A viscoelastic ellipsoidal model of the mechanics of plantar tissues Jessica DeBerardinis a,⇑ , Janet S. Dufek b , Mohamed B. Trabia a a Department of Mechanical Engineering, University of Nevada, Las Vegas, United States b Department of Kinesiology and Nutrition Sciences, University of Nevada, Las Vegas, United States article info Article history: Accepted 27 May 2019 Keywords: Varying contact area models Walking Pressure-measuring insoles Ground reaction force abstract Several assessments of the mechanics of plantar tissues, using various material models in conjunction with representing plantar regions using simple geometry, have been proposed. In this study, the plantar tissues were divided into eight regions to account for the various tissue characteristics. The plantar tissue model described each region as an ellipsoid, with a viscoelastic material model. The model combined varying elliptical contact areas with nonlinear tissue stiffness and damping. The main instruments used in this research were pressure-measuring insoles, which were used to determine the ground reaction force, as well as contact areas. The measured contact areas were fitted as elliptical areas to describe the compression of the corresponding ellipsoids. The approach was tested using walking data collected from 26 individuals: four men, 22 women, 24.4 ± 6.9 years old, 66.9 ± 21.4 kg of mass, 1.66 ± 0.12 m tall. The geometric and material variables of the proposed ellipsoidal model were optimized for each partic- ipant to match the ground reaction forces. Results suggest that the ellipsoid model is able to reproduce ground reaction force with reasonable accuracy. The largest errors were seen in heel and toe regions and were due to high-rate forces and small comparative areas, respectively. The model also showed that there are regional differences in the mechanical characteristics of plantar tissue, which confirms earlier research. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Skin, fat, muscle, and tendons in the sole of the foot are collec- tively described as the plantar soft tissues. Each section of the foot has a unique functional structure (Sarrafian, 1993). For example, the rear foot (heel) tissues include a thick layer of subcutaneous connective tissue with fatty tissue pockets, which allow the rear foot to absorb the shock associated with the heel strike during walking or running. The midfoot plantar tissues are mainly com- posed of musculature and plantar fascia, which connect the calca- neus and metatarsal bones. These tissues help maintain postural balance, and work with other foot structures to generate move- ment. The forefoot plantar tissues are comprised mainly of muscles and tendons, with small fat pads underneath the metatarsal heads and toes. These tissues are used to push the foot off the ground in preparation for the subsequent step, during gait. While each of these plantar soft tissues exhibit different mechanical behaviors, researchers have most often proposed cumulative tissue models to describe the mechanical characteristics of plantar regions. Several researchers (Gefen et al., 2001; Gilchrist and Winter, 1996; Scott and Winter, 1993), have used multiple, individual, nonlinear spring-damper systems across the plantar regions to model the plantar tissue’s response to load. Spring-damper mate- rial models are computationally simple, which allow for quick cal- culations in comparison to more complex models. These models assume a point-load, which limits their applicability for studying the behavior of plantar tissues during walking. Another researcher (Neptune et al., 2000) used multiple, nonlinear spring-damper sys- tems to represent the shoe sole and soft tissue and optimized tech- niques to improve the accuracy of the model. Others have used hyperelastic material models to represent the nonlinearity of plantar tissues. Hyperelastic models examine the nonlinearity and elasticity of materials that have experienced large strains or deformations. They are beneficial to examine plantar tis- sue without the complexity of time-dependent, viscous effects. One such model is the Ogden model, which is a material model that develops a potential function of three constants, determined from experimental stress-strain data. This model was shown to be accurate in reproducing mechanical tests, but had errors in reproducing walking data (Budhabhatti et al., 2007; Chatzistergos et al., 2018; Chen et al., 2014; Chokhandre et al., 2012; Erdemir et al., 2006; Gu et al., 2010). Bucki et al. (2016), used a https://doi.org/10.1016/j.jbiomech.2019.05.041 0021-9290/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: deberj1@unlv.nevada.edu (J. DeBerardinis). Journal of Biomechanics 92 (2019) 137–145 Contents lists available at ScienceDirect Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com