Forward simulations of walking on a variable surface-impedance treadmill: A comparison of two methods

Recent experiments with a variable stiffness treadmill (VST) suggest that modulating foot-ground contact dynamics during walking may offer an effective new paradigm for gait rehabilitation. How gait adapts to extended perturbations of asymmetrical surface stiffness is still an open question. In this study, we simulated human gait with prolonged asymmetrical changes in ground stiffness using two methods: (1) forward simulation of a muscle-reflex model and (2) optimal control via direct collocation. Simulation results showed that both models could competently describe the biomechanical trends observed in human experiments with a VST which altered the walking surface stiffness for one step. In addition, the simulations revealed important considerations for future experiments studying the effect of asymmetric ground stiffness on gait behavior. With the muscle-reflex model, we observed that although subtle, there was a difference between gait biomechanics before and after the prolonged asymmetric stiffness perturbation, showing the behavioral signature of an aftereffect despite the lack of supraspinal control in the model. In addition, the optimal control simulations showed that damping has a large effect on the overall lower-body muscle activity, with the muscle effort cost function used to optimize the biomechanics increasing 203% between 5 Ns/m and 2000 Ns/m at a stiffness of 10 kN/m. Overall, these findings point to new insights and considerations for advancing our understanding of human neuromotor control of locomotion and enhancing robot-aided gait rehabilitation.