距骨数值仿真模型的建立及有限元分析
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摘要
研究背景
距骨为人体最大的跗骨之一,是身体重力传至足部的枢纽,约60%-70%被关节软骨覆盖。了解距骨正常力学分布特点,将有助于进一步认识正常和异常情况下距骨的生理病理学行为。距骨各关节面的载荷分布异常是踝关节关节疾病发生的重要因素,是发生骨关节炎的主要病因之一。距骨及周围结构的损伤必然导致距骨生理结构的紊乱,影响距骨的应力分布。踝关节周围韧带损伤对距骨在踝穴中的稳定有重要影响。当踝关节周围韧带损伤后,将导致行走时距骨在踝穴中解剖位置的改变,影响关节接触面积及应力分布,异常的应力分布导致关节软骨发生退行性病变,最终导致骨性关节炎,故韧带损伤后应仔细对韧带原来的位置及纤维走向进行重建。由于距骨解剖结构复杂,在活体对韧带损伤后距骨的生物力学特征变化研究较为困难。
传统的骨科生物力学实验主要是以动物模型或尸体模型为基础,但存在许多弊端和局限性。动物模型的结构和功能与人类差别较大,因此生物力学结果不可能解决有关人类特性的问题；在体实验研究结果虽然最为可靠,但由于实验手段的缺陷,想在不改变其生理状态的情况下得到生物体尤其是内部组织的实验数据往往是十分困难的。尸体模型虽然在几何相似性有很大的优势,却又会改变生物体作为活组织的特性,难以获得各异的力学性能,同时一个标本不能反复利用,使对照研究的可比性下降,且实验费用较高,取材较困难,想得到实验对象内部任意部位的生物力学响应也十分困难。
随着数字仿真建模技术及有限元法的发展,数字虚拟逐渐应用到临床诊断、治疗及实验研究。与以往的生物力学实验相比,有限元方法是一种非常有用的数值计算工具,可以用几何及数字非线性进行复杂结构内部应力、应变分析。可以完成其他研究方法所不能实现的加载方式及约束条件,标本也可以进行修正以模拟任何病理状态。有限元模型也可以提供实验不能得到的正常生理信息,得到客观实体实验所难以得到的研究结果。可以通过改变载荷加载方式、改变材料特性等方法进行个体化受力分析。
由于距骨结构的复杂性、运动的多样性、个体的差异性,迄今为止,距骨生物力学研究中尚无一个可以完全模拟生理状态的有限元模型。生理状况下,距骨的结构和功能在很大程度上依赖于其所处的力学环境。本研究利用CT数据,建立合理的距骨数字仿真及三维有限元模型,研究距骨及周围结构的生物力学特性,分析正常步态下距骨应力应变情况,距骨颈骨折不同内固定方式的生物力学稳定性,距骨周围韧带损伤后距骨力学环境的改变情况,以期为足踝外科领域生物力学研究提供新的手段。
目的
1.利用数字化技术,建立距骨及周围结构的数字虚拟仿真模型,探讨数字仿真医学建模的方法及意义；
2.建立正常步态下距骨及周围结构的三维有限元模型,分析正常步态下距骨生物力学变化；
3.研究正常步态下距骨各关节面软骨的应力分布特点,分析不同步态相距骨各关节面接触特征；
4.通过三维有限元法对距骨颈骨折不同螺钉内固定方式进行对比评价,比较不同内固定方式生物力学稳定性,为临床应用提供理论依据；
5.建立踝关节韧带损伤三维有限元模型,分析不同韧带损伤后,在内旋、外旋作用力下距骨的生物力学变化。
方法
1.距骨及周围结构三维数字模型的建立：选择一例正常志愿者进行64排螺旋CT扫描。扫描平面：足底至踝关节上10cm,扫描层厚：0.45mm；存贮图像格式：DICOM格式。获得DICOM格式的二维图像数据,二维断层CT图像共663层,将其导入到三维重建软件Mimics10.01中,生成3D模型,再以STL格式导入逆向工程软件Geomagic Studio10.0中拟合曲面,最后在UG软件中缝合,建立距骨及周围结构的三维实体模型。
2.正常步态下距骨及周围结构三维有限元模型的建立：将UG中生成的实体模型导入HyperMesh10.0中,根据关节软骨边界,生成软骨实体结构,然后利用其强大的前处理功能模块划分网格,添加距骨周围韧带等附属结构,构建距骨及周围结构的三维有限元模型,之后导入ABAQUS6.9软件进行后处理。结果与以前研究进行对比来验证模型的有效性。分析距骨在不同步态相应力位移云图,探讨距骨的生物力学特性。
3.正常步态下距骨各关节面软骨接触特征的有限元分析：在上述所建有限元模型上,观察落地相、中立相、离地相时各关节面接触区域,接触面积及压强,关节软骨及软骨骨床von Mise应力分布等,了解距骨各关节面的生物力学特征。
4.距骨颈骨折螺钉固定稳定性的有限元分析：对成人正常踝关节进行CT扫描(使用64排西门子螺旋CT,层厚0.45mm),数据以DICOM格式储存。然后导入Mimics 10.0软件,根据不同组织灰度值的差异,通过阈值化及相应的擦除操作,构建得到距骨三维模型,将模型输出为STL文件,再导入逆向工程软件Geomagic Studio10.0进行光滑处理,模拟距骨颈骨折进行截骨,拟合曲面,输出为Iges文件,导入UG软件缝合生成实体模型。螺钉模型由UG软件建立,根据临床上AO/ASIF全螺纹松质骨螺钉的尺寸确定螺钉外径为4.0 mm,内径2.9mm,长度根据需要的不同而调整。由于本研究的重点与螺纹关系不大,因此为简化模型,忽略螺纹的细节,以直径4.0mm的圆柱体代替螺纹部分,输出为Iges文件。再将距骨及螺钉的几何模型导入有限元分析前处理软件Hyper Works10.0中,进行装配、网格化及赋值等前处理。根据距骨颈骨折不同固定方式,生成单螺钉、双螺钉由前向后固定及单螺钉、双螺钉由后向前固定四种不同固定的有限元模型,最后导入有限元分析软件ANSYS11.0后处理分析。通过比较不同固定方式之间螺钉的von Mises应力、骨折面接触面积及压力和骨折间隙,评价不同内固定方式的稳定性。
5.踝关节周围韧带损伤后距骨生物力学变化：建立距骨周围韧带损伤模型,分别模拟距腓前韧带、跟腓韧带、距腓后韧带、胫距前韧带、胫跟韧带、胫距后韧带及胫舟韧带断裂,施加载荷,观察距骨应变位移云图,分析不同部位韧带损伤后在内旋、外旋外力下距骨的生物力学变化,为临床上韧带损伤修复提供理论指导。
结果
1.进行足踝部CT扫描,得到DICOM数据,利用Mimics、Geomagic Studio、UG软件建立距骨及周围结构的三维模型,模型几何结构精确、逼真。
2.将实体模型导入Hypermesh进行网格划分,赋值,建立三维有限元模型,共生成21865个节点、73440个单元,导入ABAQUS软件进行后处理。通过加载载荷及施加边界条件,模型进行有限元分析,与其他生物力学实验比较,结果相似,证明模型有效。正常步态中从落地相到离地相中等效应力峰值在距骨滑车分别为3.0 MPa、4.3 MPa、4.8 MPa;在距骨颈分别为1.3 MPa、1.9 MPa、2.8 MPa;在距舟关节分别为2.8 MPa、3.0 MPa、3.4 MPa;在距下关节分别为2.2 MPa、1.8 MPa、1.5MPa。不同位相距骨Von Mises应力值及分布范围不同,等效应力在距骨滑车、距骨颈及距舟关节从落地相到离地相逐渐增大,在距下关节逐渐减小。
3.距骨滑车面软骨接触应力从落地相到离地相逐渐增加,在三个位相分别是5.6、8.3和11.8MPa。在落地相关节软骨接触应力主要分布于中后侧,中立相分布在前、外侧,离地相分布在外侧和前内侧。距舟关节面软骨接触应力主要分布在跖内侧,三个位相应力最大值分别为7.8、8.6和8.1 MPa,中立相时关节软骨所受接触应力较大。距下后关节关节软骨接触应力三个位相时接触应力最大值分别为4.5、4.7和4.0 MPa,中立相时较大,离地相关节面软骨所受接触应力较小。距骨各关节面软骨von Mises应力分布趋势同接触应力分布,从落地相至离地相,距骨滑车关节面软骨和距舟关节面软骨的von Mises应力逐渐增加,而距下后关节面软骨的von Mises应力逐渐减小。
4.模拟距骨颈骨折有限元模型,对距骨颈骨折螺钉固定方式进行生物力学分析,从应力应变云图可以看出：不同内固定方式螺钉应力分布不均匀,螺钉应力主要集中于骨折断端处。在两种载荷边界条件下,采用双螺钉由前向后固定,螺钉von Mises应力最小,在中立位和背伸时分别为14.062MPa、32.012MPa。相同内固定情况下,踝关节背伸螺钉von Mises应力值高于中立位站立时。中立位时,骨折面压力主要集中于距骨颈背外侧,双螺钉由前向后固定压力最大,为7.041MPa；踝关节背伸时,压力主要集中在内侧,双螺钉由前向后固定压力大于其他三种固定方式,为9.165 MPa。两种载荷下,四种固定方式骨折面接触面积变化不大。采用单螺钉由前向后固定在两种载荷边界条件下骨折间隙最大,双螺钉由前向后固定骨折间隙最小。
5.在内旋载荷下,胫腓后韧带、距腓前韧带和胫距后韧带不受应力作用,跟腓韧带所受应力较大,为18.91MPa。在外旋应力下,距腓后韧带、跟腓韧带、胫距前韧带、胫舟韧带不受应力作用,距腓前韧带所受应力最大,为13.75 MPa。内旋作用下,距腓前韧带损伤后,等效应力峰值在胫距关节为8.56MPa,距下后关节6.43MPa,距下前关节为1.87MPa,距舟关节为7.31 MPa。距骨的最大位移位于距骨后部,为1.21mm。跟腓韧带损伤后,等效应力峰值在胫距关节为9.29MPa,距下后关节7.19MPa,距下前关节为3.49MPa,距舟关节为6.69MPa,最大位移位于距骨后部,为1.72mm。距腓后带损伤后,等效应力峰值在胫距关节为8.86MPa,距下后关节6.88MPa,距下前关节为1.85MPa,距舟关节为7.39MPa。距骨的最大位移位于距骨后部,为1.09mm。外旋作用下,胫距前韧带、胫跟韧带、胫舟韧带损伤后,等效应力及位移变化情况相同,在胫距关节为5.79MPa,距下后关节4.91MPa,距下前关节为1.71MPa,距舟关节为6.88MPa。距骨的最大位移位于距骨体外侧及头部外侧,为0.64mm。胫距后韧带损伤后,距骨等效应力在胫距关节面前侧、距下后关节中部、距舟关节下内侧等效应力较大,在胫距关节为6.24MPa,距下后关节5.23MPa,距下前关节为1.41MPa,距舟关节为6.67 MPa。距骨的最大位移位于距骨体外侧及头部外侧,为0.72mm。
结论
1.基于CT扫描数据,利用Mimics、Geomagic Studio、UG软件,建立距骨及周围骨骼的三维数字仿真模型,这种方法可行、有效,建模速度较快,且对人体无损害。所建模型包含大量信息量,具有和实体相似的几何形状,能够较真实模拟原模型。
2.三维有限元法是生物力学研究的一种理论方法,可以模拟各种结构的几何模型,赋予各种组织的生物材料属性,能很好的反映其生物力学特性的总体趋势,因而可以作为标本实验生物力学研究方法很好的补充。本研究利用人体足踝部CT数据,借助Mimics、Geomagic Studio、Hypermesh、ABAQUS等软件,建立了距骨及周围结构的有限元模型与正常人体具有良好的几何相似性。本模型与目前文献报道的同类研究模型相比,网格划分均匀,单元质量较高,因此,分析结果更加精确。同时,由于数字模型可拆分的特点,应用具有极大的灵活性,在研究对象的选择上,可对足踝部诸骨独立研究,进一步扩大了本模型的应用范围。除此之外,作为整体,通过与解剖结构、病理生理、临床研究等多方面生物力学实验研究相关文献对比,证明本模型具有良好的物理相似性,更能够准确和完整地模拟距骨的解剖结构及其受力特点,有利于对距骨进行生物力学分析。
3.距骨各关节面接触应力及面积的分布对临床研究有重要意义,距骨各关节面软骨的异常力学机制是踝关节骨关节炎的主要病因之一,认识正常步态下距骨各关节面软骨力学分布特点,将有助于了解正常距骨关节软骨的力学机制和异常载荷下关节软骨的病理学行为。
4.有限元分析方法开始越来越多的被用于骨折内外固定方法的生物力学评价中,为临床选择有效的固定方法提供了实验依据。内固定物本身应力分布情况及骨折断面的位移是衡量内固定方式优劣的一个标准。理想的内固定物应该使应力尽可能均匀的分布在内固定物上,而不应过度集中在某一部位。高应力必然导致骨折端的高应变,从骨折愈合角度来讲,这种高应变不利于骨折局部骨痂的生长。骨折面的情况对骨折的愈合非常重要,其中的两个因素是骨折断端接触面积及接触面的压力。较大的接触面积及适量的压力能增加断端间静摩擦力,减小骨折断端间隙,加大骨折的固定刚度。距骨颈骨折采用双螺钉由前向后固定可获得可靠的生物力学稳定。
5.踝关节周围韧带损伤,对距骨的稳定性有重要影响,当距骨周围韧带损伤后,必然导致距骨在踩穴中的位置发生改变,从而影响关节接触应力及面积发生改变,导致关节软骨发生退行性变化,最终导致骨性关节炎的发生。在外旋作用力下,胫距后韧带损伤后,距骨的等效应力及位移较大,胫距关节的接触压力较大,提示胫距后韧带在外旋情况下对踝关节的稳定性具有重要作用。在内旋作用下,跟腓韧带损伤后,距骨的等效应力及位移较大,提示跟腓韧带在内旋情况下对踝关节的稳定性具有重要作用。
6.本研究的不足之处。本实验所涉及的生物材料的材料力学特性均假定为均质、连续和各向同性,骨、软骨、韧带材料本身并不是均质、连续的,也不是各向同性,而是呈各向异性的特征,也没有考虑踝关节周围软组织对模型的影响。
Background
The talus structure, a vital connection between the human body and the foot, played a highly important role in human locomotion. Up to 60% of the talus was covered by cartilage. Knowledge about the biomechanics of the talus, will contribute to further understanding of the normal and abnormal situation talus physiological pathology practices. Abnormal distribution of load on talus articular surface was an important factor of ankle joint disease, such as osteoarthritis. The injury of ankle ligaments will disrupt the physiology structure of the talus and change the distribution of stress. The ligaments of ankle were important to the stability of ankle. The injury of ligaments will lead the changes of dislocation of the talus in the tibial mortise, which will affect the contact area and stress distribution. Abnormal distribution of stress can cause the degeneration of articular cartilage, which finally developed osteoarthritis. So it must reconstruct the ligament when the ligament injured. The anatomy of the talus was complex, so it was difficult to research the change of biomechanical characteristics.
