The Most Effective VAF Threshold for Extracting the Optimum Number of Synergies for Reaching Movement in a Two-Link Arm Model with Two DoF

Purpose: Muscle synergy is a motor feature composed of synergy patterns and activation coefficients. This study aimed to combine the two-link arm model with synergy patterns and muscle activation coefficients, which in turn leads to selecting the optimum number of synergies by changing the best Variability Account For (VAF) criterion. Materials and Methods: In this paper, signals were recorded from six arm muscles involved in arm-reaching movement while carrying a certain weight (w=700 g) by 20 subjects. The synergy pattern and activation coefficient matrices were calculated by using the Non-negative Matrix Factorization method (NNMF) and VAF criterion. Subsequently, to find the best VAF threshold, the output of signal preprocessing and NNMF’s output were done on Hill’s model. Results: Average VAF% for 20 subjects in the mentioned movement was 97.34±2.0%, and four numbers of synergies were determined. Conclusion: The results of the study suggest that the output of the W*H matrix (W and H are equal to the synergy pattern matrix and the activation coefficient matrix, in turn) had harmony with the output of the signal matrix recorded from all 20 subjects (output means the endpoint position and theta 1 and theta 2 angles) when they were performed as input on the two-link arm model. This harmony can be seen when choosing the best VAF critical threshold (value≥96%) via the aforementioned procedure. This harmony in turn contributes to exerting a positive influence on optimal extracting synergy patterns and describing the arm-reaching space more clearly.