Numerical-Optimal-Control-Compliant Muscle Model for Electrically Evoked Contractions

In this paper, an existing physiological muscle model that predicts muscular force in response to electrical stimulation is adapted to be compatible with gradient-based optimization, in particular with numerical optimal control/estimation problems. The objective is to integrate biomechanical models with those that correlate muscle force generation with electrical pulses from a physiological perspective, with the aim of achieving optimal stimulation patterns in activities assisted by functional electrical stimulation. To this end, the activation dynamics of the original model, initially constrained to a stimulation train of predefined and constant length, is reformulated to account for stimulation sequences that dynamically change over time. This is typically necessary to simulate complex motions, which would otherwise be impossible to achieve with the earliest formulation. To identify the model parameters, experimental torque data of 3 participants with spinal cord injury performing electrically evoked isometric quadriceps contractions at different knee angles are used. We then employ an optimal control framework to demonstrate the model’s ability to predict knee torques and the possibility of achieving optimized stimulation patterns in simulation for controlling muscle force and knee extension. Our results reveal that the identified model allows accurate prediction of knee torque and optimization of stimulation patterns while satisfying the system’s dynamics at the skeletal and physiological muscle levels. This proof of concept is a first step towards physiological muscle model-based control of functional electrical stimulation to achieve movements that best exploit an individual’s physiological and biomechanical characteristics.