The experiment of traditional orthopedics biomechanics was based on the animal and cadaver models. There were deficiency and limit. The structure and function of animal were different from human, so the result of animal biomechanics cannot resolve the problem of human. The result in vivo was most reliability, but because of limited management, it was difficult to attain the data under the physiological state. The cadaver model gained an advantage over the geometry similarity, but it changed the characteristics of living tissue, and was difficult to attain the mechanic's characteristics. The same cadaver model cannot use again; it decreased the comparability of compared research. The cost of an experiment was high. Meanwhile it was difficult to gain the cadaver now.
Following the development of digital simulation model and finite element analysis, digit virtual model applied to clinical diagnose, treatment and experiment research. Compared with tradition biomechanical experiment, the finite element method (FEM) was a powerful mathematical tool which allows internal stress and strain analyses of complex structures with geometrical and material nonlinearities. The finite element model can build the experiment model that had similar geometry and physics. The finite element method can build the load and constrain condition that other methods cannot attain, and can simulate the pathology state. The finite element model can afford the information and get the result which the experiment model cannot get. The finite element analysis changed the load, material parameter for individual analysis.
Because of the complex structure, the kinetic variety and individual difference, so far, there was not a finite element model which can simulate the physiology status of the talus. Under the physiology status, the function and structure of the talus depended on the mechanic's environment. In this study, we established the mathematical model of the talus using the CT date. We researched the biomechanics characteristics and analysis the stress/strain during the stance phase of gait, the biomechanical stability of talus fracture fixed with different implants, and the changes of mechanic status after the ligaments' injury, in order to supply a new method to study the biomechanics in an ankle-foot field.
Objective
1. To construct the digit virtual model of the talus utilizing the mathematical technology, and discuss the method and significance with using the digit virtual model.
2. To develop a detailed, three-dimensional, finite element model of a human ankle and analysis the stress distribution of the talus during different gait phases for the biomechanics studies.
3. To construct a three-dimensional finite element model (FEM) of normal adult human ankle in order to supply a digital platform for biomechanical research of talar cartilage stress during gait, and understand the stress distribution of cartilage biomechanical characteristics.
4. To explore the biomechanical properties of different internal fixations for talar neck fracture through finite element analysis and therefore to provide a scientific foundation for clinic application.
5. To construct a three-dimensional finite element model of ankle ligament injury, analysis the changes of talus biomechanics in inversion and eversion load.
Methods
1. Constructing the talus digit virtual model:One common volunteer was chosen who was scanned by multi-slices computerized tomography in the neutral unloaded position. Scan plane was situated between the bottom of food and the plane of 10cm upper ankle. CT images were taken with intervals of 0.45 millimeters. All the slices were saved in the format of the DICOM (Digital Imaging and Communications in Medicine). Therefore, the 2D image data in the format of DICOM was obtained, and there were 663 2D-CT slices. Then these 2D-CT slices were imported into the three-dimensional reconstruction software of Mimics10.01. (Materialise's Interactive Medical Image Control System). From this data, a three-dimensional image about ankle was reconstructed with the software. Outcome was saved in the format of STL. Then the STL data was imported to Geomagic studio 10.0 software to fix surface. Finally, the surface was screwed in UG software to form the solid model of talus and other structure.
2. Constructing a finite element model of talus and around structure on normal gait: The solid model formed in UG software was imported into Hypermesh10.0 software. The solid model of articular cartilage was constructed according the articular cartilage boundary. Then the model was meshed. The ligaments were constructed according the anatomy position. Finally a three-dimensional (3D) finite element model of talus and around structure was developed. The model was imported into ABAQUS6.9 software for post-processing. The results were compared with those from previous experimental research to validate the finite element model. The stress and strain nephograms during gait were obtained and analyzed to explore the biomechanical characteristics.
3. A finite element analysis of contact characteristics of the talus articular surface on gait: according the outcome of the finite element model, the contact pressure, contact area, and the von Mises stress of articular cartilage were researched to study the contact characteristics of articular surface of the talus.
4. A finite element analysis of biomechanical stability of talar neck fracture fixed with screws. One normal ankle of an adult volunteer was scanned (multi-slices computerized tomography, intervals 0.45 millimeters) in the neutral unloaded position. All the slices were saved in the format of the DICOM (Digital Imaging and Communications in Medicine). Then these 2D-CT slices were imported into the three-dimensional reconstruction software of Mimics10.01 (Materialise's Interactive Medical Image Control System). From this data, a three-dimensional image about ankle was reconstructed with the software. Outcome was saved in the format of STL. Then the STL data was imported to Geomagic studio 10.0 software to smooth and build talar neck fracture model. Simulation of talar neck fracture was achieved by an idealized planar cut between the bone segments in the neck. Then the model was fixed surface. Finally, the surface was imported and screwed in UG software to form the solid model. The size of the screw was consulted from AO/ASIF. The outside diameter was 4.0mm, the inside was 2.9mm. The length was changed according to the actually situation. The screw model was constructed in UG software. Given the complex geometry of the screws, they were modeled as simple cylinders and the thread ignored. The solid models were then imported into Hypermesh10.0 software. Then the models were assembled, meshed and given material parameter. Corresponding to the quantity and location of screws, four different finite element models of surgical fixation methods were developed: anterior-to-posterior fixation using one 4.0 mm screw, posterior-to-anterior fixation using one 4.0 mm screw, anterior-to-posterior fixation using two 4.0 mm screws, posterior-to-anterior fixation using two 4.0 mm screws. Finally, the finite element models were imported into the FE package ANSYS (ANSYS Inc., USA) for post-processing. The von Mises stress, contact area and pressure, contact gap were compared to estimate the biomechanical stability.
5. The changes of biomechanics of the talus after ankle ligament injury:a finite element model of ankle ligament injury was constructed, that was simulated the injury of anterior talofibular ligament, calcaneofibular ligament, posterior talofibular ligament, anterior tibiotalar ligament, tibiocalcaneal ligament, posterior tibiotalar ligament, tibionavicular ligament. The injury models were loaded and post-processing. The stress and strain of the talus were researched to analysis the changes of talus biomechanics under inversion and eversion load. The result provides theory instruction for ligament repair in clinics.
Results
1. A serial precise of data of DICOM was obtained from CT scan for ankle. Using Mimics10.0, Geomagic studio10.0 and UG software, a geometric reconstruction of the ankle was developed using the data. The model has the precise structure.
2. The model was meshed and given the material properties in Hypermesh10.0 software. Finally, the model was imported to ABAQUS6.9. A three-dimensional finite element model of ankle was established, which composed of 21865 nodes,73440 elements. And the stress distribution within the bone was obtained at three phases. The stress distributions of three phases were significantly different. The peak von Mises stress from the heel-strike to push-off on the talar dome was 3.0 MPa,4.3 MPa and 4.8 MPa respectively. It was 1.3 MPa,1.9 MPa and 2.8 MPa on talar neck, and 2.8 MPa,3.0 MPa,3.4 MPa on the talonavicular joint surface. It was 2.2 MPa,1.8 MPa and 1.5 MPa on subtalar joint. The von Mises stress and distribution scope were difference in different phase. The von Mises stress in the talar dome, talar neck, talonavicular joint surface gradually increased, and decreased in the subtalar joint.
3. The contact pressure gradually increased in talar dome cartilage from the heel-strike to push-off. The contact pressure was 5.6,8.8 and 11.8MPa. The contact pressure distributed on the posterior medial side in the heel-strike, anterior and lateral in mid-stance, lateral and anterior-medial side. The contact pressure was distributed on medial metatarsus in talonavicular joint surface. The contact pressure was 7.8,8.6 and 8.1 MPa respectively. It was higher in mid-stance. The contact pressure was 4.5, 4.7 and 4.0 MPa in the posterior subtalar joint. The distribution of von Mises stress on talus articular cartilage was similar to contact pressure. It increased in talar dome and talonavicular joint articular cartilage and decreased in the posterior subtalar joint.
4. Analysis the biomechanical behaviors of the talar neck fracture with four different fixations using finite element analysis. The distribution of von Mises stress was uneven on fixation. The values of maximum von Mises stress on screws were observed near the fracture location at each fixation. It was observed from these figures that the 2-AP experience has a low von Mises stress in mid-stance loading conditions. A similar behavior was observed in active dorsiflexion. It was 14 062MPa on neutral position, and 32.012 MPa on ankle active dorsiflexion. It was noticed that the fracture surface pressure mainly in the lateral talar neck at mid-stance,2-AP had the greatest pressure for 7.041 MPa. At the ankle dorsiflexion, the pressure concentrated in the medial,2-AP was higher than the others, as 9.165 MPa. The contact areas were of equal approximately in four fixations. The largest fracture gap in every fixation was in the plantar medial of fracture surface.1-AP had the maximum fracture gap under two loading conditions.2-AP was lowest.
