Cortical correlation structure of aperiodic neuronal population activity.

Electrophysiological population signals contain oscillatory and non-oscillatory aperiodic (1/frequency-like) components. So far research has largely focused on oscillatory activity, and only recently, interest in aperiodic population activity has gained momentum. Accordingly, while the cortical correlation structure of oscillatory population activity has been characterized, little is known about the correlation of aperiodic neuronal activity. To address this, we investigated aperiodic neuronal population activity in the human brain using resting-state magnetoencephalography (MEG). We combined source-analysis, signal orthogonalization and irregular-resampling auto-spectral analysis (IRASA) to systematically characterize the cortical distribution and correlation of aperiodic neuronal activity. We found that aperiodic population activity is robustly correlated across the cortex and that this correlation is spatially well structured. Furthermore, we found that the cortical correlation structure of aperiodic activity is similar but distinct from the correlation structure of oscillatory neuronal activity. Anterior cortical regions showed the strongest differences between oscillatory and aperiodic correlation patterns. Our results suggest that correlations of aperiodic population activity serve as robust markers of cortical network interactions. Furthermore, our results show that aperiodic and oscillatory signal components provide non-redundant information about large-scale neuronal correlations. This may reflect at least partly distinct neuronal mechanisms underlying and reflected by oscillatory and aperiodic neuronal population activity.

Introduction

Neuronal population activity as measured with MEG, EEG or local field potentials (LFP) consists of oscillatory and non-oscillatory aperiodic signal components. These components are evident from the power spectra of such signals, which show a characteristic 1/frequency shape, corresponding to aperiodic signal components, and variable peaks of oscillatory activity.

Cortical oscillations have attracted strong interest and have been implicated in various functions (Singer, 1999; Buzsáki and Draguhn, 2004; Fries, 2009; Donner and Siegel, 2011; Siegel et al., 2012). The amplitudes of neuronal oscillations show characteristic patterns of correlation across the cortex (Brookes et al., 2012; Hipp et al., 2012; Siems et al., 2016; Siems and Siegel, 2020). These patterns are similar to BOLD fMRI correlation patterns (Hipp and Siegel, 2015), are distinct from phase-coupling patterns (Siems and Siegel, 2020), and serve as biomarkers of various neuropsychiatric diseases, such as e.g. major depressive disorder (Nugent et al., 2015), schizophrenia (Kim et al., 2014; Uhlhaas et al., 2008; Voytek and Knight, 2015), autism (Hong et al., 2019), Alzheimer's disease (Koelewijn et al., 2017) and congenital blindness (Hawellek et al., 2013).

In contrast, little is known about aperiodic neuronal population activity. It is not until recently that studies of the biological importance of aperiodic activity gained momentum (He, 2014). Intra-cortically, aperiodic power is closely linked to neuronal spiking (Manning et al., 2009; Ray and Maunsell, 2011) and allows to decode motor behavior and visual inputs with even better fidelity than neuronal oscillations (Miller et al., 2016, 2010, 2009). Non-invasively, EEG and MEG studies have shown that the slope of the aperiodic component is modulated by sleep (Wen and Liu, 2016b), meditation (Braboszcz et al., 2017), drugs (Muthukumaraswamy et al., 2013; Muthukumaraswamy and Liley, 2018), anesthesia (Colombo et al., 2019; Purdon et al., 2015; Zhang et al., 2018) and aging (Waschke et al., 2017). Recently, the cortical distribution of aperiodic activity has been mapped using EEG (Donoghue et al., 2020) and MEG (Mahjoory et al., 2020). However, in contrast to oscillatory activity, nothing is known about the cortical coupling of aperiodic population activity.

To address this, we investigated two specific questions. First, what is the cortical correlation structure of aperiodic activity in the human brain? And second, how does the correlation structure of aperiodic activity compare to that of oscillatory population activity?

To address these questions, we combined human resting state MEG, source reconstruction, signal orthogonalization and analytical techniques for separating oscillatory and aperiodic components (see Fig. 1 for a schematic of the complete analysis pipeline). We found that spontaneous co-fluctuations of aperiodic activity in the human cortex are spatially well structured and that, although similar, there are consistent differences between the correlation structure of aperiodic and oscillatory neuronal population activity. Our results suggest correlations of aperiodic population activity as robust markers of large-scale cortical interactions.

