跟骨骨折的有限元分析
摘要
研究背景
跟骨是足内、外侧纵弓的共同后壁和足外侧柱的重要后部。其上部具有前、中、后三个关节面,与距骨构成距下关节复合体,维持距下关节运动和力学的稳定。其后关节面的面积最大,承受大部分体重。距下关节是联系中后足和踝关节运动的中间环节,中跗关节的正常活动需要距下关节的配合。跟骨的正常形态既是保证中后足关节正常对位,维持足弓形态及稳定的重要条件,又是保证跨踝关节的小腿肌肉正常发挥作用的基础。
跟骨骨折是最常见的跗骨骨折,占跗骨骨折的60%,占全身骨折的2%,约75%为关节内骨折,20%-45%伴有跟骰关节损伤。因跟骨及周围解剖结构复杂,局部软组织覆盖质量差,故治疗困难,且后遗症多,预后较差。近20年来,随着抗生素、影像技术、内固定和微创技术的迅速发展,以及对后足部生物力学及跟骨骨折认识的深入,其临床疗效不断提高。目前,治疗跟骨骨折的方法很多,各有其适应证和优、缺点,临床上应根据患者的损伤程度、骨折类型、全身及局部情况和科室的技术条件选择合理有效的治疗方法。
跟骨骨折导致跟骨长度缩短、宽度增加、高度降低,距下关节不平整,跟骨轴侧向成角,跟骨结节关节角(Bohler角)减小、消失或反角,Gissane角缩小或增大,距骨倾斜角缩小和消失。这将造成足弓塌陷,影响足的整体外形和力学稳定,并可形成创伤性扁平足。跟骨三个关节面之间正常关系的丧失、关节面的不平整和移位必将引起距下关节受力和运动的改变,造成距下关节及其周围关节的继发性损伤,如创伤性关节炎等。跟骰关节面骨折将严重影响中跗关节的正常运动功能和距下关节的外翻活动,造成的跟骰关节创伤性关节炎,影响足的正常行走。严重距下关节面破坏和软骨缺损者可发生自发性关节融合,丧失活动功能。后足外翻、跟骨增宽短缩、高度降低和外侧壁外膨不仅造成穿鞋困难,而且造成腓骨长、短肌腱卡压。另外,下降的外踝直接接触或碰撞跟骨外侧壁可出现跟腓撞击征,长期可形成假关节。跟腱止点上移,导致腓肠肌和比目鱼肌的肌力减弱。后足力线的改变可使小腿肌肉的拉力方向、力矩和肌力发生改变,最终发生足踝部疼痛和功能障碍。此外,足踝关节的运动力线异常和双侧肢体不等长,将影响整个下肢和脊柱的正常功能,过早发生腰背痛和颈肩痛。因此,治疗跟骨骨折的目的是恢复后足的正常生物力学特点和功能,避免造成各种不良后果。
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。
由于跟骨结构的复杂性、运动的多样性、个体的差异性,迄今为止,跟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,跟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,建立合理的跟骨数字仿真及三维有限元模型,研究跟骨及周围结构的生物力学特性,对跟骨的高度改变、Bohler角度改变及两种内固定固定Sanders Ⅳ型骨折的力学固定特点进行综合分析,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,建立跟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.建立正常步态下跟骨及周围结构的三维有限元模型,分析正常步态下跟骨生物力学变化；
3.研究单足站立状态下,跟骨Bohler角度减少5°、10°、15°、20°、25°时距下关节、距骨、跟骰关节、足底的应力分布变化,分析保守治疗跟骨关节外骨折时Bolher角需要恢复的角度。
4.研究单足站立状态下,跟骨高度减少5mm、10mm、15mm、20mm时距下关节、距骨、跟骰关节、足底的应力分布变化,分析术中需要恢复跟骨的高度。
5.对跟骨锁定钢板和解剖型钢板治疗Sanders Ⅳ型跟骨骨折时距下关节、距骨、跟骨骨折块、跟骰关节的应力分布及位移进行综合比较分析,以得出SandersⅣ型跟骨骨折的治疗方案并推断出内固定的合理改进方向。
方法
1.数字化足踝部三维有限元模型的构建与验证：采用南方医科大学南方医院影像中心的LightSpeed16排螺旋CT,扫描参数：电压120～140KV,电流强度240～300mA,螺距1.375～1.75,层厚7.5mm,矩阵512×512,重建层厚0.625mm。对志愿者右足自踝关节上20cm胫腓骨远端向下扫描至足底,扫描时右足保持中立位,以DICOM格式输入个人计算机的Mimics10.01软件,经自动或手动阈值分割后三维重建出完整足踝部的28块骨骼及外围软组织的三维结构,再以点云输出并导入SolidWorks2009,利用网格处理向导及曲面生成向导生成几何模型并重建装配体,然后分别导入两种有限元分析软件：(1)方法一为导入有限元分析软件ANSYS12.0的Workbench模块建立完整的足踝部有限元模型。在踝关节的接触面两侧根据关节间隙分别建立了0.5mm关节软骨,其他关节采用仅受压的三维杆单元模拟软骨,并建立了125条弹簧模拟韧带和小腿骨间膜,5条梁单元模拟跖筋膜,材料属性分别参照文献确定。然后参照Anderson等方法,对模型仅取胫骨及距骨所构成的简单踝关节模型加以测试。通过模拟人体单足站立状态下的力学传递,对模型胫骨下端的上截面施加700N垂直载荷,对距骨予以约束。测量踝关节胫骨下关节面的接触压力、接触面积,并将结果与前者进行对照。(2)方法二为导入Simulation建立简化的踝关节有限元模型。根据研究需要,分别建立了包含胫骨、腓骨、距骨、跟骨及舟骨的5骨装配体,以及还包括骰骨及3块楔骨的9骨装配体的有限元模型。在模型中用“仅延伸”的弹簧模拟韧带连接,其中在踝关节5骨装配体中共建立了31条弹簧,而在9骨装配体中建立了42条弹簧模拟踝关节周围韧带及小腿骨间膜等连接装置。定义各组织的材料属性,并通过自动或手动方法在各关节间生成接触对,设置相应的边界条件分别在踝关节5骨装配体有限元模型上模拟人体单足站立及踝关节内、外旋运动加载,而在踝关节9骨装配体有限元模型上模拟踝关节内、外翻运动加载,然后设置好网格划分密度生成网格并设置算例属性进行运算。
2.在不改变距下关节面的条件下将Bohler角的角度逐渐减少5度、10度、15度、20度、25度,并分别进行楔形截骨,最终生成6种有限元模型。假设为骨折面完全断裂并处于接触状态,摩擦系数为0.3。将跟骨、足部负重区三维有限元模型下缘全部节点的自由度约束为零作为边界条件,即远端各节点在X、Y、Z轴上的位移为0。于胫骨端予以模型700N轴向应力,计算此应力下模型的应力分布及位移分布。
3.在不改变距下关节面的条件下将跟骨高度逐渐减少5mm、10mm、15mm、20mm、并分别进行楔形截骨。最终生成5种有限元模型。假设为骨折面完全断裂并处于接触状态,摩擦系数为0.3。将跟骨、足部负重区三维有限元模型下缘全部节点的自由度约束为零作为边界条件,即远端各节点在X、Y、Z轴上的位移为O。于胫骨端予以模型700N轴向应力,计算此应力下模型的应力分布及位移分布。
4.根据Sanders Ⅳ型骨折对跟骨进行截骨,保持关节面的平整及各骨折块摩擦关系。同时根据跟骨解剖型和锁定钢板形态重建出两种骨折内固定有限元模型。假设为骨折面完全断裂并处于接触状态,摩擦系数为0.3。解剖型钢板设置为摩擦接触,锁定钢板则设置为不接触,将跟骨、足部负重区三维有限元模型下缘全部节点的自由度约束为零作为边界条件,即远端各节点在X、Y、Z轴上的位移为0。普通加压钢板设定与跟骨接触为加压摩擦接触,锁定钢板与跟骨间不考虑加压摩擦接触。计算该状态下跟骨与钢板的应力分布、位移。
结果
1.在按方法一所建的完整的足踝部有限元模型中,将胫、距骨组成的踝关节测试结果与Anderson等实验结果对照后发现,二者在中立位踝关节垂直加载下应力主要分布于胫骨下关节面中部及前外侧,最大应力处于2.7MPa-4.0MPa之间,在分布区域和分布趋势、数值大小上基本一致,初步证明本模型是有效的。按方法二所建立的简化的两个踝关节三维有限元模型经测试可以模拟踝关节的不同受力情况,并可进行正确的加载运算,而且单元数、节点数、运算时间适中。各种加载后所产生的应力、位移的结果合理,比较贴近真实状况。将结果与Liacouras和Wayne在相同边界条件下所作的踝关节外旋模拟实验结果进行了对比,发现本模型在踝关节外旋加载中胫骨的旋转角度为3.85°,与其有限元模型计算的4.28°比较接近,另外本模型的主要关节的接触力大小也与其结果对应性较好,证明了本模型的有效性。
2.当跟骨的Bohler角分别减少5°、10°、15°、20°、25°时,距下关节面的应力峰值分别增加了11.3%、12%、18.5%、19.8%、32.1%；距骨应力峰值分别增加3%、12.6%、27.6%、54%、70.6%；跟骰关节面应力随着Bohler角减少而不断减小,应力峰值分别减少2.3%、4.7%、15.4%、20.3%、20.4%;足底应力集中于跟骨底部,应力峰值值分别增大11.3%、11.6%、18.6%、19.8%、32.1%。
3.跟骨高度分别减少5mmm、10mm、15mm、20mm时,距下关节面的应力峰值分别增加了10.3%、18.5%、35.4%、54.7%；距骨侧的应力峰值分别增加了最大应力值分别增加8.9%、9.8%、16.1%、16.7%；跟骰关节面应力随着跟骨高度减少而不断减小,应力峰值分别减少2.3%、4.4%、22.4%、67.4%、80.1%；足底应力主要集中于足跟处,应力峰值分别增大10.2%、18.4%、35.4%、54.7%。
4.使用锁定钢板固定后最大应力集中于钢板螺钉交界处,应力峰值为143.49MPa,上排螺钉中部、钢板中后部存在应力集中现象；解剖型钢板应力分布相对均匀,螺钉应力分布均匀,最大应力位于钢板中后部,应力峰值为102.49MPa;距骨及跟骨各骨折块的应力峰值均为锁定钢板大于解剖型钢板。两种钢板内固定模型主要位移均分布于近关节面的螺钉处,其中锁定钢板的位移小于解剖型钢板模型,分别为0.222mm,0.389mm;锁定钢板固定的骨折块位移峰值均小于解剖型钢板。
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、Ansys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跟骨的解剖结构及其受力特点,有利于对跟骨进行生物力学分析。
3. Bohler角改变对距下关节、跟骰关节、足底的应力影响较小,而对胫距关节的影响较大,术中需要根据骨折情况尽量恢复患者的Bohler角,对于Bohler角减小10°以内的骨折,如无其他手术指征可选择保守治疗；跟骨高度的改变对距下关节、跟骰关节及足底的应力改变较大,而对胫距关节影响较小,术中需要将跟骨高度的改变控制在15mm之内,避免远期关节功能的影响。
4.切开复位钢板内固定治疗粉碎性跟骨骨折,尤其对于Sanders Ⅳ型骨折,维持关节面平整非常重要。锁定钢板对于维持关节面的平整略显优势,而解剖型加压钢板能够分散骨折端的应力,钢板与骨块间的摩擦力作用也能起一定代偿作用。且在所有骨块中,载距突产生位移最大,因此跟骨钢板的设计需要对载距突部分进行重点固定。结合桡骨远端骨折、胫骨平台骨折治疗理论,对于跟骨骨折的钢板可以设计为,两枚锁定螺钉固定于载距突,跟骨上排螺钉采用锁定螺钉与加压螺钉间断排列,平行于关节面打入；足底部位以两枚锁定螺钉固定前后两端,其余部分均采用普通松质骨螺钉固定。此钢板能够同时满足钢板与骨折端的加压作用同时也发挥了锁定螺钉的部分优势。无论何种内固定方式关节内碎骨快可随足部负重而产生不同程度移位,存在较高创伤性关节炎的风险,建议采用一期外固定二期关节融合治疗。
Background:
The calcaneus is an odd-shaped bone. The superior surface consists of three articular facets (the anterior, middle, and posterior) that articulate with the talus. The posterior facet is the major weight-bearing surface and the largest facet. The middle facet is anterior and medial and is located on the sustentaculum; it is often contiguous with the anterior facet. The sustentaculum sits under the talar neck and is medial to the calcaneal body. It is attached to the talus by the interosseous talocalcaneal ligament and by the deltoid ligament medially. The flexor hallucis longus tendon runs below the sustentaculum. Laterally, the peroneal tendons run obliquely along the lateral wall of the calcaneus and sit in two shallow grooves, with a bony prominence between them known as the peroneal tubercle. The entire calcaneal surface behind the posterior facet is known as the posterior tuberosity. On its plantar surface, it has two processes, the lateral and medial. The medial process is the origin of the abductor hallucis muscle and the major weight-bearing structure in the hindfoot. Finally, the Achilles tendon inserts on the posterior surface of the tuberosity.
