Identification of Passive Knee Joint and Shank Dynamics in Paraplegics Using Quadriceps Stimulation

The dynamics of the knee joint-freely swinging lower leg system of three sitting paraplegic patients was identified using a parameterized analytical model. The system was excited by a knee torque, generated by randomized interpulse interval stimulation of the quadriceps. Surface electrodes were used for stimulation. The output of the knee joint-lower leg system was the angular position, velocity and acceleration. A measurement set-up using accelerometers was designed and characterized successfully. A model structure was taken from the literature and its complexity was subsequently minimized based on the experiments and off-line identification. The resulting model structure facilitates possible recursive identification. Model parameters of the lower leg dynamics were successfully estimated using a least-squares algorithm in combination with the LevenburgMarquardt algorithm, minimizing the error in estimated angular acceleration. The inter-subject variability in parameter values for the knee joint damping and the gravitational component appeared to be small when normalized to the inertia of the lower leg. A term, representing the nonlinear elastic properties in the knee joint, appeared to improve the prediction capability of the model significantly. The identified model for the knee joint and shank dynamics accurately predicted passive lower leg movements. The magnitude of active knee torque due to elicited quadriceps contraction could be estimated using the identified model.