Fig. 1

Analysis pipeline. Schematic of the main analysis steps and corresponding figures. Briefly, MEG resting state measurements were preprocessed and source localized. For co-fluctuation analyses, we orthogonalized time series for all pairs of cortical locations to discount confounding signal leakage. Then, we separated aperiodic and oscillatory power components using IRASA. For both power components, we first analyzed their distribution across the spatial and spectral dimension. Then, for each power component, we characterized its cortical co-fluctuation pattern. Finally, we compared cortical co-fluctuation patterns of aperiodic and oscillatory power at three different levels: globally (seed x brain), spectrally (frequency x frequency), and locally (inspecting correlations between local neighborhoods of each seed pair).

Methods

MEG datasets

We analyzed data from 112 healthy subjects recorded at the MEG Center Tübingen (n = 23) and at Saint Louis University as part of the Human Connectome Project (n = 89) (Van Essen et al., 2013). Two subjects were excluded because of wrong data labeling, and three further subjects were excluded for connectivity analysis because of excessive artifacts. All MEG recordings were performed continuously in magnetically shielded rooms. Fiducials were set to localize the position of the participants’ head in the scanner. EOG and ECG were measured with the MEG.

MEG Center data. All participants (n = 23) gave informed consent, and the experiment was approved by the local ethics committee. Data was collected during resting state. Participants were asked to sit still and let their mind wander, keeping their eyes open. Each recording lasted 10 min. Recordings at the MEG Center were collected with a 275-channel whole-head system (Omega 2000, CTF Systems Inc., Port Coquitlam, Canada). MEG was continuously recorded at a sampling rate of 2343.75 Hz (anti-aliasing filter at Nyquist-frequency).

HCP data. The HCP data (S900 release) was from 89 participants (45 female) aged between 22 and 35. All participants gave informed consent, and the experiment was approved by the local ethics committee. Resting state data and task data were recorded for each participant. We analyzed the first of the three resting state runs in this study. Each run lasted approximately 6 min.

The HCP data was acquired at Saint Louis University using a whole head Magnes 3600 (4D Neuroimaging, San Diego, CA) system having 248 magnetometers and 23 MEG reference channels (5 of them being gradiometers). All measurements were continuously recorded at a sampling rate of 2034.5101 Hz (400 Hz bandwidth, high pass filtered DC) (Larson-Prior et al., 2013).

Artifact rejection

We adapted the minimally preprocessed pipeline of the HCP (Larson-Prior et al., 2013) to the in-house collected data, and applied the same artifact rejection process to both datasets. The artifact rejection process consisted of three steps. First, we detected bad channels and bad sections of the data. Second, we applied ICA to the data without the bad sections and bad channels and classified each IC as “brain” or “artifact” using semiautomatic procedures.

Clean data were high-pass filtered at 0.1 Hz using a 4th order forward-reverse Butterworth filter. We removed line noise artifacts with a 1 Hz wide notch filter on 60 or 50 and 51.2 Hz, depending on the provenance of the data, and its harmonic frequencies. Data were finally resampled to 500 Hz.

Source projection

We used linearly constrained minimum variance (LCMV) beamforming (Van Veen et al., 1997) to project the sensor signals into MNI source space using a single shell model leadfield (Nolte, 2003) based on the individual subject's MRI. The beamforming filter B is obtained using the covariance matrix of the data C of dimensions channels x channels, and the leadfield L of dimensions (3 x channels):

We estimated cortical activity at 457 locations that homogeneously covered the cortical space approximately 7 mm beneath the skull. For each location, we projected the 3-dimensensional source-level data on to its first principal component. We computed the neural activity index (NAI) by dividing the source-level data by a projected noise covariance matrix.

