Complexity synchronization analysis of neurophysiological data: Theory and methods

Figures

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  FIGURE 1. Heterogeneous neurophysiological data from an example subject over the 675-s duration of a Go-NoGo task (64-chan EEG, ECG, RESP) illustrating diverse temporal dynamics, distributions, and spectra.

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  FIGURE 2. Amplitudes and temporal dynamics of EEG, ECG, and RESP within one breath cycle (4 s), showing the need of having a method to capture the different relevant features of each time series. In MDEA analysis, amplitudes of all time series are normalized to the interval [0,1], but the original amplitude and frequency scales are shown here to illustrate the different orders of magnitude scales of EEG with respect to ECG and RESP.

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  FIGURE 3. The impact of stripe size selection in the CE waiting-time PDF. Left column shows the no-IPL shape of the empirical waiting times PDF (blue curve) when the stripe size is not properly selected. Clearly, the blue curve corresponding to Femp(τ) (cf. Equation 2) does not fit any of the theoretical IPL PDFs indicated by the red curves for values of μ starting at μ=1 and increasing by 0.4 as the red curves approach the horizontal axis. The right column indicates the IPL nature of the empirical CCDF Femp(τ) defined in Equation 2 (blue curve) when the stripe size is properly selected by minimizing the KS statistic to fit an IPL PDF.

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  FIGURE 4. Bias and variance of KS-based and MDEA-based estimation of IPL parameter μ versus number of samples Nsamp utilized for the estimation.

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  FIGURE 5. Tracking ability of IPL parameter μ using MDEA with automated stripe size selection by minimizing the KS statistic.

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  FIGURE 6. Distributions of stripe sizes determined across 30 sec moving windows for EEG, ECG, RESP, and filtered RESP across 27 subjects in low and high time stress conditions.

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  FIGURE 7. RESP time series zoomed to 20 sec (upper) and spectra (lower) unfiltered (left) and high-pass filtered (right) over entire 675 sec task period.

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  FIGURE 8. Entropy (S(w)) vs. log window length (log(w)) over sliding windows for EEG, ECG, and unfiltered and filtered RESP. Red lines demarcate the median fit regions applied for estimating delta scaling indices. Different colored scatter plots for each time series reflect entropy plots from all 30-s sliding windows super-impose plotted to reveal consistency/variability across windows.

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  FIGURE 9. Complexity synchronization among EEG, ECG, and RESP using automated parameters selection.

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  FIGURE 10. CS among EEG, ECG, and filtered RESP using automated parameters selection following high-pass filtering of the RESP time series.