Calcaneal fractures are the most common tarsal bone fractures, accounted for60%of the tarsal bone fractures, accounting for2%of the body fracture, about75%refers to intra-articular fractures,20%to45%with calcaneocuboid joint injury. due to the complexity of the calcaneus anatomy and surrounding anatomical structures, poor quality of local soft tissue coverage, it is difficult to treat with much complications and poor outcome. During the past20years, with the development of antibiotics, imaging technology, internal fixation and minimally invasive techniques, as well as the research of biomechanics of calcaneal fractures, its clinical efficacy and continuously improve. Although a lot of method with differentiated indications and advantages and disadvantages has been applied to treat calcaneal fractures, it is advised that the solution should be made according to the patient's degree of injury, fracture type, systemic and local circumstances and sections of the technical conditions.
Calcaneal fractures often related to calcaneus shorten in the length, width increases, reduced height, uneven subtalar joint the calcaneal axis lateral angled, the the calcaneal tuberosity joint angle (Bohler angle) decreases, disappeared or contra-angle Gissane angle narrowing or increased talar tilt angle to shrink and disappear. This will cause the arch collapse, affect the overall shape of the foot and mechanical stability, can form traumatic flatfoot. Loss of normal relations between the articular surface of the calcaneus three articular surface uneven and the shift is bound to cause a change of the force and movement of the subtalar joint, causing secondary injury subtalar joints in and around the joints, such as trauma arthritis. Calcaneocuboid articular surface fractures will seriously affect the normal movement of the hock function and subtalar joint eversion activities caused calcaneocuboid joint traumatic arthritis, enough to affect normal walking. Serious subtalar joint surface damage and cartilage defects can occur spontaneously arthrodesis, the loss of the active function. After pronation, calcaneal widening shortening, reduced height and lateral wall of the outer expansion is not only caused by wearing shoes difficult, and the peroneus longus and brevis tendon entrapment. In addition, the decline lateral malleolus direct contact or collision the calcaneus outside sidewall calcaneofibular impingement syndrome, long-term form pseudarthrosis. Achilles tendon point enough, leading to weakness of the gastrocnemius and soleus. Hind foot line of force to change the calf muscles can pull direction, torque and muscle changes, the final occurrence of foot and ankle pain and dysfunction. In addition, the abnormal movement of the ankle joint force line and bilateral limb length inequality will affect the normal function of the entire lower extremity and spine, premature low back pain and neck pain. Therefore, the purpose of calcaneal fractures after the resumption of normal biomechanics of the foot and functions to avoid undesirable consequences.
With the development of digital simulation modeling techniques and finite element method, the digital virtual gradually applied to the clinical diagnosis, treatment, and experimental studies. Compared with the previous biomechanical experiments, the finite element method is a useful numerical tool geometry and digital nonlinear complex structure of internal stress and strain analysis. Can complete the load cannot be achieved by other research methods and constraints, the specimens can also be corrected to simulate any pathological state. The finite element model can provide the normal physiological experiments cannot be that to get the objective entities experiments difficult to get results. By changing the load loading mode, change the material properties of individual stress analysis.
Objective:
1. With the help digital technology, to establish the calcaneus and surrounding structures digital virtual simulation model to explore the of digital simulation Medicine modeling method and significance
2. Establish normal gait the calcaneus and around the structure of three-dimensional finite element model to analyze the the calcaneus biomechanics normal gait changes.
3. To analysis of the operative indication of conservative treatment as well as the intra-articular calcaneal fracture with the change of Bolher angle. Single-leg stance state, calcaneus Bohler angle decreased by5°,10°,15°,20°and25°of the subtalar joint, to test talus calcaneocuboid joint plantar stress distribution changes.
4. To analysis of the operative indication of conservative treatment as well as the intra-articular calcaneal fracture with the change of Bolher angle. Single-leg stance state, calcaneus height decreased by5mm,10mm,15mm and20mm, talus calcaneocuboid joint plantar stress distribution changes.
5. Calcaneal locking plates and anatomical plate in the treatment of Sanders Ⅳ type calcaneal fractures subtalar joint, talus, calcaneus fracture fragments, with the the calcaneocuboid joint stress distribution and displacement comprehensive comparative analysis to arrive at Sanders Ⅳ calcaneal fractures treatment programs and to infer the direction of the internal fixation reasonable improvement.
