The relationship between electrical stimulus and joint torque: a dynamic model

The knowledge of the behavior of electrically activated muscles is an important requisite for the development of functional electrical stimulation (FES) systems to restore mobility to persons with paralysis. The aim of this work was to develop a model capable of relating electrical parameters to dynamic joint torque for FES applications. The knee extensor muscles, stimulated using surface electrodes, were used for the experimental preparation. Both healthy subjects and people with paraplegia were tested. The dynamics of the lower limb were represented by a nonlinear second order model, which took account of the gravitational and inertial characteristics of the anatomical segments as well as the damping and stiffness properties of the knee joint. The viscous-elastic parameters of the system were identified experimentally through free pendular movements of the leg. Leg movements induced by quadriceps stimulation were acquired too, using a motion analysis system. Results showed that, for the considered experimental conditions, a simple one-pole transfer function is able to model the relationship between stimulus pulsewidth (PW) and active muscle torque. The time constant of the pole was found to depend on the stimulus pattern (ramp or step) while gain was directly dependent on stimulation frequency