Feasibility assessment of transfer functions describing biomechanics of the human lower limb during the gait cycle

Background and objective: Transfer functions could model biomechanical parameters to conveniently analyze the system dynamics of the lower limb during daily activities, e.g., walking. The current study evaluates the feasibility of transfer functions as a means of predicting surface electromyography (sEMG) of lower limb muscles based on axial tibial (ATA) and femoral (FA) accelerations. Since the transfer functions are comparable in accuracy to commonly used long short-term memory models (LSTM), the transfer function-based methodology can assist in the design of novel prostheses while being competitive with mainstream models. Methods: Data were collected from eight participants with no medical history that would alter their gait cycles. The data included the sEMG of four primary muscle groups, ATA and FA, and heel-strike triggering signal, while the subjects walked at 5.28 km/h on a treadmill. A fast Fourier transform (FFT) was performed on the filtered ensemble averages of the ATA, FA and normalized average rectified sEMG signals, which were used to approximate the time domain Fourier series. Transfer functions relating ATA-to-sEMG and FA-to-sEMG were derived from the Fourier series equations to generate time-domain intra-subject predictions of sEMG signals. With respect to predictive accuracy, these transfer functions were compared with sEMG-to-sEMG LSTM models trained on sEMG data from some of the participants. It was hypothesized that the transfer functions would be at least comparable to the LSTM models. Results: The results indicate that the predicted sEMG signals were able to capture the temporal characteristics of the measured sEMG signal based on either ATA or FA. The muscle activities and acceleration were in good agreement with the walking gait cycle events. Only 13 Fourier terms were needed to effectively predict the sEMG from the acceleration signals, indicating the computational efficiency of the investigated analysis framework. For the ATA-to-sEMG transfer functions, the mean square difference (MSD) between the predicted and measured sEMG signals was low and comparable to the LSTM models. Conclusions: Overall, the feasibility and competitiveness of the transfer functions with LSTM models was confirmed with respect to predictive accuracy. Potential applications of the transfer functions include the control of powered prosthetics and the detection of gait pathologies.