Multiscale entropy of ADHD children during resting state condition

Participants

A group of children and adolescents diagnosed with ADHD by clinical experts from two public hospital services participated in this study. A structured interview and the DuPaul parent questionnaire (DuPaul et al. 1998) were conducted for the diagnosis. The ADHD group, consisting of 40 children and adolescents aged 6 to 17 years, was recorded under experimental OE and CE conditions. Only subjects who (i) obtained a minimum of 50 trials without artifacts in one or both conditions (OE and CE), and (ii) showed diagnostic agreement between the administered questionnaire and the clinical diagnosis were selected for data analysis. Therefore, the ADHD group was finally composed of 32 children and adolescents for the OE condition (M = 10.94, SD = 3.18, 25 males, 7 females, 6–17 years) and 25 ADHD children and adolescents for the CE condition (M = 11.8, SD = 3, 21 males, 4 females, 7–17 years). Grouping by ADHD typology was not performed due to the low number of subjects in each group.

Thirty-two control subjects, matched in age and gender to ADHD in the experimental condition for OE (M = 10.84, SD = 3.10, 25 males, 7 females, 6–17 years) and CE (M = 11.68, SD = 2.93, 21 males, 4 females, 7–17 years), were selected from public schools through accessibility sampling. The control subjects for CE were reduced to 25 to equate them to the number of ADHD subjects in the CE condition. There were no significant differences between the two groups in age (OE: (F (1, 62) = 0.000042, p = 0.995; eta partial squared = 0.0000007) and CE: (F (1, 48) = 0.000122, p = 0.991, eta partial squared = 0.000003) or gender (OE: (F (1, 62) = 0.00, p = 1; eta partial squared = 0.00) and CE: (F (1, 48) = 0.00, p = 0.991, eta partial squared = 0.00). The equating in gender and age between controls and ADHD allowed to eliminate these factors for mean comparisons statistical analyses.

Controls did not report neurological diseases, signs of epileptic discharges, or psychological impairments. The experimental protocol was approved by the biomedical research ethics committee of the autonomous community of Andalucía. The guidelines of the Declaration of Helsinki were followed and written informed consents were obtained from the parents.

Experimental session

Spontaneous EEG activity was obtained in the OE and CE experimental conditions with a duration of 3 min. Subjects were instructed to stay still and to maintain a state of relaxation in both experimental conditions. In the OE condition, they were also instructed to blink as little as possible and to look at a cross in the center of the screen.

A 32-electrode cap (ELECTROCAP) (Fp1, Fpz, Fp2, F7, F3, Fz, F4, F8, FC5, FC1, FC2, FC6, M1, T7, C3, Cz, C4, T8, M2, CP5, CP1, CP2, CP6, P7, P3, Pz, P4, P8, POz, O1, Oz, O2) assembled according to the international 10–20 system was used for recording. Electrodes placed on the scalp were referenced off-line to the mean mastoid (M1 + M2)/2. Horizontal eye movements were recorded with two electrodes placed on the outer edge of each eye and vertical movements with two electrodes placed above and below the left eye. Impedance was obtained below 10 Kohms. Using an analog-to-digital acquisition and analysis system (ANT amplifiers, The Netherlands), data were recorded with a gain of 20,000 in direct current at 512 Hz without any filtering.

Data analysis

For EEG data analyses, the EEGLAB toolboxes (Delorme & Makeig 2004) and Matlab R2019a software package were employed.

The EEG signal was band-pass filtered from 0.5 to 35 Hz (eegfiltnew EEGLAB function). The Artifact Subspace Reconstruction (ASR) algorithm was applied to correct EEG signal artifacts that exceeded 20 times the standard deviation of the calibrated data (clean rawdata EEGLAB function). Data were reconstructed and epochs (2 s in duration) that exceeded ± 120 μV in any channel were rejected for subsequent analysis (eegthresh EEGLAB function). Subjects with less than 50 trials were not further analyzed. Table 2 shows the number of epochs accepted in each group and experimental condition. ANOVA comparisons showed no differences in the number of epochs accepted in both groups: For the OE condition (F (1, 62) = 0.147, p = 0.703, eta partial square = 0.002) and for the CE condition (F (1, 48) = 1.3, p = 0.259, eta partial square = 0.026).

