Modelling the optimal control of cyclical leg movements induced by functional electrical stimulation

An optimal control strategy for FES-induced cyclical leg movements in paraplegics is proposed. The control of the cyclical movement of a freely swinging leg is considered as an example. Quadriceps and the flexion withdrawal reflex are stimulated in order to generate a cyclical movement, of which the forward swing resembles the swing phase of gait. Optimal stimulation patterns are determined on the basis of an optimization criterion and a dynamic model of the system. The criterion is based on desired movement parameters and a minimal duration of the stimulation bursts. The movement parameters should ensure the generation of the desired cyclical movement: a desired hip angle range, sufficient foot clearance during the forward swing and knee extension at the beginning of the backward swing. Minimal duration of the stimulation bursts is assumed to yield minimal fatigue. A dynamic model, describing the dynamics of the neural system, the muscles and the leg, was constructed and its parameters identified on the basis of preliminary experiments and literature. Optimal timing of the quadriceps and flexion reflex stimulation bursts was determined by means of computer simulation. These simulations predicted that the flexion reflex should be stimulated in a short burst approximately 150 ms before the start of the forward swing. The quadriceps should be stimulated approximately starting 200 ms before the end of the forward swing in order to ensure knee extension at the beginning of the backward swing. The duration of one cycle of the movement was between 1300 and 1500 ms in these simulations. These results predict that the movement specified by the functional objectives can be realised using only two channels of stimulation. On the basis of the optimal timing, an adaptive control strategy can be designed, which varies the stimulation burst width when muscles fatigue.