INTRODUCTION:​ Applying electrical current to a limb to produce movement is not difficult;​ controlling the movements and completing the task is. Muscle fatigue, greater than that of naturally activated muscle, has hindered the progress of functional electrical stimulation (FES) systems. A mathematical model capable of predicting excursion, velocity, and force during fatiguing contractions could test combinations of independent variables to produce stimulation strategies that minimize fatigue. Models of fatigue during electrically stimulated, repetitive, non-isometric contractions in humans reported by others have not been experimentally validated, so the goal of this study was to develop and experimentally validate such a model. Since (a) muscle length changes during nonisometric contractions, (b) loads vary with different tasks, and (c) the activated area of stimulated muscle changes with pulse duration, achieving the study goal required three specific aims:​ Predict mathematically and validate the relationship between 1) knee angle and quadriceps muscle force, 2) applied load and angular velocity or excursion, and 3) stimulation pulse duration and angular velocity or excursion, all during fatiguing isometric or concentric contractions.

METHODS:​ A computer-controlled stimulator sent electrical pulses to surface electrodes on the thighs of able-bodied human subjects. Isometric and non-isometric non-fatiguing and fatiguing leg extension ankle forces and/or knee angles were measured. The independent variables were either:​ 1) knee angle (20°, 40°, 65°, and 90°), 2) applied load (0, 1.82, 4.54, 6.36, and 9.08 kg), or 3) pulse duration (170, 200, 250, 400, and 600 μs). The dependent variables were either force (isometric) or angular excursion and velocity (non-isometric). The model was fit to some of the measurements to determine which, if any, model parameters changed during fatigue. The remaining measurements were compared to predictions to validate the model.

RESULTS & DISCUSSION:​ More than 65% of the variability in the measurements was explained by the new force-fatigue model. None of the independent variables were explicitly needed in the fatigue model;​ their effects on fatigue were captured by their effects on force. The additional fatigue model parameter was a function of other model parameters. This model can help scientists investigate the etiology of non-isometric fatigue and improve the task performance of FES systems.