expanded to other software. The uniaxial tensile test of bone-cement is taken as an example. The fracture process of this model is tracked. The results display the changes of stress field and damage field in the whole fracture process. The other focus of this study is to explore the influences of the numbers of potential crack path and crack morphology upon fracture mechanism and fracture property. That the findings agree well with other published experiment data validates the feasibility of application of the coupled method as mentioned above in solving the fracture problem of quasi-brittle or brittle material. In order to improve computational efficiency, components should be divided into two zones. One is the fracture risk zone. Fractures commonly occur in the zone and the model of the zone is built by the coupled method, whereas, another zone is only built by FE method.
(5) To establish fatigue cumulative damage model with the technique of coupling of CZM and FE and to investigate the fatigue damage process of bone-cement.
Based on strength degradation theory, the technique of coupling of CZM and FE is introduced in the analysis of fatigue cumulative damage. The tensile fatigue test of bone-cement is taken as an example. A new fatigue cumulative damage model with three stages is proposed. The three stages correspond to before crack initiation (I), fatigue crack initiation (II) and fatigue crack propagation (III). This research investigates the changes of material properties in damage evolution process. A program is written in Visual C language to control Abaqus solver for the analysis of fatigue damage evolution process. The mechanism of damage is investigated and fatigue life in different stages can be predicted under linear and logarithmic strength degradation modes. Compared with published experiment data, this research confirmed the feasibility of the coupled method in the application of fatigue damage and the validation of the fatigue cumulative damage model with three stages proposed in this study.
引文
[1]Brekelmans W, Poort H, Slooff T. A new method to analyze the mechanical behavior of skeletal parts[J], Acta Orthopaedica Scandinavica,1972.43:3-17.
[2]Rybicki EF, Yang KH. On the mathematical analysis of stress in the human femur [J], Journal of Biomechanics,1972.5(2):203-215.
[3]Bandak FA, Vander Vorst MJ, et al. An imaging-based computational and experimental study of skull fracture:finite element model development [J], Journal of neurotrauma,1995.12(4): 679-688.
[4]Phillips AT, Pankaj P, Howie CR, et al. Finite element modeling of the pelvis:inclusion of muscular and ligamentous boundary conditions [J], Medical Engineering & Physics, 2007.29(7):739-748.
[5]Hagemann A, Rohr K, Stiel HS. Coupling of fluid and elastic models for biomechanical simulation of brain deformations using FEM[J], Medical Imaging Analysis,2002.6:375-388.
[6]Ecabert O, Butz T, Nabavi A et al. Brain Shift Correction Based on a Boundary Element Biomechanical Model with Different Material Properties[C], MICCAI 2003 Proceedings, PartⅠ-41-50.
[7]Lorensen WE, Cline HE. Marching Cubes:A high resolution 3D surface construction algorithm [J], Computer Graphics,1987.21(4):163-169.
[8]梁秀霞.医学影像数据可视化中若干问题研究[D],山东大学,2006.
[9]Rho JY, Hobatho MC, Ashman RB, et al. Relations of mechanical properties to density and CT numbers in human bone[J], Medical Engineering Physics,1995.17:347-355
[10]Sanjay Gupta, Prosenjit Dan. Bone geometry and mechanical properties of the human scapula using computed tomography data[J], Trends in Biomaterials and Artificial Organs,2004.17(2): 61-70.
[11]Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure [J], Journal of Bone and Joint Surgery,1977.59A:954-962.
[12]Ashman RB, Cowin SC, Van Buskirk WC, et al. A continuous wAve technique for the measurement of the elastic properties of cortical bone[J], Journal of Biomechanics,1984.17: 349-361.
[13]Shefelbine SJ, Simona U, Claes L. Prediction of fracture callus mechanical properties using micro-CT images and voxel-based finite element analysis [J], Bone,2005.36:480-488.
[14]Taddei F, Pancanti A, Viceconti M. An improved method for the automatic mapping of computed tomography numbers onto finite element models[J], Medical Engineering and Physics,2004. 26(1):61-69.
[15]Taylor WR, Roland E. Determination of orthotropic bone elastic constants using FEA and modal analysis[J], Journal of Biomechanics,2002.35:767-773.
[16]Taddei F, Schileo E, Helgason B. The material mapping strategy influences the accuracy of CT-based finite element models of bones:An evaluation against experimental measurements [J], Medical Engineering and Physics,2007.(29):973-979.
[17]Viceconti M, Zannoni C, Pierotti L, et al. An application of reverse engineering methods to the creation of CAD models of bone segments[J], Computer Methods and Programs in Biomedicine, 1998.56(3):211-220.
[18]Herman G, Liu T. Three-Dimensional Display of Human Organs from Computed Tomograms[J], Computer Graphics&Image Processing,1979.9(4):1-12.
[19]Miller JV, Breen DE, Lorensen WE, et al. Geometrically deformed models:a method for extracting closed geometric models from volume data[J], ACM SIGGRAPH Computer Graphics,1991.25(4):217-226.
[20]Gonzalez RC, Woods RE数字图像处理[M],北京：电子工业出版社,2003.
[21]Kass M, Witkin A, Terzopoulos D. Snakes:active contour models [J], International Journal of Computer Vision,1987.1(4):321-331.
[22]Osher S, Sethian JA. Fronts propagating with curvature dependent speed:Algorithms based on Hamilton-Jacobl formulation[J], Journal of Computational Physics,1988.79(1):12-49.
[23]] Pardo JM, Cabello D, Heras J. A snake for model-based segmentation of biomedical imagesfJJ, Pattern Recognition Letters,1997.18(14):1529-1538.
[24]Barbara Podda, Gianluigi Zanetti, Andrea Giachetti. Texture analysis for vascular segmentation from CT images[C], International Congress Series,2005.1281:206-211.
[25]张小萍,朱志松,王君泽.基于CT医学图像的边缘提取研究[J],生物医学工程研究,2009.28(1)：31-34.
[26]Otsu N. A threshold selection method from gray-level histograms [J], IEEE Transactions on Systems, Man and Cybernetics,1979.9(1):62-66.
[27]郑静,张建州,赵楠.基于跟踪算法的肺部CT图像血管提取[J],计算机工程与应用,2007.43(32)：204-206.
[28]涂其远,吴建华,万国金.动态阈值结合全局阈值对图像进行分割[J],南昌大学学报(工科版),2002.24(01)：37-40.
[29]Eidheim OC, Aurdal L, Omholt-Jensen T, et al. Segmentation of liver vessels as seen in MR and CT images[C], International Congress Series,2004.268:201-206.
[30]金钟,汪炳权.自动多门限CT图像的分割[J],安徽大学学报(自然科学版),2002.26(03)：57-60.
[31]Adams R, Bischof L. Seeded region growing[J], IEEE Transactions on Pattern Analysis and Machine Intelligence,1994.16(6):641-647.
[32]舒添慧,胥布工,胡战虎.基于区域生长法的医学图像分割[J],微计算机信息,2008,6-3：284-285.
[33]陈彦达,鲍苏苏.一种新的肝脏CT序列图像区域生长算法[J],计算机工程与应用, 2010.46(3)：188-190.
[34]朱玲利,王听忠.基于CT图像分析和区域生长法的CT图像分割[J],洛阳理工学院学报(自然版),2009.19(4)：55-59.
[35]何为,余晓锷.基于K均值聚类算法的CT图像金属伪影去除[J],中国医疗设备,2009.24(06)：12-14.
[36]梅媚,张力新,万柏坤.基于CT图像的势函数聚类分割人体脂肪检测[J],天津大学学报,2004.37(08)：740-744.
[37]周鲜成.图像分割方法及其应用研究综述[J],信息技术,2007.12：11-14.
[38]卢畅,韩珂,李晶.基于CT图像全颈椎三维有限元模型的建立及验证[J],中南大学学报(医学版),2008.33(5)：410-414.
[39]张秀萍.基于点云数据复杂曲面的三维重构[D],新疆大学,2004.
[40]王成焘.中国力学虚拟人[J],医用生物力学,2006.21(3)：172-178.
[41]王晓,何建英.考虑MC算法二义性后的三角化方法[J],湖北工业大学学报,2007.6：225-230.
[42]Cline HE, Lorensen WE, Ludke S. Two algorithms for the three-dimensional reconstruction of tomograms[J], Medical Physics,1988.15(3):320-397.
[43]Van Lenthe GH, Stauber M, Muller R. Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties [J], Bone,2006.39:1182-1189.
[44]Kong WZ, Geol VK. Ability of the finite element models to predict response of human spine to sinusoidal vertical vibration[J], Spine,2003.28(17):1961-1967.
[45]陈守义.椎弓骨钉在材料性质及介面状态之生物力学分析[D],台湾成功大学医学工程研究所,2003.
[46]Krone R, Schuster P. An Investigation on the Importance of Material Anisotropy in Finite-Element Modeling of the Human Femur[J], SAE International Paper Number 2006. 01-0064.
[47]Guptal S, van der Helm FCT, Sterk JC. Development and experimental validation of a three-dimensional finite element model of the human scapula[J], Proceedings of the Institution of Mechanical Engineers, Part H:Journal of Engineering in Medicine,2004.218(2):127-142.
[48]Skinner HB, Kilgus DJ, Keyak J. Correlation of computed finite element stresses to bone density after remodeling around cementless femoral implants[J], Clinical Orthopedics and Related Research,1994.305:178-189.
[49]Keyak JH, Meagher JM, Skinner HB, et al. Automated three-dimensional finite element modeling of bone:a new method[J], Journal of Biomedical Engineering,1990.12 (5):389-397.
[50]Keller TS. Predicting the compressive mechanical behavior of bone[J], Journal of Biomechanics,1994.27(9):1159-1168.
[51]van Rietbergen B, Muller R, Ulrich D, et al. Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions[J], Journal of Biomechanics, 1999.32:165-173.
[52]Muller-Karger CM, Zeman ME, Cerrolaza M. P-version of the finite-element method for highly heterogeneous simulation of human bone[J], Finite Elements in Analysis and Design, 2004.40(7):757-770.
[53]Yosibash Z, Padan R, Joskowicz L, et al. A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to In-vitro Experiments[J], Journal of Biomechanical Engineering,2007.129:297-309.
[54]Barna Szabo, Ivo Babuska. Finite Element Analysis[M], Babuska Wiley-Interscience,1991.
[55]Cowin SC. Bone poroelasticity[J], Journal of Biomechanics,1999.32(3):217-238.
[56]Ciarelli MJ, Goldstein SA, Kuhn JL, et al. Evaluation of orthogonal mechanical properties and density of human trabecular bone From the Major metaphyseal regions with materials testing and computed tomography [J], Journal of Orthopaedic Surgery and Research,1991.9:674-682.
[57]Cody D, Gross G, Hou F, et al. Femoral strength is better predicted by finite element models than QCT and DXA[J], Journal of Biomechanics,1999.32:1013-1020.
[58]Harrigan TP, Oh I, Harris WH, et al. The anisotropic properties of trabecular bone[C], Proceeding 6th NE Bio-Engineering Conference,1980:5-10.
[59]Kuhn JL, Goldstein SA, Ciarelli MJ, et al. The limitations of canine trabecular bone as a model forhuman:a biomechanical study [J], Journal of Biomechanics,1989.22:95-107.
[60]Lotz JC, Gerhart TN, Hayes WC. Mechanical properties of metaphyseal bone in the proximal femur [J], Journal of Biomechanics,1991.24:317-29.
[61]Stolk J, Janssen D, Huiskes R, et al. Finite element-based preclinical testing of cemented total hip implants[J], Clinical Orthopaedics and Related Research,2007.456:138-147.
[62]Couteau B, Labey L, Hobatho MC, et al. Validation of a three dimensional finite element model of a femur with a customized hip implant[J], Computer Methods in Biomechanics and Biomedical Engineering,1998.1(1):77-86.
[63]Rubin PJ, Rakotomanana RL, Leyvraz P, et al. Frictional interface micromotions and anisotropic stress distribution in a femoral total hip component[J], Journal of Biomechanics, 1993.26:725-739.
[64]庄茁,蒋持平.工程断裂与损伤[M],北京：机械工业出版社,2004.
[65]余天堂.含裂纹体的数值模拟[J],岩石力学与工程学报,2004.24(24)：4434-4439.
[66]陈篪等.工程断裂力学[M],北京：国防工业出版社,1977.
[67]余寿文,冯西桥.损伤力学[M],北京：清华大学出版社,1997.
[68]钱济成.损伤理论及应用[M],北京：国防工业出版社,1993.
[69]冒小萍,郎福元,柯显信.断裂力学的数值计算方法的研究现状与展望[J],商丘师范学院学报,2004.2：20-24.
[70]李尧臣,王自强.在裂纹尖端引入位移协调奇异单元的有限单元法[J],上海力学, 1983.3：79-99
[71]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用[M],北京：科学出版社,2009.
