Singular Value Decomposition for Removal of Cardiac Interference from Trunk Electromyogram

Figure 1. Schematic representation of the acquisition setup used to acquire the high-density (HD) EMG. Adapted from [35].

Figure 2. Schematic of the algorithm proposed with an illustrative synthetic trunk EMG (SNR = 10 dB). The EMG signal during the first three QRScomplexes was the minimum (rest phase), while the last three QRS were overlapped with the EMG at 50% maximal voluntary contraction (MVC). Firstly, the synthetic trunk EMG signal was processed to find the QRS complexes. For each ith QRS, a matrix X was built. Each row of X was composed by a single QRS centered 0.3 s before the R peak, with the length equal to the current RRinterval. Finally, the ECG component was extracted through inverse SVD considering n singular values, and it was subtracted from the mixed EMG.

Figure 3. The choice of the optimal number of SVs. (A) Synthetic dataset with EMG + ECG signals around a single QRS complex; (B) application of the algorithm described in the previous section selecting three SVs to obtain an estimation of the EMG and ECG components; (C) SNR estimation considering ECG3SV and EMG3SV; this approximation stands since there is a linear relationship between the real SNR and the estimated SNR with ECG3SV and EMG3SV shown in the figure (Panel C—on the right); (D) calibration curve: the choice of the optimal number of SVs on the basis of the approximation to step functions; (E) application of the algorithm with the appropriate number of SVs.

Figure 4. Relative mean squared error (MSEr) in the reconstruction selecting an increasing number of QRS complexes in the X matrix.

Figure 5. Calibration curve to establish the number of singular values to be used at each SNR level. The mean SNR and the 95% confidence interval are reported in the boxes.

Figure 6. Performance of the SVD algorithm at different values of the SNR in terms of the mean squared error (A) and mean frequency difference (B). The present results were obtained on the whole signal, including the EMG from the voluntary contraction and the signal at rest. MFD, mean frequency difference.

Figure 7. Performance of the different algorithms. SVD: singular value decomposition; GT: gating technique; HPF: high-pass filtering; TS: template subtraction; ICA: independent component analysis. The upper panels show the results in terms of the mean squared error (MSEr) with SNR of 0 dB (A), 10 dB (B), and 20 dB (C). The lower panels show the results in terms of the mean frequency difference (MFD) with an SNR of 0 dB (D), 10 dB (E), and 20 dB (F). * if p-value < 0.05 by the Bonferroni-corrected Wilcoxon test.

Figure 8. Illustrative results of the signal obtained with the algorithm applied on a real signal from trunk EMG (diaphragm). (A) Trunk EMG; (B) reconstructed ECG (Rec ECG in red) and EMG (Rec EMG in black) with the SVD-based algorithm; (C) reconstructed ECG (Rec ECG in dotted red) and EMG (Rec EMG in dotted black) with TS; (D) the envelope of the Rec EMG was computed and normalized with its maximum (gray line for the SVD-based algorithm and dotted gray line for TS). The inverted esophageal pressure is also shown (green line) as a reference of the respiratory cycle. R: correlation coefficient between EMG and esophageal pressure, * if p-value < 0.01.