Methods:
1.Construction and verification of digital three-dimensional finite element model of foot and ankle:Adopting LightSpeed16-slice spiral CT of the Imaging Center, Nanfang Hospital affiliated to Southern Medical University (scanning parameters:120～140KV,240～300mA, pitch of1.375～1.75, the layer thickness7.5mm, matrix512×512, reconstruction slice thickness0.625mm), scaned the volunteer's right foot from distal tibia and fibula20cm above the ankle down to the planta, with the right foot remaining neutral position. Then imported the scanned data of DICOM format into Mimics10.01software, by threshold segmentation automatically or manually, to reconstruct the three-dimensional structure of a complete foot and ankle composed of28bones and surrounding soft tissue. Finally, exported the data with point cloud format and reimported into SolidWorks2009, using the guide of grid processing and surface generation to form geometric models and reconfigure them, then import the data into two kinds of finite element analysis softwares:Method1: Imported into Workbench module of finite element analysis software ANSYS12.0to establish a complete finite element model of foot and ankle. To construct0.5mm of articular cartilage on both sides of contact surface according to the joint space, while to use three-dimensional rod elements which were compressed only to simulate other joints cartilage, and to establish125springs to simulate ligaments and crural interosseous membrane, five beam elements to simulate plantar fascia.The material properties were determined with reference to documents. Then refered to Anderson's method, took the tibia and talus only as a simple model of the ankle joint for test. The normal standing status of ankle joint was simulated by application a vertical load of700N on the upper section of the lower tibia while the talus constrained. To measure contact pressure and contact area of inferior articular surface of the tibia, and to compare the results with the former. Method2:Imported the data into Simulation module of Solidworks to establish a simplified finite element model of the ankle. According to the research needs, to establish a5-bones assembly finite element model containing the tibia, fibula, talus, calcaneus, and navicular, and a9-bones assembly finite element model also including the cuboid bone and the three cuneiform bones in addition to the5bones mentioned above. In the models, to use tension-only springs to simulate ligaments connection. The5-bones assembly contained31springs, while the 9-bones assembly was established42springs to simulate connected structures such as ligaments around the ankle and crural interosseous membrane. To Define the material properties of each tissue, to generate contact pair between each joints automatically or manually, and to set the corresponding boundary conditions. In the5-bone assembly finite element model of ankle, to simulate the state of human body with one foot standing and the states of internal and external rotation of ankle, while in the9-bones finite element model of ankle, to simulate the states of ankle inversion and ankle eversion. Then, regulated the mesh density to generate mesh, and set the simulation examples attribute for solution.
2.With the Subtalar joint surface unchanged, wedge osteotomy was applied to the calcaneus to make the Bohler angle gradually decreased in5degrees,10degrees,15degrees,20degrees,25degrees, respectively, then reconstruct six FE models. Assuming the fracture surface completely broken and is in contact state, and the coefficient of friction of0.3. All nodes of the calcaneus, the lower edge of the three-dimensional finite element model of the weight-bearing area of the foot degrees of freedom constrained to zero as boundary conditions, each remote node in the X, Y, Z axis displacement0. Be on the tibial end model700N axial stress calculation of stress distribution and displacement distribution of the model under this stress.
3.With the Subtalar joint surface unchanged, wedge osteotomy was applied to the calcaneus to make the calcaneus height gradually decreased in5mm,10mm,15mm and20mm respectively, then reconstruct five FE models. Assuming the fracture surface completely broken and is in contact state, and the coefficient of friction of0.3. All nodes of the calcaneus, the lower edge of the three-dimensional finite element model of the weight-bearing area of the foot degrees of freedom constrained to zero as boundary conditions, each remote node in the X, Y, Z axis displacement0. Be on the tibial end model700N axial stress calculation of stress distribution and displacement distribution of the model under this stress.
4.To stimulated Sanders IV fractures of the calcaneus and do osteotomy as well, keep the fragment of the articular surface of the friction relationship. Assuming the fracture surface completely broken and is in contact state, and the coefficient of friction of0.3. Anatomic plate set to frictional contact, locking plate is set to no contact the calcaneus foot weight-bearing area three-dimensional finite element model of the lower edge of the degrees of freedom of all nodes constrained to zero as the boundary conditions. All nodes of the calcaneus, the lower edge of the three-dimensional finite element model of the weight-bearing area of the foot degrees of freedom constrained to zero as boundary conditions, each remote node in the X, Y, Z axis displacement0. Be on the tibial end model700N axial stress calculation of stress distribution and displacement distribution of the model under this stress.
Result:
1. In the complete finite element model of foot and ankle constructed by method1, the test results of the ankle composed of tibia and talus were taken to contrast with Anderson's study. It showed that the stress on ankle joint articular surface of the tibia mainly distributed at the central and anterolateral aspects in both of them when ankle joint was in neutral position under the vertical loading, with the maximum stress between2.7MPa and4.0MPa, substantial agreement on distribution area, distribution trend, and numerical value. It was preliminarily verified this model valid. The test results of two simplified three-dimensional finite element models of the ankle established by method2showed that they could simulate various load situations of ankle for solution, with moderate number of element, node and suitable amount of computing time. The stress and displacement results in each loading were reasonable and close to the actual situation. Compared with Liacouras and Wayne's model under the same boundary conditions, it showed that the rotation angle of tibia was3.85°in our model whereas their result was4.28°after application of ankle external rotation load, comparatively close between the two values. In adition, the contact forces of major joints were also consistent with theirs. All confirmed the validity of our models.
2. When Bohler angle of the calcaneus decreased by5°,10°,15°,20°,25°, and the stress of the subtalar joint surface peak increase of11.3%,12%,18.5%,19.8%,32.1%; taluspeak stress increased by3%, respectively,12.6%,27.6%,54%,70.6%; calcaneocuboid articular surface stress reduce Bohler angle decreases, the peak stress decreased by2.3%,4.7%,15.4%,20.3%,20.4%; plantar stress concentration at the bottom of the calcaneus, the peak stress values were increased by11.3%.11.6%,18.6%,19.8%,32.1%.
3. Calcaneal height to reduce5mm,10mm,15mm,20mm, the subtalar joint surface stress peak increase of10.3%,18.5%,35.4%,54.7%; the talar side peak stress increased by8.9%,9.8%,16.1%,16.7%; calcaneocuboid articular surface stress with the reduction of the height of the calcaneus continue to decrease, the peak stress decreased by2.3%,4.4%,22.4%,67.4%,80.1%;The foot stress mainly concentrated in the heel at peak stress increased10.2%,18.4%,35.4%,54.7%.
4. Using locking plate fixation, maximum stress concentration at the plate and screw the junction stress peak to143.49MPa, stress concentrated on the middle of the upper row of screws steel plate in the rear; anatomical plate stress distribution is relatively uniform the screw stress distribution is uniform, the maximum stress in thesteel plate in the rear of the peak stress of102.49MPa; talus and calcaneus each fracture stress peak are locking plate block than anatomic plate. Major displacement of two steel plates fixed model distributed near the articular surface of the screw at which the lock plate displacement is less than the anatomical plate model were0.222mm,0.389mm; locking plate fixation peak displacement of the fracture fragments are less than anatomic steel plate.
Conclusions:
1. Based on CT scan data, the calcaneus 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 from3D reconstruction of computed tomography, a three-dimensional (3D) finite element model was developed using Mimics, Geomagic Studio, Hypermesh, Ansys 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 calcaneus and its mechanical characteristics. It was beneficial for biomechanical analysis of the calcaneus.
3. The change of Bohler angle affect little on the subtalar joint, calcaneocuboid joint, plantar stress changes but more to tibiotalar joint. It is necessary to restore the Bolher angle during operation. If the Bohler angle changes below10°, as no other surgery indication, conservative treatment could be choose; The change of calcaneus height affect more on the subtalar joint, calcaneocuboid joint, plantar stress changes but little to tibiotalar joint. It is necessary to maintain the calcaneus height under15mm, to get better joint function for long term.
4. Open reduction and internal fixation for the treatment of comminuted calcaneal fractures, especially for Sanders IV type fracture formation is very important to maintain the articular surface. Locking plate show slightly advantage for the maintenance of the articular surface of the flat, anatomical compression plate can be dispersed fracture stress, the frictional force between the plate and bone can also play a compensatory role. During all bone fragment, set out from the sudden displacement calcaneal plate design needs to set out from the sudden part fixed focus. According to the theory of treatment of tibial plateau fractures distal radial fracture theory, the calcaneal fractures can be designed for two locking screws in the set from the sudden, the calcaneus upper row of screws on the locking screw and compression screw intermittent arranged, parallel to the articular surface. Plantar parts fixed with two locking screws front and rear ends, the rest are ordinary cancellous bone screws. This plate combines the advantage of locking plate and anatomic plate. Whatever within fixed intra-articular bone fragments fast with foot weight and produce different degrees of shift, there is a higher traumatic arthritis risk, it is recommended that an external fixation two arthrodesis treatment.
