Maliheh Ahmadi

Kamran Kazemi

Katarzyna Kuc

Anita Cybulska-Klosowicz

Marta Zakrzewska

Ewa Racicka-Pawlukiewicz

Mohammad Sadegh Helfroush

PhD Ardalan Aarabi
email: ardalan.aarabi@u-picardie.fr

Cortical source analysis of resting state EEG data in children with attention deficit hyperactivity disorder

Keywords: EEG, spectral power analysis, cortical source imaging, LORETA, combined and inattentive ADHD, children

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Attention deficit hyperactivity disorder (ADHD) is characterized by inattention, hyperactivity and impulsivity, with a prevalence rate of 3-7% reported for school-aged children [START_REF] Burd | Children and adolescents with attention deficit-hyperactivity disorder: 1. Prevalence and cost of care[END_REF][START_REF] Polanczyk | Epidemiologic considerations in attention deficit hyperactivity disorder: a review and update[END_REF]. Fifty percent of children with ADHD show persistent symptoms into adulthood [START_REF] Mannuzza | Adult psychiatric status of hyperactive boys grown up[END_REF][START_REF] Spencer | Attention-deficit/hyperactivity disorder: diagnosis, lifespan, comorbidities, and neurobiology[END_REF][START_REF] Kessler | The structure and diagnosis of adult ADHD: an analysis of expanded symptom criteria from the adult ADHD clinical diagnostic scale (ACDS)[END_REF]. Despite the large number of neuroimaging studies on ADHD, the neural basis underlying this deficit is poorly understood especially in neurodevelopmental populations.

In the past decade, electroencephalography (EEG) has been extensively used to investigate neural abnormalities in ADHD [START_REF] Lenartowicz | Aberrant modulation of brain oscillatory activity and attentional impairment in attention-deficit/hyperactivity disorder[END_REF]. Resting-state EEG can provide valuable information concerning alterations in the temporal dynamics of brain functions in the absence of any tasks requiring high cognitive demands especially in children.

The majority of EEG studies performed on ADHD patients has focused on changes in spectral characteristics of scalp EEG in different physiological frequency ranges including delta, theta, alpha and beta bands [START_REF] Newson | EEG frequency bands in psychiatric disorders: a review of resting state studies[END_REF]. When compared to typically developing controls, children with ADHD have been characterized with higher and lower power in low (delta and theta) and high frequency (alpha and beta) bands, respectively [START_REF] Lubar | Discourse on the development of EEG diagnostics and biofeedback for attentiondeficit/hyperactivity disorders[END_REF]. More specifically relative to healthy controls, the ADHD population has shown elevated theta/beta (TBR) and theta/alpha power ratios, interpreted as an index of immature brain activity [START_REF] Barry | A review of electrophysiology in attentiondeficit/hyperactivity disorder: I. Qualitative and quantitative electroencephalography[END_REF][START_REF] Snyder | A meta-analysis of quantitative EEG power associated with attention-deficit hyperactivity disorder[END_REF][START_REF] Giertuga | Age-related changes in resting-state EEG activity in attention deficit/hyperactivity disorder: a cross-sectional study[END_REF]. The TBR measure has been considered as one of the neurophysiological biomarkers of ADHD by many researchers [START_REF] Lenartowicz | Use of EEG to diagnose ADHD[END_REF]. However, the use of TBR for diagnosing ADHD has been a subject of debate for many years [START_REF] Lenartowicz | Aberrant modulation of brain oscillatory activity and attentional impairment in attention-deficit/hyperactivity disorder[END_REF].

Overall, the interpretation of changes in EEG spectra at sensor level may be less reliable due to the volume conduction effect caused by the electrical conduction properties of the head [START_REF] Hassan | Electroencephalography source connectivity: toward high time/space resolution brain networks[END_REF]. To address this issue, EEG source imaging methods including the low resolution brain electromagnetic source tomography (LORETA;[START_REF] Pascual-Marqui | Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details[END_REF] have been used in many studies to analyze source activity of resting state EEG signals in the frequency domain [START_REF] Babiloni | Cortical sources of resting state electroencephalographic rhythms in Parkinson's disease related dementia and Alzheimer's disease[END_REF][START_REF] Imperatori | Aberrant EEG functional connectivity and EEG power spectra in resting state post-traumatic stress disorder: A sLORETA study[END_REF][START_REF] Adebimpe | EEG resting state analysis of cortical sources in patients with benign epilepsy with centrotemporal spikes[END_REF].

In the present study, we first tested the hypothesis that children with ADHD could be distinguished using age-related atypicalities in cortical source power of EEG rhythms in different frequency bands. We further hypothesized that children with ADHD would show elevated power in low frequency bands (delta and theta) and decreased power in high frequency bands (alpha and beta) compared to controls. To these aims, we investigated differences in current source densities of eyes-closed resting state EEG between children with combined and inattentive subtypes of ADHD and healthy controls in different frequency bands. We also explored age-dependent changes in resting-state EEG activity in ADHD and typically developing children.

Material and Methods

In this study, we included resting state EEG data collected as part of a larger study [START_REF] Giertuga | Age-related changes in resting-state EEG activity in attention deficit/hyperactivity disorder: a cross-sectional study[END_REF] from 74 healthy controls (13±2.3 years) and 67 ADHD children (12.9±2.4 years) from a total of 141 children aged 8-16 years. In this database, the ADHD children were diagnosed and classified into inattentive (n=20) and combined (n=47) subtypes in accordance with the Diagnostic and Statistical Manual of Mental Disorders (DSM) at the Public Pediatric Teaching Hospital in Warsaw, Poland [START_REF] Giertuga | Age-related changes in resting-state EEG activity in attention deficit/hyperactivity disorder: a cross-sectional study[END_REF]. The ADHD Rating Scale (ADHD-RS) has been used to rate ADHD symptom intensity [START_REF] Dupaul | ADHD Rating Scale-IV: Checklists, norms, and clinical interpretation[END_REF] with an average score of (20.3±3.8), (9±4.9) and (8.5±4.1) for inattention, hyperactivity and impulsivity, respectively. The inclusion criteria were: (1) no previous history of head injuries, somatic disorders and epilepsy, and (2) absence of loss of consciousness. The study was approved by the local Ethics Committee at the SWPS University of Social Sciences and Humanities (approval No. 9/2016) and the Medical University of Warsaw (approval No. KB/157/2010). Assent was provided from all participants. Informed written consents was also obtained from each participant's parent or caregiver in accordance with the Declaration of Helsinki. All participants were asked to complete the questionnaire concerning their health condition to assess whether the participants had any attentional problems, neurological disorders or close family members with ADHD/ADD diagnosis [START_REF] Giertuga | Age-related changes in resting-state EEG activity in attention deficit/hyperactivity disorder: a cross-sectional study[END_REF]. The patients were also requested not to take medications at least 24 h before the experiment.

EEG data collection and preprocessing

EEG data were recorded using a 64-channel EGI HydroCel Geodesic System (Electrical Geodesics Incorporation, Eugen, OR, United States) with a sampling rate of 250 Hz with respect to Cz as the reference electrode. Three one-minute eyes-closed resting-state data, each followed with one-minute eyes-open resting periods were collected from each subject. The eyes-open condition was included to prevent subjects from falling asleep during the experiment. The subjects were requested to remain fully relaxed and motion-less during the recording.

Figure 1 shows the main processing pipeline including preprocessing, scalp EEG spectral and cortical source analyses. The EEG preprocessing was performed using custom MATLAB scripts, EEGlab (v2019.0, [START_REF] Delorme | EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis[END_REF] and Fieldtrip toolbox (v2019, [START_REF] Oostenveld | FieldTrip: open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data[END_REF].

<Figure 1>

The EEG data were first inspected visually by an EEG expert using the EEGlab toolbox to identify and mark all artifacts including eye movement, eye blinking, muscular activation and movement artifacts as well as noisy/bad channels, which were replaced by interpolating their neighboring electrodes data using the Fieldtrip toolbox. The average number of interpolated electrodes was 3 (± 2.6) per subject. The artifactual portions of the EEG recordings were excluded from further analysis. The remaining EEG data were bandpass filtered between 0.5-30 Hz using a fourth-order Butterworth filter, and then re-referenced using a common average reference. The artifact-free filtered EEG data were partitioned into five-second epochs with 25% overlap to avoid information loss caused by windowing. To avoid the small sample size effect, only the EEG data of participants who contributed at least twenty artifact-free segments were included in the analysis. In total, the EEG data from 41 healthy control (13±2.3 years; 31 males/10 females) and 40 ADHD children (12.9±2.4 years; 32 males/ 8 females) including 10 inattentive and 30 combined were used for further analysis.