5. Under the internal rotation load, there was no strain/stress in posterior tibiofibular ligament, anterior talofibular ligament and posterior tibiotalar ligament. The stress in calcaneofibular ligament was higher, as 18.91 MPa. Under the external rotation load, there was no strain/stress in posterior talofibular ligament, calcaneofibular ligament, anterior tibiotalar ligament and tibionavicular ligament. The stress in anterior talofibular ligament was biggest, as 13.75 MPa. Under internal rotation, after anterior talofibular ligament injury, the von Mises peak stress was 8.56 MPa on talar dome,6.43 MPa on posterior subtalar joint,2.87 MPa on anterior subtalar joint, and 7.31 MPa on talonavicular joint. The maximum displacement was located in the posterior talus, as 1.21mm. With calcaneofibular ligament injury, the von Mises, peak stress was 9.29 MPa on talar dome,7.19 MPa on posterior subtalar joint,3.49 MPa on anterior subtalar joint, and 6.69 MPa on talonavicular joint. The maximum displacement was located in the posterior talus, as 1.72mm. With posterior talofibular injury, the von Mises peak stress was 8.86 MPa on talar dome,6.88 MPa on posterior subtalar joint,1.85 MPa on anterior subtalar joint, and 7.39 MPa on talonavicular joint. The maximum displacement was located in the posterior talus, as 1.09mm. Under the load of external rotation, the changes of von Mises and displacement was similar in anterior tibiotalar ligament, tibionavicular ligament and tibiocalcaneal ligament injury. The von Mises peak stress was 5.79 MPa on talar dome,4.91 MPa on posterior subtalar joint,1.71 MPa on anterior subtalar joint, and 6.88 MPa on talonavicular joint. The maximum displacement was located in lateral of talus body and head, as 0.63mm. With the injury of posterior tibiotalar ligament, the von Mises peak stress was 6.24 MPa on talar dome,5.23 MPa on posterior subtalar joint,1.41 MPa on anterior subtalar joint, and 6.67 MPa on talonavicular joint. The maximum displacement was located in lateral of talus body and head, as 0.72mm.
Conclusions
1. Based on CT scan data, the talus three-dimensional digital simulation models were established using Mimics, Geomagic Studio, and UG software. This approach was feasible, effective, faster and harmless to the human body. The model contained a large amount of information and entities with a similar geometry to the more realistic simulation of the original model.
2. The three-dimensional finite element method was a biomechanical study of theories and methods to simulate the geometric model of the structure to give organizations the biological material properties. It can reflect the biomechanical properties of the overall trend, which can be used as a very good supplement for experimental specimen biomechanical study. In this study, according to the actual geometry of the skeleton, which was obtained from 3D reconstruction of computed tomography, a three-dimensional (3D) finite element model was developed using Mimics, Geomagic Studio, Hypermesh, ABAQUS software. The finite element model of had a good geometric similarity. Compared with similar studies reported in the literature, the model had the more refined and uniform grid, the greater the cell density and more accurate results. Furthermore, this model can be disassembled, with great flexibility in the choice of subjects; it can be built on the foot bones of various independent study to further expand the scope of application of the model. In addition, as a whole, compared with the anatomical structure, pathophysiology, clinical research literature, and many other biomechanical researches, it indicated that this model had good physical similarity, more accurate and complete to simulate the anatomy of the talus and its mechanical characteristics. It was beneficial for biomechanical analysis of the talus.
3. The articular surface contact stress and area distribution on talus were important to the clinical research. The abnormal mechanical mechanism on cartilage was a major cause of osteoarthritis. Knowledge for the characteristics of mechanic distribution on cartilage will help to understand the mechanism of the normal talus articular cartilage and behavior of articular cartilage pathology under abnormal load.
4. Finite element analysis is a useful tool for the analysis mechanical behavior of implants in fractures of bone, which can provide an experimental basis for effective fixation. Stress distribution within the implant itself and the displacement of fracture section were a standard measure of internal fixation. Internal fixation should be the ideal uniform distribution of stress as possible on the fixture, but not overly concentrated in certain parts. High stress will inevitably lead to high fracture strain, from the point of fracture healing view, this high strain was not conducive to the growth in fracture callus. One of the measures to verify the stability was to check the bone contact status at the fracture interface surface; the two factors were contact pressure and fracture gap at the fracture site. Larger contact area and the right pressure can increase the static friction between the fracture sites, reducing the fracture site clearance; increase the stiffness of fracture fixation. Talar neck fractures by double screws from front to back fixed and reliable access to the biomechanical stability.
5. The injury of ankle ligament had a major impact on the stability of the talus, which will inevitably change the location of the talus in the ankle mortise, thus affecting the contact area and stress. It will lead to articular cartilage degeneration, eventually lead to osteoarthritis. In external rotation force, the injury of the posterior tibiotalar ligament, the von Mises stress, displacement and contact pressure was high. It was suggested that posterior tibiotalar ligament played an important role for ankle stability under external rotation force. Including the effect of rotation, with the ligament injury, the talus of the equivalent stress and the displacement of large, suggesting that spin with the ligament under the circumstances, including the stability of the ankle joint plays an important role. In internal rotation force, the injury of calcaneofibular ligament, the von Mises stress, displacement and contact pressure was high. It was suggested that calcaneofibular ligament played an important role for ankle stability under internal rotation force.
6. The limitation of this study was that mechanical characteristics of biological materials involved in this study were assumed to be homogeneous, continuous and isotropic. Actually, bone, cartilage and ligaments material itself were not homogeneous, continuous, nor was isotropic, but anisotropy. The characteristic of soft tissue around the ankle has not considered the impact of the model.
距骨为人体最大的跗骨之一,是身体重力传至足部的枢纽,约60%-70%被关节软骨覆盖。了解距骨正常力学分布特点,将有助于进一步认识正常和异常情况下距骨的生理病理学行为。距骨各关节面的载荷分布异常是踝关节关节疾病发生的重要因素,是发生骨关节炎的主要病因之一。距骨及周围结构的损伤必然导致距骨生理结构的紊乱,影响距骨的应力分布。踝关节周围韧带损伤对距骨在踝穴中的稳定有重要影响。当踝关节周围韧带损伤后,将导致行走时距骨在踝穴中解剖位置的改变,影响关节接触面积及应力分布,异常的应力分布导致关节软骨发生退行性病变,最终导致骨性关节炎,故韧带损伤后应仔细对韧带原来的位置及纤维走向进行重建。由于距骨解剖结构复杂,在活体对韧带损伤后距骨的生物力学特征变化研究较为困难。
传统的骨科生物力学实验主要是以动物模型或尸体模型为基础,但存在许多弊端和局限性。动物模型的结构和功能与人类差别较大,因此生物力学结果不可能解决有关人类特性的问题；在体实验研究结果虽然最为可靠,但由于实验手段的缺陷,想在不改变其生理状态的情况下得到生物体尤其是内部组织的实验数据往往是十分困难的。尸体模型虽然在几何相似性有很大的优势,却又会改变生物体作为活组织的特性,难以获得各异的力学性能,同时一个标本不能反复利用,使对照研究的可比性下降,且实验费用较高,取材较困难,想得到实验对象内部任意部位的生物力学响应也十分困难。
随着数字仿真建模技术及有限元法的发展,数字虚拟逐渐应用到临床诊断、治疗及实验研究。与以往的生物力学实验相比,有限元方法是一种非常有用的数值计算工具,可以用几何及数字非线性进行复杂结构内部应力、应变分析。可以完成其他研究方法所不能实现的加载方式及约束条件,标本也可以进行修正以模拟任何病理状态。有限元模型也可以提供实验不能得到的正常生理信息,得到客观实体实验所难以得到的研究结果。可以通过改变载荷加载方式、改变材料特性等方法进行个体化受力分析。
由于距骨结构的复杂性、运动的多样性、个体的差异性,迄今为止,距骨生物力学研究中尚无一个可以完全模拟生理状态的有限元模型。生理状况下,距骨的结构和功能在很大程度上依赖于其所处的力学环境。本研究利用CT数据,建立合理的距骨数字仿真及三维有限元模型,研究距骨及周围结构的生物力学特性,分析正常步态下距骨应力应变情况,距骨颈骨折不同内固定方式的生物力学稳定性,距骨周围韧带损伤后距骨力学环境的改变情况,以期为足踝外科领域生物力学研究提供新的手段。
目的
1.利用数字化技术,建立距骨及周围结构的数字虚拟仿真模型,探讨数字仿真医学建模的方法及意义；
2.建立正常步态下距骨及周围结构的三维有限元模型,分析正常步态下距骨生物力学变化；
3.研究正常步态下距骨各关节面软骨的应力分布特点,分析不同步态相距骨各关节面接触特征；
4.通过三维有限元法对距骨颈骨折不同螺钉内固定方式进行对比评价,比较不同内固定方式生物力学稳定性,为临床应用提供理论依据；
5.建立踝关节韧带损伤三维有限元模型,分析不同韧带损伤后,在内旋、外旋作用力下距骨的生物力学变化。
方法
1.距骨及周围结构三维数字模型的建立：选择一例正常志愿者进行64排螺旋CT扫描。扫描平面：足底至踝关节上10cm,扫描层厚：0.45mm；存贮图像格式：DICOM格式。获得DICOM格式的二维图像数据,二维断层CT图像共663层,将其导入到三维重建软件Mimics10.01中,生成3D模型,再以STL格式导入逆向工程软件Geomagic Studio10.0中拟合曲面,最后在UG软件中缝合,建立距骨及周围结构的三维实体模型。
2.正常步态下距骨及周围结构三维有限元模型的建立：将UG中生成的实体模型导入HyperMesh10.0中,根据关节软骨边界,生成软骨实体结构,然后利用其强大的前处理功能模块划分网格,添加距骨周围韧带等附属结构,构建距骨及周围结构的三维有限元模型,之后导入ABAQUS6.9软件进行后处理。结果与以前研究进行对比来验证模型的有效性。分析距骨在不同步态相应力位移云图,探讨距骨的生物力学特性。
3.正常步态下距骨各关节面软骨接触特征的有限元分析：在上述所建有限元模型上,观察落地相、中立相、离地相时各关节面接触区域,接触面积及压强,关节软骨及软骨骨床von Mise应力分布等,了解距骨各关节面的生物力学特征。
4.距骨颈骨折螺钉固定稳定性的有限元分析：对成人正常踝关节进行CT扫描(使用64排西门子螺旋CT,层厚0.45mm),数据以DICOM格式储存。然后导入Mimics 10.0软件,根据不同组织灰度值的差异,通过阈值化及相应的擦除操作,构建得到距骨三维模型,将模型输出为STL文件,再导入逆向工程软件Geomagic Studio10.0进行光滑处理,模拟距骨颈骨折进行截骨,拟合曲面,输出为Iges文件,导入UG软件缝合生成实体模型。螺钉模型由UG软件建立,根据临床上AO/ASIF全螺纹松质骨螺钉的尺寸确定螺钉外径为4.0 mm,内径2.9mm,长度根据需要的不同而调整。由于本研究的重点与螺纹关系不大,因此为简化模型,忽略螺纹的细节,以直径4.0mm的圆柱体代替螺纹部分,输出为Iges文件。再将距骨及螺钉的几何模型导入有限元分析前处理软件Hyper Works10.0中,进行装配、网格化及赋值等前处理。根据距骨颈骨折不同固定方式,生成单螺钉、双螺钉由前向后固定及单螺钉、双螺钉由后向前固定四种不同固定的有限元模型,最后导入有限元分析软件ANSYS11.0后处理分析。通过比较不同固定方式之间螺钉的von Mises应力、骨折面接触面积及压力和骨折间隙,评价不同内固定方式的稳定性。
5.踝关节周围韧带损伤后距骨生物力学变化：建立距骨周围韧带损伤模型,分别模拟距腓前韧带、跟腓韧带、距腓后韧带、胫距前韧带、胫跟韧带、胫距后韧带及胫舟韧带断裂,施加载荷,观察距骨应变位移云图,分析不同部位韧带损伤后在内旋、外旋外力下距骨的生物力学变化,为临床上韧带损伤修复提供理论指导。
结果
1.进行足踝部CT扫描,得到DICOM数据,利用Mimics、Geomagic Studio、UG软件建立距骨及周围结构的三维模型,模型几何结构精确、逼真。
2.将实体模型导入Hypermesh进行网格划分,赋值,建立三维有限元模型,共生成21865个节点、73440个单元,导入ABAQUS软件进行后处理。通过加载载荷及施加边界条件,模型进行有限元分析,与其他生物力学实验比较,结果相似,证明模型有效。正常步态中从落地相到离地相中等效应力峰值在距骨滑车分别为3.0 MPa、4.3 MPa、4.8 MPa;在距骨颈分别为1.3 MPa、1.9 MPa、2.8 MPa;在距舟关节分别为2.8 MPa、3.0 MPa、3.4 MPa;在距下关节分别为2.2 MPa、1.8 MPa、1.5MPa。不同位相距骨Von Mises应力值及分布范围不同,等效应力在距骨滑车、距骨颈及距舟关节从落地相到离地相逐渐增大,在距下关节逐渐减小。
3.距骨滑车面软骨接触应力从落地相到离地相逐渐增加,在三个位相分别是5.6、8.3和11.8MPa。在落地相关节软骨接触应力主要分布于中后侧,中立相分布在前、外侧,离地相分布在外侧和前内侧。距舟关节面软骨接触应力主要分布在跖内侧,三个位相应力最大值分别为7.8、8.6和8.1 MPa,中立相时关节软骨所受接触应力较大。距下后关节关节软骨接触应力三个位相时接触应力最大值分别为4.5、4.7和4.0 MPa,中立相时较大,离地相关节面软骨所受接触应力较小。距骨各关节面软骨von Mises应力分布趋势同接触应力分布,从落地相至离地相,距骨滑车关节面软骨和距舟关节面软骨的von Mises应力逐渐增加,而距下后关节面软骨的von Mises应力逐渐减小。
4.模拟距骨颈骨折有限元模型,对距骨颈骨折螺钉固定方式进行生物力学分析,从应力应变云图可以看出：不同内固定方式螺钉应力分布不均匀,螺钉应力主要集中于骨折断端处。在两种载荷边界条件下,采用双螺钉由前向后固定,螺钉von Mises应力最小,在中立位和背伸时分别为14.062MPa、32.012MPa。相同内固定情况下,踝关节背伸螺钉von Mises应力值高于中立位站立时。中立位时,骨折面压力主要集中于距骨颈背外侧,双螺钉由前向后固定压力最大,为7.041MPa；踝关节背伸时,压力主要集中在内侧,双螺钉由前向后固定压力大于其他三种固定方式,为9.165 MPa。两种载荷下,四种固定方式骨折面接触面积变化不大。采用单螺钉由前向后固定在两种载荷边界条件下骨折间隙最大,双螺钉由前向后固定骨折间隙最小。