跟骨是足内、外侧纵弓的共同后壁和足外侧柱的重要后部。其上部具有前、中、后三个关节面,与距骨构成距下关节复合体,维持距下关节运动和力学的稳定。其后关节面的面积最大,承受大部分体重。距下关节是联系中后足和踝关节运动的中间环节,中跗关节的正常活动需要距下关节的配合。跟骨的正常形态既是保证中后足关节正常对位,维持足弓形态及稳定的重要条件,又是保证跨踝关节的小腿肌肉正常发挥作用的基础。
跟骨骨折是最常见的跗骨骨折,占跗骨骨折的60%,占全身骨折的2%,约75%为关节内骨折,20%-45%伴有跟骰关节损伤。因跟骨及周围解剖结构复杂,局部软组织覆盖质量差,故治疗困难,且后遗症多,预后较差。近20年来,随着抗生素、影像技术、内固定和微创技术的迅速发展,以及对后足部生物力学及跟骨骨折认识的深入,其临床疗效不断提高。目前,治疗跟骨骨折的方法很多,各有其适应证和优、缺点,临床上应根据患者的损伤程度、骨折类型、全身及局部情况和科室的技术条件选择合理有效的治疗方法。
跟骨骨折导致跟骨长度缩短、宽度增加、高度降低,距下关节不平整,跟骨轴侧向成角,跟骨结节关节角(Bohler角)减小、消失或反角,Gissane角缩小或增大,距骨倾斜角缩小和消失。这将造成足弓塌陷,影响足的整体外形和力学稳定,并可形成创伤性扁平足。跟骨三个关节面之间正常关系的丧失、关节面的不平整和移位必将引起距下关节受力和运动的改变,造成距下关节及其周围关节的继发性损伤,如创伤性关节炎等。跟骰关节面骨折将严重影响中跗关节的正常运动功能和距下关节的外翻活动,造成的跟骰关节创伤性关节炎,影响足的正常行走。严重距下关节面破坏和软骨缺损者可发生自发性关节融合,丧失活动功能。后足外翻、跟骨增宽短缩、高度降低和外侧壁外膨不仅造成穿鞋困难,而且造成腓骨长、短肌腱卡压。另外,下降的外踝直接接触或碰撞跟骨外侧壁可出现跟腓撞击征,长期可形成假关节。跟腱止点上移,导致腓肠肌和比目鱼肌的肌力减弱。后足力线的改变可使小腿肌肉的拉力方向、力矩和肌力发生改变,最终发生足踝部疼痛和功能障碍。此外,足踝关节的运动力线异常和双侧肢体不等长,将影响整个下肢和脊柱的正常功能,过早发生腰背痛和颈肩痛。因此,治疗跟骨骨折的目的是恢复后足的正常生物力学特点和功能,避免造成各种不良后果。
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。
由于跟骨结构的复杂性、运动的多样性、个体的差异性,迄今为止,跟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,跟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,建立合理的跟骨数字仿真及三维有限元模型,研究跟骨及周围结构的生物力学特性,对跟骨的高度改变、Bohler角度改变及两种内固定固定Sanders Ⅳ型骨折的力学固定特点进行综合分析,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,建立跟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.建立正常步态下跟骨及周围结构的三维有限元模型,分析正常步态下跟骨生物力学变化；
3.研究单足站立状态下,跟骨Bohler角度减少5°、10°、15°、20°、25°时距下关节、距骨、跟骰关节、足底的应力分布变化,分析保守治疗跟骨关节外骨折时Bolher角需要恢复的角度。
4.研究单足站立状态下,跟骨高度减少5mm、10mm、15mm、20mm时距下关节、距骨、跟骰关节、足底的应力分布变化,分析术中需要恢复跟骨的高度。
5.对跟骨锁定钢板和解剖型钢板治疗Sanders Ⅳ型跟骨骨折时距下关节、距骨、跟骨骨折块、跟骰关节的应力分布及位移进行综合比较分析,以得出SandersⅣ型跟骨骨折的治疗方案并推断出内固定的合理改进方向。
方法
1.数字化足踝部三维有限元模型的构建与验证：采用南方医科大学南方医院影像中心的LightSpeed16排螺旋CT,扫描参数：电压120～140KV,电流强度240～300mA,螺距1.375～1.75,层厚7.5mm,矩阵512×512,重建层厚0.625mm。对志愿者右足自踝关节上20cm胫腓骨远端向下扫描至足底,扫描时右足保持中立位,以DICOM格式输入个人计算机的Mimics10.01软件,经自动或手动阈值分割后三维重建出完整足踝部的28块骨骼及外围软组织的三维结构,再以点云输出并导入SolidWorks2009,利用网格处理向导及曲面生成向导生成几何模型并重建装配体,然后分别导入两种有限元分析软件：(1)方法一为导入有限元分析软件ANSYS12.0的Workbench模块建立完整的足踝部有限元模型。在踝关节的接触面两侧根据关节间隙分别建立了0.5mm关节软骨,其他关节采用仅受压的三维杆单元模拟软骨,并建立了125条弹簧模拟韧带和小腿骨间膜,5条梁单元模拟跖筋膜,材料属性分别参照文献确定。然后参照Anderson等方法,对模型仅取胫骨及距骨所构成的简单踝关节模型加以测试。通过模拟人体单足站立状态下的力学传递,对模型胫骨下端的上截面施加700N垂直载荷,对距骨予以约束。测量踝关节胫骨下关节面的接触压力、接触面积,并将结果与前者进行对照。(2)方法二为导入Simulation建立简化的踝关节有限元模型。根据研究需要,分别建立了包含胫骨、腓骨、距骨、跟骨及舟骨的5骨装配体,以及还包括骰骨及3块楔骨的9骨装配体的有限元模型。在模型中用“仅延伸”的弹簧模拟韧带连接,其中在踝关节5骨装配体中共建立了31条弹簧,而在9骨装配体中建立了42条弹簧模拟踝关节周围韧带及小腿骨间膜等连接装置。定义各组织的材料属性,并通过自动或手动方法在各关节间生成接触对,设置相应的边界条件分别在踝关节5骨装配体有限元模型上模拟人体单足站立及踝关节内、外旋运动加载,而在踝关节9骨装配体有限元模型上模拟踝关节内、外翻运动加载,然后设置好网格划分密度生成网格并设置算例属性进行运算。
2.在不改变距下关节面的条件下将Bohler角的角度逐渐减少5度、10度、15度、20度、25度,并分别进行楔形截骨,最终生成6种有限元模型。假设为骨折面完全断裂并处于接触状态,摩擦系数为0.3。将跟骨、足部负重区三维有限元模型下缘全部节点的自由度约束为零作为边界条件,即远端各节点在X、Y、Z轴上的位移为0。于胫骨端予以模型700N轴向应力,计算此应力下模型的应力分布及位移分布。
3.在不改变距下关节面的条件下将跟骨高度逐渐减少5mm、10mm、15mm、20mm、并分别进行楔形截骨。最终生成5种有限元模型。假设为骨折面完全断裂并处于接触状态,摩擦系数为0.3。将跟骨、足部负重区三维有限元模型下缘全部节点的自由度约束为零作为边界条件,即远端各节点在X、Y、Z轴上的位移为O。于胫骨端予以模型700N轴向应力,计算此应力下模型的应力分布及位移分布。
4.根据Sanders Ⅳ型骨折对跟骨进行截骨,保持关节面的平整及各骨折块摩擦关系。同时根据跟骨解剖型和锁定钢板形态重建出两种骨折内固定有限元模型。假设为骨折面完全断裂并处于接触状态,摩擦系数为0.3。解剖型钢板设置为摩擦接触,锁定钢板则设置为不接触,将跟骨、足部负重区三维有限元模型下缘全部节点的自由度约束为零作为边界条件,即远端各节点在X、Y、Z轴上的位移为0。普通加压钢板设定与跟骨接触为加压摩擦接触,锁定钢板与跟骨间不考虑加压摩擦接触。计算该状态下跟骨与钢板的应力分布、位移。
结果
1.在按方法一所建的完整的足踝部有限元模型中,将胫、距骨组成的踝关节测试结果与Anderson等实验结果对照后发现,二者在中立位踝关节垂直加载下应力主要分布于胫骨下关节面中部及前外侧,最大应力处于2.7MPa-4.0MPa之间,在分布区域和分布趋势、数值大小上基本一致,初步证明本模型是有效的。按方法二所建立的简化的两个踝关节三维有限元模型经测试可以模拟踝关节的不同受力情况,并可进行正确的加载运算,而且单元数、节点数、运算时间适中。各种加载后所产生的应力、位移的结果合理,比较贴近真实状况。将结果与Liacouras和Wayne在相同边界条件下所作的踝关节外旋模拟实验结果进行了对比,发现本模型在踝关节外旋加载中胫骨的旋转角度为3.85°,与其有限元模型计算的4.28°比较接近,另外本模型的主要关节的接触力大小也与其结果对应性较好,证明了本模型的有效性。
2.当跟骨的Bohler角分别减少5°、10°、15°、20°、25°时,距下关节面的应力峰值分别增加了11.3%、12%、18.5%、19.8%、32.1%；距骨应力峰值分别增加3%、12.6%、27.6%、54%、70.6%；跟骰关节面应力随着Bohler角减少而不断减小,应力峰值分别减少2.3%、4.7%、15.4%、20.3%、20.4%;足底应力集中于跟骨底部,应力峰值值分别增大11.3%、11.6%、18.6%、19.8%、32.1%。
3.跟骨高度分别减少5mmm、10mm、15mm、20mm时,距下关节面的应力峰值分别增加了10.3%、18.5%、35.4%、54.7%；距骨侧的应力峰值分别增加了最大应力值分别增加8.9%、9.8%、16.1%、16.7%；跟骰关节面应力随着跟骨高度减少而不断减小,应力峰值分别减少2.3%、4.4%、22.4%、67.4%、80.1%；足底应力主要集中于足跟处,应力峰值分别增大10.2%、18.4%、35.4%、54.7%。
4.使用锁定钢板固定后最大应力集中于钢板螺钉交界处,应力峰值为143.49MPa,上排螺钉中部、钢板中后部存在应力集中现象；解剖型钢板应力分布相对均匀,螺钉应力分布均匀,最大应力位于钢板中后部,应力峰值为102.49MPa;距骨及跟骨各骨折块的应力峰值均为锁定钢板大于解剖型钢板。两种钢板内固定模型主要位移均分布于近关节面的螺钉处,其中锁定钢板的位移小于解剖型钢板模型,分别为0.222mm,0.389mm;锁定钢板固定的骨折块位移峰值均小于解剖型钢板。
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、Ansys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跟骨的解剖结构及其受力特点,有利于对跟骨进行生物力学分析。
3. Bohler角改变对距下关节、跟骰关节、足底的应力影响较小,而对胫距关节的影响较大,术中需要根据骨折情况尽量恢复患者的Bohler角,对于Bohler角减小10°以内的骨折,如无其他手术指征可选择保守治疗；跟骨高度的改变对距下关节、跟骰关节及足底的应力改变较大,而对胫距关节影响较小,术中需要将跟骨高度的改变控制在15mm之内,避免远期关节功能的影响。
4.切开复位钢板内固定治疗粉碎性跟骨骨折,尤其对于Sanders Ⅳ型骨折,维持关节面平整非常重要。锁定钢板对于维持关节面的平整略显优势,而解剖型加压钢板能够分散骨折端的应力,钢板与骨块间的摩擦力作用也能起一定代偿作用。且在所有骨块中,载距突产生位移最大,因此跟骨钢板的设计需要对载距突部分进行重点固定。结合桡骨远端骨折、胫骨平台骨折治疗理论,对于跟骨骨折的钢板可以设计为,两枚锁定螺钉固定于载距突,跟骨上排螺钉采用锁定螺钉与加压螺钉间断排列,平行于关节面打入；足底部位以两枚锁定螺钉固定前后两端,其余部分均采用普通松质骨螺钉固定。此钢板能够同时满足钢板与骨折端的加压作用同时也发挥了锁定螺钉的部分优势。无论何种内固定方式关节内碎骨快可随足部负重而产生不同程度移位,存在较高创伤性关节炎的风险,建议采用一期外固定二期关节融合治疗。
Background:
The calcaneus is an odd-shaped bone. The superior surface consists of three articular facets (the anterior, middle, and posterior) that articulate with the talus. The posterior facet is the major weight-bearing surface and the largest facet. The middle facet is anterior and medial and is located on the sustentaculum; it is often contiguous with the anterior facet. The sustentaculum sits under the talar neck and is medial to the calcaneal body. It is attached to the talus by the interosseous talocalcaneal ligament and by the deltoid ligament medially. The flexor hallucis longus tendon runs below the sustentaculum. Laterally, the peroneal tendons run obliquely along the lateral wall of the calcaneus and sit in two shallow grooves, with a bony prominence between them known as the peroneal tubercle. The entire calcaneal surface behind the posterior facet is known as the posterior tuberosity. On its plantar surface, it has two processes, the lateral and medial. The medial process is the origin of the abductor hallucis muscle and the major weight-bearing structure in the hindfoot. Finally, the Achilles tendon inserts on the posterior surface of the tuberosity.
