Quantification of plantar tissue behavior of the heel pad is essential in developing computational models for predictive analysis of preventive treatment options such as footwear for patients with diabetes. Simulation based studies in the past have generally adopted heel pad properties from the literature, in return using heel-specific geometry with material properties of a different heel. In exceptional cases, patient-specific material characterization was performed with simplified two-dimensional models, without further evaluation of a heel-specific response under different loading conditions. The aim of this study was to conduct an inverse finite element analysis of the heel in order to calculate heel-specific material properties in situ. Multidimensional experimental data available from a previous cadaver study by Erdemir et al. (“An Elaborate Data Set Characterizing the Mechanical Response of the Foot,” ASME J. Biomech. Eng., >131(9), pp. 094502) was used for model development, optimization, and evaluation of material properties. A specimen-specific three-dimensional finite element representation was developed. Heel pad material properties were determined using inverse finite element analysis by fitting the model behavior to the experimental data. Compression dominant loading, applied using a spherical indenter, was used for optimization of the material properties. The optimized material properties were evaluated through simulations representative of a combined loading scenario (compression and anterior-posterior shear) with a spherical indenter and also of a compression dominant loading applied using an elevated platform. Optimized heel pad material coefficients were 0.001084 MPa (μ), 9.780 (α) (with an effective Poisson’s ratio (ν) of 0.475), for a first-order nearly incompressible Ogden material model. The model predicted structural response of the heel pad was in good agreement for both the optimization (<1.05% maximum tool force, 0.9% maximum tool displacement) and validation cases (6.5% maximum tool force, 15% maximum tool displacement). The inverse analysis successfully predicted the material properties for the given specimen-specific heel pad using the experimental data for the specimen. The modeling framework and results can be used for accurate predictions of the three-dimensional interaction of the heel pad with its surroundings.
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机译：在开发用于对预防性治疗方案（例如糖尿病患者的鞋类）进行预测分析的计算模型时，量化脚跟垫的足底组织行为至关重要。过去基于模拟的研究通常采用文献中的脚跟垫特性，而使用具有不同脚跟材料特性的特定于脚跟的几何形状作为回报。在特殊情况下，使用简化的二维模型对患者进行特定的材料表征，而无需进一步评估在不同负荷条件下对后跟的响应。这项研究的目的是对脚跟进行逆向有限元分析，以便就地计算脚跟特定的材料特性。多维实验数据可从Erdemir等人先前的尸体研究中获得。 （“ ASME J. Biomech。Eng。，> 131 （9），第094502页，“表征脚部机械响应的详尽数据集”）用于模型的开发，优化和评估材料特性。建立了标本特定的三维有限元表示。通过将模型行为拟合到实验数据，使用逆向有限元分析确定了脚跟垫的材料性能。使用球形压头施加的压缩主导载荷用于优化材料性能。通过模拟来评估优化的材料性能，该模拟代表使用球形压头的组合载荷情况（压缩和前后剪切），以及使用高架平台施加的压缩主导载荷。对于一阶几乎不可压缩的奥格登材料模型，优化后跟垫材料系数为0.001084 MPa（μ），9.780（α）（有效泊松比（ν）为0.475）。在优化（最大工具力<1.05％，最大工具位移为0.9％）和验证案例（最大工具力为6.5％，最大工具位移为15％）的情况下，模型预测的脚跟垫的结构响应都非常吻合。逆分析使用样本的实验数据成功地预测了给定样本特定脚跟垫的材料特性。建模框架和结果可用于精确预测脚跟垫与其周围环境的三维交互作用。
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