Determining appropriate models for joint control using surface electrical stimulation of soleus in spinal cord injury

The mechanical impedance of the ankle joint during electrical stimulation of the soleus is studied by applying constant-velocity 10 degrees angular perturbations to the ankle and measuring the resultant torque. Both neurologically intact subjects and spinal cord injured subjects are tested. Lumped, piecewise linear models are developed to predict the torque from the measured displacement and acceleration signals. The commonly used second-order mass-spring-dashpot model fails to predict the changes in torque that occur following imposed movements. A five-element, directionally-dependent piecewise linear model is much better at predicting the measured responses for velocities up to 50 degrees s-1. Numerical least squared error identification techniques are used to estimate the model parameters for three neurologically intact and three spinal cord injured subjects. The average error between the model's response and the measured response across all subjects is 10.9%. There is some evidence that a velocity-dependent non-linear model could produce better results than the directionally-dependent piecewise linear model.