Identification of heel pad thickness and visco-hyperelastic properties by finite element analysis and Gaussian process regression

Abstract

The importance of the heel pad thickness and visco-hyperelastic material properties on gait and quality of life is clear to biomedical engineers and physicians alike. To this end, this contribution presents first an experimental methodology to measure the load-time response on the heel pad by indentation test. Afterward, finite element analysis (FEA) simulations were implemented to replicate the experimental environment and employed for the training of a Gaussian Process Regression (GPR) model, subsequently employed to estimate the hyperelastic model constants and the heel pad thickness. A second-order polynomial strain energy potential was employed in the FEA models, whereas the viscoelastic behavior was modeled with a stretched exponential formulation. The trained GPR model was tested against experimental results on 6 subjects of different ages and genders, where the visco-hyperelastic properties and heel pad thickness were determined. The predicted heel pad thickness was validated by ultrasonography. The results show that the developed methodology allows for real-time estimation (within 10 s) of the visco-elastic material properties and thickness of the heel pad with comparable accuracy to the established models, thus granting a significant reduction in the computation time with no loss in accuracy. © 2025