[72]高东宇,林臼新.飞机机翼疲劳断裂过程的有限元分析[J],哈尔滨理工大学学报,2006.11(3)：18-21.
[73]彭云.基于VUMAT的三维裂纹动态扩展有限元模拟[J],南昌航空大学学报,2010.24(2)：41-45.
[74]Moes N, Dolbow J, Belytschco T. A finite element method for crack growth without remeshing[J], InternationalJournal for Numerical Methods in Engineering,1999.46:131-150.
[75]Babuska I, Melenk JM.The partition of unity nite element method[J], International Journal for Numerical Methods in Engineering,1997.40:727-758.
[76]李录贤,手铁军.扩展有限元及其应用[J],力学进展,2005.35(1)：5-20.
[77]Dolbow J, Moes N, Belytschko T. Modeling fracture in Mindlin-Reissner plates with the extended finite element method[J], International Journal of solid and structures, 2000.57:7161-7183.
[78]梁国平,何江衡.广义有限元方法[J],力学进展,1995.25(4)：562-565.
[79]杨德全,赵忠生.边界元理论及应用[M],北京：北京理工大学出版社,2002.
[80]朱加铭,欧贵宝,何蕴增.有限元与边界元法[M],哈尔滨：哈尔滨工程大学出版社,2002.
[81]孙玉周,王锦燕,许君风.边界元法在断裂力学数值计算中的应用研究[J],中原工学院学报,2004.15(5)：21-23.
[82]彭妙娟,程玉民.断裂力学的相似边界元法及其应用[J],应用力学学报,2007.24(2)：294-297.
[83]周小平,周瑞忠.无单元法研究现状及展望[J],工程力学,2005.22(1)：12-18.
[84]Belytschko T, Lu YY, Gu L. Element-free Galerkin methods [J], International Journal for Numerical Methods in Engineering,1994.37:229-256.
[85]Belyschko T, Lu YY, Gu L. Element-free Galerkin methods for static and dynamic fracture [J], International Journal of Solids and Structures,1995.32:2547-2570.
[86]Terry T. Fatigue crack propagation modeling using the element-free Galerkin method[D], Evanston, Illinois:Northwestern University, USA.1994.
[87]顾元通,丁桦.无网格法及其最新进展[J],力学进展,2005.35(3)：323-337.
[88]曹国金,姜弘道.无单元法研究和应用现状及动态[J],力学进展,2002.32(4)：526-534.
[89]章青,周资斌,卓家寿.分区界面元-有限元-无限元混合模型[J],计算力学学报,2005.22(1)：8-12.
[90]刘凯欣,高凌天.离散元法研究的评述[J],力学进展,2003.33(4)：483-490.
[91]周先齐,徐卫亚,钮新强等.离散单元法研究进展及应用综述岩土力学[J],2007.28：409-415.
[92]卓家寿,赵宁.离散元的基本原理、方法和应用[J],河海科技进展,1993.13(2)：1-11.
[93]何传永,孙平编著,非连续变形分析方法程序与工程应用[M],中国水利水电出版社,2009.
[94]唐瑜,苏超.非连续变形分析方法的研究及应用现状[J],水利水电科技进展,2004.24：111-119.
[95]石根华.数值流形方法与非连续变形分析[M],北京：清华大学出版社,1997.
[96]苏海东.固定网格的数值流形方法研究[J],力学学报.2011.1：169-178.
[97]张湘伟,章争荣,吕文阁等.数值流形方法研究及应用进展[J],力学进展,2010.40(1)：1-12.
[98]Tsay RJ, Chiou Y J, Chuang W L. Crack growth prediction by manifold method[J], Journal of Engineering Mechanics, ASCE,1999.125(8):884-890.
[99]Kawai T. New discrete structural models and generalization of the method of limit analysis [C], International Conference on Finite Elements in Nonlinear Solid and structural Mechanics, Norway,1977a.2:885-909.
[100]钱令希,张雄.结构分析中的刚性有限元法[J],计算结构力学及其应用,1991.8(1)：1-14.
[101]卓家寿,章青.不连续介质力学问题的界面元法[M],北京：科学出版社,2001.
[102]Dugdale DS. Yielding of steel sheets containing slits [J], Journal of the Mechanics and Physics of Solids,1960.8:100-104.
[103]Barenblatt G. The mathematical theory of equilibrium cracks in brittle fracture [J], Advances in Applied Mechanics,1962.7:55-129.
[104]Shet C, Chandra N. Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Processes[J],Transactions of the ASME,2002.124:440-450.
[105]Settgasta RR, Rashid MM. Continuum coupled cohesive zone elements for analysis of fracture in solid bodies [J], Engineering Fracture Mechanics,2009.(76):1614-1635.
[106]Camanho PP, Davila CG, et al. Numerical simulation of mixed-mode progressive delamination in composite materials[J], Journal of Composite Materials,2003.37(16):1415-1438.
[107]崔浩,李玉龙,刘元镛等.基于粘聚区模型的含填充区复合材料接头失效数值模拟[J],复合材料学报,2010.(27)：161-168.
[108]周储伟,杨卫,方岱宁.内聚力界面单元与复合材料的界面损伤分析[J],力学学报,1999.31(3)：372-377.
[109]刘甫.粘弹性界面断裂与固体火箭发动机界面脱粘研究[D],国防科学技术大学,2005.
[110]刘红霞,矫桂琼,熊伟等.复合材料层合板分层分析中的界面元应用[J],机械强度,2008.2：301-304.
[111]邵国建,刘体锋.广义有限元及其应用[J],河海大学学报(自然科学版),2002.30(4)：28-31.
[112]方修君,金峰,王进廷.基于扩展有限元法的粘聚裂纹模型[J],清华大学学报(自然科学版),2007.47(3)：344-347.
[113]尹华伟,易伟建,刘艳.有限元-界面元混合模型及其应用[J],湖南科技大学学报(自然科学版),2006.21(4)：41-46.
[114]陈跃良,卞贵学,郁大照.预腐蚀铝合金典型螺栓单搭接件疲劳寿命研究[J],工程力学,2012.29(5)：251-256.
[115]NASGRO Manual (2006). http://www. nasgro.swri.org.
[116]施伟,黄小平,崔维成.基于疲劳裂纹扩展率单一曲线模型的疲劳寿命预测[J],船舶力学,2008.12(2)：264-271.
[117]Skorupa M, Machniewicz T, Schijve J, et al. Application of the strip-yield model from the NASGRO software to predict fatigue crack growth in aluminum alloys under constant and variable amplitude loading[J], Engineering Fracture Mechanics,2007.74:291-313.
[118]http://www.t-solutiongroup.com/software/frame/20090901-frc.shtml.
[119]贾学明,王启智.三维断裂分析软件FRANC3D[J],计算力学学报,2004.21(6)：764-768.
[120]孙远滔.裂纹诊断的数值分析方法与应用研究[D],武汉：武汉理工大学,2008.
[121]3D fracture mechanics simulation, Zencrack_brochure_2008, Zentech company.
[122]T-solution,3D裂纹扩展分析技术及其在航空领域的应用,2009产品创新数字化峰会征文.
[123]朱永生.颗粒流分析系统(PFC2D/3D)理论背景,中国水电顾问集团-ITASA研发中心.
[124]http://www.crackwizard.com/.
[125]肖涛,左正兴.虚拟裂纹闭合法在结构断裂分析中的应用[J],计算力学学报,2008.25：16-19.
[126]孟令兵,陈普会.层压复合材料分层扩展分析的虚拟裂纹闭合技术及其应[J],复合材料学报,2010.27(1)：190-195.
[127]姜年朝ANSYS和ANSYS/FE-SAFE软件的工程应用及实例[M],南京：河海大学出版社,2006.
[128]周传月,郑红霞,罗慧强MSC.Fatigue疲劳分析应用与实例[M],北京：科学出版社,2005.
[129]三维裂纹扩展仿真软-ALOF软件使用手册,合肥洞力信息科技有限公司,2010.
[130]http://www.sili-tech.com/article.jsp?type=6&id=90.
[131]刘达列.疲劳破坏的连续型损伤力学模型的研究[D],浙江大学,2002.
[132]吴德飞,童根树.含初始缺陷钢结构损伤累积至断裂即后期的调查分析[J],工程力学,2006.8：160-168.
[133]王军.损伤力学的理论与应用[M],北京：科学出版社,1997.
[134]余天庆,钱济成.损伤理论及应用[M],北京：国防工业出版社,1993.
[135]沈为.损伤力学[M],武汉：华中理工大学出版社,1995.
[136]Griffith AA. The phenomena of rupture and flow in solid [J], Philosophical Transactions, 1920.221(A):163-198.
[137]Orowan E. Fracture and strength of solids[J], The Physical Society,1949.12:182-232.
[138]Irwin G. Analysis of stresses and strains near the end of a crack trAver sing a plate [J], Journal of Applied Mechanics,1957.24:361-364.
[139]David Roylance, Orowan E. Fracture and strength of solids[J], The Physical Society, MIT: 2001, MA 02139 June 14.
[140]Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear[J], Journal of Basic Engineering,1963.85(4):519-527.
[141]Sih GC. Strain energy density factor applied to mixed mode crack problem[J], International Journal of Fracture Mechanics,1974.10:305-321.
[142]Palaniswamy K, Knauss WG. Propagation of a crack under general in-plane tension [J], International Journal of Fracture,1972.8:114-117.
[143]Wells AA. Application of fracture mechanics at and beyond general yielding[J], British welding journal,1963.10:563-570.
[144]Rice JR. A path independent integral and the approximate analysis of concentration by notches and cracks [J], Journal of Applied Mechanics,1968.35:379-386.
[145]杨光松.损伤力学与复合材料损伤[M],北京：国防工业出版社,1995.
[146]尹双增.断裂、损伤理论及应用[M],北京清华大学出版社,1992.
[147]KachanovL M. On the Creep Fracture Time[J], Izv Akad, Nauk USSR Otd. Tech.,1958.8: 26-31 (in Russian).
[148]Rabotnov YN. On the equations of state for creep [J], Progress in Applied Mechanics, 1963.10:307-315.
[149]吴刚,孙钧,吴中如.复杂应力状态下完整岩体卸荷破坏的损伤力学分析[J],河海大学学报,1997.25(3)：44-49.
[150]唐春安.岩石破裂过程中的灾变[M],北京：煤炭工业出版社,1993.
[151]杨更社,张长庆.岩体损伤及检测[M],西安：陕西科学技术出版社,1998.
[152]Kachanov D. Theory of creep in advances in creep design[M], London:Applied Science Publisher,1985.121-138.
[153]Lemaitre J. How to use damage mechanics [J], Nuclear Engineering and Design, 1984.80(1):233-245.
[154]谢和平,彭瑞东,鞠杨.岩石变形破坏过程中的能量耗散分析[J],岩石力学与工程学报,2004.23(21)：3565-3570.
[155]Paris PC, Erdogan F. A critical analysis of crack propagation laws [J], Journal of basic Engineering, Trans. ASME,1963.85(4):528-534.
[156]Walker EK. The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum[J], ASTM STP 462, American Society for Testing and Materials, 1970:1-14.
[157]Forman RG, Kearney VE, Englem RM. Numerical analysis of crack propagation in a cyclic-loaded structure [J], Journal of basic Engineering, Trans.ASME,1967.89:459-465.
[158]Miner MA. Cumulative damage in fatigure[J], Journal of Applied Mechanics, 1945.2:159-164.
[159]姚卫星.结构疲劳寿命分析[M],北京：国防工业出版社,2003.
[160]Wallgren G. Fatigue test with stress cycle of varying amplitude[D], Stockholm Aeronautical Research Institute of Sweden,1949.
[161 [Grover HJ. An observation concerning the cycle ratio in cumulative damage[J], Fatigue in Aircraft Structures, ASTM, STP274,1960.120-124.
[162]Manson SS, Freche JC. Ensign CR. Application of a double linear damage rule to cumulative fatigue [J], Fatigue Crack Propagation, ASTM STP 415,1967.384-412.
[163]Marco SM, Starkey WL. A concept of fatigue damage [J], Transactions of the ASME,1954.76: 627-632.
[164]Manson SS, Halford GR. Practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage[J], International Journal of Fatigue, 1981.17(2):169-192.
[165]徐灏.疲劳强度[M],北京：高等教育出版,1990.
[166]叶笃毅,王德俊.一种基于材料韧性耗散分析的疲劳损伤定量新方法[J],试验力学,1999.14(1)：80-89.
[167]Abdul-Kadir MR, Hansen U, Klabunde R, et al. Finite element modeling of primary hip stem stability:The effect of interference fit[J], Journal of Biomechanics,2008,41(3):587-594.
[168]Varini E, Bialoblocka-Juszczyk E, Lannocca MA. Assessment of implant stability of cementless hip prostheses through the frequency response function of the stem-bone system[J], Sensors and Actuators A,2010.163(2):526-532.