On average, 37 (±9) segments for each healthy subject and 31 (±10) segments for each ADHD patient were obtained. For the EEG spectral and source analyses, twenty segments were randomly selected from the artifact-free eyes-closed segments from each subject.

To test the effect of age and ADHD subtype on EEG spectra and current source densities, we grouped the patients and healthy subjects into six subgroups as listed in Table 1.

For each age range (8-10, 10-12, 12-14 and 14-16 years), an ADHD (ADHD8-10, ADHD10-12, ADHD12-14 and ADHD14-16) and an age-matched HC (HC8-10, HC10-12, HC12-14 and HC14-16) subgroup were selected from the ADHD and healthy children. To have the same sample size per subgroup, each ADHD subgroup and its corresponding HC were balanced in terms of the number of subjects by maintaining the maximum number of patients per subgroup. We also added two more ADHD subgroups, including 10 inattentive (ADHDI) and 30 combined (ADHDC) children to investigate subtype-related changes in spectral and current source density of resting-state EEG activity. For each subtype, we selected an age-matched HC (HCC and HCI) subgroup as listed in Table 1.

< Table 1>

Spectral analysis

The multi-taper spectral analysis was used to estimate the power spectral density (PSD) of the artifact-free EEG segments with the Slepian tapers and a frequency resolution of 0.25 Hz [START_REF] Jarvis | Sampling properties of the spectrum and coherency of sequences of action potentials[END_REF][START_REF] Mitra | Analysis of dynamic brain imaging data[END_REF] using the Fieldtrip toolbox. The total absolute power was then computed within four frequency bands: delta (0.5-4 Hz), theta . In each frequency band, the total absolute power was defined as the integral of all of the absolute power values within its frequency range. For each subject, this procedure was repeated on a channel-by-channel basis.

The mean absolute power for each frequency band was computed over all twenty segments at each scalp location. A subject-wise normalization was then performed on all mean absolute power values to minimize the effect of noise and non-physiological spectral power of the EEG signals. Compared to other methods, the subject-wise standardization was a crucial preprocessing step before group analysis by making the amplitude of the EEG data comparable between subjects all by keeping inter-channel differences in amplitudes [START_REF] Giaquinto | Applications of statistical equivalence to newborn EEG recordings[END_REF][START_REF] Giaquinto | Alpha increase in puerperium[END_REF][START_REF] Bigdely-Shamlo | Automated EEG mega-analysis I: Spectral and amplitude characteristics across studies[END_REF]. It also allowed us to reduce intersubject differences in global levels of signal power due to maturational factors such as skull thickness, conductivity of head tissues and gender [START_REF] Somsen | Growth spurts in brain maturation during middle childhood as indexed by EEG power spectra[END_REF].

For each subject j, the normalization factor ( ) was defined as the averaged sum of the mean absolute power values of the four frequency bands across all channels ( = 1, … , ) defined as follows:

= . ≡ + + + !"# " " $ %#& & ℎ ((# , ! )# " ) = ∑ +, -. / ( &0 1 " ( " & & ! )# " ) (1) 2 = 3 4 5 6 + 7 4 ( &0 1#8 $# "& 8#( "9 !( " ( & ℎ ((# , ! )# " )
Where was the power spectral density of channel i for subject j, and Nc was the total number of EEG channels. Supplementary Figure S1 shows the average normalized PSD across all channels and subjects for each HC and ADHD age subgroup.

The theta/beta power ratio was also calculated by dividing the average absolute theta to beta power for each channel. All the normalized average absolute power and TBR values were computed for each scalp location and each of the nine regions of interests (ROIs) shown in Fig. 1.

Cortical source analysis

The EEG cortical source analysis was performed by eLORETA (LORETA-KEY package, http://www.unizh.ch/keyinst/NewLORETA/LORETA01.htm), a linear source imaging method used in different resting state EEG studies to estimate current source densities of EEG rhythms in different frequency bands [START_REF] Babiloni | Brain neural synchronization and functional coupling in Alzheimer's disease as revealed by resting state EEG rhythms[END_REF][START_REF] Pascual-Marqui | Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details[END_REF]. Compared to other linear source localization methods, the frequency-domain eLORETA has shown to provide better results for resting-state EEG analysis in multiple source situations especially in the presence of noise [START_REF] Pascual-Marqui | Assessing interactions in the brain with exact low-resolution electromagnetic tomography[END_REF][START_REF] Pascual-Marqui | The resting microstate networks (RMN): cortical distributions, dynamics, and frequency specific information flow[END_REF].

For each subject, the cross-spectral matrices of the artifact-free EEG epochs were used to compute current source densities (CSD, intensity of the current/area, measured in A/m2) using eLORETA for each voxel in each frequency band. The Montreal Neurologic Institute average MRI head model (MNI152) was used to restrict the source space within the gray matter including 6239 voxels with 5 mm spatial resolution [START_REF] Mazziotta | A probabilistic atlas and reference system for the human brain: International Consortium for Brain Mapping (ICBM)[END_REF]. We used the electrode positions provided by EGI [START_REF] Luu | Determination of the HydroCel Geodesic Sensor Nets' average electrode positions and their 10-10 international equivalents[END_REF]. In this method, the average electrode positions have been determined by computing the approximate correspondence between the international 10-10 electrode positions and the positions of the EGI electrodes digitized using the Fastrack hardware and Locator software [START_REF] Luu | Determination of the HydroCel Geodesic Sensor Nets' average electrode positions and their 10-10 international equivalents[END_REF].

We also performed the subject-wise normalization for different frequency bands by dividing the current source density value of every single voxel by the total activity of all voxels using the same approach described in Eq. (1) with : representing the total number of cortical voxels [START_REF] Paquette | Effect of a psychoneurotherapy on brain electromagnetic tomography in individuals with major depressive disorder[END_REF][START_REF] Zinn | Intrinsic functional hypoconnectivity in core neurocognitive networks suggests central nervous system pathology in patients with myalgic encephalomyelitis: A pilot study[END_REF]. We further computed the average eLORETA solutions for the ROIs defined at the source level. Supplementary Table S1 shows the Brodmann areas for each ROI (Fig. 1).

Statistical analysis

Statistical comparisons were performed between ADHD and HC subgroups to assess group-level differences in EEG spectra and current source densities in each frequency band.

At the sensor level, we first tested for the interactions between ADHD subtypes (inattentive and combined) and electrodes/ROIs using repeated measures analysis of variance (ANOVA)

with multiple testing corrected using false discovery rates (FDR). We then assessed the interactions between age (8-10, 10-12, 12-14 and 14-16) and electrodes/ROIs. For each dependent variable (delta, theta, alpha, beta or TBR), a separate model was used with groups (ADHD and HC subtype and age subgroups) as between-subjects factors and electrodes/ROIs as within-subjects factors. We used the false discovery rate (FDR) approach [START_REF] Benjamni | Controlling the false discovery rate: a practical and powerful approach to multiple testing[END_REF] to account for collinearity among EEG electrodes or ROIs by controlling the number of false positives among the subset of electrodes/ROIs labelled as significant. The correction for multiple comparison was performed across all electrodes/ROIs and five dependent variables (delta, theta, alpha, beta or TBR) with an adjusted level of significance at p < 0.05.

At the source level, we used statistical nonparametric mapping method (SnPM) implemented in the LORETA-KEY package to assess age/subtype-related statistical differences in normalized current source densities (nCSD) between groups using voxel-byvoxel log of F-ratio tests with 5000 randomizations in each frequency band [START_REF] Holmes | Nonparametric analysis of statistic images from functional mapping experiments[END_REF].

