Resting state EEG power spectrum and functional connectivity in autism: a cross-sectional analysis

EEG signals were resampled to 1000 Hz and then band pass filtered to [1–32] Hz with a finite impulse response filter of order 2000 (using 2 s of padding at each edge of a resting state block). Higher frequencies (in the gamma range) were not included in the analysis to avoid substantial contamination with muscle activity [23]. Only data from 61 electrodes common to most contributing sites were retained for subsequent analyses. Preprocessing was performed manually and blinded to the participants diagnosis and clinical information, following these sequential steps: (a) Eliminate bad channels, (b) locate and discard sections with large transient artifacts resulting, e.g., from muscle bursts or movements, (c) perform independent component analysis with fastICA (http://​www.​cis.​hut.​fi/​projects/​ica/​fastica/​, [24]), (d) detect artefactual components (capturing: ocular, muscular, cardiac or other artifacts), (e) eliminate the contribution of artefactual components, (f) iterate points (b-e) if necessary, (g) interpolate the bad channels that were eliminated in (a), and (h) re-reference signals to the average across all channels (average reference).

Participants were excluded from subsequent analyses if they met any of the following criteria: (1) less than 15 clean 2.5 s epochs in the eyes-open or the eyes-closed condition (11 participants), (2) less than 51 usable channels or more than 3 neighboring channels eliminated (9 further participants), (3) number of good channels minus number of artefactual independent components smaller than 35 (threshold selected visually when inspecting the distribution of values, 6 further participants). Following these criteria, 26 recordings (18 ASD and 8 NT) were discarded, resulting in a sample size of 224 ASD and 203 NT.

We inspected the alpha peak of each participant. Alpha is the most prominent rhythm in the resting EEG and could reveal if there was a shift in frequencies between the ASD and the NT groups (e.g., one group having alpha at higher frequencies than the other). Power spectra were computed for each channel and condition (eyes open and eyes closed) with fast Fourier transform and 2.5 s Hanning windows with 75% overlap. Alpha peaks in the [6, 13] Hz range were detected automatically by fitting a Gaussian over a power law background to the average eyes closed power spectrum over occipital channels O1, O2, Oz, PO4, PO3 and POz, following [25]. A single alpha peak frequency was derived per participant (and not separate ones for eyes open and eyes closed). Automatic fits were verified by visual inspection and refined for 11 out of 224 ASD and 10 out of 203 NT participants. Seven participants with no clear alpha peak were discarded from subsequent analyses, yielding a total of 218 ASD and 202 NT participants.

The following summary alpha measures were derived from the alpha peak: (1) alpha peak frequency \(f_{{\text{p}}}\), (2) alpha power, defined as the absolute power in the range \(\left[ {f_{{\text{p}}} - 2 {\text{Hz}}, f_{{\text{p}}} + 2 {\text{Hz}}} \right]\) over occipital sensors (O1, O2, Oz, PO4, PO3, POz), (3) reactivity to eye opening, defined as \(R = 1 - \frac{{P_{{{\text{EO}}}} }}{{P_{{{\text{EC}}}} }}\), where \(P_{{{\text{EO}}}}\) and \(P_{{{\text{EC}}}}\) are absolute power values defined previously for the eyes-open and the eyes-closed condition.

Head models with realistic geometry were built from individual’s T1 weighted MRIs. Details on MRI acquisition can be found in [26]. T1-weighted MRIs were segmented with SPM12 [27] into gray matter, white matter, cerebrospinal fluid, bone, soft tissue and air. Then, these probabilistic images were smoothed (5 mm FWHM), thresholded and resliced to produce binary masks of 2 mm × 2 mm × 2 mm resolution for three tissue types: brain (including gray matter, white matter and cerebrospinal fluid), skull and scalp. These binary masks were transformed to hexahedral meshes with FieldTrip [28]. All three considered tissue types were assumed to have homogeneous and isotropic conductivity: 330 mS/m for the brain and scalp [29], and an age-dependent skull conductivity of 3.958 + 62.77*exp(− 0.2404*age[years]) mS/m, in line with the BESA (BESA, Gräfelfing, Germany) recommended conductivity ratios. Of note, the conductivity of cerebrospinal fluid is higher than that of gray or white matter [30], so setting the conductivity of the brain compartment as a constant and isotropic value is a simplification, but the 3-tissue model has led to similar spatial accuracy than a model including a separate CSF tissue in a previous publication [31]. Segmentations were visually inspected, and for 9 participants head models could not be built (because of either no MRI or no clean segmentations). As a consequence, subsequent analyses included 212 ASD and 199 NT participants.

The forward model was derived with FieldTrip and SimBio [32]. 365 source locations of interest were defined in gray matter in MNI space, following a 3D cubic diamond grid with 1.5 cm spacing. Source positions were transformed from MNI to each subject’s individual space with a nonlinear transformation obtained with SPM12. Electrode positions were determined by transforming standard MNI positions to subject’s space with this same transformation and projecting to the scalp surface. Source time series were estimated with linearly constrained minimum variance beamformer, using a regularization of 5% of the average trace of the covariance matrix, a common filter for resting state eyes open and eyes closed and projecting the source time series into the direction of maximal power [33].

Power spectra were computed for each sensor, source and condition: Time series (source or sensor) were convolved with Morlet wavelets of 0.6 octave frequency resolution (f/σ_f = 4.88) and \(5 \cdot \sigma_{t}\) window length, with 90% overlap between windows, for frequencies \(f\; = \;2^{1:0.15:5}\) Hz (frequencies from 2 to 32 Hz in increments of 0.15 in the exponent value). Since beamformer reconstructions suffer from power bias especially for deeper sources [34], source space PS values were normalized with the overall power over the [2 32] Hz range to produce relative PS values. Of note, all subsequent analyses were performed with source space data, except for a control analysis using absolute power at the sensor level.