[169]谢英杰,叶志前,徐庐生.医学图像可视化与相关技术及应用[J],国外医学生物医学工程分册,2001.24(3)：114-117.
[170]Jiang hsieh.计算机断层成像技术[M],北京：科学技术出版社,2006.
[171]王立功,刘伟强,于甬华等DICOM医学图像文件格式解析与应用究[J],计算机工程与应用,2006.(29)：210-212.
[172]董义兵,晁爱农DICOM标准应用深层次探讨[J],中国医学装备,2006.3(11)：31-35.
[173]刘晓燕,张春田.基于DICOM医学图像软件工具包的设计和实现[J],天津理工学院学报,2003.19(4)：84-87.
[174]李科,颜红梅.医学信息学[M],成均：电子科技大学出版社,2005.
[175]石明国.实用CT图像技术学[M],西安：陕西科学技术出版社,1995.
[176]Smith RA, Paulus MJ, Branning JM, et al. X-ray computed tomography on a cellular polysiloxane under compression[J], Journal of Cellular Plastics,2001.37(3):231-248.
[177]田培林.CT检查的窗宽窗位设置[J],医学与工程,2001.3(1)：6-10.
[178]赵以甦.骨科生物力学的基本名词[J],中华骨科杂志,2006.26(4)：286-288.
[179]ImageJ_Manual, http://rsb.info.nih.gov/ijz.
[180]Will Schroeder, Ken Martin, Bill Lorensen. An Object Oriented Approach to 3D Graphics[M], 2nd Edition. Prentice Hall old,1996.
[181]Katoozian H, Davy DT, Arshi A, et al. Material optimization of femoral component of total hip prosthesis using fiber reinforced polymeric composites [J], Medical Engineering & Physics, 2001.23:503-509.
[182]Goetzen N, Lampe F, Nassut R, et al. Load-shift-numerical evaluation of a new design philosophy for uncemented hip prostheses[J], Journal of Biomechanics,2005.28(3):595-604.
[183]Fantigrossi A, Galbusera F, Raimondi MT, et al. Biomechanical analysis of cages for posterior lumbar interbody fusion [J], Medical Engineering & Physics,2007.29(1):101-109.
[184]Wu W, Yang DZ, Qi M, et al. An FEA method to study flexibility of expanded coronary stents[J], Journal of Materials Processing Technology,2007.84(12):447-450.
[185]杨帆.数字图像处理与分析[M],北京：北京航空航天大学出版社,2010.
[186]刘相滨,向坚持,阳波.基于八邻域边界跟踪的标号算法[J],计算机工程与应用,2001.23：125-127.
[187]Fedida R, Yosibash Z, Milgrom C, et al. Femur mechanical simulation using high-order FE analysis with continuous mechanical properties[C], International Conference on Computational Bioengineering, Lisbon, Portugal, September 2005.14-16.
[188]Kowalczyk P. Design optimization of cementless femoral hip prostheses using finite element analysis[J], Journal of Biomechanical Engineering,2001.123(5):398-402.
[189]Fx W, Zhang WJ, Kusalik AJ. A genetic Kmeans clustering algorithm applied to gene expression data. Advances in Artificial Intelligence[J], Proceedings Lecture Notes in Artificial Intelligence,2003.2671:520-526.
[190]石亦平,周玉蓉ABAQUS有限元分析实例详解[M],北京：机械工业出版社,2006.
[191]郭卫.中华骨科学-骨肿瘤卷[M],北京：人民卫生出版社,2010.
[192]Weber KL. What is new in musculoskeletal on cology[J], Journal of Bone and Joint Surgery, 2005.87(6):1400-1410.
[193]Gorge H, T Andrew I, Daniel JB. Reverse obliquity fractures of the interochanteric region of the femur[J], Journal of Bone and Joint Surgery(Am),2001.83:643-647.
[194]徐旭纯.May钢板治疗股骨粗隆粉碎性骨折[J],浙江临床医学,2005.7(9)：924-925.
[195]Chao EY, Ivins JC. Tumor prostheses for bone and joint reconstruction:The design and application[M], New York:University of Michigan,1983.
[196]Charnley J. Low-friction arthroplasty of the hip[M], Theory and practice, Berlin:Springer, 1979.3-15.
[197]中国组织工程研究与临床康复编辑部.让昨天告诉今天-人工髋关节研究的学术与技术进展[J],中国组织工程研究与临床康复,2009.13(4)：690-691.
[198]宁志杰.奥斯汀-骨移植替代物[J],中国矫形外科杂志,2000.7(6)：593-594.
[199]Moore AT, Bohlman HR. Metal hip replacement:A case report[J], Journal of Bone and Joint Surgery,1943.25:688-692.
[200]Scales JT. Massive bone and joint replacement involving the upper femur, acetabulum, and iliac bone[J], Proceedings of the Open Scientific Meeting of the Hip Society,1975.3:245-275.
[201]Barr JS, Eaton RG. Elbow reconstruction with a new prosthesis to replace the distal end of the humerus. A case report [J], Journal of Bone and Joint Surgery(Am),1965.47:1408-1413.
[202]Chao EY, Sim FH, Ivins JC. Tumor prostheses for bone and joint reconstruction:The design and application[M], New York:University of Michigan,1983.
[203]Khang G, Choi K, Kim CS, et al. A study of Korean femoral geometry [J], Clinical Orthopaedics and Related Research,2007.22:116-122.
[204]Palm L, Olofsson J, Astrom SE, et al. No difference in migration or wear between cemented low-profile cups and standard cups:a randomized radio stereographic study of 53 patients over 3 years[J], Acta Orthopaedica,2007.78(4):479-484.
[205]戴尅戎,朱振安,孙月华.计算机辅助个体化人工半骨盆的设计与应用[J],中华骨科杂志,2005.25(5)：258-262.
[206]Werner A. Design and manufacture of anatomical hip jointendoprosthesis using CAD/CAM systems[J], Journal of Materials Processing Technology,2000.107(1):181-186.
[207]Kurz MJ, Stergiou N. An artificial neural network that utilizes hip joint actuations to control bifurcations and chaos in a passive dynamic bipedal walking model [J], Biological Cybernetics, 2005.93(3):213-221.
[208]康黎云,龚宪生,权威等.髋关节内置假体设计方法[J],重庆大学学报(自然科学版),2005.28(7)：18-22.
[209]Reuben JD, Chang CH, Akin JE et al. A knowledge-based computer-aided design and manufacturing system for total hip replacement [J], Clinical Orthopaedics and Related Research,1992.285:48-56.
[210]Stulberg S, Stugberg B, Wixson R. The fationable design characteristicsand ptrliminary trsults of a primary total hip prosthesis [J], Clinical Orthopaedics and Related Research,1989. 249:79-96.
[211]Huo MH, Salvati EA, Lieberman JR, et al. Custom-designed femoral prostheses in total hip arthroplasty done with cement for severe dysplasin of the hip[J], Journal of Bone and Joint Surgery (Am),1993.75:1497-1504.
[212]Frank D, Won Y, Eduardo A, et al. Long-tem results of total hip arthroplasty with a cemented custom-designed swan-neck femoral computer for congenital dislocation or severe dysplasia[J], Journal of Bone and Joint Surgery (Am),2002.84:204-207.
[213]Murphy SB, Rijeuski PK, Millis MB, et al. The palnning of orthopaedic reconstructive surgery using computer aided simulation and design[J], Computerized Medical Imaging and Graphics,1988.12(1):35-45.
[214]刘文广.套接式翻修假体设计、初步应用及三维有限元优化[D],山东大学,2008.
[215]http://www.360doc.com.
[216]Bergmann G, Deuretzbacher G, Heller M, et al. Hip contact forces and gait patterns from routine activities[J], Journal of Biomechanics,2001.(34):859-871.
[217]全国体育院校教材委员.运动解剖学[M],北京：人民体育出版社,2000.
[218]Turner RH, Matingly DA, Scheller A. Femoral revision total hip arthroplasty using a long-stem femoral component:Clinical and radiog raphic analysis [J], Journal of Arthroplasty, 1987.2:247-258.
[219]Gandhi R, Petruccelli D, Winemaker MJ, et al. Fractures at the tip of long-stem prostheses used for revision hip arthroplasty [J], Journal of Arthroplasty,2003.18 (6):741-745.
[220]张华,赵鹏,安耀荣等.股骨干骨折的生物力学研究进展[J],实用骨科杂志,2007.13(11)：669-671.
[221]Heller MO, Bergmann G, Kassi JP, et al. Determination of muscle loading at the hip joint for use in pre-clinical testing[J], Journal of Biomechanics,2005.38:1155-1163.
[222]ABAQUS 6.7 Analysis User's Manual, DS-SIMULIA.
[223]Hypermesh Advance Trainning, Altair Engineering, Inc., TX, USA.2001.
[224]Bergmann G, Graichen F, Rohlmann A. Hip joint loading during walking and running measured in two patients [J], Journal of Biomechanics,1993.26:969-990.
[225]赵钟岳.骨科实用生物力学[M],北京：人民卫生出版社,1983.
[226]戴尅戎,倪诚,王成焘等.定制型膝肿瘤假体的设计与临床应用[J],中华骨科杂志,2003.23(10)：606-610.
[227]Hsu RW, Sim FH, Chao EY. Reoperation results after segmental prosthetic replacement of bone and joint for limb salvage [J], Journal of Arthroplasty,1999.14:519-526.
[228]张鹤宇,罗先正,王志义.人工假体在骨肿瘤保肢中的应用[J],中华骨科杂志,2000.20：50-52.
[229]Lewis JL. The mechanical state of the bone-implant interface:In Non-cemented total hip arthroplasty[M]. New York:RAven Press Ltd,1988.
[230]Mjoberg B. The theory of early loosening of hip prostheses [J], Orthopedics,1997.20(12): 1169-1175.
[231]卿茂盛,李全.骨科应力遮挡的研究进展[J],中国骨伤,2003.16(1)：57-58.
[232]Sabo D, Reiter A, Simank HG, et al. Periprosthetic mineralization around cementless total hip endoprosthesis:longitudinal study and cross-sectional study on titanium threaded acetabular cup and cementless Spotorno stem with DEXA[J], Calcified tissue international, 1998.62(2):177-182.
[233]Schmidt R, Nowak TE, Mueller L, et al. Osteodensitometry after total hip replacement with uncemented taper-design stem[J], International orthopaedics,2004.28(2):74-77.
[234]Saito S, Saito M, Nishino T, et al. Long-term results of total hip arthroplasty for osteonecrosis of the femoral head-A comparison with osteoarthritis[J], Clinical Orthopaedics and Related Research,1989.244:198-207.
[235]Harris WH. The first 32 years of total hip arthroplasty. One surgeon's perspective [J], Clinical Orthopaedics and Related Research,1992.274:6-11.
[236]Weinans H, Sumner DR, Igloria R, et al. Sensitivity of periprosthetic stress-shielding to load and the bone density modulus relationship in subject-specific finite element models [J], Journal of Biomechanics,2000.33:809-817.
[237]Zannoni C, Mantovani R, Viceconti R. Material properties assignment to finite element models of bone structures:a new method [J], Medical Engineering and Physics,1998.20:735-740.
[238]Frost HM. A 2003 update of bone physiology and Wolffs Law for clinicians [J], The Angle Orthodontist,2004.74:3-15.
[239]孔庆毅,李家顺,贾连顺等.寰枢椎经关节螺钉固定的临床解剖学测量[J],中国矫形外科杂志,2002.10(13)：1328-1330.
[240]http://image.baidu.com.
[241]Doyle JS, Lauerman WC, Wood KB, et al. Complications and Long-Term Outcome of Upper Cervical Spine Arthrodesis in Patients With Down Syndrome[J], Spine,1996.21(10): 1223-1231.
[242]Dickman CA, Sonntag VK. Posterior CI-C2 Transarticular Screw Fixation for Atlantoaxial Arthrodesis [J], Neurosurgery,1998.43(2):275-280.
[243]Mitchell TC, Sadasivan KK, et al. Biomechanical Study of Atlantoaxial Arthrodesis: Transarticular Screw Fixation Versus Modified Brooks Posterior Wiring[J], Journal of Orthopaedic Trauma,1999.13(7):483-489.
[244]侍德,赵孰炎,张明.上颈椎不稳定性骨折脱位做前方融合术的探讨[J],中华骨科杂志,1992.12(3)：175.
[245]连小峰,侯铁胜.上颈椎不稳的内固定技术及其进展[J],中国矫形外科杂志,2004.7：544-546.
[246]解放军总医院等总编.实用神经外科学[M],北京：中国人民解放军战士出版社,1978.
[247]刘海兵,王文军.寰枢椎后路内同定术的研究进展[J],中国现代医药杂志,2009.11(4)：128-132.