Using this approach, a nonparametric permutation procedure (with 5000 randomization) was first used to identify cortical voxels with significant differences (p<0.05) by comparing the mean source power and the distribution of the permutated values at the voxel level. To control for Type 1 error, the empirical probability distribution was evaluated to find the ''maximal-statistic'' (the 95th percentile) under the null hypothesis. The critical probability threshold value was then determined for the actual log F-ratio values, with correction for multiple comparisons across all voxels and frequency bands [START_REF] Takamiya | Electroconvulsive therapy modulates resting-state EEG oscillatory pattern and phase synchronization in nodes of the default mode network in patients with depressive disorder[END_REF]. This procedure has been shown to be very effective in controlling for the Type I errors even for non-Gaussian distributions [START_REF] Holmes | Nonparametric analysis of statistic images from functional mapping experiments[END_REF][START_REF] Nichols | Nonparametric permutation tests for functional neuroimaging: a primer with examples[END_REF]see Hata et al., 2016 for a brief description). The group-level significant differences in nCSD were then color-coded, with colors representing the log-F-ratio value for each voxel, and projected onto the MNI brain model (MNI152; [START_REF] Mazziotta | A probabilistic atlas and reference system for the human brain: International Consortium for Brain Mapping (ICBM)[END_REF] to obtain maps of log-F-ratio statistics for corrected p < 0.05 in each frequency band.

We also compared the average nCSD between the groups in each ROI using the same statistical analysis used at the sensor level (repeated measures ANOVA, FDR corrected with p<0.05).

We further assessed linear associations between age and EEG spectra/current source densities in each frequency band using the linear regression analysis implemented in eLORETA software. We determined the critical probability threshold of the regression coefficients across all voxels/electrodes/ROIs and frequency bands with the nonparametric randomization method (5000 randomizations) based on corrections for multiple comparisons [START_REF] Nichols | Nonparametric permutation tests for functional neuroimaging: a primer with examples[END_REF]Winkler et al., 2016). The linear regression analysis was also performed to evaluate correlations between age and EEG power in each frequency band at each scalp location and ROI. The correction for multiple comparisons was performed across all electrodes/ROIs and five dependent variables (four frequency bands and TBR) with p = 0.05 [START_REF] Hata | Functional connectivity assessed by resting state EEG correlates with cognitive decline of Alzheimer's disease-An eLORETA study[END_REF].

Results

Topographic maps of scalp EEG spectral power

Age-dependent spectral patterns

Figure 2 shows topological t-maps illustrating differences (p < 0.05, FDR corrected) in the normalized power of each frequency band, and in TBR between the ADHD and HC age subgroups. Figure 3 also depicts the distribution of EEG parameters (normalized power and TBR) and the result (with p-values listed in Supplementary Table S2) of the group-level comparisons (p < 0.05, FDR corrected) for each ROI and frequency band.

Compared to HC, increased power in lower frequencies (delta and theta) was observed in frontal and/or central electrodes in all ADHD age subgroups except in ADHD12-14. This pattern also involved electrodes placed over temporal and posterior areas in ADHD14-16.

Alpha power was also significantly lower at posterior, temporal and/or frontal electrodes in ADHD subgroups (Figure 3 and Supplementary Table S2) compared to HC. In the beta band, ADHD was characterized with a more widespread decreased power in ADHD10-12 and ADHD12-14 relative to HC. In the other two subgroups (ADHD8-10 and ADHD14-16), the decrease in beta power was more restricted to channels over parietal, occipital and/or frontal areas. The ADHD14-16, however, displayed increased beta power in the left hemisphere compared to HC. The TBR showed a significant diffuse increase in ADHD10-12, ADHD12-14 and ADHD14-16. The increase in TBR for ADHD10-12 and ADHD12-14 was more due to significant decreases in beta power than increases in theta power. In ADHD14-16, however, the increased TBR was more due to significant increases in theta power (Figures 2 and3). Among all age subgroups, only ADHD8-10 showed a significant decrease in TBR in the occipital regions with higher variability across patients (Figure 3 and Supplementary Table S2) in comparison with HC.

<Figure 2> <Figure 3>

Figure 4 shows the group-level maps of beta coefficients reflecting correlations between age and EEG power in each frequency band and TBR for HC and ADHD. In these topological maps, significant associations between EEG power and age were evaluated with p<0.05 corrected with nonparametric randomization (5000 randomizations) across all frequency bands and channels.

Both groups exhibited a widespread decrease and increase in delta and alpha power with increasing age, respectively. The decline in delta power in older subjects was more pronounced in frontal-temporal locations in ADHD than in HC (Fig. 4). Interestingly, beta power also showed increases at posterior channels in both groups as well as in central-parietal channels in ADHD with increasing age. The theta power, however, displayed significant decreases at bilateral temporal and parietal electrodes in older healthy controls and increases at left temporal and parietal electrodes in older ADHD patients. The TBR also decreased significantly in HC with increasing age in central, temporal, parietal and occipital scalp locations. In ADHD, however, the decline in TBR was less pronounced with increasing age, involving electrodes over frontal, central and occipital areas. <Figure 4>

Subtype-related spectral patterns

Figures 5 and 6 illustrate the group-level differences (p < 0.05, FDR corrected) in the normalized of different frequency bands, and in TBR between ADHDI/ADHDC and HC.

Compared with the controls, ADHDC was characterized with significantly increased TBR in bilateral frontal, central and temporal measurement sites. In this subtype, the increase in TBR was more due to the widespread decrease in beta power (Fig. 5, top row). A similar pattern of differences was found for alpha power in ADHDC (Fig. 5). A significant increase in theta power only emerged in the mid-frontal regions in ADHDC relative to HC.

Compared to HC, ADHDI showed a significant increase (pFDR < 0.05) in TBR in electrodes over right frontal, bilateral temporal and posterior areas due to the widespread increase in theta power. In comparison with the control subjects, ADHDI exhibited remarkably increased beta power in fronto-central scalp locations (Fig 6). The delta t-map showed a pattern of changes similar to that found for theta in ADHDI (Fig. 5).

<Figure 5> <Figure 6> For each ROI, the results of statistical comparisons (p < 0.05, FDR corrected) between ADHD and HC are shown in Fig. 8 and Supplementary Table S3.

Topography of EEG current source densities

Age-dependent patterns

Compared to HC, higher current densities were observed for theta sources in the bilateral central and parietal regions for ADHD10-12, in the frontal regions for ADHD12-14 and in most brain regions (less pronounced in posterior areas) for ADHD14-16. In ADHD relative to HC, delta sources showed significant decreases in nCSD in children aged 12-16 years. A diffuse decrease in beta source power was observed in ADHD children aged 8-14 years (Figures 7 and8). Interestingly, beta source power (Supplementary Figure S2) in all brain regions showed no significant differences between ADHD14-16 and the controls (Supplementary Table S3). In the alpha band, however, a decrease in source power in ADHD relative to HC was observed in fronto-central (ADHD8-10) and posterior areas (ADHD10-12) or in both areas (ADHD14-16). As shown in Fig. 7, a widespread pattern of increased TBR was found for ADHD10-12, ADHD12-14 and ADHD14-16 relative to HC, with a declining pattern over age (Fig. 7).

<Figure 7> <Figure 8>

Figure 9 and Supplementary Figure S3 show group-level regression coefficient maps illustrating significant associations between nCSD and age with p<0.05 corrected with nonparametric randomization across all frequency bands and voxels. Supplementary Table S4 also shows the mean (± SD) of regression coefficients (βR) computed over voxels displaying significant positive or negative correlations between age and nCSD for both HC and ADHD.

As shown, both groups exhibited a diffuse decline in nCSD of delta cortical sources with increasing age, with a more pronounced decline rate in ADHD (Supplementary Table S4). This finding confirms the results shown in Supplementary Table S3. While for older controls, theta source power declined significantly in the bilateral temporal and left central regions, for the ADHD group, densities of theta fronto-central and temporal sources showed significantly positive correlations with age (Fig. 9). In both groups, alpha sources displayed significantly positive correlations with age in the bilateral frontal, central and temporal brain regions, with greater regression coefficients for ADHD children compared to healthy controls (Supplementary Table S4). An inverse trend was observed in both groups in posterior areas.

