Musculoskeletal modeling based on deep-nsNMF for multi-DoF motion decoding

Surface electromyography (sEMG) signals, as physiological signals generated during muscle contraction, are widely employed in human-machine interfaces for decoding continuous motion intention. Based on the muscle synergy theory, musculoskeletal models integrated with non-negative matrix factorization provide a physiologically interpretable framework (such as M-NMF-MM) for such decoding tasks. However, the framework exhibits insufficient accuracy for simultaneous movements of multiple degrees of freedom (DoFs) due to the crosstalk between signals of multiple muscles. To address this limitation, the present study proposes an improved deep non-smooth non-negative matrix factorization musculoskeletal model (Deep-nsNMF-MM) by replacing the standard non-negative matrix factorization (NMF) in the M-NMF-MM with a deep non-smooth NMF (Deep-nsNMF) algorithm, which enhances the sparsity of muscle co-excitation and reduces signal redundancy. Compared with sparse NMF and non-smooth NMF, Deep nsNMF yields a higher variance accounted for (VAF), especially with a greater number of network layers. For four DoF synchronous motions, the Deep nsNMF MM significantly outperforms the original M-NMF-MM: the Pearson's correlation coefficient for metacarpophalangeal flexion/extension (MFLX/EXT) and wrist adduction/abduction (WADD/ABD) increases from 0.75 and 0.74 to 0.80 and 0.79, respectively, while the overall normalized root mean square error decreases by 10-15%. This work provides a novel, high precision, and physiologically interpretable decoding method for synchronous proportional control in multiple DoFs human-machine interfaces.