[248]董荣华,王文宝,赵合元.实用脊柱外科内固定[M],天津：天津科学技术出版社,2006.
[249]Farey ID, Nadkarni S, Smith N. Modified Gallie Technique Versus Transarticular Screw Fixation in C1-C2 Fusion[J], Clinical Orthopaedics and Related Research,1999.359:126-135.
[250]Fielding JW, Hawkins RJ, Ratzan SA. Spine fusion for atlanto-axial instability [J], The Journal of bone and joint surgery, American volume,1976.58(3):400-407.
[251]Tucker HH. Technical report:method of fixation of subluxed or dislocated cervical spine below C1-C2[J], Journal of the Neurological Sciences,1975.2(4):381-382.
[252]Magerl F, Seemann PS. Stable posterior fusion of the atlas and axis by transarticularscrew fixation[M], Kehr P, Weidner A, eds. Cervical Spine, New York:Wien,1986:322-327.
[253]Tucker HH. Technical report:method of fixation of subluxed or dislocated cervical spine below C1-C2[J], Journal of the Neurological Sciences,1975.2(4):381-382.
[254]Aldrich EF, Weber PB, Crow WN. Halifax interlaminar clamp for posterior cervical fusion:a long-term follow-up review[J], Journal of Neurosurgery,1993.78(5):702-708.
[255]Stillerman CB, Wilson JA. Atlanto-Axial Stabilization with Posterior Transarticular Screw Fixation:Technical Description and Report of 22 Cases[J], Neurosurgery,1993.32(6):948-955.
[256]Sherk HH, Snyder B. Posterior Fusions of the Upper Cervical Spine:Indications, Techniques, and Prognosis [J], Orthopedic Clinics of North America,1978.9:1091-1099.
[257]Yoshida M, Neo M, Fujibayashi S, et al. Comparison of the anatomical risk for vertebral artery injury associated with the C2-pedicle screw and atlantoaxial transarticular screw. [J], Spine,2006.31(15):E513-E517.
[258]董荣华,王文宝.赵合元.实用脊柱外科内固定[M],天津：天津科学技术出版社,2006.
[259]Goel A, Laheri V. Plate and screw fixation for atlanto-axial subluxation[J], Acta Neurochirurgica,1994.129(1):47-53.
[260]Harms J, Meleher RP. Posterior C1-C2 fusion with polyaxial screw and rod fixation [J], Spine, 2001.16(22):2467-2471.
[261]郝定均,贺宝荣,雷伟等.寰椎侧块螺钉与枢椎弓根螺钉徒手植入技术的研究与应用[J],中国矫形外科杂志,2006.14(8)：579-581.
[262]Resnick DK, Benzel EC. C1-C2 Pedicle Screw Fixation with Rigid Cantilever Beam Construct Case Report and Technical Note [J], Neurosurgery,2002.50(2):426-428.
[263]Tan MS, Wang H, Wang Y, et al. Morphometric Evaluation of Screw Fixation in Atlas via Posterior Arch and Lateral Mass [J], Spine,2003.28(9):888-895.
[264]马向阳,尹庆水,吴增晖等.寰枢椎后路椎弓根螺钉固定治疗少儿上颈椎不稳[J],山东医药,2010.50(28)：37-39.
[265]Paramore CG, Dickman CA, Sonntag VK. The anatomical suitability of the C1-C2 complex for transarticular screw fixation[J], Journal of Neurosurgery,1996.85(2):221-224.
[266]Madawi AA, Casey AT, Solanki GA, et al. Radiological and anatomical evaluation of the atlantoaxial transarticular screw fixation technique[J], Journal of Neurosurgery,1997. 86(6):961-968.
[267]Wright NM. Posterior C2 fixation using bilateral crossing C2 laminar screws:case series and technical note[J], Journal of Spinal Disorders & Techniques,2004.17(2):158-162.
[268]Claybrooks R, Kayanja M, Milks R, et al. Atlantoaxial Fusion:a Biomechanical Analysis of two C1-C2 Fusion Techniques [J], The Spine Journal,2007.7(6):682-688.
[269]马向阳,尹庆水,吴增晖.寰枢椎后路四种钉棒固定方法的三维稳定性评价[J],中国脊柱脊髓杂志,2008.18(6)：464-468.
[270]胡巍,肖增明.寰枢关节脱位的置入物治疗技术与生物相容性及生物力学的关[J],中国 组织工程研究与临床康复,2008.12(13)：2511-2513.
[271]Saito T, Tamatouro T, Shikara J, et al. Analysis and Prevent ion of Spinal Column Deformity Following Cervical Laminectomy Pathogenic Analysis of Post Laminectomy Deformities [J], Spine,1991.16:494-502.
[272]Kleinberger M. Application of finite element techniques to the study of cervical spine mechanics[C], Proceedings of the 37th Steppe Car Crash Conference, San Antonio Tesas,1993: 7-8.
[273]Bozic KJ, Keyak JH, Skinner HB, et al. Three-dimensional finite element modeling of a cervical vertebra:an investigation of burst fracture mechanism[J], Journal of spinal disorders, 1994.7(2):102-110.
[274]Voo L, Denman J, Kumaresan S, et al. Development of 3D Finite Element Model of Cervical Spine[J], Avd Bioeng,1995.31:13-14.
[275]Teo EC, Ng HW. First cervical vertebra (atlas) fracture mechanism studies using finite element method[J], Journal of biomechanics,2001.34(1):13-21.
[276]Brolin K, Halldin P. Development of a Finite Element Model of the Upper Cervical Spine and a Parameter Study of Ligament Characteristics[J], Spine,2004.29(4):376-385.
[277]Zhang H, Bai J. Development and Validation of a Finite Element Model of the Occipito-Atlantoaxial Complex Under Physiologic Loads[J], Spine,2007.32(9):968-974.
[278]Young JK, Woo TR, Sang BL. Computerized Tomographic Measurements of Morphometric Parameters of the C2 for the Feasibility of Laminar Screw Fixation in Korean Population[J], Korean Neurosurgery Society,2008.44(1):15-18.
[279]Xu R, Burgar A, Ebraheim NA, et al. The Quantitative Anatomy of the Laminas of the Spine[J], Spine,1999.24(2):107-113.
[280]汪耀.枢椎椎板螺钉固定的有限元分析[D],山东大学,2010.
[281]Lu J, Fiala JC, Lichtman JW. Semi-Automated Reconstruction of Neural Processes from Large Numbers of Fluorescence Images[J], PLoS ONE,2009.4(5):e5655.
[282]Ulrich D, van Rietbergen B, Laib A, et al. The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone[J], Bone,1999.25(1):55-60.
[283]Kopperdahl DL, Morgan EF, KeAveny TM. Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone[J], Journal of Orthopaedic Research,2002.20(4):801-805.
[284]Pope MH, Panjabi MM. Biomechanical definitions of spinal instability [J], Spine, 1985.10:255-256.
[285]Moreo P, Pe'rez MA, Garci'a-Aznar JM. Modelling the mixed-mode failure of cement-bone interfaces [J], Engineering Fracture Mechanics,2006.73:1379-1395.
[286]Verdonschot N, Huiskes R. Mechanical effects of stem cement interface characteristics in total hip replacement [J], Clinical Orthopaedics and Related Research,1996.329:326-36.
[287]Lennon AB, Prendergast PJ. Evaluation of cement stresses in finite element analyses of cemented orthopaedic implants [J], Journal of Biomechanical Engineering,2001.123:623-628.
[288]Elena Varini, Ewa Bialoblocka-Juszczyk, Maurizio Lannocca. Assessment of implant stability of cementless hip prostheses through the frequency response function of the stem-bone system [J], Sensors and Actuators A,2010.163:526-532.
[289]Reggiani B, Cristofolini L, Varini E, et al. Predicting the subject-specific primary stability of cementless implants during pre-operative planning:Preliminary validation of subject-specific finite-element models [J], Journal of Biomechanics,2007.40:2552-2558.
[290]Bednar AH, Ziada S. Pullout strength of pedicle screwsaugmented with particulate calcium phosphate:An experimental study[J], The Spine Journal,2009.9(5):404-410.
[291]姜海波,葛世荣.骨水泥与置换髋关节的界面力学计算[J],机械工程材,2008.32：24-28.
[292]Perez MA, Grasa J, Garci'a-Aznar JM. Probabilistic analysis of the influence of the bonding degree of the stem-cement interface in the performance of cemented hip prostheses [J], Journal of Biomechanic,2006.39:1859-1872.
[293]Elices M, Guinea GV, Gomez J, et al. The cohesive zone model:advantages, limitations and challenges [J], Engineering Fracture Mechanics,2002.69(2):137-163.
[294]Chen J, Browne M, Taylor M et al. Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem [J], Computer Methods and Programs in Biomedicine,2004.73:249-256.
[295]Ural A. Prediction of Colles fracture load in human radius using cohesive finite element modeling[J], Journal of Biomechanics,2009.42:22-28.
[296]Perez MA, Garcia JM, Doblare GM. Analysis of the debonding of the stem-cement interface in intramedullary fixation using a non-linear fracture mechanics approach[J], Engineering Fracture Mechanics,2005.72:1125-1147.
[297]许金泉.界面力学[M],北京：科学出版社,2006.
[298]骆华松,徐永清.磷酸钙骨水泥的临床应用进展[J],中华创伤骨科杂志,2007.9(4)：381-383.
[299]Jui-Pin Hung, Fu-Chai Chang. Computational modeling of debonding behavior at the bone/cement interface with experimental validation[J], Materials Science and Engineering[C], 2010.30:445-453.
[300]Lewis G. Properties of Acrylic Bone-cement:State-of-the-Art Review[J], Journal of Biomedical Materials Research,1997.38:155-182.
[301]Evans AG, Ruhle M, Dalgleish BJ. The fracture energy of biomaterial interfaces [J], Metallurgical Transactions A,1990.21(9):2419-2429.
[302]Knott JF, Withey PA.断裂力学应用实例[M],北京：科学出版社,1995.
[303]Reyes G, Cantwell WJ. The mechanical properties of fiber-metal laminates based on glass fiber reinforced polypropylene [J], Composites Science and Technology, 2000.60(7):1085-1094.
[304]Andras Szekrenyes. Delamination composite specimens[D], Hungary:Budapest University of technology and Economics,2005.
[305]Kageyama K, Kikuchi M, Yanagisawa N. Stabilized end notched flexure test:characterization of mode Ⅱ crack propagation[J], Composite Materials:fatigue and fracture. ASTM STP 1110 (3rd volume),1991.243-266.
[306]Schueker C, Davidson BD. Evaluation of the accuracy of the four-point bend end-notched flexure test for mode Ⅱ delamination thoughness determination[J], Composites Science and Technology,2000.60(11):2137-2146.
[307]Qiao PZ, Wang JL, Davalos JF. Analysis of tapered ENF specimen and characterization of bonded interface fracture under Mode-II loading[J], International Journal of Solids and Structures,2003.40(8):1865-1884.
[308]Moore DR, Pavan A, Williams JG Fracture mechanics testing methods for polymers adhesives and composites[M], ESIS Publication 28. Elsevier Science Ltd,2001.
[309]Wang Y, Williams JG Corrections for mode Ⅱ fracture toughnesss specimens of composite materials[J], Composites Science and Technology,1992.43:251-256.
[310]马铝臣,冯乃谦.砂浆的柔度标定曲线与阻力曲线特性[J],硅酸盐学报,2008.36(3)：140-146.
[311]冈村弘之.线性断裂力学入门[M],南京：江苏科学技术出版社,1981.
[312]Ahmed AM, Raab S, Miller JE. Metal/Cement Interface Strength in Cemented Stem Fixation [J], Journal of Orthopaedic Research,1984.2:105-118.
[313]Ural A, Vashishth D. Cohesive finite element modelling of age-related toughness loss in human cortical bone [J], Journal of Biomechanics,2006.39:2974.2982.
[314]Morais AB, de Moura MFSF, et al. Analysis of crack propagation in double cantilever beam tests of multidirectional laminates[J], Mechanics of Materials,2003.35:641-652.
[315]Camacho GT, Ortiz M. Computational modeling of impact damage in brittle materials [J], International Journal of Solids and Structures,1996.33(20-22):2899-2938.
[316]Jianping Jing, Feng Gao, Janine Johnson, et al. Simulation of dynamic fracture along solder-pad interfaces using a cohesive zone model[J], Engineering Failure Analysis, 2009.16(5):1579-1586.
[317]Lewis G. Properties of Acrylic Bone Cement:State-of-the-Art Review [J], Journal of Biomedical Materials Research,1997.38:155-182.
[318]Geubelle PH, Baylor J. The Impact-Induced Delamination of Laminated Composites:A 2D Simulation [J], Composites, Part B:Engineering,1998.29:589-602.
[319]De Moura MFSF, Goncalve JPM, Chousal JAG. Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behavior of bonded joints [J], International Journal of Adhesion & Adhesives,2008.28(8):419-426.