We confirmed that the filters did not have an effect on the cortical distribution of the aperiodic signal parameters. For each of the 457 cortical locations we generated 3 s long timeseries with a power-law spectrum and varied the power-law exponent between 0.5 and 2. We projected these signals to the sensor space, added white noise, used the subject-specific beamforming filters B to project the signals back to the cortex space, and estimated the power-law exponent using IRASA and a power-law fit. All simulated power-law exponents were correctly estimated and there was no bias across the cortex.

Broadband signal orthogonalization

IRASA operates on time-domain signals. Thus, to discount signal leakage, we employed pair-wise time-domain orthogonalization of the broadband source-level signals (Brookes et al., 2012; Hipp et al., 2012; Siems and Siegel, 2020). Specifically, for each pair of sources, we computed the orthogonalized signal by taking the residuals of a linear regression of each signal onto the other signal (Fig. S2). We orthogonalized all pairs of sources in both directions. We analyzed log-power correlations of time-domain orthogonalized signals to confirm leakage suppression (Fig. S2).

IRASA

We applied IRASA to consecutive non-overlapping 3 s windows, which provides an efficient trade-off between computational requirements and spectral resolution (Wen and Liu, 2016b). For each window, we performed IRASA using the IRASA software toolbox with default parameters: detrending the data, irregular resampling (parameter h) from 1.1 to 1.9 in steps of 0.05, low-pass filtering the signal to avoid aliasing when down-sampling (frequency-domain multiplication with a sinusoidal transition between 125 Hz and 143.75 Hz), and limiting the output to a frequency range of 0.24–125 Hz (one fourth of the sampling rate). For the univariate analysis we performed IRASA per seed. For all pair-wise analyses on the connection level we first orthogonalized the broadband data for each seed pair and then applied IRASA on the orthogonalized signals.

Modeling the aperiodic spectrum

For each 3 s window and seed or seed-pair, we fitted a power law to the aperiodic spectrum obtained from IRASA following the same steps as in the IRASA package. We limited the frequency range from 0.7 to 125 Hz and logarithmically resampled the spectrum. Then we fitted the spectrum with either a one-range linear model, a continuous two-range linear model with a knee at 15 Hz, and a model that takes into account the effect of the ambient noise. For the model including the noise, after fitting the knee model we reversed the logarithm of the predicted model values to add the measured empty room noise multiplied by a noise coefficient d. We then again applied the logarithm and computed the mean squared error (MSE) of the model fit. We constrained the noise coefficient between 0 and 3 and minimized the MSE to find the optimal fit. The following function summarizes this model:

We compared all three models by computing their optimal MSE in the log-linear fitting space and comparing their Akaike information criterion (AIC). The AIC quantifies goodness of fit taking into account the number of model parameters k and observations n. The AIC was computed as:where c was set to 0 for all models.

To characterize the optimal knee frequency across the cortex we fitted knee-models with noise and knee frequencies ranging from 5 Hz to 70 Hz in 5 Hz steps.

Correlation structure of oscillatory and aperiodic activity

To assess the correlation of different activity components, we log-transformed power spectra and resampled them on a logarithmic frequency axis. The power at frequency f was computed as the inner product between the power spectrum and Gaussian kernels at frequencies f ranging from 1 to 64 Hz in quarter octave steps. The standard deviation of the Gaussian kernel was f/5.83 which results in a spectral bandwidth of 0.5 octaves. Finally, we computed Pearson correlation of power across time for each pair of seeds and frequency. The same approach was used for all signal components, model fits and reconstructed spectra.

Testing cortical patterns

To quantify whether cortical distributions of model parameters or correlation coefficients were consistent across subjects we performed a cluster permutation statistic (Maris and Oostenveld, 2007) (random-effects). We z-scored the cortical maps of model parameters or of Fisher-z transformed correlation coefficients per subject across space. Then, we performed a t-test against 0 per cortical location across subjects. Clusters were defined as continuous significant regions (p < 0.01), with their number of significant locations as the cluster size. Then, 1000 times, for a random set of subjects, we flipped the sign of their entire data, repeated the t-statistic, and quantified the maximum cluster size. The statistical significance of the original clusters was finally assessed against the distribution of maximum cluster sizes for the permuted data. This cluster permutation test is robust against the autocorrelation of neuronal variables because the permutation is consistently performed across the data space, and thus the autocorrelation does not change under the null hypothesis.

