An approach to a muscle force model with force-pulse amplitude relationship of human quadriceps muscles

Background: Recent advanced applications of the functional electrical stimulation (FES) mostly used closed-loop control strategies based on mathematical models to improve the performance of the FES systems. In most of them, the pulse amplitude was used as an input control. However, in controlling the muscle force, the most popular force model developed by Ding et al. does not take into account the pulse amplitude effect. The purpose of this study was to include the pulse amplitude in the existing Ding et al. model based on the recruitment curve function. Methods: Quadriceps femoris muscles of eight healthy subjects were tested. Forces responses to stimulation trains with different pulse amplitudes (30-100 mA) and frequencies (20-80 Hz) were recorded and analyzed. Then, specific model parameter values were identified by fitting the measured forces for one train (50 Hz, 100 mA). The obtained model parameters were then used to identify the recruitment curve parameter values by fitting the force responses for different pulse amplitudes at the same frequency train. Finally, the extended model was used to predict force responses for a range of stimulation pulse amplitudes and frequencies. Results: The experimental results indicated that our adapted model accurately predicts the force-pulse amplitude relationship with an excellent agreement between measured and predicted forces (R-2 = 0.998, RMSE = 6.6 N). Conclusions: This model could be used to predict the pulse amplitude effect and to design control strategies for controlling the muscle force in order to obtain precise movements during FES sessions using intensity modulation.