5.在内旋载荷下,胫腓后韧带、距腓前韧带和胫距后韧带不受应力作用,跟腓韧带所受应力较大,为18.91MPa。在外旋应力下,距腓后韧带、跟腓韧带、胫距前韧带、胫舟韧带不受应力作用,距腓前韧带所受应力最大,为13.75 MPa。内旋作用下,距腓前韧带损伤后,等效应力峰值在胫距关节为8.56MPa,距下后关节6.43MPa,距下前关节为1.87MPa,距舟关节为7.31 MPa。距骨的最大位移位于距骨后部,为1.21mm。跟腓韧带损伤后,等效应力峰值在胫距关节为9.29MPa,距下后关节7.19MPa,距下前关节为3.49MPa,距舟关节为6.69MPa,最大位移位于距骨后部,为1.72mm。距腓后带损伤后,等效应力峰值在胫距关节为8.86MPa,距下后关节6.88MPa,距下前关节为1.85MPa,距舟关节为7.39MPa。距骨的最大位移位于距骨后部,为1.09mm。外旋作用下,胫距前韧带、胫跟韧带、胫舟韧带损伤后,等效应力及位移变化情况相同,在胫距关节为5.79MPa,距下后关节4.91MPa,距下前关节为1.71MPa,距舟关节为6.88MPa。距骨的最大位移位于距骨体外侧及头部外侧,为0.64mm。胫距后韧带损伤后,距骨等效应力在胫距关节面前侧、距下后关节中部、距舟关节下内侧等效应力较大,在胫距关节为6.24MPa,距下后关节5.23MPa,距下前关节为1.41MPa,距舟关节为6.67 MPa。距骨的最大位移位于距骨体外侧及头部外侧,为0.72mm。
结论
1.基于CT扫描数据,利用Mimics、Geomagic Studio、UG软件,建立距骨及周围骨骼的三维数字仿真模型,这种方法可行、有效,建模速度较快,且对人体无损害。所建模型包含大量信息量,具有和实体相似的几何形状,能够较真实模拟原模型。
2.三维有限元法是生物力学研究的一种理论方法,可以模拟各种结构的几何模型,赋予各种组织的生物材料属性,能很好的反映其生物力学特性的总体趋势,因而可以作为标本实验生物力学研究方法很好的补充。本研究利用人体足踝部CT数据,借助Mimics、Geomagic Studio、Hypermesh、ABAQUS等软件,建立了距骨及周围结构的有限元模型与正常人体具有良好的几何相似性。本模型与目前文献报道的同类研究模型相比,网格划分均匀,单元质量较高,因此,分析结果更加精确。同时,由于数字模型可拆分的特点,应用具有极大的灵活性,在研究对象的选择上,可对足踝部诸骨独立研究,进一步扩大了本模型的应用范围。除此之外,作为整体,通过与解剖结构、病理生理、临床研究等多方面生物力学实验研究相关文献对比,证明本模型具有良好的物理相似性,更能够准确和完整地模拟距骨的解剖结构及其受力特点,有利于对距骨进行生物力学分析。
3.距骨各关节面接触应力及面积的分布对临床研究有重要意义,距骨各关节面软骨的异常力学机制是踝关节骨关节炎的主要病因之一,认识正常步态下距骨各关节面软骨力学分布特点,将有助于了解正常距骨关节软骨的力学机制和异常载荷下关节软骨的病理学行为。
4.有限元分析方法开始越来越多的被用于骨折内外固定方法的生物力学评价中,为临床选择有效的固定方法提供了实验依据。内固定物本身应力分布情况及骨折断面的位移是衡量内固定方式优劣的一个标准。理想的内固定物应该使应力尽可能均匀的分布在内固定物上,而不应过度集中在某一部位。高应力必然导致骨折端的高应变,从骨折愈合角度来讲,这种高应变不利于骨折局部骨痂的生长。骨折面的情况对骨折的愈合非常重要,其中的两个因素是骨折断端接触面积及接触面的压力。较大的接触面积及适量的压力能增加断端间静摩擦力,减小骨折断端间隙,加大骨折的固定刚度。距骨颈骨折采用双螺钉由前向后固定可获得可靠的生物力学稳定。
5.踝关节周围韧带损伤,对距骨的稳定性有重要影响,当距骨周围韧带损伤后,必然导致距骨在踩穴中的位置发生改变,从而影响关节接触应力及面积发生改变,导致关节软骨发生退行性变化,最终导致骨性关节炎的发生。在外旋作用力下,胫距后韧带损伤后,距骨的等效应力及位移较大,胫距关节的接触压力较大,提示胫距后韧带在外旋情况下对踝关节的稳定性具有重要作用。在内旋作用下,跟腓韧带损伤后,距骨的等效应力及位移较大,提示跟腓韧带在内旋情况下对踝关节的稳定性具有重要作用。
6.本研究的不足之处。本实验所涉及的生物材料的材料力学特性均假定为均质、连续和各向同性,骨、软骨、韧带材料本身并不是均质、连续的,也不是各向同性,而是呈各向异性的特征,也没有考虑踝关节周围软组织对模型的影响。
Background
The talus structure, a vital connection between the human body and the foot, played a highly important role in human locomotion. Up to 60% of the talus was covered by cartilage. Knowledge about the biomechanics of the talus, will contribute to further understanding of the normal and abnormal situation talus physiological pathology practices. Abnormal distribution of load on talus articular surface was an important factor of ankle joint disease, such as osteoarthritis. The injury of ankle ligaments will disrupt the physiology structure of the talus and change the distribution of stress. The ligaments of ankle were important to the stability of ankle. The injury of ligaments will lead the changes of dislocation of the talus in the tibial mortise, which will affect the contact area and stress distribution. Abnormal distribution of stress can cause the degeneration of articular cartilage, which finally developed osteoarthritis. So it must reconstruct the ligament when the ligament injured. The anatomy of the talus was complex, so it was difficult to research the change of biomechanical characteristics.
The experiment of traditional orthopedics biomechanics was based on the animal and cadaver models. There were deficiency and limit. The structure and function of animal were different from human, so the result of animal biomechanics cannot resolve the problem of human. The result in vivo was most reliability, but because of limited management, it was difficult to attain the data under the physiological state. The cadaver model gained an advantage over the geometry similarity, but it changed the characteristics of living tissue, and was difficult to attain the mechanic's characteristics. The same cadaver model cannot use again; it decreased the comparability of compared research. The cost of an experiment was high. Meanwhile it was difficult to gain the cadaver now.
Following the development of digital simulation model and finite element analysis, digit virtual model applied to clinical diagnose, treatment and experiment research. Compared with tradition biomechanical experiment, the finite element method (FEM) was a powerful mathematical tool which allows internal stress and strain analyses of complex structures with geometrical and material nonlinearities. The finite element model can build the experiment model that had similar geometry and physics. The finite element method can build the load and constrain condition that other methods cannot attain, and can simulate the pathology state. The finite element model can afford the information and get the result which the experiment model cannot get. The finite element analysis changed the load, material parameter for individual analysis.
Because of the complex structure, the kinetic variety and individual difference, so far, there was not a finite element model which can simulate the physiology status of the talus. Under the physiology status, the function and structure of the talus depended on the mechanic's environment. In this study, we established the mathematical model of the talus using the CT date. We researched the biomechanics characteristics and analysis the stress/strain during the stance phase of gait, the biomechanical stability of talus fracture fixed with different implants, and the changes of mechanic status after the ligaments' injury, in order to supply a new method to study the biomechanics in an ankle-foot field.
Objective
1. To construct the digit virtual model of the talus utilizing the mathematical technology, and discuss the method and significance with using the digit virtual model.
2. To develop a detailed, three-dimensional, finite element model of a human ankle and analysis the stress distribution of the talus during different gait phases for the biomechanics studies.
3. To construct a three-dimensional finite element model (FEM) of normal adult human ankle in order to supply a digital platform for biomechanical research of talar cartilage stress during gait, and understand the stress distribution of cartilage biomechanical characteristics.
4. To explore the biomechanical properties of different internal fixations for talar neck fracture through finite element analysis and therefore to provide a scientific foundation for clinic application.
5. To construct a three-dimensional finite element model of ankle ligament injury, analysis the changes of talus biomechanics in inversion and eversion load.
Methods
1. Constructing the talus digit virtual model:One common volunteer was chosen who was scanned by multi-slices computerized tomography in the neutral unloaded position. Scan plane was situated between the bottom of food and the plane of 10cm upper ankle. CT images were taken with intervals of 0.45 millimeters. All the slices were saved in the format of the DICOM (Digital Imaging and Communications in Medicine). Therefore, the 2D image data in the format of DICOM was obtained, and there were 663 2D-CT slices. Then these 2D-CT slices were imported into the three-dimensional reconstruction software of Mimics10.01. (Materialise's Interactive Medical Image Control System). From this data, a three-dimensional image about ankle was reconstructed with the software. Outcome was saved in the format of STL. Then the STL data was imported to Geomagic studio 10.0 software to fix surface. Finally, the surface was screwed in UG software to form the solid model of talus and other structure.
2. Constructing a finite element model of talus and around structure on normal gait: The solid model formed in UG software was imported into Hypermesh10.0 software. The solid model of articular cartilage was constructed according the articular cartilage boundary. Then the model was meshed. The ligaments were constructed according the anatomy position. Finally a three-dimensional (3D) finite element model of talus and around structure was developed. The model was imported into ABAQUS6.9 software for post-processing. The results were compared with those from previous experimental research to validate the finite element model. The stress and strain nephograms during gait were obtained and analyzed to explore the biomechanical characteristics.
3. A finite element analysis of contact characteristics of the talus articular surface on gait: according the outcome of the finite element model, the contact pressure, contact area, and the von Mises stress of articular cartilage were researched to study the contact characteristics of articular surface of the talus.
4. A finite element analysis of biomechanical stability of talar neck fracture fixed with screws. One normal ankle of an adult volunteer was scanned (multi-slices computerized tomography, intervals 0.45 millimeters) in the neutral unloaded position. All the slices were saved in the format of the DICOM (Digital Imaging and Communications in Medicine). Then these 2D-CT slices were imported into the three-dimensional reconstruction software of Mimics10.01 (Materialise's Interactive Medical Image Control System). From this data, a three-dimensional image about ankle was reconstructed with the software. Outcome was saved in the format of STL. Then the STL data was imported to Geomagic studio 10.0 software to smooth and build talar neck fracture model. Simulation of talar neck fracture was achieved by an idealized planar cut between the bone segments in the neck. Then the model was fixed surface. Finally, the surface was imported and screwed in UG software to form the solid model. The size of the screw was consulted from AO/ASIF. The outside diameter was 4.0mm, the inside was 2.9mm. The length was changed according to the actually situation. The screw model was constructed in UG software. Given the complex geometry of the screws, they were modeled as simple cylinders and the thread ignored. The solid models were then imported into Hypermesh10.0 software. Then the models were assembled, meshed and given material parameter. Corresponding to the quantity and location of screws, four different finite element models of surgical fixation methods were developed: anterior-to-posterior fixation using one 4.0 mm screw, posterior-to-anterior fixation using one 4.0 mm screw, anterior-to-posterior fixation using two 4.0 mm screws, posterior-to-anterior fixation using two 4.0 mm screws. Finally, the finite element models were imported into the FE package ANSYS (ANSYS Inc., USA) for post-processing. The von Mises stress, contact area and pressure, contact gap were compared to estimate the biomechanical stability.