[320]杨晓华,姚卫星,段成美.确定性疲劳累积损伤理论进展[J],中国工程科学, 2003.5(4)：81-86.
[321]刘德刚,王凤洲,林春虎.国外疲劳研究及应用领域的新发展[J],铁道车辆,2001.39(9)：10-12.
[322]黄洪钟,朱顺鹏,范志强,汪忠.基于剩余强度衰减退化的非线性累积损伤准则及其可靠性定寿[J],应用基础与工程科学学报,2011.19(20)：323-334.
[323]Bruce Philip Murphy. Aspects of the fatigue behaviour of acrylic bone cement[D], Ireland, University of Dublin,2001.
[324]谢里阳,徐灏,王德俊.疲劳过程中材料强化和弱化现象的探讨[J],机械强度,1991.13(1)：352-355.
[2]Rybicki EF, Yang KH. On the mathematical analysis of stress in the human femur [J], Journal of Biomechanics,1972.5(2):203-215.
[3]Bandak FA, Vander Vorst MJ, et al. An imaging-based computational and experimental study of skull fracture:finite element model development [J], Journal of neurotrauma,1995.12(4): 679-688.
[4]Phillips AT, Pankaj P, Howie CR, et al. Finite element modeling of the pelvis:inclusion of muscular and ligamentous boundary conditions [J], Medical Engineering & Physics, 2007.29(7):739-748.
[5]Hagemann A, Rohr K, Stiel HS. Coupling of fluid and elastic models for biomechanical simulation of brain deformations using FEM[J], Medical Imaging Analysis,2002.6:375-388.
[6]Ecabert O, Butz T, Nabavi A et al. Brain Shift Correction Based on a Boundary Element Biomechanical Model with Different Material Properties[C], MICCAI 2003 Proceedings, PartⅠ-41-50.
[7]Lorensen WE, Cline HE. Marching Cubes:A high resolution 3D surface construction algorithm [J], Computer Graphics,1987.21(4):163-169.
[8]梁秀霞.医学影像数据可视化中若干问题研究[D],山东大学,2006.
[9]Rho JY, Hobatho MC, Ashman RB, et al. Relations of mechanical properties to density and CT numbers in human bone[J], Medical Engineering Physics,1995.17:347-355
[10]Sanjay Gupta, Prosenjit Dan. Bone geometry and mechanical properties of the human scapula using computed tomography data[J], Trends in Biomaterials and Artificial Organs,2004.17(2): 61-70.
[11]Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure [J], Journal of Bone and Joint Surgery,1977.59A:954-962.
[12]Ashman RB, Cowin SC, Van Buskirk WC, et al. A continuous wAve technique for the measurement of the elastic properties of cortical bone[J], Journal of Biomechanics,1984.17: 349-361.
[13]Shefelbine SJ, Simona U, Claes L. Prediction of fracture callus mechanical properties using micro-CT images and voxel-based finite element analysis [J], Bone,2005.36:480-488.
[14]Taddei F, Pancanti A, Viceconti M. An improved method for the automatic mapping of computed tomography numbers onto finite element models[J], Medical Engineering and Physics,2004. 26(1):61-69.
[15]Taylor WR, Roland E. Determination of orthotropic bone elastic constants using FEA and modal analysis[J], Journal of Biomechanics,2002.35:767-773.
[16]Taddei F, Schileo E, Helgason B. The material mapping strategy influences the accuracy of CT-based finite element models of bones:An evaluation against experimental measurements [J], Medical Engineering and Physics,2007.(29):973-979.
[17]Viceconti M, Zannoni C, Pierotti L, et al. An application of reverse engineering methods to the creation of CAD models of bone segments[J], Computer Methods and Programs in Biomedicine, 1998.56(3):211-220.
[18]Herman G, Liu T. Three-Dimensional Display of Human Organs from Computed Tomograms[J], Computer Graphics&Image Processing,1979.9(4):1-12.
[19]Miller JV, Breen DE, Lorensen WE, et al. Geometrically deformed models:a method for extracting closed geometric models from volume data[J], ACM SIGGRAPH Computer Graphics,1991.25(4):217-226.
[20]Gonzalez RC, Woods RE数字图像处理[M],北京：电子工业出版社,2003.
[21]Kass M, Witkin A, Terzopoulos D. Snakes:active contour models [J], International Journal of Computer Vision,1987.1(4):321-331.
[22]Osher S, Sethian JA. Fronts propagating with curvature dependent speed:Algorithms based on Hamilton-Jacobl formulation[J], Journal of Computational Physics,1988.79(1):12-49.
[23]] Pardo JM, Cabello D, Heras J. A snake for model-based segmentation of biomedical imagesfJJ, Pattern Recognition Letters,1997.18(14):1529-1538.
[24]Barbara Podda, Gianluigi Zanetti, Andrea Giachetti. Texture analysis for vascular segmentation from CT images[C], International Congress Series,2005.1281:206-211.
[25]张小萍,朱志松,王君泽.基于CT医学图像的边缘提取研究[J],生物医学工程研究,2009.28(1)：31-34.
[26]Otsu N. A threshold selection method from gray-level histograms [J], IEEE Transactions on Systems, Man and Cybernetics,1979.9(1):62-66.
[27]郑静,张建州,赵楠.基于跟踪算法的肺部CT图像血管提取[J],计算机工程与应用,2007.43(32)：204-206.
[28]涂其远,吴建华,万国金.动态阈值结合全局阈值对图像进行分割[J],南昌大学学报(工科版),2002.24(01)：37-40.
[29]Eidheim OC, Aurdal L, Omholt-Jensen T, et al. Segmentation of liver vessels as seen in MR and CT images[C], International Congress Series,2004.268:201-206.
[30]金钟,汪炳权.自动多门限CT图像的分割[J],安徽大学学报(自然科学版),2002.26(03)：57-60.
[31]Adams R, Bischof L. Seeded region growing[J], IEEE Transactions on Pattern Analysis and Machine Intelligence,1994.16(6):641-647.
[32]舒添慧,胥布工,胡战虎.基于区域生长法的医学图像分割[J],微计算机信息,2008,6-3：284-285.
[33]陈彦达,鲍苏苏.一种新的肝脏CT序列图像区域生长算法[J],计算机工程与应用, 2010.46(3)：188-190.
[34]朱玲利,王听忠.基于CT图像分析和区域生长法的CT图像分割[J],洛阳理工学院学报(自然版),2009.19(4)：55-59.
[35]何为,余晓锷.基于K均值聚类算法的CT图像金属伪影去除[J],中国医疗设备,2009.24(06)：12-14.
[36]梅媚,张力新,万柏坤.基于CT图像的势函数聚类分割人体脂肪检测[J],天津大学学报,2004.37(08)：740-744.
[37]周鲜成.图像分割方法及其应用研究综述[J],信息技术,2007.12：11-14.
[38]卢畅,韩珂,李晶.基于CT图像全颈椎三维有限元模型的建立及验证[J],中南大学学报(医学版),2008.33(5)：410-414.
[39]张秀萍.基于点云数据复杂曲面的三维重构[D],新疆大学,2004.
[40]王成焘.中国力学虚拟人[J],医用生物力学,2006.21(3)：172-178.
[41]王晓,何建英.考虑MC算法二义性后的三角化方法[J],湖北工业大学学报,2007.6：225-230.
[42]Cline HE, Lorensen WE, Ludke S. Two algorithms for the three-dimensional reconstruction of tomograms[J], Medical Physics,1988.15(3):320-397.
[43]Van Lenthe GH, Stauber M, Muller R. Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties [J], Bone,2006.39:1182-1189.
[44]Kong WZ, Geol VK. Ability of the finite element models to predict response of human spine to sinusoidal vertical vibration[J], Spine,2003.28(17):1961-1967.
[45]陈守义.椎弓骨钉在材料性质及介面状态之生物力学分析[D],台湾成功大学医学工程研究所,2003.
[46]Krone R, Schuster P. An Investigation on the Importance of Material Anisotropy in Finite-Element Modeling of the Human Femur[J], SAE International Paper Number 2006. 01-0064.
[47]Guptal S, van der Helm FCT, Sterk JC. Development and experimental validation of a three-dimensional finite element model of the human scapula[J], Proceedings of the Institution of Mechanical Engineers, Part H:Journal of Engineering in Medicine,2004.218(2):127-142.
[48]Skinner HB, Kilgus DJ, Keyak J. Correlation of computed finite element stresses to bone density after remodeling around cementless femoral implants[J], Clinical Orthopedics and Related Research,1994.305:178-189.
[49]Keyak JH, Meagher JM, Skinner HB, et al. Automated three-dimensional finite element modeling of bone:a new method[J], Journal of Biomedical Engineering,1990.12 (5):389-397.
[50]Keller TS. Predicting the compressive mechanical behavior of bone[J], Journal of Biomechanics,1994.27(9):1159-1168.
[51]van Rietbergen B, Muller R, Ulrich D, et al. Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions[J], Journal of Biomechanics, 1999.32:165-173.
[52]Muller-Karger CM, Zeman ME, Cerrolaza M. P-version of the finite-element method for highly heterogeneous simulation of human bone[J], Finite Elements in Analysis and Design, 2004.40(7):757-770.
[53]Yosibash Z, Padan R, Joskowicz L, et al. A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to In-vitro Experiments[J], Journal of Biomechanical Engineering,2007.129:297-309.
[54]Barna Szabo, Ivo Babuska. Finite Element Analysis[M], Babuska Wiley-Interscience,1991.
[55]Cowin SC. Bone poroelasticity[J], Journal of Biomechanics,1999.32(3):217-238.
[56]Ciarelli MJ, Goldstein SA, Kuhn JL, et al. Evaluation of orthogonal mechanical properties and density of human trabecular bone From the Major metaphyseal regions with materials testing and computed tomography [J], Journal of Orthopaedic Surgery and Research,1991.9:674-682.
[57]Cody D, Gross G, Hou F, et al. Femoral strength is better predicted by finite element models than QCT and DXA[J], Journal of Biomechanics,1999.32:1013-1020.
[58]Harrigan TP, Oh I, Harris WH, et al. The anisotropic properties of trabecular bone[C], Proceeding 6th NE Bio-Engineering Conference,1980:5-10.
[59]Kuhn JL, Goldstein SA, Ciarelli MJ, et al. The limitations of canine trabecular bone as a model forhuman:a biomechanical study [J], Journal of Biomechanics,1989.22:95-107.
[60]Lotz JC, Gerhart TN, Hayes WC. Mechanical properties of metaphyseal bone in the proximal femur [J], Journal of Biomechanics,1991.24:317-29.
[61]Stolk J, Janssen D, Huiskes R, et al. Finite element-based preclinical testing of cemented total hip implants[J], Clinical Orthopaedics and Related Research,2007.456:138-147.
[62]Couteau B, Labey L, Hobatho MC, et al. Validation of a three dimensional finite element model of a femur with a customized hip implant[J], Computer Methods in Biomechanics and Biomedical Engineering,1998.1(1):77-86.
[63]Rubin PJ, Rakotomanana RL, Leyvraz P, et al. Frictional interface micromotions and anisotropic stress distribution in a femoral total hip component[J], Journal of Biomechanics, 1993.26:725-739.
[64]庄茁,蒋持平.工程断裂与损伤[M],北京：机械工业出版社,2004.
[65]余天堂.含裂纹体的数值模拟[J],岩石力学与工程学报,2004.24(24)：4434-4439.
[66]陈篪等.工程断裂力学[M],北京：国防工业出版社,1977.
[67]余寿文,冯西桥.损伤力学[M],北京：清华大学出版社,1997.
[68]钱济成.损伤理论及应用[M],北京：国防工业出版社,1993.
[69]冒小萍,郎福元,柯显信.断裂力学的数值计算方法的研究现状与展望[J],商丘师范学院学报,2004.2：20-24.
[70]李尧臣,王自强.在裂纹尖端引入位移协调奇异单元的有限单元法[J],上海力学, 1983.3：79-99
[71]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用[M],北京：科学出版社,2009.
[72]高东宇,林臼新.飞机机翼疲劳断裂过程的有限元分析[J],哈尔滨理工大学学报,2006.11(3)：18-21.
[73]彭云.基于VUMAT的三维裂纹动态扩展有限元模拟[J],南昌航空大学学报,2010.24(2)：41-45.
[74]Moes N, Dolbow J, Belytschco T. A finite element method for crack growth without remeshing[J], InternationalJournal for Numerical Methods in Engineering,1999.46:131-150.
[75]Babuska I, Melenk JM.The partition of unity nite element method[J], International Journal for Numerical Methods in Engineering,1997.40:727-758.
[76]李录贤,手铁军.扩展有限元及其应用[J],力学进展,2005.35(1)：5-20.
[77]Dolbow J, Moes N, Belytschko T. Modeling fracture in Mindlin-Reissner plates with the extended finite element method[J], International Journal of solid and structures, 2000.57:7161-7183.