Calcaneal fractures are the most common tarsal bone fractures, accounted for60%of the tarsal bone fractures, accounting for2%of the body fracture, about75%refers to intra-articular fractures,20%to45%with calcaneocuboid joint injury. due to the complexity of the calcaneus anatomy and surrounding anatomical structures, poor quality of local soft tissue coverage, it is difficult to treat with much complications and poor outcome. During the past20years, with the development of antibiotics, imaging technology, internal fixation and minimally invasive techniques, as well as the research of biomechanics of calcaneal fractures, its clinical efficacy and continuously improve. Although a lot of method with differentiated indications and advantages and disadvantages has been applied to treat calcaneal fractures, it is advised that the solution should be made according to the patient's degree of injury, fracture type, systemic and local circumstances and sections of the technical conditions.
Calcaneal fractures often related to calcaneus shorten in the length, width increases, reduced height, uneven subtalar joint the calcaneal axis lateral angled, the the calcaneal tuberosity joint angle (Bohler angle) decreases, disappeared or contra-angle Gissane angle narrowing or increased talar tilt angle to shrink and disappear. This will cause the arch collapse, affect the overall shape of the foot and mechanical stability, can form traumatic flatfoot. Loss of normal relations between the articular surface of the calcaneus three articular surface uneven and the shift is bound to cause a change of the force and movement of the subtalar joint, causing secondary injury subtalar joints in and around the joints, such as trauma arthritis. Calcaneocuboid articular surface fractures will seriously affect the normal movement of the hock function and subtalar joint eversion activities caused calcaneocuboid joint traumatic arthritis, enough to affect normal walking. Serious subtalar joint surface damage and cartilage defects can occur spontaneously arthrodesis, the loss of the active function. After pronation, calcaneal widening shortening, reduced height and lateral wall of the outer expansion is not only caused by wearing shoes difficult, and the peroneus longus and brevis tendon entrapment. In addition, the decline lateral malleolus direct contact or collision the calcaneus outside sidewall calcaneofibular impingement syndrome, long-term form pseudarthrosis. Achilles tendon point enough, leading to weakness of the gastrocnemius and soleus. Hind foot line of force to change the calf muscles can pull direction, torque and muscle changes, the final occurrence of foot and ankle pain and dysfunction. In addition, the abnormal movement of the ankle joint force line and bilateral limb length inequality will affect the normal function of the entire lower extremity and spine, premature low back pain and neck pain. Therefore, the purpose of calcaneal fractures after the resumption of normal biomechanics of the foot and functions to avoid undesirable consequences.
With the development of digital simulation modeling techniques and finite element method, the digital virtual gradually applied to the clinical diagnosis, treatment, and experimental studies. Compared with the previous biomechanical experiments, the finite element method is a useful numerical tool geometry and digital nonlinear complex structure of internal stress and strain analysis. Can complete the load cannot be achieved by other research methods and constraints, the specimens can also be corrected to simulate any pathological state. The finite element model can provide the normal physiological experiments cannot be that to get the objective entities experiments difficult to get results. By changing the load loading mode, change the material properties of individual stress analysis.
Objective:
1. With the help digital technology, to establish the calcaneus and surrounding structures digital virtual simulation model to explore the of digital simulation Medicine modeling method and significance
2. Establish normal gait the calcaneus and around the structure of three-dimensional finite element model to analyze the the calcaneus biomechanics normal gait changes.
3. To analysis of the operative indication of conservative treatment as well as the intra-articular calcaneal fracture with the change of Bolher angle. Single-leg stance state, calcaneus Bohler angle decreased by5°,10°,15°,20°and25°of the subtalar joint, to test talus calcaneocuboid joint plantar stress distribution changes.
4. To analysis of the operative indication of conservative treatment as well as the intra-articular calcaneal fracture with the change of Bolher angle. Single-leg stance state, calcaneus height decreased by5mm,10mm,15mm and20mm, talus calcaneocuboid joint plantar stress distribution changes.
5. Calcaneal locking plates and anatomical plate in the treatment of Sanders Ⅳ type calcaneal fractures subtalar joint, talus, calcaneus fracture fragments, with the the calcaneocuboid joint stress distribution and displacement comprehensive comparative analysis to arrive at Sanders Ⅳ calcaneal fractures treatment programs and to infer the direction of the internal fixation reasonable improvement.