5. The changes of biomechanics of the talus after ankle ligament injury:a finite element model of ankle ligament injury was constructed, that was simulated the injury of anterior talofibular ligament, calcaneofibular ligament, posterior talofibular ligament, anterior tibiotalar ligament, tibiocalcaneal ligament, posterior tibiotalar ligament, tibionavicular ligament. The injury models were loaded and post-processing. The stress and strain of the talus were researched to analysis the changes of talus biomechanics under inversion and eversion load. The result provides theory instruction for ligament repair in clinics.
Results
1. A serial precise of data of DICOM was obtained from CT scan for ankle. Using Mimics10.0, Geomagic studio10.0 and UG software, a geometric reconstruction of the ankle was developed using the data. The model has the precise structure.
2. The model was meshed and given the material properties in Hypermesh10.0 software. Finally, the model was imported to ABAQUS6.9. A three-dimensional finite element model of ankle was established, which composed of 21865 nodes,73440 elements. And the stress distribution within the bone was obtained at three phases. The stress distributions of three phases were significantly different. The peak von Mises stress from the heel-strike to push-off on the talar dome was 3.0 MPa,4.3 MPa and 4.8 MPa respectively. It was 1.3 MPa,1.9 MPa and 2.8 MPa on talar neck, and 2.8 MPa,3.0 MPa,3.4 MPa on the talonavicular joint surface. It was 2.2 MPa,1.8 MPa and 1.5 MPa on subtalar joint. The von Mises stress and distribution scope were difference in different phase. The von Mises stress in the talar dome, talar neck, talonavicular joint surface gradually increased, and decreased in the subtalar joint.
3. The contact pressure gradually increased in talar dome cartilage from the heel-strike to push-off. The contact pressure was 5.6,8.8 and 11.8MPa. The contact pressure distributed on the posterior medial side in the heel-strike, anterior and lateral in mid-stance, lateral and anterior-medial side. The contact pressure was distributed on medial metatarsus in talonavicular joint surface. The contact pressure was 7.8,8.6 and 8.1 MPa respectively. It was higher in mid-stance. The contact pressure was 4.5, 4.7 and 4.0 MPa in the posterior subtalar joint. The distribution of von Mises stress on talus articular cartilage was similar to contact pressure. It increased in talar dome and talonavicular joint articular cartilage and decreased in the posterior subtalar joint.
4. Analysis the biomechanical behaviors of the talar neck fracture with four different fixations using finite element analysis. The distribution of von Mises stress was uneven on fixation. The values of maximum von Mises stress on screws were observed near the fracture location at each fixation. It was observed from these figures that the 2-AP experience has a low von Mises stress in mid-stance loading conditions. A similar behavior was observed in active dorsiflexion. It was 14 062MPa on neutral position, and 32.012 MPa on ankle active dorsiflexion. It was noticed that the fracture surface pressure mainly in the lateral talar neck at mid-stance,2-AP had the greatest pressure for 7.041 MPa. At the ankle dorsiflexion, the pressure concentrated in the medial,2-AP was higher than the others, as 9.165 MPa. The contact areas were of equal approximately in four fixations. The largest fracture gap in every fixation was in the plantar medial of fracture surface.1-AP had the maximum fracture gap under two loading conditions.2-AP was lowest.
5. Under the internal rotation load, there was no strain/stress in posterior tibiofibular ligament, anterior talofibular ligament and posterior tibiotalar ligament. The stress in calcaneofibular ligament was higher, as 18.91 MPa. Under the external rotation load, there was no strain/stress in posterior talofibular ligament, calcaneofibular ligament, anterior tibiotalar ligament and tibionavicular ligament. The stress in anterior talofibular ligament was biggest, as 13.75 MPa. Under internal rotation, after anterior talofibular ligament injury, the von Mises peak stress was 8.56 MPa on talar dome,6.43 MPa on posterior subtalar joint,2.87 MPa on anterior subtalar joint, and 7.31 MPa on talonavicular joint. The maximum displacement was located in the posterior talus, as 1.21mm. With calcaneofibular ligament injury, the von Mises, peak stress was 9.29 MPa on talar dome,7.19 MPa on posterior subtalar joint,3.49 MPa on anterior subtalar joint, and 6.69 MPa on talonavicular joint. The maximum displacement was located in the posterior talus, as 1.72mm. With posterior talofibular injury, the von Mises peak stress was 8.86 MPa on talar dome,6.88 MPa on posterior subtalar joint,1.85 MPa on anterior subtalar joint, and 7.39 MPa on talonavicular joint. The maximum displacement was located in the posterior talus, as 1.09mm. Under the load of external rotation, the changes of von Mises and displacement was similar in anterior tibiotalar ligament, tibionavicular ligament and tibiocalcaneal ligament injury. The von Mises peak stress was 5.79 MPa on talar dome,4.91 MPa on posterior subtalar joint,1.71 MPa on anterior subtalar joint, and 6.88 MPa on talonavicular joint. The maximum displacement was located in lateral of talus body and head, as 0.63mm. With the injury of posterior tibiotalar ligament, the von Mises peak stress was 6.24 MPa on talar dome,5.23 MPa on posterior subtalar joint,1.41 MPa on anterior subtalar joint, and 6.67 MPa on talonavicular joint. The maximum displacement was located in lateral of talus body and head, as 0.72mm.
Conclusions
1. Based on CT scan data, the talus three-dimensional digital simulation models were established using Mimics, Geomagic Studio, and UG software. This approach was feasible, effective, faster and harmless to the human body. The model contained a large amount of information and entities with a similar geometry to the more realistic simulation of the original model.
2. The three-dimensional finite element method was a biomechanical study of theories and methods to simulate the geometric model of the structure to give organizations the biological material properties. It can reflect the biomechanical properties of the overall trend, which can be used as a very good supplement for experimental specimen biomechanical study. In this study, according to the actual geometry of the skeleton, which was obtained from 3D reconstruction of computed tomography, a three-dimensional (3D) finite element model was developed using Mimics, Geomagic Studio, Hypermesh, ABAQUS software. The finite element model of had a good geometric similarity. Compared with similar studies reported in the literature, the model had the more refined and uniform grid, the greater the cell density and more accurate results. Furthermore, this model can be disassembled, with great flexibility in the choice of subjects; it can be built on the foot bones of various independent study to further expand the scope of application of the model. In addition, as a whole, compared with the anatomical structure, pathophysiology, clinical research literature, and many other biomechanical researches, it indicated that this model had good physical similarity, more accurate and complete to simulate the anatomy of the talus and its mechanical characteristics. It was beneficial for biomechanical analysis of the talus.
3. The articular surface contact stress and area distribution on talus were important to the clinical research. The abnormal mechanical mechanism on cartilage was a major cause of osteoarthritis. Knowledge for the characteristics of mechanic distribution on cartilage will help to understand the mechanism of the normal talus articular cartilage and behavior of articular cartilage pathology under abnormal load.
4. Finite element analysis is a useful tool for the analysis mechanical behavior of implants in fractures of bone, which can provide an experimental basis for effective fixation. Stress distribution within the implant itself and the displacement of fracture section were a standard measure of internal fixation. Internal fixation should be the ideal uniform distribution of stress as possible on the fixture, but not overly concentrated in certain parts. High stress will inevitably lead to high fracture strain, from the point of fracture healing view, this high strain was not conducive to the growth in fracture callus. One of the measures to verify the stability was to check the bone contact status at the fracture interface surface; the two factors were contact pressure and fracture gap at the fracture site. Larger contact area and the right pressure can increase the static friction between the fracture sites, reducing the fracture site clearance; increase the stiffness of fracture fixation. Talar neck fractures by double screws from front to back fixed and reliable access to the biomechanical stability.
5. The injury of ankle ligament had a major impact on the stability of the talus, which will inevitably change the location of the talus in the ankle mortise, thus affecting the contact area and stress. It will lead to articular cartilage degeneration, eventually lead to osteoarthritis. In external rotation force, the injury of the posterior tibiotalar ligament, the von Mises stress, displacement and contact pressure was high. It was suggested that posterior tibiotalar ligament played an important role for ankle stability under external rotation force. Including the effect of rotation, with the ligament injury, the talus of the equivalent stress and the displacement of large, suggesting that spin with the ligament under the circumstances, including the stability of the ankle joint plays an important role. In internal rotation force, the injury of calcaneofibular ligament, the von Mises stress, displacement and contact pressure was high. It was suggested that calcaneofibular ligament played an important role for ankle stability under internal rotation force.
6. The limitation of this study was that mechanical characteristics of biological materials involved in this study were assumed to be homogeneous, continuous and isotropic. Actually, bone, cartilage and ligaments material itself were not homogeneous, continuous, nor was isotropic, but anisotropy. The characteristic of soft tissue around the ankle has not considered the impact of the model.
引文
[1]钟世镇.虚拟人体将为创伤骨科研究提供新技术[J].中华创伤骨科杂志,2003,5(02)：81-84.
[2]钟世镇.从数字人到数字医学[J].医学研究杂志,2009,38(08)：1-2.
[3]徐遄,吴勇,贾克斌,等.数字医学影像与通信的重要标准—Dicom标准[J]. 中国医学影像技术,2002,18(09)：952-54.
[4]傅征.数字医学的提出与发展[J].中国数字医学,2007,2(11)：9-13.
[5]张绍祥.数字化人体与数字医学的研究概况及发展趋势[J].第三军医大学学报,2009,31(01)：1-2.
[6]Jacob S, M. K. Patil. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. J Rehabil Res Dev,1999,36(3):252-63.
[7]Wu L. JS. Z ZhongR. M Zheng, et al. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus[J]. Surg Radiol Anat,2007,29:561-67.
[8]Wu L. J. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures[J]. Clin Biomech 2007,22(2):221-29.
[9]王剑利.足骨三维有限元模型对足跖骨缺损重建的指导意义[J].实用手外科杂志,2007,21(1)：6-8.
[10]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[11]Chen W. M, T Lee, P. V. S Lee, et al. Effects of internal stress concentrations in plantar soft-tissue-A preliminary three-dimensional finite element analysis[J]. Med Eng Phys,2010,32(4):324-31.
[12]罗之军,何彪.基于Geomagic Studio的逆向工程技术[J].贵州工业大学学报(自然科学版),2008,38(05)：102-04.
[13]李燕,黄凯.基于Geomagic的三维人体建模技术[J].纺织学报,2008,29(05)：130-34.
[14]胡影峰.Geomagic Studio软件在逆向工程后处理中的应用[J].制造业自动化,2009,31(09)：135-37.
[15]李华才.开创数字医学研究与实践新纪元[J].中国数字医学,2008,1(05)：1.
[1]Sangeorzan B. J, U. A Wagner, R. M Harrington, et al. Contact characteristics of the subtalar joint:the effect of talar neck misalignment[J]. J Orthop Res,1992, 10(4):544-51.
[2]Daniels T. R, J. W Smith, T. I. Ross. Varus malalignment of the talar neck-Its effect on the position of the foot and on subtalar motion[J]. J Bone Joint Surg [Am],1996,78A(10):1559-67.
[3]陶凯,王冬梅,王成焘,等.基于三维有限元静态分析的人体足部生物力学研究[J].中国生物医学工程学报,2007,26(05)：763-66.
[4]张明,张德文,余嘉,等.足部三维有限元建模方法及其生物力学应用[J].医用生物力学,2007,22(04)：339-44.
[5]王旭,马听,陶凯,等.足踝有限元模型的建立与初步临床应用[J].中国生物医学工程学报,2008,27(02)：287-91.
[6]Golano P, J Vega, P. A. J Leeuw, et al. Anatomy of the ankle ligaments:a pictorial essay[J]. Knee Surg Sports Tr A,2010,18(5):557-69.
[7]Reggiani B, A Leardini, F Corazza, et al. Finite element analysis of a total ankle replacement during the stance phase of gait[J]. J Biomech,2006,39(8):1435-43.