In ADHD, beta CSD also showed a significant positive association with age in all regions except in posterior areas, demonstrating increased beta source power in older patients. In HC, the increase in beta source power with increasing age was only observed in the bilateral frontal regions. Finally, the TBR showed a widespread decreasing pattern with increasing age in ADHD. In HC, this pattern was observed in most brain regions except in prefrontal and posterior areas, however, with a greater decline rate compared to ADHD (Supplementary Figure S3 and Supplementary Table S4). <Figure 9>

Subtype-related patterns

Figure 10 and Supplementary Figure S4 show statistical p-maps (p<0.05, corrected for multiple comparison with non-parametric randomization) illustrating significant differences in nCSD (eLORETA solutions) between the ADHD subtypes (ADHDI and ADHDC) and HC in different frequency bands. Group differences in each ROI are also shown in Fig. 11.

As shown, ADHDC exhibited a significant diffuse decrease in beta and also alpha source densities in comparison with HC. This decrease has led to an overall increase in TBR in ADHDC (Figures 10 and 11). In this subtype, a significant increase in theta CSD was observed in the central, parietal and occipital regions. In the delta band, a significant decrease in power was only observed in right frontal areas in ADHDC compared to the controls.

In ADHDI, however, low frequency (delta and theta) sources showed significant increases in current density in the fronto-central regions (for both delta and theta) as well as in temporal and posterior areas (for theta only) (Fig. 11). Within the beta and alpha bands, the fronto-central sources displayed decreased nCSD in ADHDI relative to HC. An inverse trend was observed for in the beta and alpha bands in prefrontal and posterior areas (Figure 10 and Supplementary Figure S4). Overall, except in the posterior areas, other cortical regions showed increased TBR in ADHDI relative to HC. <Figure 10> <Figure 11>

Discussion

In this study, we investigated the effect of ADHD (combined and inattentive) subtypes and age on EEG power spectra and current source densities in comparison with the agematched HC subgroups using high-density resting-state EEG data. Our results revealed

several key findings about the electrophysiological signatures of the immature brain activity in ADHD children. Compared to the typically developing children, ADHDC was characterized with a significant diffuse increase in TBR with a widespread decrease in beta CSDs. The ADHDC subgroup also exhibited a significant increase in theta source power in the central, parietal and occipital regions. The ADHDI subgroup, however, presented increased TBR values in the frontal, central and temporal regions with a global increase in theta current source densities. In this subtype relative to HC, the beta fronto-central sources displayed significantly decreased current densities. Overall, compared to HC, the ADHD group showed significant distinct age-dependent increases and decreases in current source densities of slow (delta and theta) and fast (alpha and beta) EEG oscillations, respectively.

Slow oscillations

Several resting-state EEG studies in children with ADHD have shown increased power in the lower frequency bands (delta and theta) concomitant with decreased power in the higher frequency bands (alpha and beta) [START_REF] Arns | A decade of EEG theta/beta ratio research in ADHD: a meta-analysis[END_REF], resulting in an elevated TBR considered as a diagnostic neuromarker in ADHD [START_REF] Barry | A review of electrophysiology in attentiondeficit/hyperactivity disorder: I. Qualitative and quantitative electroencephalography[END_REF][START_REF] Sangal | Use of EEG beta-1 power and theta/beta ratio over Broca's area to confirm diagnosis of attention deficit/hyperactivity disorder in children[END_REF].

Delta band:

We found increased delta source power in ADHDI compared to HC in the fronto-central regions. Compared to the healthy controls, ADHD8-10 and ADHD10-12 also exhibited elevated delta power in posterior areas and front-central regions, respectively. This result is in line with the findings of other studies on ADHD children and adults [START_REF] Clarke | EEG analysis in attentiondeficit/hyperactivity disorder: a comparative study of two subtypes[END_REF](Clarke et al., , 2001a[START_REF] Clarke | Age and sex effects in the EEG: differences in two subtypes of attention-deficit/hyperactivity disorder[END_REF][START_REF] Bresnahan | Age-related changes in quantitative EEG in attention-deficit/hyperactivity disorder[END_REF][START_REF] Bresnahan | Specificity of quantitative EEG analysis in adults with attention deficit hyperactivity disorder[END_REF][START_REF] Koehler | Increased EEG power density in alpha and theta bands in adult ADHD patients[END_REF][START_REF] Kamida | EEG power spectrum analysis in children with ADHD[END_REF][START_REF] Shephard | Resting-state neurophysiological activity patterns in young people with ASD, ADHD, and ASD+ ADHD[END_REF]. Using a scalp EEG spectral analysis, [START_REF] Kamida | EEG power spectrum analysis in children with ADHD[END_REF] have also reported increases in mean delta power in the frontal and parietal regions in a relatively large group of 80 ADHD children aged 4-15 years. The increased power of delta rhythms has been considered as an 'EEG slowing' signature in childhood ADHD, an indicator of maturational lags (Clarke et al., 2002).

In contrast, Clarke et al. (2001c) have reported decreased frontal delta power in ADHD children. In our study, we also observed a decrease in delta source power in ADHDC as well as in ADHD children aged 12-16 years. Both HC (βR : -0.176±0.031) and ADHD (βR :

-0.298±0.043) showed a diffuse decline in power of delta cortical sources with increasing age, with a more pronounced decline rate in ADHD (Supplementary Table S4). Similarly, [START_REF] Giertuga | Age-related changes in resting-state EEG activity in attention deficit/hyperactivity disorder: a cross-sectional study[END_REF] have shown age-dependent decreases in the spectral power of slow oscillations, consistent with findings of other studies on healthy controls [START_REF] Gibbs | Growth of the electrical activity of the cortex[END_REF][START_REF] Matousek | Frequency analysis of the EEG in normal children and adolescents[END_REF][START_REF] Matsuura | Age development and sex differences of various EEG elements in healthy children and adults-quantification by a computerized wave form recognition method[END_REF][START_REF] Gasser | Development of the EEG of school-age children and adolescents. I. Analysis of band power[END_REF][START_REF] Somsen | Growth spurts in brain maturation during middle childhood as indexed by EEG power spectra[END_REF][START_REF] Dustman | Life-span changes in EEG spectral amplitude, amplitude variability and mean frequency[END_REF].

Theta band:

In children with ADHD compared to healthy controls, increases in theta power have been reported in many resting state EEG studies [START_REF] Bresnahan | Age-related changes in quantitative EEG in attention-deficit/hyperactivity disorder[END_REF]Clarke et al., 2001c;[START_REF] Barry | Electroencephalogram θ/β ratio and arousal in attention-deficit/hyperactivity disorder: Evidence of independent processes[END_REF][START_REF] Koehler | Increased EEG power density in alpha and theta bands in adult ADHD patients[END_REF][START_REF] Kitsune | A matter of time: the influence of recording context on EEG spectral power in adolescents and young adults with ADHD[END_REF]. In typically developing children, enhanced theta rhythms reflect neural plasticity, new information coding [START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF][START_REF] Kahana | Theta returns[END_REF] and memory and attention processing [START_REF] Dietl | Orienting response and frontal midline theta activity: a somatosensory spectral perturbation study[END_REF][START_REF] Rol Başar | The selectively distributed theta system: functions[END_REF][START_REF] Michels | Simultaneous EEG-fMRI during a working memory task: modulations in low and high frequency bands[END_REF]. In ADHD children, however, the elevated theta power has been interpreted as an indicator of drowsiness or 'cortical slowing' during resting state, keeping ADHD children in an underarousal state causing inattentiveness [START_REF] Saha | Neural oscillations in resting state EEG in ADHD children-A preliminary study[END_REF].

The increased theta power especially in mid-frontal areas might be also associated with increased attentional loading during memory tasks in ADHD children [START_REF] Onton | Frontal midline EEG dynamics during working memory[END_REF]. Moreover, the power increase in the theta band can be caused by the delayed (about 2-3 years) maturation in cortical thickening, with largest delays observed in the prefrontal cortex [START_REF] Shaw | Attention-deficit/hyperactivity disorder is characterized by a delay in cortical maturation[END_REF][START_REF] Shaw | Development of cortical surface area and gyrification in attention-deficit/hyperactivity disorder[END_REF][START_REF] Giertuga | Age-related changes in resting-state EEG activity in attention deficit/hyperactivity disorder: a cross-sectional study[END_REF]. However, this atypical change in electrophysiological signatures has been suggested to indicate persistent abnormalities in ADHD children [START_REF] Barry | A review of electrophysiology in attentiondeficit/hyperactivity disorder: I. Qualitative and quantitative electroencephalography[END_REF].

