# Effects of Arm Swing in Lower Limb Muscle Activation and Coordination During Treadmill Walking
## 2 Materials and Methods
From left to right: EMG envelopes of the eight measured muscles: four synergies extracted (red Syn 1, purple Syn 2, blue Syn 3, green Syn 4); and performance indicators extracted from the EMG data and muscle synergies. (**d**) Schematic representation of \(max_{X}^{EMG}\), \(max_{Y}^{EMG}\), \(max_{Y}^{H}\), and (\(FWHM^{H}\)), all explained in the Supplementary Material (Table S1). GLM, Gluteus Medius; RF, Rectus Femoris; VL, Vastus Lateralis; BP, Biceps Femoris; ST, Semitendinos; GaM, Gastrocnemius Medialis; SOL, soleus; TA, Tibialis Anterior; ref., reference electrode; W and H, matrices that represent the spatial time-independent and the time-dependent coefficients of a synergy, respectively. The EMG signals were analyzed in Matlab R2021a using SynergyLab [24] and custom Matlab scripts. Signals were first high-pass filtered with a third-order Butterworth filter with a cutoff frequency of 20 Hz, then demeaned, rectified, and low-pass filtered with a third-order Butterworth filter with a cutoff frequency of 5 Hz to obtain the EMG envelopes (\(EMG_{0}\)). The EMG envelopes were then segmented based on the events recorded by the sensorized treadmill. Segmentation was carried out for 30 cycles, normally the central cycles [46]. Each selected cycle was interpolated to 101 samples (from 0% to 100%), de-offset, and normalized to the mean value of the peaks of the selected 30 cycles. Finally, synergies were calculated from the selected cycles using the non-negative matrix factorization algorithm (NNMF) [47], as this method has been shown to effectively estimate LL joint movements by leveraging muscle patterns [48]. For each task and subject, four synergies were extracted [24; 38; 39], each including the spatial time-independent and the time-dependent coefficients of activation (matrices W and H, respectively), which are used to reconstruct \(EMG_{0}\) with an error \(e\), based on the following equation:  
\[EMG_{0}=EMG_{R}+e=WH+e\]  
The size of the EMG\({}_{0}\) and EMG\({}_{\text{R}}\) matrices is 8 \(\times\) 101, with each row corresponding to a muscle and each column to a gait cycle percentage. The size of the H matrix is 4 \(\times\) 101, with each row corresponding to a synergy and each column to a gait cycle percentage. The size of the W matrix is 8 \(\times\) 4, with each row corresponding to a muscle and each column to a synergy. The \(EMG_{0}\) and the reconstructed EMG (\(EMG_{R}\)) were used to calculate the _variability accounted for_ (VAF) metric, which quantifies the accuracy of the EMG reconstruction [36]. The VAF was computed for each muscle individually (VAF\({}_{\text{muscle}}\)) and for all of them together (VAF\({}_{\text{global}}\)). Minimum values of 90% for VAF\({}_{\text{global}}\)[49] and 75% for VAF\({}_{\text{muscle}}\)[50] were selected to accept the reconstruction. A diagram of the EMG signals and synergy extraction is shown in Figure 1c. Muscle activation and coordination were compared between WWA and WNA using 10 performance indicators from the EMG\({}_{0}\) and spatial time-independent (W) and time-dependent (H) coefficients of activation. The performance indicators considered were: the position of the EMG peak (\(max_{x}^{EMG}\)) as a function of gait cycle (GC) [51], the difference (in %) between the value of the EMG peak in \(\mu\)V (\(\text{max}_{y}^{EMG}\)) during WWA and WNA (\(\Delta\)), as in [33], the position of the synergy peak (\(max_{x}^{H}\)) in % of GC [33; 51], the cross-correlation between the EMG activity of WWA and WNA (\(crosscorr^{EMG}\)) [24; 37; 40], the lag of \(crosscorr^{EMG}\) (\(lag^{EMG}\)) [37], the cross-correlation between time-dependent H coefficients of WWA and WNA (\(crosscorr^{H}\)) [37; 40], the lag of \(crosscorr^{H}\) (\(lag^{H}\)) [37; 40], the full width at half maximum of the time-dependent H coefficients (\(FWHM^{H}\)) [37; 52], the root mean square of \(FWHM^{H}\) (\(RMSE_{FWHM}^{H}\)) [37; 52], and the normalized dot product between W of WWA and WNA (\(dot^{W}\)) [24; 33; 53; 54].