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Research Papers

A Three-Dimensional Inverse Finite Element Analysis of the Heel Pad

[+] Author and Article Information
Snehal Chokhandre, Jason P. Halloran

 Department of Biomedical Engineering, Cleveland Clinic, Cleveland, OH 44195; Computational Biomodeling (CoBi) Core, Lerner Research Institute, Cleveland Clinic, Cleveland, OH 44195

Antonie J. van den Bogert

 Orchard Kinetics LLC, Cleveland, OH 44106

Ahmet Erdemir1

 Department of Biomedical Engineering, Cleveland Clinic, Cleveland, OH 44195; Computational Biomodeling (CoBi) Core, Lerner Research Institute, Cleveland Clinic, Cleveland, OH 44195,erdemira@ccf.org

1

Corresponding author.

J Biomech Eng 134(3), 031002 (Mar 20, 2012) (9 pages) doi:10.1115/1.4005692 History: Received October 14, 2011; Revised January 03, 2012; Posted February 21, 2012; Published March 16, 2012; Online March 20, 2012

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 (“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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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Model development: (a) cadaver specimen for which the mechanical testing and imaging data was used in the finite element model development, (b) three-dimensional surface geometries created for the specimen with a plane illustrating the separation of the region of interest (heel), (c) hexahedral mesh of the heel, and (d) finite element model showing heel and indenter.

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Figure 2

Experimental load-tool combinations used for inverse finite element analysis and validation purposes: (a) tools—a spherical indenter (25.4 mm in diameter) and a flat elevated platform (86 mm × 51 mm × 151 mm; width × height × length), (b) compression dominant indentation conditions used for material properties optimization, and (c) combined loading of compression and anterior-posterior shear applied using the indenter and compression dominant loading applied using the flat elevated platform; both used for validation.

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Figure 3

A hybrid control was used to apply the experimental tool trajectory in the model, consisting of a spring component driving the tool (indenter or elevated platform). A control point was defined and a linear spring was attached between the control point and the indenter reference point. Displacements of the control point implicitly applied experimental forces (see text for details). In the model, the control point is defined at the same location as the indenter reference point and is shown separately in the figure for illustration purposes.

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Figure 4

Structural response (forces and displacements) of the heel pad under the compression dominant indentation data. Both experimental and model predicted values are shown. The data set was used for the inverse finite element analysis and the model predictions utilized the final optimized material coefficients.

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Figure 5

Structural response of the heel under the combined loading of compression and anterior-posterior shear applied using a spherical indenter. Experimental forces and displacements are compared with the model predictions. The experimental data set was used for validation where the model predictions relied on optimized material coefficients obtained through another experimental data set (see Fig. 4). A compressive load application (1), was followed by an anterior shear (2), maintaining the approximate compressive displacement. The data for return of the tool to its original position (unloading) (3) was not considered in the analysis. Upon returning to the initial position, a posterior shear was applied (4).

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Figure 6

Structural response of the heel under a compression dominant loading applied using an elevated platform. Experimental forces and displacements are compared with the model predictions.

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Figure 7

Evaluation of the effect of misalignment between the foot and the load transducer coordinate systems on the force components. This sensitivity analysis was performed to assess the causes of deviations observed between the experimental force values and those predicted by the model, in particular, the anterior-posterior forces.

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Figure 8

As the indenter gets closer to the bony landmark (from position (i) to position (ii)), internal loading of the heel (as illustrated by the von Mises stress distribution) may cause large off-axis forces that may not necessarily align with the direction of the tool movement. Note that the dominant shear displacement (anterior) is approximately perpendicular to the plane of the cut, where the mediolateral reaction force is higher in an unexpected fashion.

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