Predicting the effect of muscle length on fatigue during electrical stimulation

Mathematical models have been developed to predict fatigue during functional electrical stimulation, but the predictive accuracy at different muscle lengths is unknown. The objectives of our study were to: (1) experimentally determine the relationship between knee extension angle (20°, 40°, 65°, and 90°) and fatigue of the quadriceps muscles, and (2) predict that relationship using a mathematical model. A computer-controlled stimulator sent trains of pulses to surface electrodes on the thighs of five subjects while forces were measured at the ankle. A two-component mathematical model was developed. One component accounted for force, and the other accounted for fatigue. The model was fit to the data, and parameters were identified at 90°. The fitted subject-averaged r² value was 0.89. The model was used to predict fatigue at the remaining angles, and the subject-averaged r² values were >0.75. Therefore, at least 75% of the variability in the measurements was explained by the model. The force model is explicitly dependent on angle, and the fatigue model is explicitly dependent on force; therefore, the dependence of fatigue on knee angle was implicit.