A novel force-constrained non-negative matrix factorization algorithm reveals the effectiveness of muscle synergies in the task space

According to the synergy hypothesis, the motor system recruits a small number of synergies in a task-dependent manner. Existing synergy extraction algorithms typically only consider the muscle pattern and it remains unclear to which extent muscle synergies encode task-relevant variations of muscle activity. We propose a novel force-constrained non-negative matrix algorithm (FCNMF) based on a gradient descent update rule that considers also the task space by adding a term penalizing force reconstruction error in the cost function. We validated the FCNMF algorithm using simulated muscle data and corrupted them by noise. We compared task performances with reconstructed trajectories using synergies (RS) extracted from the FCNMF algorithm and from the standard multiplicative non-negative matrix factorization NMF algorithm. We found that FCNMF outperforms NMF for different types of noise. Finally, we demonstrated the effectiveness of FCNMF on EMG data collected during an isometric reaching task. The new algorithm accurately reconstructs the trajectories in all participants, even in those for which the NMF algorithm fails. These findings show the effectiveness of muscle synergies extracted considering the task space, possibly thanks to the robustness of FCNMF against non-isotropic noise present in muscle data, suggesting that they provide an effective strategy for motor coordination.