Our results concerning increased theta power are consistent with similar observations in ADHD children [START_REF] Satterfield | Physiological studies of the hyperkinetic child: I[END_REF][START_REF] Mann | Quantitative analysis of EEG in boys with attention-deficit-hyperactivity disorder: Controlled study with clinical implications[END_REF][START_REF] Janzen | Differences in baseline EEG measures for ADD and normally achieving preadolescent males[END_REF][START_REF] Chabot | Quantitative electroencephalographic profiles of children with attention deficit disorder[END_REF][START_REF] Lazzaro | Quantified EEG activity in adolescent attention deficit hyperactivity disorder[END_REF][START_REF] Clarke | EEG analysis in attentiondeficit/hyperactivity disorder: a comparative study of two subtypes[END_REF][START_REF] Clarke | Age and sex effects in the EEG: differences in two subtypes of attention-deficit/hyperactivity disorder[END_REF][START_REF] Clarke | Electroencephalogram differences in two subtypes of attention-deficit/hyperactivity disorder[END_REF]. In our study, relative to HC, ADHDC was characterized with significantly increased theta source power in the central, parietal and occipital regions. The ADHDI subgroup, also, presented a similar pattern in all cortical regions, slightly less pronounced in posterior areas. The statistical comparison between the four age subgroups also revealed higher CSD for theta sources in specific brain regions depending on age. Our results are partly in agreement with the findings reported by Clarke et al. (2001c), who have found a generalized increase in theta power in ADHD children aged 8-12 years. We also observed a diffuse increase in theta power but only for ADHD14-16. In other age subgroups, we found local increases in theta CSD in the bilateral central regions for ADHD10-12 and in the bilateral frontal regions for ADHD12-14 relative to HC. This result is partly consistent with the increased theta power found by [START_REF] Kamida | EEG power spectrum analysis in children with ADHD[END_REF] in the frontal and parietal regions for ADHD children aged 4-15 years.

With regard to the neurodevelopmental process, age-dependent decreases in delta or theta power have been reported in typical development [START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF]. We also found a decline (βR : -0.149±0.013) in theta cortical source power with increasing age in the bilateral temporal and left central regions in typically developing children. An increase in theta power has been reported for children (8-12 years) with ADHD relative to age-matched controls (Clarke et al., 2001c). In our study, a significant increase (βR: 0.167±0.021) in current densities of theta fronto-central and temporal sources was observed with increasing age in ADHD children compared to HC (Figure 9 and Supplementary Table S4). The differences in the trend of changes in theta power between ADHD patients and HC might reflect delayed brain maturation in ADHD [START_REF] Barry | A review of electrophysiology in attentiondeficit/hyperactivity disorder: I. Qualitative and quantitative electroencephalography[END_REF].

Fast oscillations

Alpha band: Changes in resting-state alpha power may depend on developmental level, ADHD subtype, and psychiatric comorbidities [START_REF] Lenartowicz | Aberrant modulation of brain oscillatory activity and attentional impairment in attention-deficit/hyperactivity disorder[END_REF]. Studies of resting state EEG in adults with ADHD have revealed two biotypes for alpha power, the 'low-alpha' biotype [START_REF] Loo | Cortical activity patterns in ADHD during arousal, activation and sustained attention[END_REF][START_REF] Woltering | Resting state EEG oscillatory power differences in ADHD college students and their peers[END_REF] and the 'high-alpha' biotype [START_REF] Bresnahan | Specificity of quantitative EEG analysis in adults with attention deficit hyperactivity disorder[END_REF][START_REF] Koehler | Increased EEG power density in alpha and theta bands in adult ADHD patients[END_REF][START_REF] Poil | Age dependent electroencephalographic changes in attentiondeficit/hyperactivity disorder (ADHD)[END_REF]. Changes in resting-state alpha power (8-12 Hz) in healthy subjects have been shown to be associated with cortical inhibition or excitation [START_REF] Romei | Spontaneous fluctuations in posterior α-band EEG activity reflect variability in excitability of human visual areas[END_REF][START_REF] Haegens | α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking[END_REF][START_REF] Mathewson | Pulsed out of awareness: EEG alpha oscillations represent a pulsed-inhibition of ongoing cortical processing[END_REF][START_REF] Klimesch | Alpha-band oscillations, attention, and controlled access to stored information[END_REF]. During cognitive tasks, however, alpha oscillations reflect levels of selective attention and sustained attention [START_REF] Foxe | The role of alpha-band brain oscillations as a sensory suppression mechanism during selective attention[END_REF].

Compared to healthy children, the majority of EEG studies performed on ADHD children have reported reduced alpha activity especially in the posterior regions [START_REF] Lazzaro | Quantified EEG activity in adolescent attention deficit hyperactivity disorder[END_REF][START_REF] Clarke | Age and sex effects in the EEG: differences in two subtypes of attention-deficit/hyperactivity disorder[END_REF]Clarke et al., , 2001c;;[START_REF] Bresnahan | Specificity of quantitative EEG analysis in adults with attention deficit hyperactivity disorder[END_REF][START_REF] Loo | Cortical activity patterns in ADHD during arousal, activation and sustained attention[END_REF][START_REF] Loo | Clinical utility of EEG in attention-deficit/hyperactivity disorder: a research update[END_REF][START_REF] Woltering | Resting state EEG oscillatory power differences in ADHD college students and their peers[END_REF][START_REF] Poil | Age dependent electroencephalographic changes in attentiondeficit/hyperactivity disorder (ADHD)[END_REF][START_REF] Ponomarev | Group independent component analysis (gICA) and current source density (CSD) in the study of EEG in ADHD adults[END_REF][START_REF] Deiber | Linking alpha oscillations, attention and inhibitory control in adult ADHD with EEG neurofeedback[END_REF]. In ADHD patients, the attenuated alpha activity is associated with a state of cortical hyper-activation, increased excitability of sensory cortices or attentional self-control problems [START_REF] Romei | Spontaneous fluctuations in posterior α-band EEG activity reflect variability in excitability of human visual areas[END_REF][START_REF] Haegens | α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking[END_REF][START_REF] Woltering | Resting state EEG oscillatory power differences in ADHD college students and their peers[END_REF][START_REF] Deiber | Linking alpha oscillations, attention and inhibitory control in adult ADHD with EEG neurofeedback[END_REF]. The reduced alpha power may also reflect impairment in processing visuo-spatial information and failure in sustained attention in ADHD children [START_REF] Saha | Neural oscillations in resting state EEG in ADHD children-A preliminary study[END_REF].

Our results similar to those reported by [START_REF] Deiber | Linking alpha oscillations, attention and inhibitory control in adult ADHD with EEG neurofeedback[END_REF] are more consistent with a 'low-alpha' biotype. We found a significant decrease in alpha source power globally for ADHDC and locally in fronto-central and posterior areas or in both areas for ADHD children aged 8-12 and 14-16 years in comparison with the age-matched HC. The global decrease in alpha activity has also been reported in adults with ADHD (combined type) when compared to healthy controls [START_REF] Loo | Familial clustering and DRD4 effects on electroencephalogram measures in multiplex families with attention deficit/hyperactivity disorder[END_REF]. Consistent with our findings, [START_REF] Kamida | EEG power spectrum analysis in children with ADHD[END_REF] have found slightly lower alpha power in the ADHD children compared to HC, reflecting poor sustained attention [START_REF] Foxe | The role of alpha-band brain oscillations as a sensory suppression mechanism during selective attention[END_REF]. A few studies have reported increased alpha activity in ADHD children [START_REF] Chabot | Quantitative electroencephalographic profiles of children with attention deficit disorder[END_REF][START_REF] Bresnahan | Specificity of quantitative EEG analysis in adults with attention deficit hyperactivity disorder[END_REF][START_REF] Koehler | Increased EEG power density in alpha and theta bands in adult ADHD patients[END_REF][START_REF] Clarke | Behavioural differences between EEG-defined subgroups of children with attention-deficit/hyperactivity disorder[END_REF][START_REF] Poil | Age dependent electroencephalographic changes in attentiondeficit/hyperactivity disorder (ADHD)[END_REF]. We only observed increases in alpha source power in ADHDI compared to HC in prefrontal and posterior areas.