Methods:
1.Construction and verification of digital three-dimensional finite element model of foot and ankle:Adopting LightSpeed16-slice spiral CT of the Imaging Center, Nanfang Hospital affiliated to Southern Medical University (scanning parameters:120～140KV,240～300mA, pitch of1.375～1.75, the layer thickness7.5mm, matrix512×512, reconstruction slice thickness0.625mm), scaned the volunteer's right foot from distal tibia and fibula20cm above the ankle down to the planta, with the right foot remaining neutral position. Then imported the scanned data of DICOM format into Mimics10.01software, by threshold segmentation automatically or manually, to reconstruct the three-dimensional structure of a complete foot and ankle composed of28bones and surrounding soft tissue. Finally, exported the data with point cloud format and reimported into SolidWorks2009, using the guide of grid processing and surface generation to form geometric models and reconfigure them, then import the data into two kinds of finite element analysis softwares:Method1: Imported into Workbench module of finite element analysis software ANSYS12.0to establish a complete finite element model of foot and ankle. To construct0.5mm of articular cartilage on both sides of contact surface according to the joint space, while to use three-dimensional rod elements which were compressed only to simulate other joints cartilage, and to establish125springs to simulate ligaments and crural interosseous membrane, five beam elements to simulate plantar fascia.The material properties were determined with reference to documents. Then refered to Anderson's method, took the tibia and talus only as a simple model of the ankle joint for test. The normal standing status of ankle joint was simulated by application a vertical load of700N on the upper section of the lower tibia while the talus constrained. To measure contact pressure and contact area of inferior articular surface of the tibia, and to compare the results with the former. Method2:Imported the data into Simulation module of Solidworks to establish a simplified finite element model of the ankle. According to the research needs, to establish a5-bones assembly finite element model containing the tibia, fibula, talus, calcaneus, and navicular, and a9-bones assembly finite element model also including the cuboid bone and the three cuneiform bones in addition to the5bones mentioned above. In the models, to use tension-only springs to simulate ligaments connection. The5-bones assembly contained31springs, while the 9-bones assembly was established42springs to simulate connected structures such as ligaments around the ankle and crural interosseous membrane. To Define the material properties of each tissue, to generate contact pair between each joints automatically or manually, and to set the corresponding boundary conditions. In the5-bone assembly finite element model of ankle, to simulate the state of human body with one foot standing and the states of internal and external rotation of ankle, while in the9-bones finite element model of ankle, to simulate the states of ankle inversion and ankle eversion. Then, regulated the mesh density to generate mesh, and set the simulation examples attribute for solution.
2.With the Subtalar joint surface unchanged, wedge osteotomy was applied to the calcaneus to make the Bohler angle gradually decreased in5degrees,10degrees,15degrees,20degrees,25degrees, respectively, then reconstruct six FE models. Assuming the fracture surface completely broken and is in contact state, and the coefficient of friction of0.3. All nodes of the calcaneus, the lower edge of the three-dimensional finite element model of the weight-bearing area of the foot degrees of freedom constrained to zero as boundary conditions, each remote node in the X, Y, Z axis displacement0. Be on the tibial end model700N axial stress calculation of stress distribution and displacement distribution of the model under this stress.
3.With the Subtalar joint surface unchanged, wedge osteotomy was applied to the calcaneus to make the calcaneus height gradually decreased in5mm,10mm,15mm and20mm respectively, then reconstruct five FE models. Assuming the fracture surface completely broken and is in contact state, and the coefficient of friction of0.3. All nodes of the calcaneus, the lower edge of the three-dimensional finite element model of the weight-bearing area of the foot degrees of freedom constrained to zero as boundary conditions, each remote node in the X, Y, Z axis displacement0. Be on the tibial end model700N axial stress calculation of stress distribution and displacement distribution of the model under this stress.
4.To stimulated Sanders IV fractures of the calcaneus and do osteotomy as well, keep the fragment of the articular surface of the friction relationship. Assuming the fracture surface completely broken and is in contact state, and the coefficient of friction of0.3. Anatomic plate set to frictional contact, locking plate is set to no contact the calcaneus foot weight-bearing area three-dimensional finite element model of the lower edge of the degrees of freedom of all nodes constrained to zero as the boundary conditions. All nodes of the calcaneus, the lower edge of the three-dimensional finite element model of the weight-bearing area of the foot degrees of freedom constrained to zero as boundary conditions, each remote node in the X, Y, Z axis displacement0. Be on the tibial end model700N axial stress calculation of stress distribution and displacement distribution of the model under this stress.
Result:
1. In the complete finite element model of foot and ankle constructed by method1, the test results of the ankle composed of tibia and talus were taken to contrast with Anderson's study. It showed that the stress on ankle joint articular surface of the tibia mainly distributed at the central and anterolateral aspects in both of them when ankle joint was in neutral position under the vertical loading, with the maximum stress between2.7MPa and4.0MPa, substantial agreement on distribution area, distribution trend, and numerical value. It was preliminarily verified this model valid. The test results of two simplified three-dimensional finite element models of the ankle established by method2showed that they could simulate various load situations of ankle for solution, with moderate number of element, node and suitable amount of computing time. The stress and displacement results in each loading were reasonable and close to the actual situation. Compared with Liacouras and Wayne's model under the same boundary conditions, it showed that the rotation angle of tibia was3.85°in our model whereas their result was4.28°after application of ankle external rotation load, comparatively close between the two values. In adition, the contact forces of major joints were also consistent with theirs. All confirmed the validity of our models.
2. When Bohler angle of the calcaneus decreased by5°,10°,15°,20°,25°, and the stress of the subtalar joint surface peak increase of11.3%,12%,18.5%,19.8%,32.1%; taluspeak stress increased by3%, respectively,12.6%,27.6%,54%,70.6%; calcaneocuboid articular surface stress reduce Bohler angle decreases, the peak stress decreased by2.3%,4.7%,15.4%,20.3%,20.4%; plantar stress concentration at the bottom of the calcaneus, the peak stress values were increased by11.3%.11.6%,18.6%,19.8%,32.1%.
3. Calcaneal height to reduce5mm,10mm,15mm,20mm, the subtalar joint surface stress peak increase of10.3%,18.5%,35.4%,54.7%; the talar side peak stress increased by8.9%,9.8%,16.1%,16.7%; calcaneocuboid articular surface stress with the reduction of the height of the calcaneus continue to decrease, the peak stress decreased by2.3%,4.4%,22.4%,67.4%,80.1%;The foot stress mainly concentrated in the heel at peak stress increased10.2%,18.4%,35.4%,54.7%.
4. Using locking plate fixation, maximum stress concentration at the plate and screw the junction stress peak to143.49MPa, stress concentrated on the middle of the upper row of screws steel plate in the rear; anatomical plate stress distribution is relatively uniform the screw stress distribution is uniform, the maximum stress in thesteel plate in the rear of the peak stress of102.49MPa; talus and calcaneus each fracture stress peak are locking plate block than anatomic plate. Major displacement of two steel plates fixed model distributed near the articular surface of the screw at which the lock plate displacement is less than the anatomical plate model were0.222mm,0.389mm; locking plate fixation peak displacement of the fracture fragments are less than anatomic steel plate.
Conclusions:
1. Based on CT scan data, the calcaneus 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 from3D reconstruction of computed tomography, a three-dimensional (3D) finite element model was developed using Mimics, Geomagic Studio, Hypermesh, Ansys 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 calcaneus and its mechanical characteristics. It was beneficial for biomechanical analysis of the calcaneus.
3. The change of Bohler angle affect little on the subtalar joint, calcaneocuboid joint, plantar stress changes but more to tibiotalar joint. It is necessary to restore the Bolher angle during operation. If the Bohler angle changes below10°, as no other surgery indication, conservative treatment could be choose; The change of calcaneus height affect more on the subtalar joint, calcaneocuboid joint, plantar stress changes but little to tibiotalar joint. It is necessary to maintain the calcaneus height under15mm, to get better joint function for long term.
4. Open reduction and internal fixation for the treatment of comminuted calcaneal fractures, especially for Sanders IV type fracture formation is very important to maintain the articular surface. Locking plate show slightly advantage for the maintenance of the articular surface of the flat, anatomical compression plate can be dispersed fracture stress, the frictional force between the plate and bone can also play a compensatory role. During all bone fragment, set out from the sudden displacement calcaneal plate design needs to set out from the sudden part fixed focus. According to the theory of treatment of tibial plateau fractures distal radial fracture theory, the calcaneal fractures can be designed for two locking screws in the set from the sudden, the calcaneus upper row of screws on the locking screw and compression screw intermittent arranged, parallel to the articular surface. Plantar parts fixed with two locking screws front and rear ends, the rest are ordinary cancellous bone screws. This plate combines the advantage of locking plate and anatomic plate. Whatever within fixed intra-articular bone fragments fast with foot weight and produce different degrees of shift, there is a higher traumatic arthritis risk, it is recommended that an external fixation two arthrodesis treatment.
