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

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

A Comprehensive Specimen-Specific Multiscale Data Set for Anatomical and Mechanical Characterization of the Tibiofemoral Joint.

Understanding of tibiofemoral joint mechanics at multiple spatial scales is essential for developing effective preventive measures and treatments for both pathology and injury management. Currently, there is a distinct lack of specimen-specific biomechanical data at multiple spatial scales, e.g., joint, tissue, and cell scales. Comprehensive multiscale data may improve the understanding of the relationship between biomechanical and anatomical markers across various scales. Furthermore, specimen-specific multiscale data for the tibiofemoral joint may assist development and validation of specimen-specific computational models that may be useful for more thorough analyses of the biomechanical behavior of the joint. This study describes an aggregation of procedures for acquisition of multiscale anatomical and biomechanical data for the tibiofemoral joint. Magnetic resonance imaging was used to acquire anatomical morphology at the joint scale. A robotic testing system was used to quantify joint level biomechanical response under various loading scenarios. Tissue level material properties were obtained from the same specimen for the femoral and tibial articular cartilage, medial and lateral menisci, anterior and posterior cruciate ligaments, and medial and lateral collateral ligaments. Histology data were also obtained for all tissue types to measure specimen-specific cell scale information, e.g., cellular distribution. This study is the first of its kind to establish a comprehensive multiscale data set for a musculoskeletal joint and the presented data collection approach can be used as a general template to guide acquisition of specimen-specific comprehensive multiscale data for musculoskeletal joints

Time history of applied varus and external rotation moments and resulting joint rotations during combined loading.

<p>Tibiofemoral flexion was set at 30° during this particular test. The loads are represented in the tibia fixed coordinate system; movements are described in the anatomical joint coordinate system.</p

Joint kinematics-kinetics response in dominant axes for various laxity tests.

<p>The loads are represented in the tibia fixed coordinate system; movements are described in the anatomical joint coordinate system.</p

Overview of multiscale data acquisition on the tibiofemoral joint.

<p>Data collection includes magnetic resonance imaging (to reconstruct joint anatomy), joint mechanical testing (to interpret the mechanical behavior of the joint), tissue mechanical testing (to understand tissue material properties), and histology (to evaluate cell level and microstructural information).</p

Reconstructed stress-strain response of all tissues at target strain levels, for instantaneous and relaxed states.

<p>Nominal stresses and grip-to-grip strains are reported. For estimates of moduli, refer to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0138226#pone.0138226.t002" target="_blank">Table 2</a>. The posterior cruciate ligament failed during the second ramp loading (10% strain); this describes the unexpected decrease in the stiffness of this tissue for larger strains. At the relaxed state, the stress response of the menisci during compression was low; the values reported may potentially be hindered by experimentation capacity.</p

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

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

Tissue sample locations.

<p>a) & b) Confined compression samples of cartilage from the medial and lateral femoral condyles and tibial plateaus. c) Confined compression and tensile test samples from the menisci. d) Tensile test samples from the mid-substance region of the ligaments. Solid lines represent mechanical testing samples; dashed lines represent histology samples.</p

Magnetic resonance images of the tibiofemoral joint.

<p>a) Axial section; cartilage is highlighted. b) Coronal section; anterior cruciate ligament, medial collateral ligament, and medial meniscus are highlighted. c) Sagittal section; anterior cruciate ligament is highlighted.</p

Details of the locations and dimensions for all samples for mechanical tissue testing.

<p>Diameter was assumed from punch diameter. Width was assumed from punch width, length was estimated from grip-to-grip distance at pre-load; and thickness was measured using a probe. ACL: anterior cruciate ligament; PCL; posterior cruciate ligament; MCL: medical collateral ligament; LCL: lateral collateral ligament.</p><p>Details of the locations and dimensions for all samples for mechanical tissue testing.</p