With regard to the brain maturation, the healthy children studied in the present work exhibited a significant positive correlation between age and alpha source power in the bilateral frontal, central and temporal brain regions (Figure 9 and Supplementary Table S4).

In ADHD children, the alpha frontal, temporal and central source power increased with increasing age with a greater mean regression coefficient (βR : 0.249 ± 0.070) in comparison with HC (βR : 0.198±0.045). In ADHD, the parietal and occipital sources, however, showed decreases in alpha CSD with increasing age. This decrease clearly shows abnormality in the neurodevelopmental process in ADHD children as the posterior regions usually show the earliest sign of maturation in typically developing children [START_REF] Gasser | Topographic factor analysis of the EEG with applications to development and to mental retardation[END_REF]Clarke et al., 2001a). Our results are partly in contrast with those reported by [START_REF] Kamida | EEG power spectrum analysis in children with ADHD[END_REF], who have found an age-dependent decrease in alpha power in HC and ADHD children with age.

This inconsistency can be explained by the fact that we have used a common average montage, which has been widely used for EEG source imaging in different EEG studies. [START_REF] Kamida | EEG power spectrum analysis in children with ADHD[END_REF], however, have used a bipolar montage, which can seriously reduce local spectral power by removing common brain activity of nearby electrodes in the subtraction operation [START_REF] Zaveri | On the use of bipolar montages for time-series analysis of intracranial electroencephalograms[END_REF].

Beta band: In children and adults with ADHD, the increased resting-state theta activity has been shown to be accompanied by significant decreases in beta power [START_REF] Bresnahan | Age-related changes in quantitative EEG in attention-deficit/hyperactivity disorder[END_REF][START_REF] Clarke | Quantitative EEG in low-IQ children with attention-deficit/hyperactivity disorder[END_REF][START_REF] Barry | Electroencephalogram θ/β ratio and arousal in attention-deficit/hyperactivity disorder: Evidence of independent processes[END_REF][START_REF] Koehler | Increased EEG power density in alpha and theta bands in adult ADHD patients[END_REF][START_REF] Buyck | Resting electroencephalogram in attention deficit hyperactivity disorder: developmental course and diagnostic value[END_REF][START_REF] Tye | Genetic overlap between ADHD symptoms and EEG theta power[END_REF][START_REF] Kitsune | A matter of time: the influence of recording context on EEG spectral power in adolescents and young adults with ADHD[END_REF][START_REF] Lenartowicz | Aberrant modulation of brain oscillatory activity and attentional impairment in attention-deficit/hyperactivity disorder[END_REF]. In healthy individuals, the increased beta activity is associated with increased attention during physical and mental activities [START_REF] Ackerman | EEG power spectra of children with dyslexia, slow learners, and normally reading children with ADD during verbal processing[END_REF][START_REF] Andreassi | Psychophysiology: human behavior and physiological response[END_REF]. In several studies, the reduced beta power has been reported for children with ADHD during cognitive tasks [START_REF] Lubar | Discourse on the development of EEG diagnostics and biofeedback for attentiondeficit/hyperactivity disorders[END_REF].

In our study, ADHDC exhibited a significant diffuse decrease in beta source power in comparison with HC. In ADHDI, however, beta sources in posterior areas displayed slightly increased current densities. We also found a global decrease in beta source power in ADHD children aged 8-14 years. Our findings confirm the results of other studies reporting increased frontal beta power in a subgroup (~10-15 %) of children with Combined Type of ADHD compared to controls [START_REF] Chabot | Quantitative electroencephalographic profiles of children with attention deficit disorder[END_REF]Clarke et al., 2002;[START_REF] Clarke | Behavioural differences between EEG-defined subgroups of children with attention-deficit/hyperactivity disorder[END_REF].

Inconsistent with our findings, Kamida et al. ( 2016) have reported higher beta power for the ADHD children aged 4-15 years compared to healthy controls.

Relative to HC, we found increased beta source power for ADHDI in the prefrontal and posterior regions (Fig. 10). The increased beta power in the frontal regions may explain poor inhibitory control and hyperactivity in ADHD children [START_REF] Clarke | Electroencephalogram differences in two subtypes of attention-deficit/hyperactivity disorder[END_REF].

With increasing age, HC showed an increase (βR : 0.171±0.034) in beta source power in the bilateral frontal regions close to central regions. This finding is in agreement with the observations of [START_REF] Bresnahan | Specificity of quantitative EEG analysis in adults with attention deficit hyperactivity disorder[END_REF], who found age-dependent increasing levels of beta power in healthy children. These findings are also supported by the fact that the beta maturation first occurs in the central regions in typically developing children (Clarke et al., 2001a;[START_REF] Gasser | Topographic factor analysis of the EEG with applications to development and to mental retardation[END_REF]. In ADHD, we also found a significant positive association (βR : 0.226±0.053) between beta source power and age in most brain regions except in posterior areas (Figure 9 and Supplementary Table S4). Our results are in contrast with the findings of [START_REF] Kamida | EEG power spectrum analysis in children with ADHD[END_REF], who have reported an age-dependent decrease in beta power in the frontal region in both ADHD and healthy children.

Theta/beta power ratio

In typically developing children, decreases and increases in slow and fast-wave brain activities have been reported, respectively [START_REF] Segalowitz | Electrophysiological changes during adolescence: a review[END_REF]Uhlhaas et al., 2010). The decreased slow-wave (delta and theta) power may be caused by the age-dependent reduction in gray matter density [START_REF] Whitford | Brain maturation in adolescence: concurrent changes in neuroanatomy and neurophysiology[END_REF], more likely related to the reduction of neuropil and elimination of synapses from childhood to adolescence [START_REF] Feinberg | Sleep EEG changes during adolescence: an index of a fundamental brain reorganization[END_REF][START_REF] Buchmann | Anatomical markers of sleep slow wave activity derived from structural magnetic resonance images[END_REF]. In ADHD, however, it has been shown that the process of cortical thinning is delayed [START_REF] Shaw | Cortical development in typically developing children with symptoms of hyperactivity and impulsivity: support for a dimensional view of attention deficit hyperactivity disorder[END_REF].

Overall, the elevated theta/ beta ratio (TBR) resulted from increased theta/decreased beta power has been largely considered as the most reliable feature reflecting immature resting-state brain activity, more likely due to delays in the neurodevelopmental process in children with ADHD [START_REF] Janzen | Differences in baseline EEG measures for ADD and normally achieving preadolescent males[END_REF][START_REF] Lubar | Discourse on the development of EEG diagnostics and biofeedback for attentiondeficit/hyperactivity disorders[END_REF][START_REF] Clarke | EEG analysis in attentiondeficit/hyperactivity disorder: a comparative study of two subtypes[END_REF][START_REF] Clarke | Age and sex effects in the EEG: differences in two subtypes of attention-deficit/hyperactivity disorder[END_REF]Clarke et al., , 2001c;;[START_REF] Chabot | Quantitative electroencephalographic profiles of children with attention deficit disorder[END_REF][START_REF] Bresnahan | Age-related changes in quantitative EEG in attention-deficit/hyperactivity disorder[END_REF][START_REF] Barry | A review of electrophysiology in attentiondeficit/hyperactivity disorder: I. Qualitative and quantitative electroencephalography[END_REF][START_REF] Koehler | Increased EEG power density in alpha and theta bands in adult ADHD patients[END_REF][START_REF] Sangal | Use of EEG beta-1 power and theta/beta ratio over Broca's area to confirm diagnosis of attention deficit/hyperactivity disorder in children[END_REF]. The increased TBR may also reflect ADHD-specific unbalanced interactions between local cortical networks and long-range cortico-cortical/subcortical activities [START_REF] Woltering | Resting state EEG oscillatory power differences in ADHD college students and their peers[END_REF].

