Assessing the robustness of the muscle synergies decomposition algorithm

The theory of “Muscle Synergies” has been formulated in the last few decades to have a better understanding of the optimization strategies applied by the Central Nervous System (CNS) in the control of the activation and coordination of the many muscles involved in any voluntary movement. The synergies can be considered as patterns of co-activation corresponding to the activity of few muscles: having to control a number of these modules lower than the actual number of muscles involved, the computational cost of every task is significantly reduced. The synergies are modeled as a time-invariant profile of activation across muscles, activated by a time-varying coefficient. Summing the individual synergies, after having scaled them by their coefficient, the profile of muscle activation should be faithfully reconstructed. Different algorithms have been used in literature to extract the synergies from the sEMG data, in this study the Non-Negative Matrix Factorization (NNMF) decomposition algorithm was analyzed. The NNMF algorithm operates a data projection from a n-dimensional space to a lower k-dimensional space, where n is the number of channels considered and k the basis vectors, representing the synergies. The focus of this thesis is analyzing the changes in the final factorization performed by the NNMF algorithm when one or more input channels are removed. During real data collection loss of channels can occur frequently due to bad quality of the recording. Having a different number of channels, it wouldn’t be possible to compare synergies obtained from signals collected from the same muscles, both for different subjects and for the same subject multiple times. To approach the problem, sEMG data were synthetized, obtaining them from the linear combination of a simulated set of synergies, and an increasing number of channels was removed from the original signals. The performances of the NNMF algorithm were evaluated comparing its outputs, i.e. synergies weights W and temporal coefficients H, for the starting signals where all the channels were still present and the signals with a decreasing number of channels. The metrics used for the comparison of the weights W and the temporal coefficients H were, respectively, the Cosine Similarity (CS) and the Correlation Coefficient (CC). The analysis of the results of the various simulation performed pointed out that losing a limited number of channels doesn’t compromise the ability of the NNMF algorithm to detect the same synergies and to reconstruct in a satisfying way the original signals, as long as not all the strategic channels or all the peculiar ones for a certain synergy are lost. To test the algorithm in conditions as close as possible to the physiological ones, data from a gait analysis was simulated replicating the averaged EMG activity from 25 muscles during a single cycle of over-ground locomotion that could be found in literature. Also with this set of data the performances of the algorithm were good and the original synergies were preserved even when an high number of channels was removed.