Chokhandre Snehal, Halloran Jason P, van den Bogert Antonie J, Erdemir Ahmet
Department of Biomedical Engineering, Cleveland Clinic, Cleveland, OH 44195, USA.
J Biomech Eng. 2012 Mar;134(3):031002. doi: 10.1115/1.4005692.
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.
量化足跟垫的足底组织行为对于开发计算模型以预测糖尿病患者预防性治疗方案（如鞋类）的分析至关重要。过去基于模拟的研究通常采用文献中的足跟垫属性，转而使用具有不同足跟材料属性的特定足跟几何形状。在特殊情况下，使用简化的二维模型进行患者特定的材料表征，而没有进一步评估不同加载条件下的特定足跟响应。本研究的目的是对足跟进行逆有限元分析，以原位计算特定足跟的材料属性。来自Erdemir等人先前尸体研究（“表征足部力学响应的详细数据集”，《美国机械工程师学会生物医学工程杂志》，第131卷第9期，第094502页）的多维实验数据用于模型开发、优化和材料属性评估。开发了一个特定标本的三维有限元表示。通过将模型行为与实验数据拟合，使用逆有限元分析确定足跟垫材料属性。使用球形压头施加的压缩主导加载用于材料属性的优化。通过代表球形压头的组合加载场景（压缩和前后剪切）以及使用升高平台施加的压缩主导加载的模拟来评估优化后的材料属性。对于一阶近似不可压缩的Ogden材料模型，优化后的足跟垫材料系数为0.001084 MPa（μ）、9.780（α）（有效泊松比（ν）为0.475）。该模型预测的足跟垫结构响应在优化（最大工具力<1.05%，最大工具位移0.9%）和验证案例（最大工具力6.5%，最大工具位移15%）中都具有良好的一致性。逆分析使用标本的实验数据成功预测了给定标本特定足跟垫的材料属性。该建模框架和结果可用于准确预测足跟垫与其周围环境的三维相互作用。
