Results of the FEA for real and artificial bone.

Introduction
Subtalar joint arthrodesis is primarily indicated for advanced osteoarthritis, hindfoot deformity, and/or instability. During the first 6-10 weeks after surgery, there is an intermediary structurally weaker state before complete bony fusion of the calcaneus and talus occurs. Loading of the foot can lead to mechanical stresses and relative movements in the former joint gap, which can impede the fusion process. The objective of this study was to examine the mechanical healing conditions for a subtalar arthrodesis with a calcaneal locking nail.
Methods
A probabilistic finite element model of the subtalar joint with a calcaneal locking nail was created to represent the foot post-surgery that accounts for the uncertainty of the material properties. The model differentiates between cortical and cancellous bone and includes non-linear contact definitions in the subtalar joint. Multiple loading scenarios, including hindfoot inversion/eversion, were simulated to determine bone and implant stresses. Utilizing local articular coordinate systems, a displacement analysis was established to separate normal and tangential components and account for their separate effects. The loading of the locking nail was assessed through section moments.
Results
Under inversion/eversion loading, the area near the locking screws and upper end of the nail experienced the highest stresses. The maximum stresses in cortical and cancellous bone were 112±8.3 MPa and 2.1±0.2 MPa, respectively. The comparison of the von Mises and maximum principal stresses for the bones showed a load case dependency with strong effect on tensile loading states. The proposed method for the analysis of relative displacement in the local articular coordinate systems showed joint regions exhibiting normal and tangential movements that changed with the considered loading states. It was found that tangential displacements of up to 0.19 mm are related to the torsional loading of the calcaneal locking nail, which is connected to the corresponding torsional stiffness of the implant and its fixation in the calcaneus and talus. Normal displacements in the joint gap of up to -0.18 mm can be shown to be governed by the bending moments acting on the calcaneal locking nail, which are linked to the nail’s bending stiffness. The ratio of tangential and normal displacement in the critical inversion configuration was determined to be -1.1.
Conclusions
Inversion and eversion loads can lead to significant mechanical loading of the bones and to bending and torsional loading of the locking nail. The bending leads to normal displacements in the articular gap. Torsions can lead to significant tangential displacements that have been shown to promote non-union instead of bony fusion.

引言
距下关节融合术（subtalar joint arthrodesis）主要适应症为晚期骨关节炎、后足畸形及/或关节不稳定。术后6~10周为过渡期，此时跟骨（calcaneus）与距骨（talus）尚未完成完全骨性融合，骨结构处于力学强度较弱的状态。足部负重会使该关节间隙产生机械应力与相对微动，进而阻碍融合进程。本研究旨在探讨采用跟骨锁定钉（calcaneal locking nail）行距下关节融合术的力学愈合条件。

方法
构建带跟骨锁定钉的距下关节概率有限元模型，以模拟术后足部状态，并纳入材料属性的不确定性。该模型区分皮质骨（cortical bone）与松质骨（cancellous bone），并在距下关节中定义了非线性接触界面。模拟包括后足内翻（inversion）/外翻（eversion）在内的多种负重工况，以分析骨组织与植入物的应力分布。采用局部关节坐标系建立位移分析方法，将位移分解为法向与切向分量，并分别考量其影响。通过截面弯矩评估锁定钉的受力状态。

结果
在内翻/外翻负重工况下，锁定螺钉附近区域及钉体上端的应力水平最高。皮质骨与松质骨的最大应力分别为112±8.3 MPa与2.1±0.2 MPa。对骨组织的冯·米塞斯（von Mises）应力与最大主应力进行对比后发现，应力分布与负重工况高度相关，且受拉伸载荷状态影响显著。基于局部关节坐标系的相对位移分析方法显示，关节区域的法向与切向位移随负重工况发生变化。研究发现，最大可达0.19 mm的切向位移与跟骨锁定钉的扭转受力相关，而该受力与植入物自身扭转刚度及其在跟骨、距骨内的固定效果密切相关。关节间隙内最大可达-0.18 mm的法向位移，则由作用于跟骨锁定钉的弯矩所主导，该弯矩与钉体的弯曲刚度直接相关。在内翻临界工况下，切向位移与法向位移的比值为-1.1。

结论
内翻与外翻负重可对骨组织造成显著力学载荷，并使锁定钉承受弯曲与扭转应力。弯曲应力会引发关节间隙的法向位移。扭转应力则会引发显著的切向位移，而此类位移已被证实会阻碍骨性融合，进而导致骨不连（non-union）。