Multiscale Sample Entropy of Cardiovascular Signals: Does the Choice between Fixed- or Varying-Tolerance among Scales Influence Its Evaluation and Interpretation?

Abstract

Abstract:Multiscale entropy (MSE) quantifies the cardiovascular complexity evaluating Sample Entropy (SampEn) on coarse-grained series at increasing scales τ. Two approaches exist, one using a fixed tolerance r at all scales (MSE FT ), the other a varying tolerance r(τ) adjusted following the standard-deviation changes after coarse graining (MSE VT ). The aim of this study is to clarify how the choice between MSE FT and MSE VT influences quantification and interpretation of cardiovascular MSE, and whether it affects some signals more than others. To achieve this aim, we considered 2-h long beat-by-beat recordings of inter-beat intervals and of systolic and diastolic blood pressures in male (N = 42) and female (N = 42) healthy volunteers. We compared MSE estimated with fixed and varying tolerances, and evaluated whether the choice between MSE FT and MSE VT estimators influence quantification and interpretation of sex-related differences. We found substantial discrepancies between MSE FT and MSE VT results, related to the degree of correlation among samples and more important for heart rate than for blood pressure; moreover the choice between MSE FT and MSE VT may influence the interpretation of gender differences for MSE of heart rate. We conclude that studies on cardiovascular complexity should carefully choose between fixed-or varying-tolerance estimators, particularly when evaluating MSE of heart rate.

Changes in EEG multiscale entropy and power‐law frequency scaling during the human sleep cycle

“…These remained constant across all scale factors, analogous to keeping the tolerance fixed for sample entropy calculations which, for physiological signals, is preferable to recalculating tolerance at each scale factor (Castiglioni, Coruzzi, Bini, Parati, & Faini, 2017). These remained constant across all scale factors, analogous to keeping the tolerance fixed for sample entropy calculations which, for physiological signals, is preferable to recalculating tolerance at each scale factor (Castiglioni, Coruzzi, Bini, Parati, & Faini, 2017).…”

“…Dispersion entropy is related to sample and permutation entropy, but it is more tolerant to the presence of noise in time series signals and has a considerably shorter computation time (Rostaghi & Azami, 2016 (Kuntzelman, Rhodes, Harrington, & Miskovic, 2018). A schematic depicting some of the major steps in the calculation of dispersion entropy is provided in Figure 1 analogous to keeping the tolerance fixed for sample entropy calculations which, for physiological signals, is preferable to recalculating tolerance at each scale factor (Castiglioni, Coruzzi, Bini, Parati, & Faini, 2017). Note that using NCDF for mapping makes this approach nonlinear, resulting in a classified signal (see Figure 1b) matching the size of the original.…”

Information-Domain Analysis of Cardiovascular Complexity: Night and Day Modulations of Entropy and the Effects of Hypertension

“…Unlike the refined-MSE [7], which originally proposed the Butterworth filter for coarse-graining, our MSE estimator does not downsample the series and does not update the tolerance threshold at each scale by re-calculating r as a fraction of the standard deviation of the filtered series. This latter choice is based on our previous analysis suggesting that a fixed threshold may provide more stable estimates and better highlight physiological differences between heart-rate and BP dynamics [23].…”

“…Another methodological aspect regards the use of the classic "fixed-threshold" approach, as originally proposed for the multiscale entropy [6], which means that the entropy is calculated with the same tolerance threshold r at all the scales, as in Equation (5). Other authors proposed using a tolerance threshold that varies at each scale as the standard deviation of the coarse-grained series [7]: With such a "varying-threshold" approach, the results could be different [23]. Finally, we selected two groups of NT and HT subjects of the same size with non-dissimilar age range (p = 0.41 after Student's t-test) and sex composition (p = 0.57 after Fisher's exact test); however, with a larger population of participants, we could have excluded more safely possible age and gender biases in our results.…”

“…However, an integrated approach for characterizing the MSE of cardiovascular time series is still missing. In fact, very few works also considered the MSE of beat-by-beat blood pressure [9,[22][23][24], and none of them investigated the interactions between heart rate and blood pressure in terms of multiscale cross-entropy. Furthermore, all of the HRV studies but one [10] considered a limited number of entropy scales.…”