Hyperelastic compressive mechanical properties of the subcalcaneal soft tissue: An inverse finite element analysis

Abstract

Finite element (FE) foot models can provide insight into soft tissue internal stresses and allow researchers to effectively conduct parametric analyses. Accurate plantar soft tissue material properties are essential for the development of FE foot models for clinical interventions. The aim of this study was to identify the first-order and second-order Ogden hyperelastic material properties of the subcalcaneal fat using an inverse FE analysis. The cylindrical soft tissue FE model was developed based on a priori in vitro dynamic compression experiment. The model simulated a 1Hz triangle wave displacement to apply a compressive strain up to 48%. The hyperelastic properties were identified by systematically varying the material parameters to minimize the difference between the model predicted force and the target experimental data. Optimal material properties were obtained (μ1=0.0235kPa and α1=12.07 for the first-order Ogden model and μ1=−4.629×10−6kPa, α1=−16.829; μ2=−1.613kPa and α2=−1.043 for the second-order Ogden model). The second-order Ogden model was superior in capturing the highly nonlinear force–deformation response when compared to the first-order model (root mean square error (RMSE) 0.169N vs. 0.570N). The material sensitivity analysis indicated that the predicted force was strongly affected by the Poisson׳s ratio (12-fold increase in RMSE when reducing Poisson׳s ratio by 10% from the baseline) and the coefficient α1 (3.2-fold and 32-fold increase in RMSE for both first-order and second-order Ogden models when increasing α1 by 10% from the optimal value).