[8]Jacob S, M. K. Patil. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. J Rehabil Res Dev,1999,36(3):252-63.
[9]Cheung J. T. M, M Zhang, A. K. L Leung, et al. Three-dimensional finite element analysis of the foot during standing - a material sensitivity study[J]. J Biomech, 2005,38(5):1045-54.
[10]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait: A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[11]Corazza F, J. J O'connor, A Leardini, et al. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint[J]. J Biomech,2003, 36(3):363-72.
[12]Funk J. R, G. W Hall, J. R Crandall, et al. Linear and quasi-linear viscoelastic characterization of ankle ligaments[J]. J Biomech Eng-T Asme,2000, 122(1):15-22.
[13]Frigg A, R Frigg, B Hintermann, et al. The biomechanical influence of tibio-talar containment on stability of the ankle joint[J]. Knee Surg Sports Tr A,2007, 15:1355-62.
[14]Bottlang M, J. L Marsh, T. D. Brown. Articulated external fixation of the ankle: minimizing motion resistance by accurate axis alignment[J]. J Biomech,1999, 32(1):63-70.
[15]Anderson D. D, J. K Goldsworthy, K Shivanna, et al. Intra-articular contact stress distributions at the ankle throughout stance phase-patient-specific finite element analysis as a metric of degeneration propensity[J]. Biomech Model Mechan,2006,5(2-3):82-89.
[16]Giddings Virginia L, Gary S Beaupre, Robert T Whalen, et al. Calcaneal loading during walking and running[J]. Med Sci Sport Exer,2000,32(3):627-34.
[17]Suckel A, O Muller, N Wachter, et al. In vitro measurement of intraarticular pressure in the ankle joint[J]. Knee Surg Sports Tr A,2010,18(5):664-68.
[18]Anderson D. D, J. K Goldsworthy, W Li, et al. Physical validation of a patient-specific contact finite element model of the ankle[J]. J Biomech,2007, 40(8):1662-69.
[19]Hurschler C, J Emmerich, N. Wulker. In vitro simulation of stance phase gait-Part Ⅰ: Model verification[J]. Foot Ankle Int,2003,24(8):614-22.
[20]Brekelmans W. A, H. W Poort, T. J. Slooff. A new method to analyse the mechanical behaviour of skeletal parts[J]. Acta Orthop Scand,1972, 43(5):301-17.
[21]Li L. P, J. T. M Cheung, W Herzog. Three-dimensional fibril-reinforced finite element model of articular cartilage[J]. Med Biol Eng Comput,2009, 47(6):607-15.
[22]杨云峰,俞光荣,牛文鑫,等.人体足主要骨-韧带结构三维有限元模型的建立及分析[J].中国运动医学杂志,2007,26(05)：542-46.
[23]Matricali G. A, W Bartels, L Labey, et al. High inter-specimen variability of baseline data for the tibio-talar contact area[J]. Clin Biomech,2009, 24(1):117-20.
[24]刘立峰,蔡锦方.不同步态位相跟、距骨应力分布的三维有限元分析[J].第二军医大学学报,2003,24(9)：1006-08.
[1]Wan L, R. J De Asia, H. E Rubash, et al. In vivo cartilage contact deformation of human ankle joints under full body weight[J]. J Orthop Res,2008,26(8):1081-89.
[2]Kimizuka M, H Kurosawa, T. Fukubayashi. Load-Bearing Pattern of The Ankle Joint-Contact Area and Pressure[J]. Arch Orthop Traum Su,1980,96(1):45-49.
[3]Bertsch C, D Rosenbaum, L. Claes. Intra-articular and plantar pressure distribution of the ankle joint complex in relation to foot position[J]. Unfallchirurg,2001,104(5):426-33.
[4]Michelson J. D, M Checcone, T Kuhn, et al. Intra-articular load distribution in the human ankle joint during motion[J]. Foot Ankle Int,2001,22(3):226-33.
[5]Matricali G. A, W Bartels, L Labey, et al. High inter-specimen variability of baseline data for the tibio-talar contact area[J]. Clin Biomech,2009, 24(1):117-20.
[6]Suckel A, O Muller, N Wachter, et al. In vitro measurement of intraarticular pressure in the ankle joint[J]. Knee Surg Sports Tr A,2010,18(5):664-68.
[7]Goldring Mary B, Steven R. Goldring, Articular cartilage and subchondral bone in the pathogenesis of osteoarthritis, in Skeletal Biology and Medicine, M. Zaidi, Editor.2010, Blackwell Publishing. p.230-37.
[8]Hwang Jennifer, Won C Bae, Wendy Shieu, et al. Increased hydraulic conductance of human articular cartilage and subchondral bone plate with progression of osteoarthritis[J]. Arthritis Rheum,2008,58(12):3831-42.
[9]Katta J, Z. M Jin, E Ingham, et al. Biotribology of articular cartilage-A review of the recent advances[J]. Med Eng Phys,2008,30(10):1349-63.
[10]Wan L, R. J De Asla, H. E Rubash, et al. Determination of in-vivo articular cartilage contact areas of human talocrural joint under weightbearing conditions[J]. Osteoarthritis and Cartilage,2006,14(12):1294-301.
[11]Wang C. L, C. K Cheng, C. W Chen, et al. Contact areas and pressure distributions in the subtalar joint[J]. J Biomech,1995,28(3):269-79.
[12]Anderson D. D, J. K Goldsworthy, K Shivanna, et al. Intra-articular contact stress distributions at the ankle throughout stance phase-patient-specific finite element analysis as a metric of degeneration propensity[J]. Biomech Model Mechan,2006,5(2-3):82-89.
[1]Archdeacon M, R. Wilber. Fractures of the talar neck[J]. Orthopedic Clinics of North America,2002,33(1):247-62.
[2]Sangeorzan B. J, U. A Wagner, R. M Harrington, et al. Contact characteristics of the subtalar joint: the effect of talar neck misalignment[J]. J Orthop Res,1992, 10(4):544-51.
[3]Wolff Julius. The classic:on the theory of fracture healing.1873[J]. Clin Orthop Relat Res,2010,468(4):1052-5.
[4]Cheung J. T. M, M Zhang, A. K. L Leung, et al. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study[J]. J Biomech, 2005,38(5):1045-54.
[5]Sowmianarayanan S, A Chandrasekaran, R. Krishna. Kumar. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants--a comparative study[J]. Proc Inst Mech Eng H,2008,222(1):117-27.
[6]Jacob S, M. K. Patil. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. J Rehabil Res Dev,1999,36(3):252-63.
[7]刘立峰,蔡锦方.不同步态位相跟、距骨应力分布的三维有限元分析[J].第二军医大学学报,2003,24(9)：1006-08.
[8]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[9]Rammelt S, H. Zwipp. Talar neck and body fractures[J]. Injury,2009, 40(2):120-35.
[10]Klein Petra, Hanna Schell, Florian Streitparth, et al. The initial phase of fracture healing is specifically sensitive to mechanical conditions [J]. J Orthop Res,2003, 21(4):662-69.
[11]Swanson T. V, T. J Bray, G. B. Holmes. Fracture of the talar neck-a mechanical study of fixation[J]. J Bone Joint Surg [Am],1992,74A(4):544-51.
[12]Attiah M, D. W Sanders, G Valdivia, et al. Comminuted talar neck fractures:A mechanical comparison of fixation techniques[J]. J OrthopTrauma,2007, 21(1):47-51.
[1]Ferran Nicholas A, Francesco Oliva, Nicola Maffulli. Ankle instability [J]. Sports Med Arthrosc,2009,17(2):139-45.
[2]Windisch G, B Odehnal, R Reimann, et al. Contact areas of the tibiotalar joint[J]. Journal of Orthop Res,2007,25:1481-87.
[3]Wan L, R. J De Asia, H. E Rubash, et al. In vivo cartilage contact deformation of human ankle joints under full body weight[J]. J Orthop Res,2008,26(8):1081-89.
[4]Caputo Adam M, Jun Y Lee, Chuck E Spritzer, et al. In Vivo Kinematics of the Tibiotalar Joint After Lateral Ankle Instability[J]. Am J Sports Med,2009, 37(11):2241-48.
[5]Earll M, J Wayne, C Brodrick, et al. Contribution of the deltoid ligament to ankle joint contact characteristics:a cadaver study[J]. Foot Ankle Int,1996, 17(6):317-24.
[6]Michelson J. D. Fractures about the ankle[J]. J Bone Joint Surg Am,1995, 77(1):142-52.
[7]梁庆威,范广宇,吕刚.踝部骨折的治疗及距骨生物力学观察[J].中华骨科杂志,1998,18(05)：290-92.
[8]Beals T. C, J Crim, F. Nickisch. Deltoid Ligament Injuries in Athletes:Techniques of Repair and Reconstruction[J]. Oper Techn Sport Med,2010,18(1):11-17.
[9]Bahr R, F Pena, J Shine, et al. Biomechanics of ankle ligament reconstruction. An in vitro comparison of the Brostrom repair, Watson-Jones reconstruction, and a new anatomic reconstruction technique[J]. Am J Sports Med,1997,25(4):424-32.
[10]Boss A. P., B. Hintermann. Anatomical study of the medial ankle ligament complex[J]. Foot Ankle Int,2002,23(6):547-53.
[11]Milner C. E, R. W. Soames. The medial collateral ligaments of the human ankle joint:Anatomical variations[J]. Foot Ankle Int,1998,19(5):289-92.
[12]Leardini A, J. J O'connor, F Catani, et al. The role of the passive structures in the mobility and stability of the human ankle joint: A literature review[J]. Foot Ankle Int,2000,21(7):602-15.
[13]Rasmussen O. Stability of the ankle joint. Analysis of the function and traumatology of the ankle ligaments[J]. Acta Orthop Scand Suppl,1985, 211:1-75.
[14]Weindel S, R Schmidt, S Rammelt, et al. Subtalar instability:a biomechanical cadaver study [J]. Arch Orthop Traum Su,2010,130(3):313-19.
[15]Hintermann B, C Sommer, B. M. Nigg. Influence of ligament transection on tibial and calcaneal rotation with loading and dorsi-plantarflexion[J]. Foot Ankle Int,1995,16(9):567-71.
[1]Brekelmans W. A, H. W Poort, T. J. Slooff. A new method to analyse the mechanical behaviour of skeletal parts[J]. Acta Orthop Scand,1972, 43(5):301-17.
[2]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait: A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[3]Mesfar W, A. Shirazi-Adl. Computational biomechanics of knee joint in open kinetic chain extension exercises[J]. Comput Method Biomec,2008,11(1):55-61.
[4]Moore D. C, K. A Hogan, J. J Crisco, et al. Three-dimensional in vivo kinematics of the distal radioulnar joint in malunited distal radius fractures[J]. Journal of Hand Surgery-American Volume,2002,27A(2):233-42.
[5]Sowmianarayanan S, A Chandrasekaran, R. Krishna. Kumar. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants--a comparative study[J]. Proc Inst Mech Eng H,2008,222(1):117-27.
[6]Chen W. M, T Lee, P. V. S Lee, et al. Effects of internal stress concentrations in plantar soft-tissue-A preliminary three-dimensional finite element analysis[J]. Med Eng Phys,2010,32(4):324-31.
[7]Paul J. P. Three-dimensional finite element stress analysis of the polypropylene ankle-foot orthoses:Static analysis[J]. Med Eng Phys,1996,18(7):607-07.
[8]Saunders Mamie M, Edwards P Schwentker, David B Kay, et al. Finite element analysis as a tool for parametric prosthetic foot design and evaluation. Technique development in the solid ankle cushioned heel (SACH) foot[J]. Comput Method Biomec,2003,6(1):75-87.
[9]Syngellakis S, M. A Arnold, H. Rassoulian. Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method[J]. Proceedings of the Institution of Mechanical Engineers Part H-Journal of Engineering in Medicine,2000,214(H5):527-39.
[10]Patil K. M, L. H Braak, A. Huson. Analysis of stresses in two-dimensional models of normal and neuropathic feet[J]. Med Biol Eng Comput,1996, 34(4):280-84.
[11]Giddings Virginia L, Gary S Beaupre, Robert T Whalen, et al. Calcaneal loading during walking and running[J]. Med Sci Sport Exer,2000,32(3):627-34.
[12]Garcia-Aznar J. M, J Bayod, A Rosas, et al. Load transfer mechanism for different metatarsal geometries:a finite element study[J]. J Biomech Eng,2009, 131(2):021011.
