A real-time and convex model for the estimation of muscle force from surface electromyographic signals in the upper and lower limbs

Surface electromyography (sEMG) is a signal consisting of different motor unit action potential trains and records from the surface of the muscles. One of the applications of sEMG is the estimation of muscle force. We proposed a new real-time convex and interpretable model for solving the sEMG—force estimation. We validated it on the upper limb during isometric voluntary flexions-extensions at 30%, 50%, and 70% Maximum Voluntary Contraction in five subjects, and lower limbs during standing tasks in thirty-three volunteers, without a history of neuromuscular disorders. Moreover, the performance of the proposed method was statistically compared with that of the state-of-the-art (13 methods, including linear-in-the-parameter models, Artificial Neural Networks and Supported Vector Machines, and non-linear models). The envelope of the sEMG signals was estimated, and the representative envelope of each muscle was used in our analysis. The convex form of an exponential EMG-force model was derived, and each muscle’s coefficient was estimated using the Least Square method. The goodness-of-fit indices, the residual signal analysis (bias and Bland-Altman plot), and the running time analysis were provided. For the entire model, 30% of the data was used for estimation, while the remaining 20% and 50% were used for validation and testing, respectively. The average R-square (%) of the proposed method was 96.77 ± 1.67 [94.38, 98.06] for the test sets of the upper limb and 91.08 ± 6.84 [62.22, 96.62] for the lower-limb dataset (MEAN ± SD [min, max]). The proposed method was not significantly different from the recorded force signal (p-value = 0.610); that was not the case for the other tested models. The proposed method significantly outperformed the other methods (adj. p-value < 0.05). The average running time of each 250 ms signal of the training and testing of the proposed method was 25.7 ± 4.0 [22.3, 40.8] and 11.0 ± 2.9 [4.7, 17.8] in microseconds for the entire dataset. The proposed convex model is thus a promising method for estimating the force from the joints of the upper and lower limbs, with applications in load sharing, robotics, rehabilitation, and prosthesis control for the upper and lower limbs.