Cepstral Analysis for Scoring the Quality of Electrocardiograms for Heart Rate Variability

Figures

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  FIGURE 1. Power spectra and power cepstra of a sinusoid, sawtooth function and synthesised ECG. The signals were sampled at 200 Hz, the spectra were calculated over 2048 points by Fast Fourier Transform (FFT) and the cepstra were calculated by FFT of the log-transformed spectra between 0 and 100 Hz (for clarity, spectra are plotted up to 40 Hz, signals and cepstra up to 4 s). The cepstra of the sawtooth function and synthesized ECG show peaks at 1, 2, and 3 s representing the train of power spectrum harmonics multiple of the fundamental frequency f 0 = 1 Hz; the sawtooth cepstrum also shows peaks at 0.24 s and its multiples representing the modulation with period of 4.2 Hz visible in its log-spectrum; the ECG cepstrum shows a large peak at the lowest quefrency representing the decreasing spectral trend.

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  FIGURE 2. Definition of data windows for ECG cepstral analysis. (A): power spectrum of a synthesised ECG (dotted line) with interpolation of the maxima at the fundamental harmonic and its multiples (continuous line). (B): average and 95% confidence interval of the lines interpolating the spectral maxima of 8 synthesised ECG. The average interpolating line is relatively constant up to 20 Hz and rapidly decreases at higher frequencies, suggesting to limit the length of the frequency-domain data window up to 20 Hz. (C): relative power of the main cepstral peak: median and interquartile range over 8 synthesised ECGs calculated by six different time-domain data windows and by smoothing the spectral lines using moving average filters with bandwidth between 98 and 684 mHz. The best performance is obtained with the Blackmann window and smoothing bandwidth between 250 and 500 mHz.

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  FIGURE 3. Examples of ECG cepstral analysis. Left: 10-s ECG segments from the Physionet/Computing in Cardiology datasets of the 2011 (A–C) and 2017 (D) Challenges; centre: log-spectra with polynomial trends (red line); right: cepstra before (dotted black) and after (red) liftering by polynomial detrending, with τ 0 the quefrency of the estimated first harmonic. (A) shows a high quality ECG and a cepstrum with a single harmonic; the corresponding CQI is 91.1%. (B) shows a high quality ECG, its cepstrum with 3 harmonics multiple of τ 0, and CQI is 67.2%. (C) shows a low-quality ECG with a single harmonic identifiable in the liftered cepstrum and CQI is 29.3% due to consistent low-quefrency noise. (D) shows a high quality ECG during atrial fibrillation: the log-spectrum does not have a periodic structure, the liftered cepstrum does not show a clear first harmonic, and CQI is 22.1% only. When a clear cepstral first harmonic is identifiable (A–C), its quefrency τ 0 practically coincides with the mean R-R interval, RRm.

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  FIGURE 4. Effects of noise and deviations from periodicity on CQI. CQI median and interquartile range over 8 synthesised ECGs. (A): CQI at decreasing levels of signal-to-noise ratios, SNR (SNR = ∞ means no noise, SNR = 0 means noise only) with * indicating statistically significant difference vs. SNR = 0 at p < 0.05; the inset is an example of ECG with SNR = 4. (B) : CQI at increasing values of variation coefficient, VC, of R-R interval when the heart rate dynamics consists in monotonic ramps (solid circles) or random changes (open circles): median and interquartile range over 8 synthesised ECGs with * indicating statistically significant difference between ramp and random changes at p < 0.05. (C): CQI without or with 1, 2 or 3 premature beats, with * indicating statistically significant difference vs. no premature beats at p < 0.05: inset is an example of simulated supraventricular premature beat.

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  FIGURE 5. Examples of multi-lead ECGs from the dataset of Physionet/Computing in Cardiology 2011 Challenge. The recordings were classified as “acceptable” (left) or “unacceptable” (right). CQI scores of individual leads correctly detect Lead I of sufficient quality for heart rate variability analysis in the “unacceptable” recording and Lead V6 as inadequate for heart rate variability analysis in the “acceptable” recording.

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  FIGURE 6. Physionet/Computing in Cardiology Challenge 2011 datasets. CQI median and interquartile range for each of 12 leads of ECG recordings classified as “acceptable” (A) or “unacceptable” (B): for each lead, the * indicates statistically significant difference between groups at p < 0.01.

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  FIGURE 7. Physionet/Computing in Cardiology Challenge 2017 datasets. (A) CQI as median and interquartile range for single-lead ECGs manually classified as in normal rhythm, atrial fibrillation or noisy recording. The * indicates a statistically significant difference vs. the normal rhythm group at p < 0.01 (B) ROC analysis on 5050 recordings adequate for heart rate variability analysis (normal rhythm) vs. 1022 recordings inadequate for heart rate variability analysis (in atrial fibrillation or noisy); the red dot on the curve identifies the classification cut-off (CQI > 47%) according to the Youden’s criterion; AUC = Area Under the Curve.

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  FIGURE 8. Examples of discarded ECG segments by running cepstral analysis. Colors represent four CQI levels. (A) : low CQI values identify a short burst of muscle noise and a following movement artefact. (B) : low CQI values detect signal loss likely due to a poor contact between textile electrodes and skin. (C): premature beats in a high quality recording are locally associated to low CQI values. (D) : atrial fibrillation is associated to persistently low CQI even in high quality ECG recording.

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  FIGURE 9. Examples of running cepstral during ramp-like heart-rate changes. Upper panels: ECG (A), R-R intervals, RRI (B), and respiratory movements of the thorax (C) during sleep apneas; color codes represent the CQI levels. Even if apnea/deep breathing events produced large ramp-like changes of heart rate, the CQI score remained relatively high classifying the data segment of good quality for heart rate variability analysis. Lower panels: R-R intervals (D) and ECG (E) during an incremental exercise test on the cycloergometer: the ECG was in normal sinus rhythm (see insets) and the CQI score remained high even when RRI progressively decreased during the exercise.

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  FIGURE 10. Overall quality of very long-term ECG recordings from the distribution of running CQI values. Distributions (relative frequencies) of CQIs calculated second-by-second on ECG Holters recorded for 7 consecutive days continuously with a wearable device (RootiRx®, Rooti Labs Ltd., Taipei, Taiwan) at 250 Hz in two subjects. The recording of the subject on the right (#1556) is almost completely analysable having good quality (CQI > 50%) for 97% of the time; by contrast, assessing heart rate variability in the recording on the left (#38F) might be problematic for a not negligible fraction of the time, being the quality “very low” or “unacceptable” (CQI ≤ 40%) for 12% of the recording.