Removal of ECG Artifacts Affects Respiratory Muscle Fatigue Detection—A Simulation Study

Figure A1. ECG preprocessing and epoch construction. (A) displays a single QRS complex of baseline-filtered ECGIBLFt and ECGISGt pre-processed by the application of a Savitzky–Golay filter. (B) shows the 60% MVC sEMG signal taken from a previous study [16]. (C) shows the artificial test signal ATS60,0.05,At. The detected and time-refined position of the QRS is indicated by the orange diamond. Ranges of the signal close to the QRS complex designated to be excluded from the following fatigue analysis are drawn in purple. (D,E) display the epoch construction based on ATS60,0.05,ATSW15t obtained by template subtraction. A fatigue value is calculated every 125 ms (symbolized by dots), yielding a fatigue signal with 8 Hz sample rate. The epoch that forms the basis of each fatigue value is indicated by the timeline to the left of the dot at the same height. As an example, the fatigue value assigned to time t=35.2 s (as indicated by the red dot) is based on the epoch drawn in blue. This example uses an epoch size of a 0.25 s (256 samples). Subsegments as used in the Welch PSD estimation, with kw=7 subsegments shown in green for the exemplary epoch (shown in blue). (D) visualizes the gating strategy…

Figure A2. An evaluation of heartbeat irregularity. (A) visualizes three characteristic properties evaluated for each heart cycle. The evaluation is performed for both ECGIt and ECGAt. The resulting distributions of these characteristic properties for both ECG channels I and A are shown in (B) for each subject. ECG channel A is artificially mixed and features increased heartbeat irregularity. The violin plot visualizes the variation of the characteristic property within the same channel of one subject. The subject number is stated on the horizontal axis. An alternative way to evaluate the heartbeat irregularity is based on the amount of cardiogenic artifacts that could not be eliminated by the artifact removal step and is still present in ATSΛ,η,chcrt. The analysis is preferably used in combination with template subtraction TSW15 as the artifact removal method. A rectified segment of ATSΛ,η,chcrt is extracted for each heart cycle, as shown in (C). These segments are superimposed by the same QRS times used for template subtraction. A raw version of an average remaining cardiogenic artifact signal rARCAΛ,η,chcrτc is constructed by averaging all segments at the same relative heart cycle time…

Figure A3. A block diagram visualizing the test signal generation. See Section 2.1 for the corresponding description.

Figure A4. Table stating the utilized combinations of EMG recordings (differential signals originating from electrodes 1 and 3—subject numbers from [16]) and ECG recordings (identifiers from [20]). Further indicated is the number of heartbeats (# HB) within the analyzed segment of pure ECG. False positive (FP) and false negative (FN) detected QRS complexes from signals ATSΛ,η,At are stated for different EMG levels η and MVC loads Λ.

Figure A5. Block diagram displaying different methods to reduce cardiogenic artifacts. See Section 2.2 for a detailed description. For clarity reasons, the TSWD algorithm is only depicted for a single wavelet scale and suggested for two other instead of the utilized 8 scales. Not depicted are the methods TSWD35 and DSO. Both are variants to TSWD15 and differ in the signal that is fed into the stationary wavelet transform (SWT). TSWD35 uses the signal ATSΛ,η,chTSW35 as input. In the case of DSO, the unpreprocessed signal ATSΛ,η,ch is used as input. The ECG removal methods featuring a high pass with fc=35 Hz are only relevant for fApEn fatigue detection. PSD-based fatigue detection relies solely on the 15 Hz version as the PSD lower bound bl is applied.

Figure A6. (A) displays the template that is subtracted QRS synchronously in the first step. To limit its influence on the current cardiac cycle, values outside the average cardiac cycle length are set to zero, being the additive identity. (B) visualizes the average remaining cardiogenic artifact signal wARCAΛ,η,chTSW15_SWT,iτc for different, color-coded wavelet levels i. It is constructed by averaging all rectified heart cycle segments of the signal ATSΛ,η,chTSW15_SWT,it at the same relative heart cycle time τc. The signal ATSΛ,η,chTSW15_SWT,it is obtained by the application of the stationary wavelet transform with eight different levels to the result of the template subtraction from the first step. Dash-dotted lines indicate the threshold θi. Damping is carried out only at heart cycle times τc where the average remaining cardiogenic artifact signal wARCAΛ,η,chTSW15_SWT,iτc is above the threshold θi. (C) shows the resulting damping templates dTempτc,i for different, color-coded wavelet levels i. Again, values outside the average cardiac cycle length are set to identity, in this case, 1 due to the multiplication. The remaining subpanels compare the results of different template subtraction…

Figure A7. Block diagram of applied fatigue detection methods. See Section 2.3 for a detailed description. Fatigue detection is performed based on signals ATSΛ,η,chcr. These signals feature reduced cardiogenic artifacts produced with the cardiogenic artifact elimination method cr. The resulting fatigue index signals are denoted ΦΛ,η,chcr,gs,Ne,fd, where gs denotes the gating strategy, Ne the epoch size and fd the fatigue detection method. The prefix se_ in front of MNF and SMR5 fatigue detection methods denotes the applied spectral estimation method (Welch or Burg method).

