Directional tuning of arm muscle activation in isometric force generation and its prediction by flexible and synergistic models

Because of the redundancy in the musculoskeletal system, to generate a force at the hand in a given direction and with a given magnitude the central nervous system (CNS) has to select one of infinitely many possible muscle activation patterns. What strategies and constraints underlie such selection is an open and debated issue. The CNS might select muscle activations that optimize some performance criterion, such as accuracy or effort, or it might simplify the solution by constraining it to be a combination of a few muscle synergies. Flexible optimization of individual muscle recruitment or muscle synergies should give rise to distinct directional tuning of muscle activations. In this study we compared the activation of arm muscles observed during the generation of isometric force at the hand in 16 different directions with the activation predicted by flexible recruitment of individual muscles selected, for each direction, minimizing the sum of squared muscle activations and by flexible recruitment of a set of muscle synergies, by minimization of the sum of squared synergy activations. Muscle synergies were identified from the recorded muscle pattern using non-negative matrix factorization. To perform both optimizations we approximated the mapping between muscle activations and end-point force with a matrix that we estimated using multiple linear regression. We found that, in most cases, the synergistic model predicted the observed directional tuning with smaller error than the flexible model. While this result might be due to some of the assumptions and approximations used in the models, it supports the hypothesis that the CNS employs a small number of muscle synergies to simplify the control of the many degrees-of-freedom of the musculoskeletal apparatus.