Entropy and Multifractal-Multiscale Indices of Heart Rate Time Series to Evaluate Intricate Cognitive-Autonomic Interactions

Figures

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  Figure 1. Stroop Color and Word Task (SCWT). Displayed sequences for the SCWT.

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  Figure 2. Go/no-go task (GNGT). Displayed sequences for the GNGT. In this task, the participants respond as rapidly as possible to a go stimulus. In a minority of trials (30%), the go stimulus is replaced by a no-go stimulus that instructs participants to not respond.

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  Figure 3. Stop signal Task (SST). Displayed sequences for the SST. In this task, participants responded to a “go” stimulus, and, in a minority of trials (30%), the “go” stimulus is followed by a stop signal that instructs participants to withhold their response.

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  Figure 4. Typical RR time series for one subject in each phase (baseline, SCWT, SST, GNGT). (a) Original RR time series, (b) 1-Hz resampled RR series.

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  Figure 5. Surfaces of multifractal multiscale DFA average over all participants obtained on each condition (baseline (a), SCWT (b), SST (c) and GNGT (d)). Surface computed with the method described in [16] on the left side or with the fast one described in [40] on the right side.

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  Figure 6. Multifractal index (MFi) computed as a function of observational scales n with the method described in [16] (a) or with the fast one described in [40] (b). Computation for each experimental situation, baseline, SCWT, SST and GNGT.

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  Figure 7. Significance of repeated measures ANOVA conducted on MFi parameter at each observational scale. Blue line indicates the end of the range of scales where multifractality differed according to the situation, between n=10s and n=17s.

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  Figure 8. Values of the nonlinear dynamic measures on RR time series for a typical subject, obtained on each experimental condition (baseline, SCWT, SST and GNGT). The markers are the original values and the errors bars are the 5th and 95th percentiles of the surrogates’ distribution.

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  Figure 9. Percentage of stationary signals obtained by counting the subjects. Stationarity was tested using the RWS method. Results are presented for each experimental condition, baseline, Stroop color and word task (SCWT), stop signal task (SST) and go/no-go task (GNGT).

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  Figure 10. Refined composite multiscale entropy (RCMSE) analysis of RR interval time series. Sample entropy values at time scales 1 to 4 during all conditions (baseline, Stroop color and word task (SCWT), stop signal task (SST) and go/no-go task (GNGT) (mean ± SD)). The RCMSE curves for the surrogate shuffled time series (black curves) are also presented. The entropy index Ei represents the trapezoid approximation of the area under each curve.

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  Figure 11. (a) Surrogate data testing for entropy measurement. Open red circles represent the mean entropy value and standard deviation of the 97.5th and 2.5th percentiles from 50 surrogate series, green circles represent subjects’ individual values. (b) The percentage of significant nonlinear dynamics obtained by counting the subjects. For these subjects, the original RR time series presented an entropy value below the 2.5th percentile of 50 surrogates’ values. Results are presented for each experimental condition, baseline, Stroop color and word task (SCWT), stop signal task (SST) and go/no-go task (GNGT).

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  Figure 12. Effect of cognitive tasks (SCWT = Stroop color and word task; SST = stop signal task and GNGT = go/no-go task) on the entropy index (Ei) value. a.u. = arbitrary unit. Interpretation scale: H1 **** and H1 ** mean, respectively, extreme and strong evidence for the alternative hypothesis.