[78]梁国平,何江衡.广义有限元方法[J],力学进展,1995.25(4)：562-565.
[79]杨德全,赵忠生.边界元理论及应用[M],北京：北京理工大学出版社,2002.
[80]朱加铭,欧贵宝,何蕴增.有限元与边界元法[M],哈尔滨：哈尔滨工程大学出版社,2002.
[81]孙玉周,王锦燕,许君风.边界元法在断裂力学数值计算中的应用研究[J],中原工学院学报,2004.15(5)：21-23.
[82]彭妙娟,程玉民.断裂力学的相似边界元法及其应用[J],应用力学学报,2007.24(2)：294-297.
[83]周小平,周瑞忠.无单元法研究现状及展望[J],工程力学,2005.22(1)：12-18.
[84]Belytschko T, Lu YY, Gu L. Element-free Galerkin methods [J], International Journal for Numerical Methods in Engineering,1994.37:229-256.
[85]Belyschko T, Lu YY, Gu L. Element-free Galerkin methods for static and dynamic fracture [J], International Journal of Solids and Structures,1995.32:2547-2570.
[86]Terry T. Fatigue crack propagation modeling using the element-free Galerkin method[D], Evanston, Illinois:Northwestern University, USA.1994.
[87]顾元通,丁桦.无网格法及其最新进展[J],力学进展,2005.35(3)：323-337.
[88]曹国金,姜弘道.无单元法研究和应用现状及动态[J],力学进展,2002.32(4)：526-534.
[89]章青,周资斌,卓家寿.分区界面元-有限元-无限元混合模型[J],计算力学学报,2005.22(1)：8-12.
[90]刘凯欣,高凌天.离散元法研究的评述[J],力学进展,2003.33(4)：483-490.
[91]周先齐,徐卫亚,钮新强等.离散单元法研究进展及应用综述岩土力学[J],2007.28：409-415.
[92]卓家寿,赵宁.离散元的基本原理、方法和应用[J],河海科技进展,1993.13(2)：1-11.
[93]何传永,孙平编著,非连续变形分析方法程序与工程应用[M],中国水利水电出版社,2009.
[94]唐瑜,苏超.非连续变形分析方法的研究及应用现状[J],水利水电科技进展,2004.24：111-119.
[95]石根华.数值流形方法与非连续变形分析[M],北京：清华大学出版社,1997.
[96]苏海东.固定网格的数值流形方法研究[J],力学学报.2011.1：169-178.
[97]张湘伟,章争荣,吕文阁等.数值流形方法研究及应用进展[J],力学进展,2010.40(1)：1-12.
[98]Tsay RJ, Chiou Y J, Chuang W L. Crack growth prediction by manifold method[J], Journal of Engineering Mechanics, ASCE,1999.125(8):884-890.
[99]Kawai T. New discrete structural models and generalization of the method of limit analysis [C], International Conference on Finite Elements in Nonlinear Solid and structural Mechanics, Norway,1977a.2:885-909.
[100]钱令希,张雄.结构分析中的刚性有限元法[J],计算结构力学及其应用,1991.8(1)：1-14.
[101]卓家寿,章青.不连续介质力学问题的界面元法[M],北京：科学出版社,2001.
[102]Dugdale DS. Yielding of steel sheets containing slits [J], Journal of the Mechanics and Physics of Solids,1960.8:100-104.
[103]Barenblatt G. The mathematical theory of equilibrium cracks in brittle fracture [J], Advances in Applied Mechanics,1962.7:55-129.
[104]Shet C, Chandra N. Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Processes[J],Transactions of the ASME,2002.124:440-450.
[105]Settgasta RR, Rashid MM. Continuum coupled cohesive zone elements for analysis of fracture in solid bodies [J], Engineering Fracture Mechanics,2009.(76):1614-1635.
[106]Camanho PP, Davila CG, et al. Numerical simulation of mixed-mode progressive delamination in composite materials[J], Journal of Composite Materials,2003.37(16):1415-1438.
[107]崔浩,李玉龙,刘元镛等.基于粘聚区模型的含填充区复合材料接头失效数值模拟[J],复合材料学报,2010.(27)：161-168.
[108]周储伟,杨卫,方岱宁.内聚力界面单元与复合材料的界面损伤分析[J],力学学报,1999.31(3)：372-377.
[109]刘甫.粘弹性界面断裂与固体火箭发动机界面脱粘研究[D],国防科学技术大学,2005.
[110]刘红霞,矫桂琼,熊伟等.复合材料层合板分层分析中的界面元应用[J],机械强度,2008.2：301-304.
[111]邵国建,刘体锋.广义有限元及其应用[J],河海大学学报(自然科学版),2002.30(4)：28-31.
[112]方修君,金峰,王进廷.基于扩展有限元法的粘聚裂纹模型[J],清华大学学报(自然科学版),2007.47(3)：344-347.
[113]尹华伟,易伟建,刘艳.有限元-界面元混合模型及其应用[J],湖南科技大学学报(自然科学版),2006.21(4)：41-46.
[114]陈跃良,卞贵学,郁大照.预腐蚀铝合金典型螺栓单搭接件疲劳寿命研究[J],工程力学,2012.29(5)：251-256.
[115]NASGRO Manual (2006). http://www. nasgro.swri.org.
[116]施伟,黄小平,崔维成.基于疲劳裂纹扩展率单一曲线模型的疲劳寿命预测[J],船舶力学,2008.12(2)：264-271.
[117]Skorupa M, Machniewicz T, Schijve J, et al. Application of the strip-yield model from the NASGRO software to predict fatigue crack growth in aluminum alloys under constant and variable amplitude loading[J], Engineering Fracture Mechanics,2007.74:291-313.
[118]http://www.t-solutiongroup.com/software/frame/20090901-frc.shtml.
[119]贾学明,王启智.三维断裂分析软件FRANC3D[J],计算力学学报,2004.21(6)：764-768.
[120]孙远滔.裂纹诊断的数值分析方法与应用研究[D],武汉：武汉理工大学,2008.
[121]3D fracture mechanics simulation, Zencrack_brochure_2008, Zentech company.
[122]T-solution,3D裂纹扩展分析技术及其在航空领域的应用,2009产品创新数字化峰会征文.
[123]朱永生.颗粒流分析系统(PFC2D/3D)理论背景,中国水电顾问集团-ITASA研发中心.
[124]http://www.crackwizard.com/.
[125]肖涛,左正兴.虚拟裂纹闭合法在结构断裂分析中的应用[J],计算力学学报,2008.25：16-19.
[126]孟令兵,陈普会.层压复合材料分层扩展分析的虚拟裂纹闭合技术及其应[J],复合材料学报,2010.27(1)：190-195.
[127]姜年朝ANSYS和ANSYS/FE-SAFE软件的工程应用及实例[M],南京：河海大学出版社,2006.
[128]周传月,郑红霞,罗慧强MSC.Fatigue疲劳分析应用与实例[M],北京：科学出版社,2005.
[129]三维裂纹扩展仿真软-ALOF软件使用手册,合肥洞力信息科技有限公司,2010.
[130]http://www.sili-tech.com/article.jsp?type=6&id=90.
[131]刘达列.疲劳破坏的连续型损伤力学模型的研究[D],浙江大学,2002.
[132]吴德飞,童根树.含初始缺陷钢结构损伤累积至断裂即后期的调查分析[J],工程力学,2006.8：160-168.
[133]王军.损伤力学的理论与应用[M],北京：科学出版社,1997.
[134]余天庆,钱济成.损伤理论及应用[M],北京：国防工业出版社,1993.
[135]沈为.损伤力学[M],武汉：华中理工大学出版社,1995.
[136]Griffith AA. The phenomena of rupture and flow in solid [J], Philosophical Transactions, 1920.221(A):163-198.
[137]Orowan E. Fracture and strength of solids[J], The Physical Society,1949.12:182-232.
[138]Irwin G. Analysis of stresses and strains near the end of a crack trAver sing a plate [J], Journal of Applied Mechanics,1957.24:361-364.
[139]David Roylance, Orowan E. Fracture and strength of solids[J], The Physical Society, MIT: 2001, MA 02139 June 14.
[140]Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear[J], Journal of Basic Engineering,1963.85(4):519-527.
[141]Sih GC. Strain energy density factor applied to mixed mode crack problem[J], International Journal of Fracture Mechanics,1974.10:305-321.
[142]Palaniswamy K, Knauss WG. Propagation of a crack under general in-plane tension [J], International Journal of Fracture,1972.8:114-117.
[143]Wells AA. Application of fracture mechanics at and beyond general yielding[J], British welding journal,1963.10:563-570.
[144]Rice JR. A path independent integral and the approximate analysis of concentration by notches and cracks [J], Journal of Applied Mechanics,1968.35:379-386.
[145]杨光松.损伤力学与复合材料损伤[M],北京：国防工业出版社,1995.
[146]尹双增.断裂、损伤理论及应用[M],北京清华大学出版社,1992.
[147]KachanovL M. On the Creep Fracture Time[J], Izv Akad, Nauk USSR Otd. Tech.,1958.8: 26-31 (in Russian).
[148]Rabotnov YN. On the equations of state for creep [J], Progress in Applied Mechanics, 1963.10:307-315.
[149]吴刚,孙钧,吴中如.复杂应力状态下完整岩体卸荷破坏的损伤力学分析[J],河海大学学报,1997.25(3)：44-49.
[150]唐春安.岩石破裂过程中的灾变[M],北京：煤炭工业出版社,1993.
[151]杨更社,张长庆.岩体损伤及检测[M],西安：陕西科学技术出版社,1998.
[152]Kachanov D. Theory of creep in advances in creep design[M], London:Applied Science Publisher,1985.121-138.
[153]Lemaitre J. How to use damage mechanics [J], Nuclear Engineering and Design, 1984.80(1):233-245.
[154]谢和平,彭瑞东,鞠杨.岩石变形破坏过程中的能量耗散分析[J],岩石力学与工程学报,2004.23(21)：3565-3570.
[155]Paris PC, Erdogan F. A critical analysis of crack propagation laws [J], Journal of basic Engineering, Trans. ASME,1963.85(4):528-534.
[156]Walker EK. The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum[J], ASTM STP 462, American Society for Testing and Materials, 1970:1-14.
[157]Forman RG, Kearney VE, Englem RM. Numerical analysis of crack propagation in a cyclic-loaded structure [J], Journal of basic Engineering, Trans.ASME,1967.89:459-465.
[158]Miner MA. Cumulative damage in fatigure[J], Journal of Applied Mechanics, 1945.2:159-164.
[159]姚卫星.结构疲劳寿命分析[M],北京：国防工业出版社,2003.
[160]Wallgren G. Fatigue test with stress cycle of varying amplitude[D], Stockholm Aeronautical Research Institute of Sweden,1949.
[161 [Grover HJ. An observation concerning the cycle ratio in cumulative damage[J], Fatigue in Aircraft Structures, ASTM, STP274,1960.120-124.
[162]Manson SS, Freche JC. Ensign CR. Application of a double linear damage rule to cumulative fatigue [J], Fatigue Crack Propagation, ASTM STP 415,1967.384-412.
[163]Marco SM, Starkey WL. A concept of fatigue damage [J], Transactions of the ASME,1954.76: 627-632.
[164]Manson SS, Halford GR. Practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage[J], International Journal of Fatigue, 1981.17(2):169-192.
[165]徐灏.疲劳强度[M],北京：高等教育出版,1990.
[166]叶笃毅,王德俊.一种基于材料韧性耗散分析的疲劳损伤定量新方法[J],试验力学,1999.14(1)：80-89.
[167]Abdul-Kadir MR, Hansen U, Klabunde R, et al. Finite element modeling of primary hip stem stability:The effect of interference fit[J], Journal of Biomechanics,2008,41(3):587-594.
[168]Varini E, Bialoblocka-Juszczyk E, Lannocca MA. Assessment of implant stability of cementless hip prostheses through the frequency response function of the stem-bone system[J], Sensors and Actuators A,2010.163(2):526-532.
[169]谢英杰,叶志前,徐庐生.医学图像可视化与相关技术及应用[J],国外医学生物医学工程分册,2001.24(3)：114-117.
[170]Jiang hsieh.计算机断层成像技术[M],北京：科学技术出版社,2006.
[171]王立功,刘伟强,于甬华等DICOM医学图像文件格式解析与应用究[J],计算机工程与应用,2006.(29)：210-212.
[172]董义兵,晁爱农DICOM标准应用深层次探讨[J],中国医学装备,2006.3(11)：31-35.
[173]刘晓燕,张春田.基于DICOM医学图像软件工具包的设计和实现[J],天津理工学院学报,2003.19(4)：84-87.
[174]李科,颜红梅.医学信息学[M],成均：电子科技大学出版社,2005.