Comparing correlation structures

We computed attenuation corrected correlations (Hipp et al., 2015; Siems et al., 2016; Siems and Siegel, 2020; Spearman, 1904) to compare the correlation structures of aperiodic and oscillatory components. In short, attenuation correction computes the correlation between those components of two quantities (here: correlation patterns) that are reliable across samples of interest (here: subjects). Critically, attenuation corrected correlations are unbiased, which allows to directly test against 0 and 1.

First, we Fisher-z transformed and z-scored all cortical correlation matrices. Here, matrices are of dimension cortical sources x cortical sources and represent the correlation between each pair of orthogonalized sources at a specific frequency and for either the aperiodic or oscillatory signal, per subject. Then we computed the correlation of each seed correlation pattern, i.e. of each column of the correlation matrix, between all pairs of subjects separately for the aperiodic component and for the oscillatory component. This yielded the reliabilities and for seed i and frequency band f. We then computed the correlation of the same columns, but now between oscillatory and aperiodic correlation matrices, for all pairs of non-identical subjects. This yielded the non-corrected correlation between oscillatory and aperiodic correlation patterns . Finally, we computed the corrected correlation between oscillatory and aperiodic correlation patterns as . Critically, this correction is only possible for seed patterns, where both oscillatory and aperiodic components are reliable (i.e. and ). Thus, we determined which seeds had reliable correlation patterns using a one-sided t-test against 0 (p < 0.05). We tested attenuation corrected correlations against 0 and 1 using t-statistics across subjects. We performed FDR-correction (Benjamini and Hochberg, 1995) of the resulting p-values to control for multiple tests across frequencies. Single subject attenuation corrected correlations and reliabilities were estimated as pseudo-values using a leave-one-out bootstrap.

Differences between oscillatory and aperiodic correlation patterns

For each subject and frequency, we vectorized and z-scored the upper triangular matrix of cortical correlation coefficients. For each subject and frequency, we subtracted the standardized correlation vector of oscillatory activity from the standardized correlation vector of aperiodic activity. We then computed attenuation corrected correlations of the resulting difference vectors between frequencies. We computed reliabilities within frequencies across subjects , we computed the correlation between frequencies , and we used those values to compute the corrected cross frequency correlation .

Comparison of oscillatory and aperiodic correlation patterns at the connection level

We computed attenuation corrected correlations between oscillatory and aperiodic correlation patterns at the connection level (Hipp and Siegel, 2015). The analysis is analogous to the global attenuation corrected correlation analysis, but, in contrast to the global analysis, which compares the full cortical correlation patterns for each seed, this analysis compares the correlation patterns between the local neighborhoods of each pair of seeds, i.e. of each cortico-cortical connection. Local neighborhoods covered about 19 seed locations within a radius of about 2.5 cm surrounding each seed. This analysis resulted in full cortical correlation matrices of attenuation corrected correlations between oscillatory and aperiodic correlation patterns. We determined connections with reliabilities > 0 using a t-test on Fisher z-transformed reliabilities (p < 0.01) and excluded absolute z-scored corrected correlation larger than 4 to stabilize variance.

Results

We analyzed combined data from two datasets of resting state MEG recordings in healthy human participants (n = 112). One dataset (n = 89 subjects) was from the Human Connectome Project (Larson-Prior et al., 2013; Van Essen et al., 2013) and the other dataset (n = 23) was recorded at the MEG Center, Tübingen. Fig. 1 shows a flowchart of the entire analysis pipeline and corresponding results figures.

Aperiodic cortical population activity

In a first step, we source reconstructed cortical activity from the MEG data using beamforming (Van Veen et al., 1997) and separated oscillatory and aperiodic components using irregular-resampling auto-spectral analysis (IRASA) (Wen and Liu, 2016b). IRASA extracts the scale free characteristic, i.e., spectral self-similarity, of the broadband signal. It applies a series of re-samplings to generate power spectra that displace the oscillatory peaks, but do not alter the scale free aspect of the spectrum. The aperiodic component is then derived as the median over all re-samplings (see Methods). IRASA has several key advantages. It is non-parametric, i.e. there is no need to pre-specify the number or width of oscillatory modes, it can automatically detect different aperiodic regimes and it operates across a large frequency range.