[13]刘立峰,蔡锦方.不同步态位相跟、距骨应力分布的三维有限元分析[J].第二军医大学学报,2003,24(9)：1006-08.
[14]Wu L. J. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures[J]. Clin Biomech 2007,22(2):221-29.
[15]Wu L. JS. Z ZhongR. M Zheng, et al. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus[J]. Surg Radiol Anat,2007,29:561-67.
[16]杨璇.手法复位先天性马蹄内翻足过程中的力学变化[J].临床骨科杂志,2010,13(3)：323-26.
[17]刘立峰,蔡锦方,梁进.跟骨骨折内固定方法的有限元模拟比较[J].中国矫形外科杂志,2003,11(08)：557-58.
[18]Reggiani B, A Leardini, F Corazza, et al. Finite element analysis of a total ankle replacement during the stance phase of gait[J]. J Biomech,2006,39(8):1435-43.
[19]Espinosa N, M Walti, P Favre, et al. Misalignment of Total Ankle Components Can Induce High Joint Contact Pressures[J]. J Bone Joint Surg [Am],2010, 92A(5):1179-87.
[20]Lee Jun Young, Yeon Soo Lee. Optimal double screw configuration for subtalar arthrodesis: a finite element analysis[J]. Knee Surg Sports Traumatol Arthrosc, 2011,19(5):842-9.
[21]Alonso-Vazquez Ana, Henrik Lauge-Pedersen, Lars Lidgren, et al. The effect of bone quality on the stability of ankle arthrodesis. A finite element study[J]. Foot Ankle Int,2004,25(11):840-50.
[22]Nakamura S., R. D. Crowninshield, R. R. Cooper. An analysis of soft tissue loading in the foot-a preliminary report[J]. Bull Prosthet Res,1981,10-35:27-34.
[23]Scott S. H, D. A. Winter. Biomechanical model of the human foot: kinematics and kinetics during the stance phase of walking[J]. J Biomech,1993, 26(9):1091-104.
[24]Garcia-Gonzalez A, J Bayod, U. C Prados-Frutos, et al. Finite-element simulation of flexor digitorum longus or flexor digitorum brevis tendon transfer for the treatment of claw toe deformity [J]. J Biomech,2009,42(11):1697-704.
[25]顾耀东.基于踏跳阶段跟腱的有限元分析[J].体育科研,2007,28(1)：62-64.
[26]牛文鑫,杨云峰,俞光荣,等.人体足部三维有限元模型的有效构建方法及其合理性的实验分析研究[J].生物医学工程学杂志,2009,26(1)：80-84.
[27]陶凯,王冬梅,王成焘,等.韧带和跖腱膜在足部有限元分析中的力学作用[J].生物医学工程学杂志,2008,25(02)：336-40.
[28]Chu T. M, N. P Reddy, J. Padovan. Three-dimensional finite element stress analysis of the polypropylene, ankle-foot orthosis:static analysis [J]. Med Eng Phys,1995,17(5):372-79.
[29]Yu J, J. T. M Cheung, Y. B Fan, et al. Development of a finite element model of female foot for high-heeled shoe design[J]. Clin Biomech 2008,23:S31-S38.
[30]张明,张德文,余嘉,等.足部三维有限元建模方法及其生物力学应用[J].医用生物力学,2007,22(04)：339-44.
[31]孙卫东,温建民.足部有限元建模方法应用现状[J].中国组织工程研究与临床康复,2010,74(13)：2458-61.
[32]Yc. Funq. Biomechanics-mechanical properties of living tissues[J]. Springer, 1993,2th Ed.
[33]Funk J. R, G. W Hall, J. R Crandall, et al. Linear and quasi-linear viscoelastic characterization of ankle ligaments[J]. J Biomech Eng-T Asme,2000, 122(1):15-22.
[34]Jia X. H, M Zhang, X. B Li, et al. A quasi-dynamic nonlinear finite element model to investigate prosthetic interface stresses during walking for trans-tibial amputees[J]. Clin Biomech 2005,20(6):630-35.
[35]Duerr Hans R, Heiner Martin, Christoph Pellengahr, et al. The cause of subchondral bone cysts in osteoarthrosis - A finite element analysis [J]. Acta Orthop Scand,2004,75(5):554-58.
[36]Li L. P, J. T. M Cheung, W Herzog. Three-dimensional fibril-reinforced finite element model of articular cartilage[J]. Med Biol Eng Comput,2009, 47(6):607-15.
[37]Susilo Monica E, Blayne A Roeder, Sherry L Voytik-Harbin, et al. Development of a three-dimensional unit cell to model the micromechanical response of a collagen-based extracellular matrix[J]. Acta Biomater,2010,6(4):1471-86.
[2]钟世镇.从数字人到数字医学[J].医学研究杂志,2009,38(08)：1-2.
[3]徐遄,吴勇,贾克斌,等.数字医学影像与通信的重要标准—Dicom标准[J]. 中国医学影像技术,2002,18(09)：952-54.
[4]傅征.数字医学的提出与发展[J].中国数字医学,2007,2(11)：9-13.
[5]张绍祥.数字化人体与数字医学的研究概况及发展趋势[J].第三军医大学学报,2009,31(01)：1-2.
[6]Jacob S, M. K. Patil. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. J Rehabil Res Dev,1999,36(3):252-63.
[7]Wu L. JS. Z ZhongR. M Zheng, et al. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus[J]. Surg Radiol Anat,2007,29:561-67.
[8]Wu L. J. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures[J]. Clin Biomech 2007,22(2):221-29.
[9]王剑利.足骨三维有限元模型对足跖骨缺损重建的指导意义[J].实用手外科杂志,2007,21(1)：6-8.
[10]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[11]Chen W. M, T Lee, P. V. S Lee, et al. Effects of internal stress concentrations in plantar soft-tissue-A preliminary three-dimensional finite element analysis[J]. Med Eng Phys,2010,32(4):324-31.
[12]罗之军,何彪.基于Geomagic Studio的逆向工程技术[J].贵州工业大学学报(自然科学版),2008,38(05)：102-04.
[13]李燕,黄凯.基于Geomagic的三维人体建模技术[J].纺织学报,2008,29(05)：130-34.
[14]胡影峰.Geomagic Studio软件在逆向工程后处理中的应用[J].制造业自动化,2009,31(09)：135-37.
[15]李华才.开创数字医学研究与实践新纪元[J].中国数字医学,2008,1(05)：1.
[1]Sangeorzan B. J, U. A Wagner, R. M Harrington, et al. Contact characteristics of the subtalar joint:the effect of talar neck misalignment[J]. J Orthop Res,1992, 10(4):544-51.
[2]Daniels T. R, J. W Smith, T. I. Ross. Varus malalignment of the talar neck-Its effect on the position of the foot and on subtalar motion[J]. J Bone Joint Surg [Am],1996,78A(10):1559-67.
[3]陶凯,王冬梅,王成焘,等.基于三维有限元静态分析的人体足部生物力学研究[J].中国生物医学工程学报,2007,26(05)：763-66.
[4]张明,张德文,余嘉,等.足部三维有限元建模方法及其生物力学应用[J].医用生物力学,2007,22(04)：339-44.
[5]王旭,马听,陶凯,等.足踝有限元模型的建立与初步临床应用[J].中国生物医学工程学报,2008,27(02)：287-91.
[6]Golano P, J Vega, P. A. J Leeuw, et al. Anatomy of the ankle ligaments:a pictorial essay[J]. Knee Surg Sports Tr A,2010,18(5):557-69.
[7]Reggiani B, A Leardini, F Corazza, et al. Finite element analysis of a total ankle replacement during the stance phase of gait[J]. J Biomech,2006,39(8):1435-43.
[8]Jacob S, M. K. Patil. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. J Rehabil Res Dev,1999,36(3):252-63.
[9]Cheung J. T. M, M Zhang, A. K. L Leung, et al. Three-dimensional finite element analysis of the foot during standing - a material sensitivity study[J]. J Biomech, 2005,38(5):1045-54.
[10]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait: A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[11]Corazza F, J. J O'connor, A Leardini, et al. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint[J]. J Biomech,2003, 36(3):363-72.
[12]Funk J. R, G. W Hall, J. R Crandall, et al. Linear and quasi-linear viscoelastic characterization of ankle ligaments[J]. J Biomech Eng-T Asme,2000, 122(1):15-22.
[13]Frigg A, R Frigg, B Hintermann, et al. The biomechanical influence of tibio-talar containment on stability of the ankle joint[J]. Knee Surg Sports Tr A,2007, 15:1355-62.
[14]Bottlang M, J. L Marsh, T. D. Brown. Articulated external fixation of the ankle: minimizing motion resistance by accurate axis alignment[J]. J Biomech,1999, 32(1):63-70.
[15]Anderson D. D, J. K Goldsworthy, K Shivanna, et al. Intra-articular contact stress distributions at the ankle throughout stance phase-patient-specific finite element analysis as a metric of degeneration propensity[J]. Biomech Model Mechan,2006,5(2-3):82-89.
[16]Giddings Virginia L, Gary S Beaupre, Robert T Whalen, et al. Calcaneal loading during walking and running[J]. Med Sci Sport Exer,2000,32(3):627-34.
[17]Suckel A, O Muller, N Wachter, et al. In vitro measurement of intraarticular pressure in the ankle joint[J]. Knee Surg Sports Tr A,2010,18(5):664-68.
[18]Anderson D. D, J. K Goldsworthy, W Li, et al. Physical validation of a patient-specific contact finite element model of the ankle[J]. J Biomech,2007, 40(8):1662-69.
[19]Hurschler C, J Emmerich, N. Wulker. In vitro simulation of stance phase gait-Part Ⅰ: Model verification[J]. Foot Ankle Int,2003,24(8):614-22.
[20]Brekelmans W. A, H. W Poort, T. J. Slooff. A new method to analyse the mechanical behaviour of skeletal parts[J]. Acta Orthop Scand,1972, 43(5):301-17.
[21]Li L. P, J. T. M Cheung, W Herzog. Three-dimensional fibril-reinforced finite element model of articular cartilage[J]. Med Biol Eng Comput,2009, 47(6):607-15.
[22]杨云峰,俞光荣,牛文鑫,等.人体足主要骨-韧带结构三维有限元模型的建立及分析[J].中国运动医学杂志,2007,26(05)：542-46.
[23]Matricali G. A, W Bartels, L Labey, et al. High inter-specimen variability of baseline data for the tibio-talar contact area[J]. Clin Biomech,2009, 24(1):117-20.
[24]刘立峰,蔡锦方.不同步态位相跟、距骨应力分布的三维有限元分析[J].第二军医大学学报,2003,24(9)：1006-08.
[1]Wan L, R. J De Asia, H. E Rubash, et al. In vivo cartilage contact deformation of human ankle joints under full body weight[J]. J Orthop Res,2008,26(8):1081-89.
[2]Kimizuka M, H Kurosawa, T. Fukubayashi. Load-Bearing Pattern of The Ankle Joint-Contact Area and Pressure[J]. Arch Orthop Traum Su,1980,96(1):45-49.
[3]Bertsch C, D Rosenbaum, L. Claes. Intra-articular and plantar pressure distribution of the ankle joint complex in relation to foot position[J]. Unfallchirurg,2001,104(5):426-33.
[4]Michelson J. D, M Checcone, T Kuhn, et al. Intra-articular load distribution in the human ankle joint during motion[J]. Foot Ankle Int,2001,22(3):226-33.
[5]Matricali G. A, W Bartels, L Labey, et al. High inter-specimen variability of baseline data for the tibio-talar contact area[J]. Clin Biomech,2009, 24(1):117-20.
[6]Suckel A, O Muller, N Wachter, et al. In vitro measurement of intraarticular pressure in the ankle joint[J]. Knee Surg Sports Tr A,2010,18(5):664-68.
[7]Goldring Mary B, Steven R. Goldring, Articular cartilage and subchondral bone in the pathogenesis of osteoarthritis, in Skeletal Biology and Medicine, M. Zaidi, Editor.2010, Blackwell Publishing. p.230-37.
[8]Hwang Jennifer, Won C Bae, Wendy Shieu, et al. Increased hydraulic conductance of human articular cartilage and subchondral bone plate with progression of osteoarthritis[J]. Arthritis Rheum,2008,58(12):3831-42.
[9]Katta J, Z. M Jin, E Ingham, et al. Biotribology of articular cartilage-A review of the recent advances[J]. Med Eng Phys,2008,30(10):1349-63.