In several studies, enhanced TBR values have been reported for ADHDC in comparison with ADHDI [START_REF] Dupuy | Sex differences between the combined and inattentive types of attention-deficit/hyperactivity disorder: an EEG perspective[END_REF][START_REF] Loo | Characterization of the theta to beta ratio in ADHD: identifying potential sources of heterogeneity[END_REF]. We, however, found a global increase in TBR in both ADHDI and ADHDC relative to HC using the scalp EEG spectral power analysis. Our results from the current source density analysis indicated significantly higher TBR values almost in all brain regions in both ADHDI and ADHDC except in the posterior cortical regions in ADHDI.

Using the scalp EEG spectral and clustering analyses, Clarke et al. (2001c) have classified 184 ADHD children aged 8-12 years into three clusters with distinct electrophysiological signatures, all showing abnormally high TBR values. Associated with cortical hypoarousal, Cluster 1 has been characterized with high theta power, particularly in the frontal regions, concomitant with reduced delta and beta power. In our work, ADHDC exhibited the same characteristics as Cluster 1, with alpha activity found at the normal level observed for HC in the frontal regions.

Associated with maturational lags, Cluster 2 identified by Clarke et al. (2001c) presented stronger slow (delta and theta) oscillations and reduced beta power wave activity. In this cluster, they have found the largest differences in delta/alpha power in the posterior regions and in beta power in the central regions between ADHD and healthy children. They have also identified a third cluster (Cluster 3) in which, ADHD showed a decreased theta/beta power ratio with increased beta and decreased alpha activity across all measurement sites as well as with decreased delta power in the frontal and central regions. In our work, ADHDI showed mixed characteristics similar to those of Cluster 2 and Cluster 3, which exhibited high power beta activity, with deficiencies in delta and alpha activity (Clarke et al., 2001c). We found elevated delta and theta source densities in the fronto-central regions in ADHDI compared to HC. We also observed an excess in beta source densities in the prefrontal and posterior regions for the inattentive subtype (Fig. 10). The stronger beta activity has been suggested to be associated with hyperarousal, which could cause the hyperactive and inattentive problems in ADHD children (Clarke et al., 2001c).

With regard to the brain development, we found widespread increases in TBR for ADHD10-12, ADHD12-14 and ADHD14-16 compared to HC. The correlation between TBR and age showed a decreasing pattern (βR : -0.146±0.014) all over the brain in ADHD. In HC, this pattern was only observed in the bilateral frontal, central and temporal regions, however, with a greater decline rate (βR : -0.172±0.030) compared to ADHD (Figure 9 and Supplementary Table S4).

Overall, the prediction value of TBR for ADHD diagnosis and its clinical acceptance have been a subject of debate [START_REF] Magee | Examining the diagnostic utility of EEG power measures in children with attention deficit/hyperactivity disorder[END_REF][START_REF] Snyder | A meta-analysis of quantitative EEG power associated with attention-deficit hyperactivity disorder[END_REF][START_REF] Lenartowicz | Use of EEG to diagnose ADHD[END_REF][START_REF] Loo | Research review: Use of EEG biomarkers in child psychiatry research-current state and future directions[END_REF]. In a recent study on adults with ADHD, [START_REF] Kiiski | EEG spectral power, but not theta/beta ratio, is a neuromarker for adult ADHD[END_REF] have suggested that the best predictors of ADHD status were changes in EEG spectra of different frequency bands rather than TBR, including increased power in low frequency (delta and theta) and low-alpha oscillations over centro-parietal regions as well as in frontal low-beta and parietal mid-beta activity under the eyes-open condition [START_REF] Kiiski | EEG spectral power, but not theta/beta ratio, is a neuromarker for adult ADHD[END_REF].

It has been shown that the TBR value might be used to predict the age with relatively high accuracy, but its diagnostic prediction value for ADHD remains marginal [START_REF] Buyck | Resting electroencephalogram in attention deficit hyperactivity disorder: developmental course and diagnostic value[END_REF][START_REF] Liechti | Diagnostic value of resting electroencephalogram in attention-deficit/hyperactivity disorder across the lifespan[END_REF]. In other words, more than the ADHD pathology, the age-dependent brain development affects the value of TBR [START_REF] Arns | A decade of EEG theta/beta ratio research in ADHD: a meta-analysis[END_REF][START_REF] Liechti | Diagnostic value of resting electroencephalogram in attention-deficit/hyperactivity disorder across the lifespan[END_REF]. It is of note that for clinical assessment of children and adolescents with ADHD, TBR has been approved by Food and Drug Administration (FDA) as a valid discriminator of ADHD diagnosis [START_REF] Food | De novo classification request for neuropsychiatric EEG-based assessment aid for ADHD (NEBA) system[END_REF][START_REF] Snyder | Integration of an EEG biomarker with a clinician's ADHD evaluation[END_REF].

Scalp EEG analysis vs. cortical source imaging

To obtain a more detailed view concerning the effect of age and ADHD subtype, we cross-validated the patterns of differences in EEG spectral power and cortical source densities between the ADHD and healthy children. Overall, both approaches resulted in concordant findings presenting similar trends of changes in resting EEG within different frequency bands. However, several discrepancies were observed between the results of the analyses performed at the sensor and source levels. This can be seen from the differences in beta power and TBR between ADHDI and HC (Figures 5 and 10) or those observed between ADHD12-14 and HC in alpha band or between ADHD14-16 and HC in beta band (Figures 2 and7). In some frequency bands, significant differences were found between the ADHD and HC subgroups in the sensor space with inconsistencies across age subgroups. In the source space, however, the source imaging analysis could identify consistent results across age subgroups. The main reason for these inconsistent results remains in the fact that the recorded signals at different scalp locations are resulted from the volume conduction effect caused by a linear mixture of source activities from all brain regions [START_REF] Loo | Clinical utility of EEG in attention-deficit/hyperactivity disorder: a research update[END_REF]. Our results clearly emphasize the importance of the EEG source imaging analysis for studying abnormalities in resting state brain activities associated with ADHD.

Limitations

Our study has several limitations. First, the sample size per subgroup is relatively small limiting the statistical power, especially in the 8-10 age subgroup. However, we used statistical tests based on randomization to improve the reliability of significance of the statistical differences. Second, we performed both the channel-wise EEG analysis and voxelwise source analysis. In these analyses, the interactions between brain regions are ignored. To study the brain as a complex system, the EEG-based connectivity methods would provide additional complementary information concerning the effect of the ADHD pathology on the temporal dynamics of the brain networks. Third, in studies on ADHD children, two electrophysiological subtypes have been observed, a subgroup with true enhanced theta activity and a subgroup with increased power of slow alpha peak frequency, rather than increased 'theta' power [START_REF] Arns | EEG phenotypes predict treatment outcome to stimulants in children with ADHD[END_REF]. Both of these subgroups show elevated theta/beta power ratios. In our study, we did not investigate the presence of these subgroups as studied by [START_REF] Lansbergen | The increase in theta/beta ratio on resting-state EEG in boys with attention-deficit/hyperactivity disorder is mediated by slow alpha peak frequency[END_REF]. Such a study requires individualized frequency bands instead of using fixed frequency bands [START_REF] Lansbergen | The increase in theta/beta ratio on resting-state EEG in boys with attention-deficit/hyperactivity disorder is mediated by slow alpha peak frequency[END_REF]. Fourth, we used a standard head model (MNI152) and standard electrode positions determined according to the 10-10 international standard system for source analysis using eLORETA. It has been shown that electrode misplacement (compared to the actual positions of the electrodes during the recording) and other head modeling errors can affect the accuracy of EEG source localization methods [START_REF] Michel | EEG source imaging: a practical review of the analysis steps[END_REF]. Finally, we used cross-sectional EEG data rather than longitudinal data from the same subjects. Compared to cross-sectional data providing average group changes, longitudinal data can be very useful to investigate the neurodevelopmental process at the subject level especially in atypical development [START_REF] Morgan | A network neuroscience approach to typical and atypical brain development[END_REF]. We plan to perform further analyses to overcome some of these limitations in our future work.

Conclusions

In the present study, we assessed differences in scalp EEG power spectra and cortical source densities between ADHD children relative to

Figure 7

 7 Figure 7 and Supplementary Figure S2 depict p-maps displaying significant differences (p<0.05, corrected for multiple comparison with non-parametric randomization) in nCSD (eLORETA solutions) between the HC and ADHD age subgroups in each frequency band.

Figure 1 .