The 365 sources (see above) were grouped into 50 regions of interests (ROIs) (25 symmetrical ROIs per hemisphere, obtained through k-means clustering of the source positions, leading to 4–13 sources per ROI). The representative time series for a given ROI was defined as the first principal component of all the source time series in this ROI. For each combination of ROIs and frequency, functional connectivity (FC) was quantified with orthogonalized power correlations (orthPowCorr) and weighted phase lag index (wPLI), which evaluate complementary phase and amplitude synchronization while discarding zero-lag synchronization which could be driven by volume conduction. OrthPowCorr and wPLI were implemented following [35] and [36], respectively. In order to avoid introducing sample size-related bias in wPLI, resting state data were segmented into non-overlapping 2.5 s clean epochs, and wPLI was estimated across 15 epochs. These 15 epochs were selected randomly from all the clean epochs from a given subject and condition, this process was repeated 100 times, and values were averaged across the 100 repetitions. Control analyses with other FC metrics are performed using direct power correlations (PowCorr), coherence (COH), imaginary coherence (iCOH) and phase locking value (PLV), following [6, 35, 37]. More details on the FC metrics can be found in Additional file 1.

Each summary alpha measure, PS and FC feature was submitted to the following linear mixed effects (LME) models:

All models were fit with the nlme package in R version 3.4.0 [39], using maximum likelihood estimation. Models 1 and 2 assumed homoscedastic residual errors, while model 3 allowed for different residual variances in the ASD and NT groups. Model 3 is the full model shown in Fig. 1. Age and IQ were mean centered and variance normalized before entering the statistical models. The statistical significance of group differences in mean was determined through the log-likelihood ratio between models 2 and 1. Log-likelihood tests have been reported to be “anticonservative”: They may output p values that are lower than the nominal p values [40]. Therefore, significant group effects were confirmed by using F-tests on the individual parameters after fitting the models with a restricted maximum likelihood method [39]. The statistical significance of group differences in variance was determined through the log-likelihood ratio between models 3 and 2. The following transformations were applied before LME in order to convert the feature distributions to normality: \(x \to \log \left( x \right)\) (absolute power), \(x \to x^{4}\) (alpha reactivity), \(x \to a\tanh \left( x \right)\) (orthPowCorr) and \(x \to x^{0.11}\) (wPLI). The optimal transformations to normality were obtained by evaluating the Kolmogorov–Smirnov goodness-of-fit test for several families of transformations. For information on site and medication effects, refer to Additional file 1.

Cluster-based permutation tests were used to control for multiple comparisons for the PS and FC measures, following [41]. First, clusters of frequencies and electrodes/sources/links with significant effects (p < 0.05, uncorrected) were created. For PS, two sources/electrodes were considered neighbors if they were spatially adjacent. For FC, two links were considered neighbors if they had one common node and one spatially adjacent node. (Two ROIs are considered adjacent if they have at least one pair of neighboring sources.) Then, the cluster size was compared with the null-hypothesis distribution derived from the maximal cluster sizes obtained in randomized datasets (2000 randomizations were performed by randomizing group labels exclusively). P values were defined as the proportion of randomizations, which yielded a larger cluster size than the original dataset.

To test whether a multivariate combination of PS and FC features, respectively, can discriminate ASD from NT, we used machine learning techniques. Before subjecting the data to the multivariate analyses, the effects of age, sex, IQ and site were removed by building PS and FC datasets containing the residuals of the LME models y ~ 1 + age + sex + IQ + (1|site) trained on individual PS and FC features. The PS dataset consists in the space x frequency PS values for eyes-open and eyes-closed condition (19,710 features). The FC dataset contains FC strength across links, frequencies and conditions (66,150 features). Principal component analysis was applied to the PS and FC datasets (matrices of EEG features x subjects), and the principal components explaining at least 98% of the variance were used as input for the classification algorithms (160, 392 and 389 components for PS, OrthPowCorr and wPLI, respectively; each of these principal components is a linear combination of EEG features).

To date, a plethora of classification approaches has been introduced and proven useful [42]. The performance of the models depends greatly on the feature selection approach, classification algorithm and hyperparameter values. Here, we use three different classification approaches that have been successfully used in previous neuroimaging studies and are implemented with scikit-learn [43]: First, we use the L2-penalized support vector classifier (linSVC) which is one of the most common approaches in neuroimaging [44, 45]. Second, we estimate an elastic net logistic regression, which combines L1 and L2 regularization and could perform better if only a small number of features was sufficient for the differentiation between two groups [45, 46]. Third, we combine a Boruta feature selection (based on random forests) with a radial basis kernel support vector classifier, which can detect nonlinear patterns differentiating between two groups [47]. Classifier hyperparameters were tuned using grid search (sklearn.model_selection.GridSearchCV) and nested tenfold cross-validation. The harmonic mean of sensitivity and specificity (also known as S1 score) was employed as the scoring metric, since it prevents algorithmic convergence into a trivial single class prediction in unbalanced datasets [48]. Further details on the classification models employed can be found in Additional file 1: Table S4. Repeated random splits [49] were used to evaluate the cross-validation performance of the classification models (15 random splits with 20% left-out data, using sklearn.model_selection.StratifiedShuffleSplit) within the training set. The significance of the classification performance of the classifiers was assessed by comparing the scoring metric in the original PS and FC datasets with the corresponding values obtained when training the classifiers in datasets with randomized group labels (1000 randomizations).