Table 2 Mean and Standard Deviation of accepted trials in controls and ADHD subjects in open (OE) and closed eyes (CE) conditionsMultiscale entropy analysis

MSE was computed for all channels (except M1 and M2) with the "multiscaleSampleEntropy" function of Matlab (Malik 2022) based on Costa et al. (2005). MSE analysis is a derivation of Shannon entropy (Shannon & Weaver 1949) and Pincus approximate entropy (Pincus 1991). It is based on the calculation of the sampling entropy (SampEn) of the EEG signal at multiple time scales (Costa et al. 2002, 2005; Richman & Moorman 2000). MSE is an index of signal complexity (Garrett et al. 2013) and is computed using a process known as coarse-graining. Each time scale is defined by averaging the different neighboring points of the original time series (of length τ), dividing the EEG signal in non-overlapping windows of a different number of samples. Subsequently, the SampEn is calculated for each time scale. This analysis evaluates the similarity of the repetition frequency of patterns of m data points (p^m) versus another of m + 1 points (p^(m + 1)). It is necessary, for this purpose, to define a similarity limit (r) that delimits the tolerance range for individual data points to be considered similar (k). The similarity limit is normalized by the EEG Standard Deviation (SD) k < r × SD (Malik 2022).

Recently, it has been suggested that the coarse-grained process is comparable to Haar wavelet approximations on power-of-two scales, relating the different frequency bands of traditional spectral power analysis to different scales of the MSE (Bosl et al. 2022). In this sense, the coarser scales would contain the lower frequencies with filtering of the high frequencies (Kosciessa et al. 2020), and the lower scales are the original signal with the high frequencies, with all scales containing also low frequencies (Bosl et al. 2022).

In our study, we set the parameters m = 2 and r = 0.5 considering the recommendations given by previous EEG signal complexity studies (Richman & Moorman 2000; McIntosh et al. 2008; Miskovic et al. 2016; Kosciessa et al. 2020; Kloosterman et al. 2019), in which the SD parameter permits normalizing the r parameter by the EEG standard deviation in each particular scale. MSE was calculated for time scale 1 to 34, which allows analysis of entropy from the finest to the coarsest scales, as well as indirect analysis of low frequency bands (≤ 7.73 Hz). The last time scale corresponds to a time of 64.6 ms per time point and 31 time points per trial.

The equation used to compute SampEn was (Malik 2022), following the notation of Kosciessa et al. (2020):

$$\mathrm=log\frac^(r)}^(r)}$$

High values of SampEn would indicate the presence of low temporal regularity or high complexity (i.e., many patterns of length m do not repeat over length m + 1) whereas low values would indicate high similarity/regularity or low complexity indicating the poverty of information (McIntosh et al. 2008; Garrett et al. 2013).

EEG standard deviation analysis

The EEG standard deviation (SDs) was computed in the same scales as MSE for both conditions and groups. The EEG SDs were computed as the EEG variability in each trial, and then, the mean of SDs across trials was obtained in the different scales. This parameter could inform if the variability of the EEG was different between both groups at the different scales and at different ages (by correlating SDs with age). The SDs parameter provides the basal variability of EEG and would be complementary to the PSD, which provides the energy of each EEG frequency, and the MSE, which provides the data complexity.

Absolute and relative PSD analyses

The mean of absolute PSD in each trial was calculated for each subject in both experimental conditions (OE and CE). PSD was calculated in 2 s windows (1024 sampling points at a sampling rate of 512 Hz) with the EEGLAB spectopo function which employs the Matlab pwelch function applying a hamming window. As spectopo calculates the logarithm of absolute PSD (Y = 10 * Log (PSD)), each subject's PSD values (PSD mean (M) and standard deviation (SDp) across trials) were calculated by removing the logarithms (PSD = eY/10) to visualize the data and calculate the coefficient of variation (CV) across trials. Four frequency bands averaged in different ranges were taken into account for subsequent analysis: delta (1–2 Hz), theta (4–7 Hz), alpha (8–11 Hz), and beta (13–20 Hz). The gamma band was not calculated due to the bandpass filter (0.5–35 Hz) used in the data analysis in order to eliminate high-frequency electromyographical artifacts.