Aperiodic power of human brain activity has been described either by a single power law or by a model with two power laws joined with a knee (Chaudhuri et al., 2017; Muthukumaraswamy and Liley, 2018; Wen and Liu, 2016a). Importantly, MEG recordings also pick-up ambient noise, which can be power law shaped (Bédard et al., 2010) and may thus affect estimates of aperiodic population activity. Thus, before investigating the co-fluctuation of aperiodic activity, we first aimed to dissociate these factors by modeling the aperiodic power spectrum with a parametric model. Furthermore, we determined the number of aperiodic regimens using model selection, which has biological implications that may help to elucidate the mechanisms underlying the aperiodic power spectrum. We fitted three increasingly complex models: a single power law (Fig. 2A, left), two power laws connected by a knee at 15 Hz (Fig. 2A, middle), and two connected power laws with added noise of empty room MEG recordings (Fig. 2A, right).

Fig. 2

Aperiodic cortical population activity. (A) Average power spectrum of the mixed broad-band signal, of the aperiodic signal component isolated by IRASA and of three different models of aperiodic power (one power law without knee, two power laws with knee, and two power laws with knee and noise). Model fits for one power law (no knee) and two power laws (knee) without noise fail to capture the shape of the aperiodic power spectrum. Shaded regions indicate SEM across subjects. SEMs are small and thus often occluded by the mean trace. (B) AIC for the three different models (all comparisons p < 10−14, n = 109, two tailed t-test). A lower AIC value indicates a better fit. (C) Mean squared error (MSE) of model fits with knee frequencies ranging from 5 to 70 Hz. For all brain regions 15 Hz was the optimal knee frequency. (D) Cortical distribution of the three neuronal parameters (β and c) of the optimum model (see Fig. S1 for noise coefficient). β: 0.7–15 Hz slope, β: 15–125 Hz slope, o: offset. P-values are from cluster permutation statistics across subjects (n = 109, 1000 permutations).

The third model with two power laws and noise best described the data and was optimal according to the Akaike Information Criterion (AIC) (Fig. 2B) (AIC one power law vs. AIC two power laws: p < 10−15, t-test, n = 109; AIC two power-laws vs AIC two power-laws and noise p < 10−15, two tailed t-test, n = 109). We next fitted different power law models with a knee and noise component with different knee frequencies between 5 and 70 Hz to test if a knee at 15 Hz was appropriate across the entire cortex (Fig. 2C). Indeed, we found that, irrespective of cortical location, 15 Hz provided the best fit.

The final optimal model had four parameters: the two slopes of the power laws (β and β), the offset of the power (o), and the amount of MEG noise. The model revealed a highly specific cortical distribution of aperiodic neuronal activity (Fig. 2D). All model parameters had consistent non-random cortical patterns across subjects (all p < 0.01, cluster permutation test; see Fig. S1A for the cortical distribution of the noise component). The 0.7 to 15 Hz power law slope β was steepest in anterior areas with minima in sensorimotor and visual cortex (β= 0.46 +/- 0.12, mean +/- SD). In contrast, the 15 to 125 Hz slope β was steepest in posterior regions, excluding the occipital pole (β1.99 +/- 0.39, mean +/- SD). The offset (o=-19.6, +/- 0.3, mean +/- SD) was lowest in prefrontal and medial temporal cortex and the noise term (d= 0.5 +/- 0.09, mean +/- SD) peaked in the temporal regions that are often contaminated by muscle artifacts (Fig. S1A). The cortical pattern of slope parameter β, was negatively correlated with the patterns of β and offset (r = -0.4, p < 10−4; r = -0.09, p < 10−4). β showed no significant spatial correlation with the offset (r = -0.004, p = 0.9).

