Strain-rate dependence of viscous properties of the plantar soft tissue identified by a spherical indentation test

The mechanical properties of the plantar soft tissue are known to vary in diabetic patients, indicating that parameter identification of the mechanical properties of the foot tissue using an indentation test is clinically important for possible early diagnosis and interventions of diabetic foot. However, accurate mechanical characterization of the viscous properties of the plantar soft tissue has been difficult, as measured force-relaxation curves of the same soft tissue differ depending on how the material is loaded. In the present study, we attempted to clarify how the indentation rate of the plantar soft tissue affects the measured force-relaxation curves, which is necessary in order to identify the viscoelastic properties. The force-relaxation curves of the heel pads were obtained from the indentation experiment in vivo at indentation rates of 15, 25, 50, 75, and 100 mm/s. The curves were fit to an analytical contact model of spherical indentation incorporating a five-element Maxwell model. The results of the present study demonstrated that, although experimentally obtained force-relaxation curves were actually variable depending on the indentation rate, similar viscous parameters could be identified for the same heel if the effects of (1) the underestimation of the peak force due to the energy dissipation occurring during indentation and (2) the deceleration of the indenter at the target position were incorporated in the parameter identification process. The indentation-rate-independent viscous properties could therefore be estimated using the proposed method.