Figure A8. Detailed description of fatigue detection algorithms and exemplary fatigue detection signals. The mean frequency and spectral moments ratio depend on an estimation of the power spectral density (PSD) of the underlying epoch. The PSD was calculated in a nonparametric way by the Welch method [37]. Epochs are subdivided into subsegments with a quarter, an eighth or a sixteenth of the epoch size. Subsegments had a 50% overlap and were tapered by a Hamming window function. This led to kw=7,15or31 subsegments for each epoch. In the case of the gating strategy GO, all subsegments affected by gating are excluded from the averaging in the Welch method. Alternatively, a parametric estimate was calculated by the Burg algorithm [37]. The Burg algorithm is performed individually for all fragments separated by gating in the case of the gating strategy GO. A final PSD estimation is obtained as the weighted average of PSDs from all fragments. The weight is chosen according to the length of the fragment in relation to the total length of all fragments. Fragments shorter than a quarter of the intended epoch size are excluded. In practice, the presented cardiogenic artifact removal will only…

Figure A9. Temporal and spectral evaluation of ECG “cleaned” signals. The evaluation is based on the different error variants quantifying the deviation of the ECG “cleaned” signal ATSΛ,η,cht compared to the scaled EMG component SMCΛ,ηt. The properly scaled, pure ECG component is defined as SMCΛ,ηt=ATSΛ,η,cht−ECGcht=η0.2·RSMΛt. The squared error of the ECG attenuated signal with removal method “cr” is defined as: esqη,ch,cr=∥SMC60,ηt−ATS60,η,chcrt∥2∥SMC60,ηt∥2|0 s<t<60 s. This corresponds to the definition of the error for synthetic signals by Petersen et al. [15]. Subpanels (A,B) show the pure EMG component SMC60,0.05t and the ECG “cleaned” signal ATS60,0.05,ATSWDt, respectively. The mean removal esqη,A,cr error across all nine subjects is displayed in (C) for different ECG removal logarithms and EMG levels η. The influence of ECG removal variants on a subsequently calculated envelope signal is quantified by an error eenv, as known from Petersen et al. [15]. The mean average value MAV with a centralized sliding window (size 128) is calculated for both the pure EMG component and the cleaned signal. Exemplary envelope signals are shown in (D). The envelope error is defined as:…

Figure A10. A comparison of the best-working ECG removal methods for PSD-based fatigue detection algorithms. Depicted are template subtraction without (TSW15) and with (TSWD15) subsequent wavelet-based damping step. Both methods are shown as variants without (GN) and with gating (GO). The utilized fatigue detection algorithms include MNF with Welch PSD estimation (kw=15) on the left side and SMR5 in combination with Burg spectral estimation on the right side. Both fatigue detection methods are based on an epoch size of Ne=256 and incorporate a PSD lower bound bl of 35 Hz. The white dots indicate the median value.

Figure A11. The left side displays the influence of the epoch size and gating strategy in case of entropy-based fatigue detection with fApEn. The main blocks on the horizontal axis denote different EMG levels η again. For each of these main blocks, different epoch sizes are shown on the horizontal axis. To assure a balanced comparison of epoch sizes, results from smaller epochs are filtered the same way as described in Figure A12. The applied gating strategy is denoted by the marker and line style. The three applied evaluation criteria (A, B, C) are again covered by the rows of subfigures. Each data point is obtained by averaging over all subjects. The right side compares the best working ECG removal methods for fApEn fatigue detection. Depicted are template subtraction without (TSW35) and with (TSWD35) subsequent wavelet-based damping step. Both methods are shown as variants without (GN) and with gating (GO). The results are based on an epoch size of Ne=256. In contrast to the left side, no filtering of the fatigue index to incorporate one second of EMG was utilized. Because there was no filter, each fatigue index value incorporates only a quarter second of EMG, and the results are…

Figure A12. The influence of epoch size Ne in the case of PSD-based fatigue detection for different combinations of ECG removal method, gating strategy and PSD estimation method. The main blocks on the horizontal axis denote different EMG levels η. Connected data points denote the same EMG level. For each of these main blocks, different epoch sizes are shown on the horizontal axis. To assure a balanced comparison of epoch sizes, the results from smaller epochs underlying fatigue detection signals Φt are filtered. The length of the moving average filter is chosen in a way that each filtered fatigue index data point incorporates EMG from a 1s long window. The results displayed are based on TSWD15 in combination without gating (GN) as well as TSW15 in combination with the gating strategy GO. In the case of pure EMG, a sole high-pass filter (HP15) is applied instead of template subtraction. The applied PSD estimation is color-coded. The Burg method is drawn in red, while Welch methods with kw= 7, 15 and 31 subsegments are shown in green, blue and purple, respectively. The number of values in each Welch subsegment depends on the epoch size. The three applied evaluation criteria (A, B, C) are…