The present MEG data consisted of two independent datasets recorded with different MEG systems at different sites. Thus, we next tested if results were consistent across datasets. This was indeed the case. For both datasets independently, the two power law model including the noise component was the optimal aperiodic model (all model comparisons p < 10−4, two tailed t-test, n = 109). Also, the specific model parameters were consistent across datasets. In fact, the first and second slope of the aperiodic model as well as the noise coefficient were not significantly different between the two datasets (all p > 0.05, t-tests). Only the offset showed a significant difference (p = 2 × 10−7, t-test; HCP: -19.45+/-0.18, Tübingen: -20.04+/-0.17).

In summary, consistent across two independent MEG datasets, we identified aperiodic neuronal population activity that was well described by a two power law model. The spectral shape and strength of this aperiodic activity showed a specific cortical distribution with anterior-posterior gradients.

Oscillatory cortical population activity

If IRASA performed a valid separation of broad-band signal power, the retained oscillatory components should resemble the known spectral and cortical specificity of rhythmic brain activity. Indeed, this is what we found. Fig. 3A shows the oscillatory power for three characteristic seeds: left auditory, left somatosensory and medial prefrontal cortex with peaks in the alpha, beta and theta band, respectively. The cortical distribution of oscillatory power (Fig. 3B) showed strongest theta band activity (6 Hz) in frontal areas, a prominent alpha peak (11.3 Hz) over visual cortex and a beta peak (22.3 Hz) over sensorimotor cortices (all p < 0.05; cluster permutation test). Thus, oscillatory power derived with IRASA well resembled the expected spectral and cortical profile of cortical rhythms.

Fig. 3

Oscillatory cortical population activity. (A) Power spectra of the oscillatory component derived by IRASA for left auditory cortex, left somatosensory cortex and medial prefrontal cortex. (B) Cortical distribution of oscillatory power. p-values are from cluster permutation tests across subjects (n = 109).

Cortical correlation structure of aperiodic activity

We next turned to our first question – if the correlation of aperiodic cortical activity is spatially structured. Signal leakage confounds the direct correlation of MEG signals. Thus, we applied pairwise orthogonalization of source-reconstructed MEG signals to rule out such confounds (Brookes et al., 2012; Hipp et al., 2012; Siems and Siegel, 2020). We confirmed that orthogonalization suppressed leakage effects (Fig. S2) but did not alter the power spectrum (Fig. S3). We then applied IRASA across time using a sliding window approach (3s windows), fitted the aperiodic model for each time window, and analyzed cortical co-fluctuations of activity across time for the different parameters of the aperiodic model.

For each cortical location and aperiodic model parameter, we quantified the mean correlation to all other cortical locations (Fig. 4A). We found that all aperiodic parameters had a consistent cortical distribution of correlations that peaked in parietal cortex (p < 0.01, cluster permutation test; see Fig. S1 for noise component). Thus, overall parietal cortex showed the strongest correlation of aperiodic activity to other brain regions resembling a hub of aperiodic power correlations. While overall the correlation structure was similar for all model parameters, descriptively β peaked more anterior than β, which supports the application of a two power law model.

Fig. 4

Cortical correlation structure of aperiodic activity. (A) Cortical distribution of the average correlation of aperiodic model parameters across time (β: 0.7–15 Hz slope, β: 15–125 Hz slope, o offset). Maximum correlations are in parentheses. (B) Cortical correlation structure of aperiodic model parameters for three cortical seeds (left auditory cortex, left somatosensory cortex and medial prefrontal cortex). In parentheses are the maximum correlations values. All p-values are from cluster permutation tests, masked at p < 0.05, n = 107.

We next analyzed the cortical correlation pattern of aperiodic parameters for specific cortical regions (Fig. 4B). We focused on early auditory and somatosensory cortices, which show strong interhemispheric coupling for fMRI (Cordes et al., 2001), intracranial recordings (Nir et al., 2008) and rhythmic M/EEG activity (Hipp et al., 2012; Siems et al., 2016). Furthermore, we investigated medial prefrontal cortex, which shows rhythmic coupling with frontoparietal cortices (Hipp et al., 2012; Siems and Siegel, 2020). If aperiodic signal components reflect interactions between brain regions, these components should show similar correlation structures. This is what we found (Fig. 4B). Across model parameters, all seeds showed the expected bilateral correlation structures with most distinct patterns for somatosensory cortex. Furthermore, correlation structures were generally consistent across model parameters with strongest correlation patterns for the 15 to 125 Hz slope (β).