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[37]Cheung JT, An KN, Zhang M. Consequences of partial and total plantar fascia release:a finite element study[J]. Foot Ankle Int,2006,27(2):125-132.
[38]Cheung JT, Zhang M, An KN. Effect of Achilles tendon loading on plantar fascia tension in the standing foo[J]t. Clin Biomech (Bristol, Avon),2006,21(2):194-203.
[39]Cheung JT, Zhang M. A 3-dimensional finite element model of the human foot and ankle for insole design[J]. Arch Phys Med Rehabil,2005,86(2):353-358.
[40]Yu J, Cheung JT, Fan Y, Zhang Y, Leung AK, Zhang M. Development of a finite element model of female foot for high-heeled shoe design[J]. Clin Biomech (Bristol, Avon),2008,23 Suppl 1:S31-38.
[41]Cheung JT, Zhang M. Parametric design of pressure-relieving foot orthosis using statistics-based finite element method[J]. Med Eng Phys,2008,30(3):269-277.
[42]Actis RL, Ventura LB, Smith KE,et al. Numerical simulation of the plantar pressure distribution in the diabetic foot during the push-off stance [J]. Med Biol Eng Comput,2006,44(8):653-63.
1. Harnroongroj T, Chuckpaiwong B, Angthong C, Nanakorn P, Sudjai N. Displaced articular calcaneus fractures:classification and fracture scores:a preliminary study. J Med Assoc Thai 2012;95(3):366-77.
2.俞光荣燕.跟骨骨折治疗方法的选择.中华骨科杂志2006；26(2).
3. Carr JB. Surgical treatment of the intra-articular calcaneus fracture. Orthop Clin North Am 1994;25(4):665-75.
4. Jacob S, Patil MK. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis. J Rehabil Res Dev 1999;36(3):252-63.
5. Cheung JTM, Zhang M, Leung AKL, Fan YB. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study. J Biomech 2005;38(5):1045-54.
6. Gefen A, Megido-Ravid M, Itzchak Y, Arcan M. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications. J Biomech Eng-T Asme 2000; 122(6):630-39.
7. Corazza F, O'Connor JJ, Leardini A, Castelli VP. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech 2003;36(3): 363-72.
8. Funk JR, Hall GW, Crandall JR, Pilkey WD. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng-TAsme 2000; 122(1):15-22.
9. Burdeaux BD. Reduction of calcaneal fractures by the McReynolds medial approach technique and its experimental basis. Clin Orthop Relat Res 1983(177): 87-103.
10. Nemeth J, Scherfel T, Nabradi S. The principle and practice of the minimal invasivity in the course of our traumatological work. Acta Chir Hung 1997;36(1-4): 258-9.
11. Ogut T, Ayhan E, Kantarci F, Unlu MC, Salih M. Medial fracture line significance in calcaneus fracture. J Foot Ankle Surg 2011;50(5):517-21.
12. Badoux DM. Some biomechanical aspects of the structure of the equine tarsus. Anat Anz 1987;164(1):53-61.
13. Scott SH, Winter DA. Biomechanical model of the human foot:kinematics and kinetics during the stance phase of walking. J Biomech 1993;26(9):1091-104.
14. Lespessailles E, Jullien A, Eynard E, et al. Biomechanical properties of human os calcanei:relationships with bone density and fractal evaluation of bone microarchitecture. J Biomech 1998;31(9):817-24.
15. Vogler HW, Bojsen-Moller F. Tarsal functions, movement, and stabilization mechanisms in foot, ankle, and leg performance. J Am Podiatr Med Assoc 2000;90(3): 112-25.
16. Kirby KA. Subtalar joint axis location and rotational equilibrium theory of foot function. J Am Podiatr Med Assoc 2001;91(9):465-87.
17. Cohen JC. Anatomy and biomechanical aspects of the gastrocsoleus complex. Foot Ankle Clin 2009;14(4):617-26.
18. Wu L, Zhong S, Zheng R, et al. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus. Surg Radiol Anat 2007;29(7):561-7.
19. Szaro P, Witkowski G, Smigielski R, Krajewski P, Ciszek B. Fascicles of the adult human Achilles tendon-an anatomical study. Ann Anat 2009; 191 (6):586-93.
1. 俞光荣,燕晓宇.跟骨骨折治疗方法的选择[J].中华骨科杂志,2006,26(2)：134-141.
2. 陈滨,黎润光,王钢.跟骨骨折的手术治疗策略及疗效分析[J].中华创伤骨折杂志,2010,12：746-751.
3.俞光荣.跟骨骨折的治疗策略[J].上海医学,2005,28：541-543.
4. Jacob S, Patil MK. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis. J Rehabil Res Dev 1999;36(3):252-63.
5. Cheung JTM, Zhang M, Leung AKL, Fan YB. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study. J Biomech 2005;38(5):1045-54.
6. Gefen A, Megido-Ravid M, Itzchak Y, Arcan M. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications. J Biomech Eng-T Asme 2000; 122(6):630-39.
7. Corazza F, O'Connor JJ, Leardini A, Castelli VP. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech 2003;36(3):363-72.
8. Funk JR, Hall GW, Crandall JR, Pilkey WD. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng-T Asme 2000;122(1):15-22.
9. Sowmianarayanan S, Chandrasekaran A, Kumar RK. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants-a comparative study. Proc Inst Mech Eng H 2008;222(1):117-27.
10. Wirtz DC, Pandorf T, Portheine F, et al. Concept and development of an orthotropic FE model of the proximal femur[J]. J Biomech,2003;36(2):289-93.
11.刘清华,余斌,金丹等.解剖结构完整的踝关节有限元模型构建及意义[J].山东医药,2010；50(14)：1-3.
12.王亦璁.骨与关节损伤[M].4版.人民卫生出版社.2009：1529.
13. Ogut T, Ayhan E, Kantarci F, Unlu MC, Salih M. Medial fracture line significance in calcaneus fracture[J]. J Foot Ankle Surg,2011; 50:517-521.
14. Goldzak M, Mittlmeier T, Simon P. Locked nailing for the treatment of displaced articular fractures of the calcaneus:description of a new procedure with calcanail((?))[J].Eur J Orthop Surg Traumatol.2012 May;22(4):345-349.
1. Sanders R. Intra-articular fractures of the calcaneus:present state of the art. J Orthop Trauma 1992;6(2):252-65.
2. Sanders R. Displaced intra-articular fractures of the calcaneus. J Bone Joint Surg Am 2000;82(2):225-50.
3. Poeze M, Verbruggen JP, Brink PR. The relationship between the outcome of operatively treated calcaneal fractures and institutional fracture load. A systematic review of the literature. J Bone Joint Surg Am 2008;90(5):1013-21.
4. acob S, Patil MK. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis. J Rehabil Res Dev 1999;36(3):252-63.
5. Cheung JTM, Zhang M, Leung AKL, Fan YB. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study. J Biomech 2005;38(5):1045-54.
6. Wirtz DC, Pandorf T, Portheine F, et al. Concept and development of an orthotropic FE model of the proximal femur. J Biomech 2003;36(2):289-93.
7. Sitthiseripratip K, Van Oosterwyck H, Vander Sloten J, et al. Finite element study of trochanteric gamma nail for trochanteric fracture. Med Eng Phys 2003;25(2): 99-106.
8. Kobayashi E, Wang TJ, Doi H, Yoneyama T, Hamanaka H. Mechanical properties and corrosion resistance of Ti-6A1-7Nb alloy dental castings. J Mater Sci Mater Med 1998;9(10):567-74.
9. Pioletti DP, Rakotomanana LR. Can the increase of bone mineral density following bisphosphonates treatments be explained by biomechanical considerations? Clin Biomech (Bristol, Avon) 2004;19(2):170-4.
10. Corazza F, O'Connor JJ, Leardini A, Castelli VP. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech 2003;36(3): 363-72.
11. Funk JR, Hall GW, Crandall JR, Pilkey WD. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng-T Asme 2000; 122(1):15-22.
12. Sowmianarayanan S, Chandrasekaran A, Kumar RK. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants--a comparative study. Proc Inst Mech Eng H 2008;222(1):117-27.
13. Levine DS, Helfet DL. An introduction to the minimally invasive osteosynthesis of intra-articular calcaneal fractures. Injury 2001;32 Suppl 1:SA51-4.
14. Randle JA, Kreder HJ, Stephen D, Williams J, Jaglal S, Hu R. Should calcaneal fractures be treated surgically? A meta-analysis. Clin Orthop Relat Res 2000(377): 217-27.
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18. Tarng YW, Yang SW, Hsu CJ. Palmar locking plates for corrective osteotomy of latent malunion of dorsally tilted distal radial fractures without structural bone grafting. Orthopedics 2011;34(6):178.
19. Sugun TS, Gurbuz Y, Ozaksar K, Toros T, Kayalar M, Bal E. Results of volar locking plating for unstable distal radius fractures. Acta Orthop Traumatol Turc 2012;46(1):22-5.
