## 2 Materials and Methods
### Data Analysis
#### 2.4.2 Work of Breathing Estimation  
Figure 3 summarizes the methodology to estimate the level of WOB from sEMG signals. The first part consists of determining which indexes from the sEMG signals are relevant in describing the breathing pattern and the work of breathing. The second part includes two classification steps. The first one identifies whether the breathing pattern corresponds to a restrictive or obstructive one. Once the breathing pattern is identified, the subjects are classified into one of the three WOB levels, as established in the literature [4; 5; 6; 7; 8]. Lastly, the work of breathing is estimated using information from respiratory muscle sEMG signals. \(\bullet\) Relevant Indexes Selection  
Before the first classification, a dimension reduction was performed to choose the most relevant indexes (see Section 2.3.1). The following two algorithms of relevant indexes selection were used: the stepwise regression and the mutual information criterion. Statistically significant indexes were examined using Kruskal-Wallis test, followed by the post hoc Tukey-Kramer test for multiple \begin{table}
\begin{tabular}{c c c c} \hline
**Index** & **Time Domain** & **Index** & **Frequency Domain** \\ \hline \multirow{2}{*}{**MaxAmpj**} & Maximum amplitude of the sEMG signal of muscle j: Dia, Int or Strn & \multirow{2}{*}{**Fcj**} & The central frequency of power spectral density of sEMG signal of muscle j \\ \hline \multirow{2}{*}{**Rj-k**} & Pearson correlation between pairs of amplitudes of sEMG signals of the muscles j and k & \multirow{2}{*}{**RHLj**} & The ratio between high and low frequencies of power spectral density of sEMG signal of muscle j \\ \hline \multirow{2}{*}{**Cj-k**} & \multirow{2}{*}{**Cj-k**} & Spectral coherence between pairs of sEMG signals of the muscles j and k \\ \cline{1-1} \cline{3-3}  & & & \\ \end{tabular}
\end{table} 
Table 1: sEMG indexes in time and frequency domains for each one of the recorded muscles, diaphragm (Dia), intercostal (Int) and sternocleidomastoid (Strn). Figure 3: Methodology to estimate the level of WOB from sEMG signals. 1—determining which of 15 indexes from the sEMG signals are relevant to describe the breathing pattern and the work of breathing. 2—classification steps: 2.1—identifying if the breathing pattern corresponds to a restrictive or obstructive one; 2.2—classifying the subject in one of three groups of WOB. 3—estimating work of breathing. The results of each step of the methodology are presented in Figure 5.  
comparisons. Additionally, a Mann-Whitney test on each pair of groups was done to determine which groups differed from each other. 1. Stepwise Regression  
The stepwise regression is a systematic method for adding and removing indexes based on their statistical significance in a regression [35]. In this study, the p-value for determining the use of an index was 0.05. The summarized sequential algorithm steps are [35]:  
* Calculus of correlation coefficients of n-indexes with the response variable Y. * Sort the n-indexes from highest to lowest correlation coefficient X = [x1, x2.....xn]. * Add index xi to the P vector. * Calculus of regression and partial F\({}_{j}\)-values between response variable Y and P, where j is the index in the P vector. * Selection of the lowest F\({}_{j}\)-value and comparison between this and the F-value at \(\alpha\) = 0.05 in the F-distribution. * If the F\({}_{j}\)-value is higher than the F-value at \(\alpha\) = 0.05, i is incremented by one, the index P\({}_{j}\) is removed from the P vector. * Steps 3-6 are repeated until the last index enters the P vector. The final P vector contains the relevant indexes. 2. Mutual Information  
The mutual information gives an idea of the general statistical dependence between two variables [36]. In this study, the mutual information was calculated between each one of the sEMG indexes and the target group through Equation (4). \[I(X;Y)=H(X)-H(X,Y) \tag{4}\]  
where X was each one of the indexes, Y the target group, and H the entropy of a random variable defined by Equation (5).