 1 Figure 1. EEG spectral and cortical source analysis pipeline. The output of each analysis is t-maps or p-maps obtained through statistical comparisons between ADHD children and HC in four frequency bands (δ, θ, α, β) and nine regions of interest (ROI). HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; R/LFR: right/left frontal regions, R/LTP: right/left temporal regions, R/LCN: right/left central regions, R/LPR: right/left parietal regions, OC: occipital regions.

Figure 2 .

 2 Figure2. Group-level t-maps (p < 0.05, FDR corrected) showing differences in the normalized power of delta (δ), theta (θ), alpha (α) and beta (β) between the HC and ADHD age subgroups(8-10, 10-12, 12-14 and 14-16 years). The bottom row shows differences in the theta/beta power ratio (θ/β) for each subgroup. The colorbar indicates statistical differences based on t-values with p<0.05 corrected for multiple comparison using FDR across all frequency bands and electrodes. The blue (red) color shows electrodes at which differences were significant, with higher (lower) power for ADHD compared to HC. Electrode positions are indicated by black dots. Non-significant regions are shown in green. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; FDR: false discovery rate.

Figure 3 .

 3 Figure 3. Boxplots displaying the median and interquartile range of the normalized power of delta (δ), theta (θ), alpha (α) and beta (β) for HC and ADHD age subgroups (8-10, 10-12, 12-14 and 14-16 years) in each ROI. The top row shows the boxplots of the theta/beta power ratio (θ/β) in each region. The asterisks reflect statistically significant differences (p<0.05, FDR corrected across all frequency bands and regions) between ADHD and HC. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; R/LFR: right/left frontal regions; R/LTP: right/left temporal regions; R/LCN: right/left central regions; R/LPR: right/left parietal regions; OC: occipital regions; ROI: region of interest; FDR: false discovery rate.

Figure 4 .

 4 Figure 4. Group-level beta coefficient maps showing regression coefficients between age and the normalized power of delta (δ), theta (θ), alpha (α) and beta (β) for HC and ADHD. The rightmost column shows the results for the theta/beta power ratio (θ/β). The red (blue) colors indicate electrodes at which the regression coefficient was significantly positive (negative) with p<0.05 corrected with nonparametric randomization (5000 randomizations) across all frequency bands and electrodes. Electrode positions are indicated by black dots. Non-

Figure 5 .

 5 Figure5. FDR corrected) showing differences in the normalized power of delta (δ), theta (θ), alpha (α) and beta (β) between HC and ADHD subtypes. The rightmost column shows differences in the theta/beta power ratio (θ/β) for each subtype. The colorbar indicates statistical differences based on t-values with p<0.05 corrected for multiple comparison using FDR across all frequency bands and electrodes. The blue (red) color shows electrodes at which differences were significant with higher (lower) power for ADHD compared to HC. Electrode positions are indicated by black dots. Non-significant regions are shown in green. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; ADHDC: ADHD combined; ADHDI: ADHD inattentive; FDR: false discovery rate.

Figure 6 .

 6 Figure 6. Boxplots displaying the median and interquartile range of the normalized power of delta (δ), theta (θ), alpha (α) and beta (β) for HC and ADHD subtypes in each ROI. The top row shows the boxplots of the theta/beta power ratio (θ/β) in each ROI. The asterisks indicate statistically significant differences (p<0.05, FDR corrected across all frequency bands and regions) between ADHD and HC. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; ADHDC: ADHD combined; ADHDI: ADHD inattentive; R/LFR: right/left frontal regions; R/LTP: right/left temporal regions; R/LCN: right/left central regions; R/LPR: right/left parietal regions; OC: occipital regions; ROI: region of interest; FDR: false discovery rate.

Figure 7 .

 7 Figure7. Statistical p-maps (axial view) displaying significant differences in nCSD (eLORETA solutions) between HC and ADHD age subgroups(8-10, 10-12, 12-14 and 14-16 years) in the delta (δ), theta (θ), alpha (α) and beta (β) bands. The bottom row shows the pmaps of differences in the theta/beta power ratio (θ/β) for each subgroup. The colorbar shows statistical differences based on p-values with p<0.05 corrected for multiple comparison using non-parametric statistical analyses (log F-ratio statistics with 5000 randomizations) across all frequency bands and voxels. The color scale represents log F-ratio values with a threshold (for p<0.05) of ±0.44, ±0.27, ±0.27 and ±0.24 for the 8-10, 10-12, 12-14 and 14-16 subgroups, respectively. The blue (red) color indicates greater (weaker) nCSD for ADHD compared to HC. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; nCSD: normalized current source density.

Figure 8 .

 8 Figure 8. Boxplots displaying the median and interquartile range of nCSD (LORETA solutions) within the delta (δ), theta (θ), alpha (α), beta (β) bands for HC and ADHD age subgroups (8-10, 10-12, 12-14 and 14-16 years) in each ROI. The top row shows the boxplots of the theta/beta power ratios (θ/β) in each region. The asterisks indicate statistically significant differences (p<0.05, FDR corrected across all frequency bands and regions) between ADHD and HC. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; R/LFR: right/left frontal regions; R/LTP: right/left temporal regions; R/LCN: right/left central regions; R/LPR: right/left parietal regions; OC: occipital regions; ROI: region of interest; nCSD: normalized current source density.

Figure 9 .

 9 Figure9. Group-level beta coefficient maps(axial view) showing regression coefficients between age and nCSD (eLORETA solutions) within the delta (δ), theta (θ), alpha (α) and beta (β) bands for HC and ADHD. The rightmost column shows the maps for the theta/beta power ratio (θ/β) for each group. The red (blue) color indicates voxels at which the correlation between age and nCSD was significantly positive (negative) with p<0.05 corrected with nonparametric randomization (5000 randomizations) across all frequency bands and voxels. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; nCSD: normalized current source density.

Figure 10 .Figure 11 .

 1011 Figure 10. Statistical p-maps (axial view) displaying significant differences in nCSD (eLORETA solutions) between HC and ADHD subtypes (ADHDC and ADHDI) within the delta (δ), theta (θ), alpha (α) and beta (β) bands. The rightmost column shows the p-maps for the theta/beta power ratio (θ/β) for each subgroup. The colorbar shows statistical differences based on p-values with p<0.05 corrected for multiple comparison with non-parametric randomization (5000 randomizations) across all frequency bands and voxels. The color scale represents log F-ratio values with a threshold (for p<0.05) of ±0.16 and ±0.29 for ADHDC and ADHDI, respectively. The blue (red) color indicates greater (weaker) nCSD for ADHD compared to HC. HC: Healthy controls; ADHD: Attention deficit and hyperactivity disorder; ADHDC: ADHD combined; ADHDI: ADHD inattentive; nCSD: normalized current source density.

  typically developing controls. We performed statistical comparisons to investigate the effect of age and ADHD subtypes on EEG in different frequency bands during the eyes-closed resting state condition. Our results indicate major alterations in cortical source densities across different frequency bands. The ADHD combined subtype exhibited significantly increased diffuse TBR with a widespread significant decrease in beta cortical source densities. The ADHD inattentive subtype, however, presented increased TBR values in all the cortical regions except in posterior regions due to the global increase in theta source power. The ADHD group also showed significant age-dependent increases and decreases in cortical source densities of slow (delta and theta) and fast (alpha and beta) oscillations, respectively. Our results emphasize the importance of TBR in differentiating ADHD from healthy children at both the source and sensor levels. However, cautions should be taken in interpreting the results with regard to the age and subtypes if TBR is used for ADHD diagnosis.

Acknowledgements

All authors contributed to the final manuscript. This research was supported by the National Science Centre Poland Grants: 2011/01/D/NZ4/04958 for A.C.-K. and 2015/17/N/HS6/03020 for K.K. It was also partially supported by the Iran National Science Foundation (INSF) and Cognitive Sciences and Technologies Council (CSTC) under the grant numbers 97008049 and 6672. The study sponsors had no role in the study design, data collection and analysis, or preparation of the manuscript.

Disclosures

None of the authors have potential conflicts of interest to be disclosed.

subtypes in each ROI. The top row shows the boxplots of the theta/beta power ratios (θ/β) for each region. The asterisks indicate statistically significant differences (p<0.05, FDR corrected across all frequency bands and regions) between ADHD and HC.