[175]石明国.实用CT图像技术学[M],西安：陕西科学技术出版社,1995.
[176]Smith RA, Paulus MJ, Branning JM, et al. X-ray computed tomography on a cellular polysiloxane under compression[J], Journal of Cellular Plastics,2001.37(3):231-248.
[177]田培林.CT检查的窗宽窗位设置[J],医学与工程,2001.3(1)：6-10.
[178]赵以甦.骨科生物力学的基本名词[J],中华骨科杂志,2006.26(4)：286-288.
[179]ImageJ_Manual, http://rsb.info.nih.gov/ijz.
[180]Will Schroeder, Ken Martin, Bill Lorensen. An Object Oriented Approach to 3D Graphics[M], 2nd Edition. Prentice Hall old,1996.
[181]Katoozian H, Davy DT, Arshi A, et al. Material optimization of femoral component of total hip prosthesis using fiber reinforced polymeric composites [J], Medical Engineering & Physics, 2001.23:503-509.
[182]Goetzen N, Lampe F, Nassut R, et al. Load-shift-numerical evaluation of a new design philosophy for uncemented hip prostheses[J], Journal of Biomechanics,2005.28(3):595-604.
[183]Fantigrossi A, Galbusera F, Raimondi MT, et al. Biomechanical analysis of cages for posterior lumbar interbody fusion [J], Medical Engineering & Physics,2007.29(1):101-109.
[184]Wu W, Yang DZ, Qi M, et al. An FEA method to study flexibility of expanded coronary stents[J], Journal of Materials Processing Technology,2007.84(12):447-450.
[185]杨帆.数字图像处理与分析[M],北京：北京航空航天大学出版社,2010.
[186]刘相滨,向坚持,阳波.基于八邻域边界跟踪的标号算法[J],计算机工程与应用,2001.23：125-127.
[187]Fedida R, Yosibash Z, Milgrom C, et al. Femur mechanical simulation using high-order FE analysis with continuous mechanical properties[C], International Conference on Computational Bioengineering, Lisbon, Portugal, September 2005.14-16.
[188]Kowalczyk P. Design optimization of cementless femoral hip prostheses using finite element analysis[J], Journal of Biomechanical Engineering,2001.123(5):398-402.
[189]Fx W, Zhang WJ, Kusalik AJ. A genetic Kmeans clustering algorithm applied to gene expression data. Advances in Artificial Intelligence[J], Proceedings Lecture Notes in Artificial Intelligence,2003.2671:520-526.
[190]石亦平,周玉蓉ABAQUS有限元分析实例详解[M],北京：机械工业出版社,2006.
[191]郭卫.中华骨科学-骨肿瘤卷[M],北京：人民卫生出版社,2010.
[192]Weber KL. What is new in musculoskeletal on cology[J], Journal of Bone and Joint Surgery, 2005.87(6):1400-1410.
[193]Gorge H, T Andrew I, Daniel JB. Reverse obliquity fractures of the interochanteric region of the femur[J], Journal of Bone and Joint Surgery(Am),2001.83:643-647.
[194]徐旭纯.May钢板治疗股骨粗隆粉碎性骨折[J],浙江临床医学,2005.7(9)：924-925.
[195]Chao EY, Ivins JC. Tumor prostheses for bone and joint reconstruction:The design and application[M], New York:University of Michigan,1983.
[196]Charnley J. Low-friction arthroplasty of the hip[M], Theory and practice, Berlin:Springer, 1979.3-15.
[197]中国组织工程研究与临床康复编辑部.让昨天告诉今天-人工髋关节研究的学术与技术进展[J],中国组织工程研究与临床康复,2009.13(4)：690-691.
[198]宁志杰.奥斯汀-骨移植替代物[J],中国矫形外科杂志,2000.7(6)：593-594.
[199]Moore AT, Bohlman HR. Metal hip replacement:A case report[J], Journal of Bone and Joint Surgery,1943.25:688-692.
[200]Scales JT. Massive bone and joint replacement involving the upper femur, acetabulum, and iliac bone[J], Proceedings of the Open Scientific Meeting of the Hip Society,1975.3:245-275.
[201]Barr JS, Eaton RG. Elbow reconstruction with a new prosthesis to replace the distal end of the humerus. A case report [J], Journal of Bone and Joint Surgery(Am),1965.47:1408-1413.
[202]Chao EY, Sim FH, Ivins JC. Tumor prostheses for bone and joint reconstruction:The design and application[M], New York:University of Michigan,1983.
[203]Khang G, Choi K, Kim CS, et al. A study of Korean femoral geometry [J], Clinical Orthopaedics and Related Research,2007.22:116-122.
[204]Palm L, Olofsson J, Astrom SE, et al. No difference in migration or wear between cemented low-profile cups and standard cups:a randomized radio stereographic study of 53 patients over 3 years[J], Acta Orthopaedica,2007.78(4):479-484.
[205]戴尅戎,朱振安,孙月华.计算机辅助个体化人工半骨盆的设计与应用[J],中华骨科杂志,2005.25(5)：258-262.
[206]Werner A. Design and manufacture of anatomical hip jointendoprosthesis using CAD/CAM systems[J], Journal of Materials Processing Technology,2000.107(1):181-186.
[207]Kurz MJ, Stergiou N. An artificial neural network that utilizes hip joint actuations to control bifurcations and chaos in a passive dynamic bipedal walking model [J], Biological Cybernetics, 2005.93(3):213-221.
[208]康黎云,龚宪生,权威等.髋关节内置假体设计方法[J],重庆大学学报(自然科学版),2005.28(7)：18-22.
[209]Reuben JD, Chang CH, Akin JE et al. A knowledge-based computer-aided design and manufacturing system for total hip replacement [J], Clinical Orthopaedics and Related Research,1992.285:48-56.
[210]Stulberg S, Stugberg B, Wixson R. The fationable design characteristicsand ptrliminary trsults of a primary total hip prosthesis [J], Clinical Orthopaedics and Related Research,1989. 249:79-96.
[211]Huo MH, Salvati EA, Lieberman JR, et al. Custom-designed femoral prostheses in total hip arthroplasty done with cement for severe dysplasin of the hip[J], Journal of Bone and Joint Surgery (Am),1993.75:1497-1504.
[212]Frank D, Won Y, Eduardo A, et al. Long-tem results of total hip arthroplasty with a cemented custom-designed swan-neck femoral computer for congenital dislocation or severe dysplasia[J], Journal of Bone and Joint Surgery (Am),2002.84:204-207.
[213]Murphy SB, Rijeuski PK, Millis MB, et al. The palnning of orthopaedic reconstructive surgery using computer aided simulation and design[J], Computerized Medical Imaging and Graphics,1988.12(1):35-45.
[214]刘文广.套接式翻修假体设计、初步应用及三维有限元优化[D],山东大学,2008.
[215]http://www.360doc.com.
[216]Bergmann G, Deuretzbacher G, Heller M, et al. Hip contact forces and gait patterns from routine activities[J], Journal of Biomechanics,2001.(34):859-871.
[217]全国体育院校教材委员.运动解剖学[M],北京：人民体育出版社,2000.
[218]Turner RH, Matingly DA, Scheller A. Femoral revision total hip arthroplasty using a long-stem femoral component:Clinical and radiog raphic analysis [J], Journal of Arthroplasty, 1987.2:247-258.
[219]Gandhi R, Petruccelli D, Winemaker MJ, et al. Fractures at the tip of long-stem prostheses used for revision hip arthroplasty [J], Journal of Arthroplasty,2003.18 (6):741-745.
[220]张华,赵鹏,安耀荣等.股骨干骨折的生物力学研究进展[J],实用骨科杂志,2007.13(11)：669-671.
[221]Heller MO, Bergmann G, Kassi JP, et al. Determination of muscle loading at the hip joint for use in pre-clinical testing[J], Journal of Biomechanics,2005.38:1155-1163.
[222]ABAQUS 6.7 Analysis User's Manual, DS-SIMULIA.
[223]Hypermesh Advance Trainning, Altair Engineering, Inc., TX, USA.2001.
[224]Bergmann G, Graichen F, Rohlmann A. Hip joint loading during walking and running measured in two patients [J], Journal of Biomechanics,1993.26:969-990.
[225]赵钟岳.骨科实用生物力学[M],北京：人民卫生出版社,1983.
[226]戴尅戎,倪诚,王成焘等.定制型膝肿瘤假体的设计与临床应用[J],中华骨科杂志,2003.23(10)：606-610.
[227]Hsu RW, Sim FH, Chao EY. Reoperation results after segmental prosthetic replacement of bone and joint for limb salvage [J], Journal of Arthroplasty,1999.14:519-526.
[228]张鹤宇,罗先正,王志义.人工假体在骨肿瘤保肢中的应用[J],中华骨科杂志,2000.20：50-52.
[229]Lewis JL. The mechanical state of the bone-implant interface:In Non-cemented total hip arthroplasty[M]. New York:RAven Press Ltd,1988.
[230]Mjoberg B. The theory of early loosening of hip prostheses [J], Orthopedics,1997.20(12): 1169-1175.
[231]卿茂盛,李全.骨科应力遮挡的研究进展[J],中国骨伤,2003.16(1)：57-58.
[232]Sabo D, Reiter A, Simank HG, et al. Periprosthetic mineralization around cementless total hip endoprosthesis:longitudinal study and cross-sectional study on titanium threaded acetabular cup and cementless Spotorno stem with DEXA[J], Calcified tissue international, 1998.62(2):177-182.
[233]Schmidt R, Nowak TE, Mueller L, et al. Osteodensitometry after total hip replacement with uncemented taper-design stem[J], International orthopaedics,2004.28(2):74-77.
[234]Saito S, Saito M, Nishino T, et al. Long-term results of total hip arthroplasty for osteonecrosis of the femoral head-A comparison with osteoarthritis[J], Clinical Orthopaedics and Related Research,1989.244:198-207.
[235]Harris WH. The first 32 years of total hip arthroplasty. One surgeon's perspective [J], Clinical Orthopaedics and Related Research,1992.274:6-11.
[236]Weinans H, Sumner DR, Igloria R, et al. Sensitivity of periprosthetic stress-shielding to load and the bone density modulus relationship in subject-specific finite element models [J], Journal of Biomechanics,2000.33:809-817.
[237]Zannoni C, Mantovani R, Viceconti R. Material properties assignment to finite element models of bone structures:a new method [J], Medical Engineering and Physics,1998.20:735-740.
[238]Frost HM. A 2003 update of bone physiology and Wolffs Law for clinicians [J], The Angle Orthodontist,2004.74:3-15.
[239]孔庆毅,李家顺,贾连顺等.寰枢椎经关节螺钉固定的临床解剖学测量[J],中国矫形外科杂志,2002.10(13)：1328-1330.
[240]http://image.baidu.com.
[241]Doyle JS, Lauerman WC, Wood KB, et al. Complications and Long-Term Outcome of Upper Cervical Spine Arthrodesis in Patients With Down Syndrome[J], Spine,1996.21(10): 1223-1231.
[242]Dickman CA, Sonntag VK. Posterior CI-C2 Transarticular Screw Fixation for Atlantoaxial Arthrodesis [J], Neurosurgery,1998.43(2):275-280.
[243]Mitchell TC, Sadasivan KK, et al. Biomechanical Study of Atlantoaxial Arthrodesis: Transarticular Screw Fixation Versus Modified Brooks Posterior Wiring[J], Journal of Orthopaedic Trauma,1999.13(7):483-489.
[244]侍德,赵孰炎,张明.上颈椎不稳定性骨折脱位做前方融合术的探讨[J],中华骨科杂志,1992.12(3)：175.
[245]连小峰,侯铁胜.上颈椎不稳的内固定技术及其进展[J],中国矫形外科杂志,2004.7：544-546.
[246]解放军总医院等总编.实用神经外科学[M],北京：中国人民解放军战士出版社,1978.
[247]刘海兵,王文军.寰枢椎后路内同定术的研究进展[J],中国现代医药杂志,2009.11(4)：128-132.
[248]董荣华,王文宝,赵合元.实用脊柱外科内固定[M],天津：天津科学技术出版社,2006.
[249]Farey ID, Nadkarni S, Smith N. Modified Gallie Technique Versus Transarticular Screw Fixation in C1-C2 Fusion[J], Clinical Orthopaedics and Related Research,1999.359:126-135.
[250]Fielding JW, Hawkins RJ, Ratzan SA. Spine fusion for atlanto-axial instability [J], The Journal of bone and joint surgery, American volume,1976.58(3):400-407.
[251]Tucker HH. Technical report:method of fixation of subluxed or dislocated cervical spine below C1-C2[J], Journal of the Neurological Sciences,1975.2(4):381-382.
[252]Magerl F, Seemann PS. Stable posterior fusion of the atlas and axis by transarticularscrew fixation[M], Kehr P, Weidner A, eds. Cervical Spine, New York:Wien,1986:322-327.
