A Multiscale Partition-Based Kolmogorov–Sinai Entropy for the Complexity Assessment of Heartbeat Dynamics

Figures

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  Figure 1. Block scheme of the experimental procedure. HRV series are derived from ECG series and are eventually preprocessed to correct artifacts. Then, artifact-free series are coarse-grained according to a multiscale approach and converted into symbolic series. The lossless data compression CASToRe is then applied to compute K-S entropy at each partition and scaling time, for which group-wise inferential statistics are finally performed to evaluate the elderly vs. young and CHF vs. NS vs. AF differences.

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  Figure 2. Median across all subjects (i.e., both young and elderly groups) of the MKSE as a function of the cardinality of the uniform partitions considered.

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  Figure 3. MKSE values for the two groups. Orange lines refer to MKSE values extracted in the young groups, whereas blue lines represent MKSE for the elderly ones. Thick lines indicate the median across subjects, whereas chromatic shaded areas represent the median absolute deviations. Each subfigure reports MKSE values (vertical axis) as a function of the time scaling τ (horizontal axis) for a different partition cardinality (even), increasing in the left-right and top-down directions from 2 to 18. Asterisks indicate corrected p-value <α=0.005 from a nonparametric Mann–Whitney test for unpaired samples.

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  Figure 4. Distribution of p-values from nonparametric Mann–Whitney test for unpaired samples for the young vs. elderly comparison for each scale and partition.

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  Figure 5. Median MKSE values as a function of scaling time. Orange lines refer to MKSE values extracted in the CHF group, green lines represent MKSE for healthy controls, and blue lines stand for the MKSE of arrhythmic HRV series. Thick lines indicate the median across subjects, whereas chromatic shaded areas represent the median absolute deviations. Each subfigure reports MKSE values (vertical axis) as a function of the time scaling τ (horizontal axis) for a different partition cardinality (even), increasing in the left-right and top-down directions from 2 to 18. Asterisks indicate the corrected p-value <α=0.005 from a nonparametric group-wise Kruskal–Wallis test.

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  Figure 6. Graphical representation of the statistical analysis results. Top-left corner: p-values from a nonparametric Kruskal–Wallis test (i.e., AF vs. CHF vs. NS) for each scale and partition. The other images represent results of pairwise comparisons through non-parametric Mann–Whitney test for unpaired samples: light grey areas represent non-significant differences in terms of MKSE with p-value >α1=0.00167, whereas blue areas denote p-value <α1.