The number and choice of muscles impact the results of muscle synergy analyses

Abstract

One theory for how humans control movement is that muscles are activated in weighted groups or synergies. Studies have shown that electromyography (EMG) from a variety of tasks can be described by a low-dimensional space thought to reflect synergies. These studies use algorithms, such as nonnegative matrix factorization, to identify synergies from EMG. Due to experimental constraints, EMG can rarely be taken from all muscles involved in a task. However, it is unclear if the choice of muscles included in the analysis impacts estimated synergies. The aim of our study was to evaluate the impact of the number and choice of muscles on synergy analyses. We used a musculoskeletal model to calculate muscle activations required to perform an isometric upper-extremity task. Synergies calculated from the activations from the musculoskeletal model were similar to a prior experimental study. To evaluate the impact of the number of muscles included in the analysis, we randomly selected subsets of between 5 and 29 muscles and compared the similarity of the synergies calculated from each subset to a master set of synergies calculated from all muscles. We determined that the structure of synergies is dependent upon the number and choice of muscles included in the analysis. When five muscles were included in the analysis, the similarity of the synergies to the master set was only 0.57 ± 0.54; however, the similarity improved to over 0.8 with more than ten muscles. We identified two methods, selecting dominant muscles from the master set or selecting muscles with the largest maximum isometric force, which significantly improved similarity to the master set and can help guide future experimental design. Analyses that included a small subset of muscles also over-estimated the variance accounted for (VAF) by the synergies compared to an analysis with all muscles. Thus, researchers should use caution using VAF to evaluate synergies when EMG is measured from a small subset of muscles.

Keywords: electromyography; muscle synergy; musculoskeletal model; nonnegative matrix factorization; simulation.

Figure 1

Synergies calculated from a subset of muscles were compared to the master set of synergies calculated from all 30 muscles. The master set of synergies was calculated using NNMF from the activations of all 30 muscles required to perform the isometric upper-extremity force task. Random subsets of muscles (varying between 5 and 29 muscles) were then selected and four synergies were calculated from the subset of muscle activations. The same subset of muscles was isolated from the master set and the similarity of the synergies was compared as the average correlation coefficient.

Figure 2

Comparison of synergies calculated from the musculoskeletal model (dark gray bars) and experimental EMG (black outlined bars showing average ± one standard deviation and light gray bars showing synergies of individual subjects). The similarity of the synergies from the musculoskeletal model and the experimental EMG were not significantly different from the inter-subject similarity of synergies.

Figure 3

Synergies calculated from all 30 muscles included in the model during an upper-extremity isometric force task. The dominant muscles of each synergy (defined as within 20% of the maximum value of each synergy) are shown in dark gray and on the musculoskeletal models.

Figure 4

Directional tuning of the four synergies calculated from all 30 muscles and the subset of eight muscles included in the experimental analysis. The direction for each synergy was calculated from the activation level of each synergy across all force directions and normalized to unit length.

Figure 5

(A) Non-normalized similarity calculated as the average correlation coefficients of synergies calculated from random subsets that included between 5 and 29 muscles to the synergies calculated from all 30 muscles (light gray bars − average ± 1 standard deviation). The dark gray bars show the similarity expected by chance for each number of muscles included in the analysis. (B) Average similarity of synergies from random subsets to synergies calculated from all 30 muscles normalized by similarity expected by chance. (C) Average total variance accounted for by synergies from random subsets. As the number of muscles in the analysis increased, the total variance accounted for approached the variance accounted for when all 30 muscles were included in the analysis (dotted line).

Figure 6

Average normalized similarity vs. number of muscles included in the synergy analysis for varying levels of noise. Noise was specified according to a signal-to-noise ratio between 0 and 20 dB.

Figure 7

Average normalized similarity of subsets of muscles chosen randomly (dotted black line), muscles chosen from subsets of dominant muscles from the master set (dark gray line), and muscles selected by size starting with the largest muscles (light gray line).