Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment

Figures

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  Figure A1. Empirical mode decomposition (EMD) results on a sinusoidal input signal with five frequency components: 10, 50, 100, 300, and 500 Hz, with an amplitude of 30, 10, 1, 20 and 5, respectively.

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  Figure A2. Ratio approach: empirical distribution of R vectors of EEG signals used in this work. The vertical red line represents the mean of the distribution of the R vectors (Ri≈2). Vertical black lines represent the left and right thresholds using a value of p=15.

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  Figure A3. Energy approach: G vectors of the EEG signals used in this work.

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  Figure A4. Trend filtering process applied on a sinusoidal input signal with five frequency components.

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  Figure 1. Multiscale analysis with refined multiscale entropy (RMSE), using sample entropy (SampEn) (a–c), fuzzy entropy (FuzEn) (d–f), translated FuzEn (TFuzEn) (g–i), inherent FuzEn (IFuzEn) (j–l), inherent translated FuzEn (ITFuzEn) (m–o), from 60 realizations of the type-1 simulated series (Gaussian white noise (GWN), 1/f, and AR025) for length N = 100 (left column), 1000 (middle column), and 10,000 (right column). In each case, the length of the simulated series was cropped up to the Nth sample.

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  Figure 2. Multiscale analysis with RMSE, using SampEn (a–c), FuzEn (d–e), TFuzEn (g–i), anslated-reflected FuzEn (TRFuzEn) (j–l), IFuzEn (m–o), and ITFuzEn (p–r), from 30 realizations of the type-2 simulated series (LM-3.5, LM-3.7, LM-3.9, and Henon map (HM)) for length N = 100 (left column), 1000 (middle column), and 10,000 (right column).

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  Figure 3. Prediction probability (Pk values) of the RMSE metrics, using SampEn, FuzEn, TFuzEn, IFuzEn, and ITFuzEn, for nociception assessment (2 ≤ Ramsay sedation scale (RSS) ≤ 5 vs. RSS = 6) after a firm nail-bed pressure. Pk = 0.5 represents a complete randomness and Pk = 1 a perfect prediction.

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  Figure 4. Prediction probability (Pk values) of the RMSE metrics, using SampEn, FuzEn, TFuzEn, IFuzEn, and ITFuzEn, for nociception assessment (gag reflex (GAG) = 1 vs. GAG = 0) after endoscopy tube insertion. Pk = 0.5 means a complete randomness and Pk = 1 a perfect prediction.

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  Figure 5. Mean values of the SampEn (blue-continuous lines) and FuzEn (red-dotted lines) as a function of the time scales TS, obtained from the electroencephalogram (EEG) segments in responsive states 2 ≤ RSS ≤ 5 (square marker), and; unresponsive state RSS = 6 (circle marker).

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  Figure 6. Pk values as a function of the time scales TS, for different values of the tolerance parameter r (0.10, 0.15, 0.20, 0.25, and 0.30). Results were obtained comparing responsive states (2 ≤ RSS ≤ 5) vs. unresponsive state (RSS = 6), using RMSE with (a) SampEn; (b) FuzEn.