2.4. Data Analysis
This protocol is extracted from research article:
Comparison of Modular Control during Side Cutting before and after Fatigue
Appl Bionics Biomech, Jan 7, 2021; DOI: 10.1155/2021/8860207

We analyzed the third round of sidestep motion during the test exercise. We determined the timing of landing using the acceleration of the edge of the toe marker. The EMG data were obtained from 200 ms before landing to 200 ms after push-off based on the kinematic data. A custom MATLAB (MATLAB R2016, MathWorks, Inc., Natick, MA, USA) code was used to analyze the EMG data. The raw data were band-pass filtered between 20 and 450 Hz and full-wave rectified. Then, they were interpolated to 200 time points. The EMG data were normalized relative to the associated MVC data of the muscle. As previously described, NMF was performed to extract modules [1], as follows:

where E is a p-by-n initial matrix (p is the number of muscles and n is the number of time points). The initial matrix comprised normalized EMG data and a cycle for each of the 8 muscles; therefore, E is a matrix with 8 rows and 200 columns. W is a p-by-s matrix (s is the number of synergies) and represents muscle synergy, C is an s-by-n matrix and represents the time-varying component, and e is a p-by-n residual error matrix. Formula 2 indicates that matrix “e” calculated using formula 1 reaches a minimum. W is a vector; therefore, the calculated W is written as W. For each subject, we iterated the analysis by varying the number of synergies between 1 and 8, and then selected the least number of synergies that accounted for >90% of the variance accounted for (VAF) [5, 24, 25]. Global VAF was calculated based on the findings of previous studies.

where i goes from 1 to p and j goes from 1 to n. Thus, i increases from 1 to 8, and j increases from 1 to 200 in this study. In addition, to confirm the reliability of our analysis, we also calculated the local VAF based on Hug et al. [24]:

where m represents the muscle. We defined the adoption standard for a local VAF >75% [24].

To compare W before and after the intervention, the scalar product (SP) was calculated based on the findings reported by Cheung et al. [4]:

The SP for the use of the correlation coefficients can assess the similarity of W. We defined the module as similar if the SP was above 0.75 [4].

In addition, to evaluate the level of fatigue, wavelet transform was performed based on the findings reported by Smale et al. [8], and the instantaneous mean frequencies (IMF) were calculated.

where  P(t, ω) is the time-dependent power spectral density. After that, the IMF was averaged to calculate the mean frequency. The analyzed range of data was the same as that of the NMF analysis.

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