Relative PSD was calculated using the mean of absolute PSD (removing logarithms) of each subject at each electrode and using the following formula:

where X(fi) is the relative PSD for a given frequency, PSD (fi) is the absolute PSD for a given frequency, and \(\sum PSD(fi)\) is the sum of absolute PSD across all the considered frequencies (1–20 Hz). This analysis was performed for controls and ADHD in both experimental conditions (OE and CE).

Statistical analysis

To calculate the difference between groups of MSE, SDs, absolute PSD (mean and CV), and mean of relative PSD metrics, the values of these parameters in neighboring electrodes, as defined in Fig. 1, were collapsed to reduce the dimensionality of the data (Fig. 1), for both OE and CE. For the same purpose, the MSE results for the 34 temporal scales were organized into three broader scales (values in ms correspond to the scales time sampling): fine scales (1.9 ms (scale 1)—24.7 ms (scale 13)); medium scales (26.6 ms (scale 14)—43.7 ms (scale 23)); and coarse scales (45.6 ms (scale 24)—64.6 ms (scale 34)) as proposed by Szostakiwskyj et al. (2017). The period of the scales was computed by multiplying the EEG sample period by the scale order.

Fig. 1figure 1

Localization and collapse of electrodes by regions. The colors indicate the nine defined scalp areas for electrodes collapse. The 30 electrodes are divided into two spatial dimensions (lateral and anterior–posterior) which have three values each one: left, middle, and right; and anterior, central, and posterior, respectively

Employing the Statistical Package for the Social Sciences 25 (SPSS) three analyses of variance (ANOVA) were performed with the mean of the MSE for each type of scale (fine, medium, and coarse) in each brain area as defined above and in Fig. 1. For the first and second ANOVA, the within-subject factors were: type of scale (levels: fine, medium, and coarse), anteroposterior areas (levels: anterior, central, and posterior), and lateral areas (levels: left, medial and right); and the between-subject factor was the group (Control and ADHD subjects). The first two ANOVAs correspond to the independent analysis of OE and CE conditions, respectively. And for the third ANOVA, the experimental condition (OE and CE) was added as a within-subject factor, maintaining the previously considered factors. To have the same subjects in both OE and CE conditions only 23 controls and 25 ADHD remained for the third ANOVA, respectively. When significant group differences were found in the ANOVA analysis, the independent samples t-test (False Discovery Rate (FDR) corrected) were computed as post-hoc tests (Benjamini & Hochberg 1995). Statistically significant results of ANOVA are presented for all the considered factors, but only those including the group factor were discussed and analyzed in post-hoc tests, given that the main objective of the present report is the between-groups differences.

Additionally, a Spearman correlation analysis of the MSE with the age of the subjects (expressed in days) was applied to controls and ADHD independently, in both experimental conditions (OE and CE). For the correlational analysis, the values of MSE in all the electrodes were collapsed to reduce dimensionality. The collapse of electrodes was also applied for other variables in which correlational analysis was computed.

The SDs of the EEG for the 34 scales, collapsed by electrodes, followed the same statistical analysis procedure as the MSE. (i) Spearman correlation with age, (ii) Three analyses of variance (ANOVA), with and without factor "experimental condition" (OE and CE), and (iii) Independent samples t-tests (FDR corrected) for post-hoc analysis.

For absolute PSD statistical analysis, Spearman correlation was performed between the collapse of the mean PSD across electrodes for each considered frequency (1–20 Hz) and the age of the subject (expressed in days). The same correlational analysis was calculated for SDp, CV, and relative PSD. Additionally, for the relative PSD, a correlation analysis was performed between the relative PSD at different frequencies with the different MSE scales for each group and experimental condition. The coefficient of variation was calculated by dividing the standard deviation across trials of absolute PSD (SDp) by the mean of the absolute PSD (CV = SDp/M) in all subjects and the two experimental conditions (OE and CE) and each frequency (1–20 Hz). The means of absolute and relative PSD and CV were analyzed through three ANOVAs. The first (for OE condition), and second (for CE condition) ANOVA included as within-subjects factors: anteroposterior areas, and lateral areas, and as a between-subject factor the group. The third ANOVA added the within-subject factor "experimental condition" (OE vs CE). The ANOVAs were computed independently for the four different considered frequency bands (delta, theta, alpha, and beta).

The FDR, which was applied to the post-hoc and to correlational analysis, was calculated according to Benjamini & Hochberg (1995) as a control measure for multiple comparisons and Spearman correlations.

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