Optimal stimulation patterns for knee joint movement restoration during co-contraction of antagonist muscles

Co-contraction of antagonistic muscles may yield a stable joint movement, force regulation and an increasing joint stiffness. In biomechanics, the force-sharing problem is often solved through minimization of an energetic criterion under given constraints. This criterion has been used in this paper to compute the necessary stimulation parameters as provided by a functional electrical stimulator, during knee joint movement restoration. An analytical solution is presented that gives the muscular activities and the stimulation parameters for the flexion/extension of the knee joint actuated by two antagonistic muscles: quadriceps and hamstrings. An inverse model taking into account the muscular dynamic contraction (i.e. force-length relationship, force velocity relationship and the maximal force that can be generated) is computed. Moreover, redundancy induced by co-contraction has been solved by minimizing the sum of the stress in the antagonistic muscles under kinematics and dynamics constraints while maintaining the computed muscular activities within its lower and upper bounds.