[253]Tucker HH. Technical report:method of fixation of subluxed or dislocated cervical spine below C1-C2[J], Journal of the Neurological Sciences,1975.2(4):381-382.
[254]Aldrich EF, Weber PB, Crow WN. Halifax interlaminar clamp for posterior cervical fusion:a long-term follow-up review[J], Journal of Neurosurgery,1993.78(5):702-708.
[255]Stillerman CB, Wilson JA. Atlanto-Axial Stabilization with Posterior Transarticular Screw Fixation:Technical Description and Report of 22 Cases[J], Neurosurgery,1993.32(6):948-955.
[256]Sherk HH, Snyder B. Posterior Fusions of the Upper Cervical Spine:Indications, Techniques, and Prognosis [J], Orthopedic Clinics of North America,1978.9:1091-1099.
[257]Yoshida M, Neo M, Fujibayashi S, et al. Comparison of the anatomical risk for vertebral artery injury associated with the C2-pedicle screw and atlantoaxial transarticular screw. [J], Spine,2006.31(15):E513-E517.
[258]董荣华,王文宝.赵合元.实用脊柱外科内固定[M],天津：天津科学技术出版社,2006.
[259]Goel A, Laheri V. Plate and screw fixation for atlanto-axial subluxation[J], Acta Neurochirurgica,1994.129(1):47-53.
[260]Harms J, Meleher RP. Posterior C1-C2 fusion with polyaxial screw and rod fixation [J], Spine, 2001.16(22):2467-2471.
[261]郝定均,贺宝荣,雷伟等.寰椎侧块螺钉与枢椎弓根螺钉徒手植入技术的研究与应用[J],中国矫形外科杂志,2006.14(8)：579-581.
[262]Resnick DK, Benzel EC. C1-C2 Pedicle Screw Fixation with Rigid Cantilever Beam Construct Case Report and Technical Note [J], Neurosurgery,2002.50(2):426-428.
[263]Tan MS, Wang H, Wang Y, et al. Morphometric Evaluation of Screw Fixation in Atlas via Posterior Arch and Lateral Mass [J], Spine,2003.28(9):888-895.
[264]马向阳,尹庆水,吴增晖等.寰枢椎后路椎弓根螺钉固定治疗少儿上颈椎不稳[J],山东医药,2010.50(28)：37-39.
[265]Paramore CG, Dickman CA, Sonntag VK. The anatomical suitability of the C1-C2 complex for transarticular screw fixation[J], Journal of Neurosurgery,1996.85(2):221-224.
[266]Madawi AA, Casey AT, Solanki GA, et al. Radiological and anatomical evaluation of the atlantoaxial transarticular screw fixation technique[J], Journal of Neurosurgery,1997. 86(6):961-968.
[267]Wright NM. Posterior C2 fixation using bilateral crossing C2 laminar screws:case series and technical note[J], Journal of Spinal Disorders & Techniques,2004.17(2):158-162.
[268]Claybrooks R, Kayanja M, Milks R, et al. Atlantoaxial Fusion:a Biomechanical Analysis of two C1-C2 Fusion Techniques [J], The Spine Journal,2007.7(6):682-688.
[269]马向阳,尹庆水,吴增晖.寰枢椎后路四种钉棒固定方法的三维稳定性评价[J],中国脊柱脊髓杂志,2008.18(6)：464-468.
[270]胡巍,肖增明.寰枢关节脱位的置入物治疗技术与生物相容性及生物力学的关[J],中国 组织工程研究与临床康复,2008.12(13)：2511-2513.
[271]Saito T, Tamatouro T, Shikara J, et al. Analysis and Prevent ion of Spinal Column Deformity Following Cervical Laminectomy Pathogenic Analysis of Post Laminectomy Deformities [J], Spine,1991.16:494-502.
[272]Kleinberger M. Application of finite element techniques to the study of cervical spine mechanics[C], Proceedings of the 37th Steppe Car Crash Conference, San Antonio Tesas,1993: 7-8.
[273]Bozic KJ, Keyak JH, Skinner HB, et al. Three-dimensional finite element modeling of a cervical vertebra:an investigation of burst fracture mechanism[J], Journal of spinal disorders, 1994.7(2):102-110.
[274]Voo L, Denman J, Kumaresan S, et al. Development of 3D Finite Element Model of Cervical Spine[J], Avd Bioeng,1995.31:13-14.
[275]Teo EC, Ng HW. First cervical vertebra (atlas) fracture mechanism studies using finite element method[J], Journal of biomechanics,2001.34(1):13-21.
[276]Brolin K, Halldin P. Development of a Finite Element Model of the Upper Cervical Spine and a Parameter Study of Ligament Characteristics[J], Spine,2004.29(4):376-385.
[277]Zhang H, Bai J. Development and Validation of a Finite Element Model of the Occipito-Atlantoaxial Complex Under Physiologic Loads[J], Spine,2007.32(9):968-974.
[278]Young JK, Woo TR, Sang BL. Computerized Tomographic Measurements of Morphometric Parameters of the C2 for the Feasibility of Laminar Screw Fixation in Korean Population[J], Korean Neurosurgery Society,2008.44(1):15-18.
[279]Xu R, Burgar A, Ebraheim NA, et al. The Quantitative Anatomy of the Laminas of the Spine[J], Spine,1999.24(2):107-113.
[280]汪耀.枢椎椎板螺钉固定的有限元分析[D],山东大学,2010.
[281]Lu J, Fiala JC, Lichtman JW. Semi-Automated Reconstruction of Neural Processes from Large Numbers of Fluorescence Images[J], PLoS ONE,2009.4(5):e5655.
[282]Ulrich D, van Rietbergen B, Laib A, et al. The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone[J], Bone,1999.25(1):55-60.
[283]Kopperdahl DL, Morgan EF, KeAveny TM. Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone[J], Journal of Orthopaedic Research,2002.20(4):801-805.
[284]Pope MH, Panjabi MM. Biomechanical definitions of spinal instability [J], Spine, 1985.10:255-256.
[285]Moreo P, Pe'rez MA, Garci'a-Aznar JM. Modelling the mixed-mode failure of cement-bone interfaces [J], Engineering Fracture Mechanics,2006.73:1379-1395.
[286]Verdonschot N, Huiskes R. Mechanical effects of stem cement interface characteristics in total hip replacement [J], Clinical Orthopaedics and Related Research,1996.329:326-36.
[287]Lennon AB, Prendergast PJ. Evaluation of cement stresses in finite element analyses of cemented orthopaedic implants [J], Journal of Biomechanical Engineering,2001.123:623-628.
[288]Elena Varini, Ewa Bialoblocka-Juszczyk, Maurizio Lannocca. Assessment of implant stability of cementless hip prostheses through the frequency response function of the stem-bone system [J], Sensors and Actuators A,2010.163:526-532.
[289]Reggiani B, Cristofolini L, Varini E, et al. Predicting the subject-specific primary stability of cementless implants during pre-operative planning:Preliminary validation of subject-specific finite-element models [J], Journal of Biomechanics,2007.40:2552-2558.
[290]Bednar AH, Ziada S. Pullout strength of pedicle screwsaugmented with particulate calcium phosphate:An experimental study[J], The Spine Journal,2009.9(5):404-410.
[291]姜海波,葛世荣.骨水泥与置换髋关节的界面力学计算[J],机械工程材,2008.32：24-28.
[292]Perez MA, Grasa J, Garci'a-Aznar JM. Probabilistic analysis of the influence of the bonding degree of the stem-cement interface in the performance of cemented hip prostheses [J], Journal of Biomechanic,2006.39:1859-1872.
[293]Elices M, Guinea GV, Gomez J, et al. The cohesive zone model:advantages, limitations and challenges [J], Engineering Fracture Mechanics,2002.69(2):137-163.
[294]Chen J, Browne M, Taylor M et al. Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem [J], Computer Methods and Programs in Biomedicine,2004.73:249-256.
[295]Ural A. Prediction of Colles fracture load in human radius using cohesive finite element modeling[J], Journal of Biomechanics,2009.42:22-28.
[296]Perez MA, Garcia JM, Doblare GM. Analysis of the debonding of the stem-cement interface in intramedullary fixation using a non-linear fracture mechanics approach[J], Engineering Fracture Mechanics,2005.72:1125-1147.
[297]许金泉.界面力学[M],北京：科学出版社,2006.
[298]骆华松,徐永清.磷酸钙骨水泥的临床应用进展[J],中华创伤骨科杂志,2007.9(4)：381-383.
[299]Jui-Pin Hung, Fu-Chai Chang. Computational modeling of debonding behavior at the bone/cement interface with experimental validation[J], Materials Science and Engineering[C], 2010.30:445-453.
[300]Lewis G. Properties of Acrylic Bone-cement:State-of-the-Art Review[J], Journal of Biomedical Materials Research,1997.38:155-182.
[301]Evans AG, Ruhle M, Dalgleish BJ. The fracture energy of biomaterial interfaces [J], Metallurgical Transactions A,1990.21(9):2419-2429.
[302]Knott JF, Withey PA.断裂力学应用实例[M],北京：科学出版社,1995.
[303]Reyes G, Cantwell WJ. The mechanical properties of fiber-metal laminates based on glass fiber reinforced polypropylene [J], Composites Science and Technology, 2000.60(7):1085-1094.
[304]Andras Szekrenyes. Delamination composite specimens[D], Hungary:Budapest University of technology and Economics,2005.
[305]Kageyama K, Kikuchi M, Yanagisawa N. Stabilized end notched flexure test:characterization of mode Ⅱ crack propagation[J], Composite Materials:fatigue and fracture. ASTM STP 1110 (3rd volume),1991.243-266.
[306]Schueker C, Davidson BD. Evaluation of the accuracy of the four-point bend end-notched flexure test for mode Ⅱ delamination thoughness determination[J], Composites Science and Technology,2000.60(11):2137-2146.
[307]Qiao PZ, Wang JL, Davalos JF. Analysis of tapered ENF specimen and characterization of bonded interface fracture under Mode-II loading[J], International Journal of Solids and Structures,2003.40(8):1865-1884.
[308]Moore DR, Pavan A, Williams JG Fracture mechanics testing methods for polymers adhesives and composites[M], ESIS Publication 28. Elsevier Science Ltd,2001.
[309]Wang Y, Williams JG Corrections for mode Ⅱ fracture toughnesss specimens of composite materials[J], Composites Science and Technology,1992.43:251-256.
[310]马铝臣,冯乃谦.砂浆的柔度标定曲线与阻力曲线特性[J],硅酸盐学报,2008.36(3)：140-146.
[311]冈村弘之.线性断裂力学入门[M],南京：江苏科学技术出版社,1981.
[312]Ahmed AM, Raab S, Miller JE. Metal/Cement Interface Strength in Cemented Stem Fixation [J], Journal of Orthopaedic Research,1984.2:105-118.
[313]Ural A, Vashishth D. Cohesive finite element modelling of age-related toughness loss in human cortical bone [J], Journal of Biomechanics,2006.39:2974.2982.
[314]Morais AB, de Moura MFSF, et al. Analysis of crack propagation in double cantilever beam tests of multidirectional laminates[J], Mechanics of Materials,2003.35:641-652.
[315]Camacho GT, Ortiz M. Computational modeling of impact damage in brittle materials [J], International Journal of Solids and Structures,1996.33(20-22):2899-2938.
[316]Jianping Jing, Feng Gao, Janine Johnson, et al. Simulation of dynamic fracture along solder-pad interfaces using a cohesive zone model[J], Engineering Failure Analysis, 2009.16(5):1579-1586.
[317]Lewis G. Properties of Acrylic Bone Cement:State-of-the-Art Review [J], Journal of Biomedical Materials Research,1997.38:155-182.
[318]Geubelle PH, Baylor J. The Impact-Induced Delamination of Laminated Composites:A 2D Simulation [J], Composites, Part B:Engineering,1998.29:589-602.
[319]De Moura MFSF, Goncalve JPM, Chousal JAG. Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behavior of bonded joints [J], International Journal of Adhesion & Adhesives,2008.28(8):419-426.
[320]杨晓华,姚卫星,段成美.确定性疲劳累积损伤理论进展[J],中国工程科学, 2003.5(4)：81-86.
[321]刘德刚,王凤洲,林春虎.国外疲劳研究及应用领域的新发展[J],铁道车辆,2001.39(9)：10-12.
[322]黄洪钟,朱顺鹏,范志强,汪忠.基于剩余强度衰减退化的非线性累积损伤准则及其可靠性定寿[J],应用基础与工程科学学报,2011.19(20)：323-334.
[323]Bruce Philip Murphy. Aspects of the fatigue behaviour of acrylic bone cement[D], Ireland, University of Dublin,2001.
[324]谢里阳,徐灏,王德俊.疲劳过程中材料强化和弱化现象的探讨[J],机械强度,1991.13(1)：352-355.