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21. Blake MH, Owen JR, Sanford TS, Wayne JS, Adelaar RS. Biomechanical evaluation of a locking and nonlocking reconstruction plate in an osteoporotic calcaneal fracture model. Foot Ankle Int 2011;32(4):432-6.
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[39]Cheung JT, Zhang M. A 3-dimensional finite element model of the human foot and ankle for insole design[J]. Arch Phys Med Rehabil,2005,86(2):353-358.
[40]Yu J, Cheung JT, Fan Y, Zhang Y, Leung AK, Zhang M. Development of a finite element model of female foot for high-heeled shoe design[J]. Clin Biomech (Bristol, Avon),2008,23 Suppl 1:S31-38.
[41]Cheung JT, Zhang M. Parametric design of pressure-relieving foot orthosis using statistics-based finite element method[J]. Med Eng Phys,2008,30(3):269-277.
[42]Actis RL, Ventura LB, Smith KE,et al. Numerical simulation of the plantar pressure distribution in the diabetic foot during the push-off stance [J]. Med Biol Eng Comput,2006,44(8):653-63.
1. Harnroongroj T, Chuckpaiwong B, Angthong C, Nanakorn P, Sudjai N. Displaced articular calcaneus fractures:classification and fracture scores:a preliminary study. J Med Assoc Thai 2012;95(3):366-77.
2.俞光荣燕.跟骨骨折治疗方法的选择.中华骨科杂志2006；26(2).
3. Carr JB. Surgical treatment of the intra-articular calcaneus fracture. Orthop Clin North Am 1994;25(4):665-75.
4. Jacob S, Patil MK. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis. J Rehabil Res Dev 1999;36(3):252-63.
5. Cheung JTM, Zhang M, Leung AKL, Fan YB. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study. J Biomech 2005;38(5):1045-54.
6. Gefen A, Megido-Ravid M, Itzchak Y, Arcan M. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications. J Biomech Eng-T Asme 2000; 122(6):630-39.
7. Corazza F, O'Connor JJ, Leardini A, Castelli VP. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech 2003;36(3): 363-72.
8. Funk JR, Hall GW, Crandall JR, Pilkey WD. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng-TAsme 2000; 122(1):15-22.
9. Burdeaux BD. Reduction of calcaneal fractures by the McReynolds medial approach technique and its experimental basis. Clin Orthop Relat Res 1983(177): 87-103.
10. Nemeth J, Scherfel T, Nabradi S. The principle and practice of the minimal invasivity in the course of our traumatological work. Acta Chir Hung 1997;36(1-4): 258-9.
11. Ogut T, Ayhan E, Kantarci F, Unlu MC, Salih M. Medial fracture line significance in calcaneus fracture. J Foot Ankle Surg 2011;50(5):517-21.
12. Badoux DM. Some biomechanical aspects of the structure of the equine tarsus. Anat Anz 1987;164(1):53-61.
13. Scott SH, Winter DA. Biomechanical model of the human foot:kinematics and kinetics during the stance phase of walking. J Biomech 1993;26(9):1091-104.
14. Lespessailles E, Jullien A, Eynard E, et al. Biomechanical properties of human os calcanei:relationships with bone density and fractal evaluation of bone microarchitecture. J Biomech 1998;31(9):817-24.
15. Vogler HW, Bojsen-Moller F. Tarsal functions, movement, and stabilization mechanisms in foot, ankle, and leg performance. J Am Podiatr Med Assoc 2000;90(3): 112-25.
16. Kirby KA. Subtalar joint axis location and rotational equilibrium theory of foot function. J Am Podiatr Med Assoc 2001;91(9):465-87.
17. Cohen JC. Anatomy and biomechanical aspects of the gastrocsoleus complex. Foot Ankle Clin 2009;14(4):617-26.
18. Wu L, Zhong S, Zheng R, et al. Clinical significance of musculoskeletal finite element model of the second and the fifth foot ray with metatarsal cavities and calcaneal sinus. Surg Radiol Anat 2007;29(7):561-7.
19. Szaro P, Witkowski G, Smigielski R, Krajewski P, Ciszek B. Fascicles of the adult human Achilles tendon-an anatomical study. Ann Anat 2009; 191 (6):586-93.
1. 俞光荣,燕晓宇.跟骨骨折治疗方法的选择[J].中华骨科杂志,2006,26(2)：134-141.
2. 陈滨,黎润光,王钢.跟骨骨折的手术治疗策略及疗效分析[J].中华创伤骨折杂志,2010,12：746-751.
3.俞光荣.跟骨骨折的治疗策略[J].上海医学,2005,28：541-543.
4. Jacob S, Patil MK. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis. J Rehabil Res Dev 1999;36(3):252-63.
5. Cheung JTM, Zhang M, Leung AKL, Fan YB. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study. J Biomech 2005;38(5):1045-54.
6. Gefen A, Megido-Ravid M, Itzchak Y, Arcan M. Biomechanical analysis of the three-dimensional foot structure during gait:A basic tool for clinical applications. J Biomech Eng-T Asme 2000; 122(6):630-39.
7. Corazza F, O'Connor JJ, Leardini A, Castelli VP. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech 2003;36(3):363-72.
8. Funk JR, Hall GW, Crandall JR, Pilkey WD. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng-T Asme 2000;122(1):15-22.
9. Sowmianarayanan S, Chandrasekaran A, Kumar RK. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants-a comparative study. Proc Inst Mech Eng H 2008;222(1):117-27.
10. Wirtz DC, Pandorf T, Portheine F, et al. Concept and development of an orthotropic FE model of the proximal femur[J]. J Biomech,2003;36(2):289-93.
11.刘清华,余斌,金丹等.解剖结构完整的踝关节有限元模型构建及意义[J].山东医药,2010；50(14)：1-3.
12.王亦璁.骨与关节损伤[M].4版.人民卫生出版社.2009：1529.
13. Ogut T, Ayhan E, Kantarci F, Unlu MC, Salih M. Medial fracture line significance in calcaneus fracture[J]. J Foot Ankle Surg,2011; 50:517-521.
14. Goldzak M, Mittlmeier T, Simon P. Locked nailing for the treatment of displaced articular fractures of the calcaneus:description of a new procedure with calcanail((?))[J].Eur J Orthop Surg Traumatol.2012 May;22(4):345-349.
1. Sanders R. Intra-articular fractures of the calcaneus:present state of the art. J Orthop Trauma 1992;6(2):252-65.
2. Sanders R. Displaced intra-articular fractures of the calcaneus. J Bone Joint Surg Am 2000;82(2):225-50.
3. Poeze M, Verbruggen JP, Brink PR. The relationship between the outcome of operatively treated calcaneal fractures and institutional fracture load. A systematic review of the literature. J Bone Joint Surg Am 2008;90(5):1013-21.
4. acob S, Patil MK. Three-dimensional foot modeling and analysis of stresses in normal and early stage Hansen's disease with muscle paralysis. J Rehabil Res Dev 1999;36(3):252-63.
5. Cheung JTM, Zhang M, Leung AKL, Fan YB. Three-dimensional finite element analysis of the foot during standing-a material sensitivity study. J Biomech 2005;38(5):1045-54.
6. Wirtz DC, Pandorf T, Portheine F, et al. Concept and development of an orthotropic FE model of the proximal femur. J Biomech 2003;36(2):289-93.
7. Sitthiseripratip K, Van Oosterwyck H, Vander Sloten J, et al. Finite element study of trochanteric gamma nail for trochanteric fracture. Med Eng Phys 2003;25(2): 99-106.
8. Kobayashi E, Wang TJ, Doi H, Yoneyama T, Hamanaka H. Mechanical properties and corrosion resistance of Ti-6A1-7Nb alloy dental castings. J Mater Sci Mater Med 1998;9(10):567-74.
9. Pioletti DP, Rakotomanana LR. Can the increase of bone mineral density following bisphosphonates treatments be explained by biomechanical considerations? Clin Biomech (Bristol, Avon) 2004;19(2):170-4.
10. Corazza F, O'Connor JJ, Leardini A, Castelli VP. Ligament fibre recruitment and forces for the anterior drawer test at the human ankle joint. J Biomech 2003;36(3): 363-72.
11. Funk JR, Hall GW, Crandall JR, Pilkey WD. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng-T Asme 2000; 122(1):15-22.
12. Sowmianarayanan S, Chandrasekaran A, Kumar RK. Finite element analysis of a subtrochanteric fractured femur with dynamic hip screw, dynamic condylar screw, and proximal femur nail implants--a comparative study. Proc Inst Mech Eng H 2008;222(1):117-27.
13. Levine DS, Helfet DL. An introduction to the minimally invasive osteosynthesis of intra-articular calcaneal fractures. Injury 2001;32 Suppl 1:SA51-4.
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