# Effects of Arm Swing in Lower Limb Muscle Activation and Coordination During Treadmill Walking
## 3 Results
### Muscle Synergies Components  
For all subjects, four synergies (shown in Figure 4a,b) were computed, with a median VAF\({}_{\text{global}}\) of 95% (minimum value of 92%) for WWA and WNA and a median VAF\({}_{\text{muscle}}\) of 95% for WWA (minimum value of 84%) and 95% for WNA (minimum value of 83%). Detailed VAF values for each subject, muscle, and task are provided in Table S7 of the Supplementary Material. For both WWA and WNA, Synergy 1 consisted mainly of the activity of GLM, RF, and VL, with a median maximum value occurring at 3.5% of GC for WWA and 3% of GC for WNA (Figure 4c). Synergy 2 involved GaM and SOL, with a median maximum value at 39% of GC for WWA and WNA. Synergy 3 involved mainly BF and ST, with a median maximum value of 94% of GC for WWA and 92.5% for WNA. Synergy 4 was mainly explained by bimodal activity of TA, with the main peak at 97% of GC for WWA and 96.5% for WNA. Detailed data on the spatial time-independent coefficients of activation of all muscles in each synergy can be found in the Supplementary Material for WWA (Table S8) and WNA (Table S9). Statistically significant differences were observed for the time-dependent H of all synergies in specific phases of the gait cycle: around 0% of GC for Synergy 1 (minimum \(p\)-value = 0.019 and Cohen's d = 0.64), around 5% and 90% of GC for Synergy 2 (respectively, minimum \(p\)-value = 0.048 and [PERSON]'s d = 0.31 and minimum \(p\)-value = 0.027 and [PERSON]'s d = 0.55), around 95% of GC for Synergy 3 (minimum \(p\)-value = 0.027 and [PERSON]'s d = 0.78), and around 75% of GC for Synergy 4 (minimum \(p\)-value = 0.01 and [PERSON]'s d = 0.44). No statistically significant differences were observed in the SPM analysis. More detailed data on the time-dependent coefficients of activation for all subjects performing both tasks can be found in Table S10 of the Supplementary Material. FWHM was around 15% of GC for Synergies 1, 3, and 4 and around 25% of GC for Synergy 2 (see Figure 4b, lower plot). The FWHM values of the time-dependent coefficients of activation for all subjects performing both tasks can be found in Table S11 of the Supplementary Material.  
As shown in Figure 4d, spatial time-independent coefficients (W) were very similar between WWA and WNA, with median \(dot_{W}\) values higher than 0.97 for all synergies. The only \(dot_{W}\) value lower than 0.90 occurred for Subject 4 in Synergy 1 (\(dot_{W}=0.86\)) and Synergy 4 (\(dot_{W}=0.89\)). Regarding the time-dependent coefficients (H), median cross-correlation was higher than 0.97 for all synergies. The only cross-correlation lower than 0.90 occurred for Subject 4 in Synergy 4 (\(crosscorr^{H}=0.80\)). Additionally, Synergy 2 presented lags between \(-2\%\) and 3% of GC. Detailed statistical results of the muscle synergy components for all synergies and subjects can be found in Table S12 of the Supplementary Material. Finally, median \(RMS_{FWHM}\) was lower than 0.12 for all synergies. The highest variability was observed for Synergy 1 and Synergy 4, with an IQR of 0.16 and 0.12, respectively. More detailed data on the \(RMS_{FWHM}\) of both tasks for all synergies and all subjects can be found in Table S13 of the Supplementary Material.  
Figure 4: Muscle synergy components extracted for walking with arms (WWA) and walking with no arms (WNA), considering four synergies (Syn 1, Syn 2, Syn 3, Syn 4). (**a**) Mean \(\pm\) std of the spatial time-invariant coefficients (W) during WWA (upper plots) and WNA (lower plots). (**b**) Time-dependent coefficients (H) for all subjects (thin lines) and mean of all subjects (bold lines). Vertical black lines show the statistically significant differences between WWA and WNA. (**c**) Distribution of the peak position (\(max_{x}^{H}\)) as a function of the gait cycle (GC) (upper plot) and full width at half maximum (FWHM) (lower plot). (**d**) Distribution of the dot product (\(dot^{W}\)), root mean square error (\(RMSE_{FWHM}^{H}\)), cross-correlation (\(crosscorr^{H}\)), and \(lag^{H}\) between WWA and WNA, for each H.