[10]Wan L, R. J De Asla, H. E Rubash, et al. Determination of in-vivo articular cartilage contact areas of human talocrural joint under weightbearing conditions[J]. Osteoarthritis and Cartilage,2006,14(12):1294-301.
[11]Wang C. L, C. K Cheng, C. W Chen, et al. Contact areas and pressure distributions in the subtalar joint[J]. J Biomech,1995,28(3):269-79.
[12]Anderson D. D, J. K Goldsworthy, K Shivanna, et al. Intra-articular contact stress distributions at the ankle throughout stance phase-patient-specific finite element analysis as a metric of degeneration propensity[J]. Biomech Model Mechan,2006,5(2-3):82-89.
[1]Archdeacon M, R. Wilber. Fractures of the talar neck[J]. Orthopedic Clinics of North America,2002,33(1):247-62.
[2]Sangeorzan B. J, U. A Wagner, R. M Harrington, et al. Contact characteristics of the subtalar joint: the effect of talar neck misalignment[J]. J Orthop Res,1992, 10(4):544-51.
[3]Wolff Julius. The classic:on the theory of fracture healing.1873[J]. Clin Orthop Relat Res,2010,468(4):1052-5.
[4]Cheung J. T. M, M Zhang, A. K. L Leung, et al. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study[J]. J Biomech, 2005,38(5):1045-54.
[5]Sowmianarayanan S, A Chandrasekaran, R. Krishna. Kumar. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants--a comparative study[J]. Proc Inst Mech Eng H,2008,222(1):117-27.
[6]Jacob S, M. K. Patil. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis[J]. J Rehabil Res Dev,1999,36(3):252-63.
[7]刘立峰,蔡锦方.不同步态位相跟、距骨应力分布的三维有限元分析[J].第二军医大学学报,2003,24(9)：1006-08.
[8]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[9]Rammelt S, H. Zwipp. Talar neck and body fractures[J]. Injury,2009, 40(2):120-35.
[10]Klein Petra, Hanna Schell, Florian Streitparth, et al. The initial phase of fracture healing is specifically sensitive to mechanical conditions [J]. J Orthop Res,2003, 21(4):662-69.
[11]Swanson T. V, T. J Bray, G. B. Holmes. Fracture of the talar neck-a mechanical study of fixation[J]. J Bone Joint Surg [Am],1992,74A(4):544-51.
[12]Attiah M, D. W Sanders, G Valdivia, et al. Comminuted talar neck fractures:A mechanical comparison of fixation techniques[J]. J OrthopTrauma,2007, 21(1):47-51.
[1]Ferran Nicholas A, Francesco Oliva, Nicola Maffulli. Ankle instability [J]. Sports Med Arthrosc,2009,17(2):139-45.
[2]Windisch G, B Odehnal, R Reimann, et al. Contact areas of the tibiotalar joint[J]. Journal of Orthop Res,2007,25:1481-87.
[3]Wan L, R. J De Asia, H. E Rubash, et al. In vivo cartilage contact deformation of human ankle joints under full body weight[J]. J Orthop Res,2008,26(8):1081-89.
[4]Caputo Adam M, Jun Y Lee, Chuck E Spritzer, et al. In Vivo Kinematics of the Tibiotalar Joint After Lateral Ankle Instability[J]. Am J Sports Med,2009, 37(11):2241-48.
[5]Earll M, J Wayne, C Brodrick, et al. Contribution of the deltoid ligament to ankle joint contact characteristics:a cadaver study[J]. Foot Ankle Int,1996, 17(6):317-24.
[6]Michelson J. D. Fractures about the ankle[J]. J Bone Joint Surg Am,1995, 77(1):142-52.
[7]梁庆威,范广宇,吕刚.踝部骨折的治疗及距骨生物力学观察[J].中华骨科杂志,1998,18(05)：290-92.
[8]Beals T. C, J Crim, F. Nickisch. Deltoid Ligament Injuries in Athletes:Techniques of Repair and Reconstruction[J]. Oper Techn Sport Med,2010,18(1):11-17.
[9]Bahr R, F Pena, J Shine, et al. Biomechanics of ankle ligament reconstruction. An in vitro comparison of the Brostrom repair, Watson-Jones reconstruction, and a new anatomic reconstruction technique[J]. Am J Sports Med,1997,25(4):424-32.
[10]Boss A. P., B. Hintermann. Anatomical study of the medial ankle ligament complex[J]. Foot Ankle Int,2002,23(6):547-53.
[11]Milner C. E, R. W. Soames. The medial collateral ligaments of the human ankle joint:Anatomical variations[J]. Foot Ankle Int,1998,19(5):289-92.
[12]Leardini A, J. J O'connor, F Catani, et al. The role of the passive structures in the mobility and stability of the human ankle joint: A literature review[J]. Foot Ankle Int,2000,21(7):602-15.
[13]Rasmussen O. Stability of the ankle joint. Analysis of the function and traumatology of the ankle ligaments[J]. Acta Orthop Scand Suppl,1985, 211:1-75.
[14]Weindel S, R Schmidt, S Rammelt, et al. Subtalar instability:a biomechanical cadaver study [J]. Arch Orthop Traum Su,2010,130(3):313-19.
[15]Hintermann B, C Sommer, B. M. Nigg. Influence of ligament transection on tibial and calcaneal rotation with loading and dorsi-plantarflexion[J]. Foot Ankle Int,1995,16(9):567-71.
[1]Brekelmans W. A, H. W Poort, T. J. Slooff. A new method to analyse the mechanical behaviour of skeletal parts[J]. Acta Orthop Scand,1972, 43(5):301-17.
[2]Gefen A, M Megido-Ravid, Y Itzchak, et al. Biomechanical analysis of the three-dimensional foot structure during gait: A basic tool for clinical applications[J]. J Biomech Eng-T Asme,2000,122(6):630-39.
[3]Mesfar W, A. Shirazi-Adl. Computational biomechanics of knee joint in open kinetic chain extension exercises[J]. Comput Method Biomec,2008,11(1):55-61.
[4]Moore D. C, K. A Hogan, J. J Crisco, et al. Three-dimensional in vivo kinematics of the distal radioulnar joint in malunited distal radius fractures[J]. Journal of Hand Surgery-American Volume,2002,27A(2):233-42.
[5]Sowmianarayanan S, A Chandrasekaran, R. Krishna. Kumar. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants--a comparative study[J]. Proc Inst Mech Eng H,2008,222(1):117-27.
[6]Chen W. M, T Lee, P. V. S Lee, et al. Effects of internal stress concentrations in plantar soft-tissue-A preliminary three-dimensional finite element analysis[J]. Med Eng Phys,2010,32(4):324-31.
[7]Paul J. P. Three-dimensional finite element stress analysis of the polypropylene ankle-foot orthoses:Static analysis[J]. Med Eng Phys,1996,18(7):607-07.
[8]Saunders Mamie M, Edwards P Schwentker, David B Kay, et al. Finite element analysis as a tool for parametric prosthetic foot design and evaluation. Technique development in the solid ankle cushioned heel (SACH) foot[J]. Comput Method Biomec,2003,6(1):75-87.
[9]Syngellakis S, M. A Arnold, H. Rassoulian. Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method[J]. Proceedings of the Institution of Mechanical Engineers Part H-Journal of Engineering in Medicine,2000,214(H5):527-39.
[10]Patil K. M, L. H Braak, A. Huson. Analysis of stresses in two-dimensional models of normal and neuropathic feet[J]. Med Biol Eng Comput,1996, 34(4):280-84.
[11]Giddings Virginia L, Gary S Beaupre, Robert T Whalen, et al. Calcaneal loading during walking and running[J]. Med Sci Sport Exer,2000,32(3):627-34.
[12]Garcia-Aznar J. M, J Bayod, A Rosas, et al. Load transfer mechanism for different metatarsal geometries:a finite element study[J]. J Biomech Eng,2009, 131(2):021011.
[13]刘立峰,蔡锦方.不同步态位相跟、距骨应力分布的三维有限元分析[J].第二军医大学学报,2003,24(9)：1006-08.
[14]Wu L. J. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures[J]. Clin Biomech 2007,22(2):221-29.
[15]Wu L. JS. Z ZhongR. M Zheng, et al. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus[J]. Surg Radiol Anat,2007,29:561-67.
[16]杨璇.手法复位先天性马蹄内翻足过程中的力学变化[J].临床骨科杂志,2010,13(3)：323-26.
[17]刘立峰,蔡锦方,梁进.跟骨骨折内固定方法的有限元模拟比较[J].中国矫形外科杂志,2003,11(08)：557-58.
[18]Reggiani B, A Leardini, F Corazza, et al. Finite element analysis of a total ankle replacement during the stance phase of gait[J]. J Biomech,2006,39(8):1435-43.
[19]Espinosa N, M Walti, P Favre, et al. Misalignment of Total Ankle Components Can Induce High Joint Contact Pressures[J]. J Bone Joint Surg [Am],2010, 92A(5):1179-87.
[20]Lee Jun Young, Yeon Soo Lee. Optimal double screw configuration for subtalar arthrodesis: a finite element analysis[J]. Knee Surg Sports Traumatol Arthrosc, 2011,19(5):842-9.
[21]Alonso-Vazquez Ana, Henrik Lauge-Pedersen, Lars Lidgren, et al. The effect of bone quality on the stability of ankle arthrodesis. A finite element study[J]. Foot Ankle Int,2004,25(11):840-50.
[22]Nakamura S., R. D. Crowninshield, R. R. Cooper. An analysis of soft tissue loading in the foot-a preliminary report[J]. Bull Prosthet Res,1981,10-35:27-34.
[23]Scott S. H, D. A. Winter. Biomechanical model of the human foot: kinematics and kinetics during the stance phase of walking[J]. J Biomech,1993, 26(9):1091-104.
[24]Garcia-Gonzalez A, J Bayod, U. C Prados-Frutos, et al. Finite-element simulation of flexor digitorum longus or flexor digitorum brevis tendon transfer for the treatment of claw toe deformity [J]. J Biomech,2009,42(11):1697-704.
[25]顾耀东.基于踏跳阶段跟腱的有限元分析[J].体育科研,2007,28(1)：62-64.
[26]牛文鑫,杨云峰,俞光荣,等.人体足部三维有限元模型的有效构建方法及其合理性的实验分析研究[J].生物医学工程学杂志,2009,26(1)：80-84.
[27]陶凯,王冬梅,王成焘,等.韧带和跖腱膜在足部有限元分析中的力学作用[J].生物医学工程学杂志,2008,25(02)：336-40.
[28]Chu T. M, N. P Reddy, J. Padovan. Three-dimensional finite element stress analysis of the polypropylene, ankle-foot orthosis:static analysis [J]. Med Eng Phys,1995,17(5):372-79.
[29]Yu J, J. T. M Cheung, Y. B Fan, et al. Development of a finite element model of female foot for high-heeled shoe design[J]. Clin Biomech 2008,23:S31-S38.
[30]张明,张德文,余嘉,等.足部三维有限元建模方法及其生物力学应用[J].医用生物力学,2007,22(04)：339-44.
[31]孙卫东,温建民.足部有限元建模方法应用现状[J].中国组织工程研究与临床康复,2010,74(13)：2458-61.
[32]Yc. Funq. Biomechanics-mechanical properties of living tissues[J]. Springer, 1993,2th Ed.
[33]Funk J. R, G. W Hall, J. R Crandall, et al. Linear and quasi-linear viscoelastic characterization of ankle ligaments[J]. J Biomech Eng-T Asme,2000, 122(1):15-22.
[34]Jia X. H, M Zhang, X. B Li, et al. A quasi-dynamic nonlinear finite element model to investigate prosthetic interface stresses during walking for trans-tibial amputees[J]. Clin Biomech 2005,20(6):630-35.
[35]Duerr Hans R, Heiner Martin, Christoph Pellengahr, et al. The cause of subchondral bone cysts in osteoarthrosis - A finite element analysis [J]. Acta Orthop Scand,2004,75(5):554-58.
[36]Li L. P, J. T. M Cheung, W Herzog. Three-dimensional fibril-reinforced finite element model of articular cartilage[J]. Med Biol Eng Comput,2009, 47(6):607-15.
[37]Susilo Monica E, Blayne A Roeder, Sherry L Voytik-Harbin, et al. Development of a three-dimensional unit cell to model the micromechanical response of a collagen-based extracellular matrix[J]. Acta Biomater,2010,6(4):1471-86.
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