How well do the muscular synergies extracted via nonnegative matrix factorization explain the variation of torque at shoulder joint?

The way central nervous system manages the excess degrees of freedom to solve kinetic redundancy of musculoskeletal system remains an open question. In this study, we utilise the concept of synergy formation as a simplifying control strategy to find the muscle recruitment based on summation of identified muscle synergies to balance the biomechanical demands (biaxial external torque) during an isometric shoulder task. A numerical optimisation-based shoulder model was used to obtain muscle activation levels when a biaxial external isometric torque is imposed at the shoulder glenohumeral joint. In the numerical simulations, 12 different shoulder torque vectors in the transverse plane are considered. For each selected direction for the torque vector, the resulting muscle activation data are calculated. The predicted muscle activation data are used for grouping muscles in some fixed element synergies by the non-negative matrix factorisation method. Next, torque produced by these synergies are computed and projected in the 2D torque space to investigate the magnitude and direction of torques that each muscle synergy generated. The results confirmed our expectation that few dominant synergies are sufficient to reconstruct the torque vectors and each muscle contributed to more than one synergy. Decomposition of the concatenated data, combining the activation and external torque, provided functional muscle synergies that produced torques in the four principal directions. Four muscle synergies were able to account for more than 95% of variation of the original data.