In summary, we found that spontaneous fluctuations of aperiodic power were correlated across the brain. These correlations were spatially well structured, with parietal regions as major hubs and with prominent interhemispheric correlations of homologous sensory areas.

Comparison of aperiodic and oscillatory correlation structures

After establishing that the cortical correlation of aperiodic activity was indeed spatially structured, we focused on our second question: How does the correlation structure of aperiodic activity compare to the correlation structure of oscillatory activity? To perform this comparison in a frequency-specific fashion, we reconstructed the power spectrum of aperiodic activity from the aperiodic model, discarding the noise component (Fig. 5). In analogy to the aperiodic model parameters above, we then correlated the power of aperiodic and oscillatory components between all pairs of brain regions across time. In addition, we performed the same analysis for the original mixed signal, that contained both, aperiodic and oscillatory components.

Fig. 5

Comparison of oscillatory and aperiodic correlation patterns. (A) Average correlation of the mixed cortical signal as well as of oscillatory and aperiodic signal component. The mean correlations of the individual aperiodic model parameters are on the right. Shaded areas and error bars denote SEM across subjects. (B) Cortical seed locations. (C) Cortical correlation structure of aperiodic activity for three seeds and frequencies. (D) Cortical correlation structure of oscillatory activity. Numbers in parenthesis are the maximum t-scores of significant clusters. All p-values are from cluster permutation tests, n = 107.

Averaged across all pairs of brain regions, oscillatory activity showed a spectrally narrower and bimodal distribution of correlation than aperiodic activity (Fig. 5A). However, correlations were generally stronger for aperiodic signal components (see Fig. S4 for correlations of the raw aperiodic output of IRASA and of the suboptimal aperiodic models).

Next, we directly compared the cortical correlation patterns between aperiodic and oscillatory activity for the same seed regions that we employed for the aperiodic model parameters for three frequencies with strong average correlations (Fig. 5C and D). In accordance with the correlation structure of the aperiodic model parameters, we found strong interhemispheric correlations for auditory and somatosensory cortex as well as bilateral frontoparietal correlations for medial prefrontal cortex. In general, these correlation structures were similar between aperiodic and oscillatory activity. However, aperiodic correlations were stronger and with more distinct spatial structure. Thus, we next systematically quantified the similarity of aperiodic and oscillatory correlation structures (Fig. 6).

Fig. 6

Attenuation corrected correlation of aperiodic and oscillatory correlation patterns. (A) Diagram of attenuation correction procedure. (B) Corrected and non-corrected mean correlation of aperiodic and oscillatory correlation patterns. Shaded regions denote SEM across subjects’ median cortical correlation values. Significance bars indicate corrected correlations < 1 (p < 0.01 FDR corrected, n = 107, one tailed t-test). (C) Aperiodic and oscillatory reliabilities (top), and the proportion of cortical seeds with reliable correlation patterns (p < 0.05; bottom) (D) Cortical distribution of attenuation corrected correlation between oscillatory and aperiodic correlation (rOAc) and reliabilities (rAA for aperiodic and rOO for oscillatory) for different frequencies. Minimum and maximum corrected correlations are in parentheses. Desaturated or gray regions have < 50% or no reliable subjects, respectively.

Aperiodic and oscillatory correlation patterns are distinct

For each seed region and frequency, we correlated the correlation patterns of aperiodic and oscillatory components (Fig. 6B, purple). Averaged across all seed regions, correlation coefficients between aperiodic and oscillatory correlation patterns were positive and up to 0.2. Furthermore, correlation patterns were most similar in the frequency range between 8 and 16 Hz. On the one hand, this may indicate that oscillatory and aperiodic correlation patterns are most similar in this frequency range. On the other hand, this may indicate however, that in this frequency range correlation patterns can be detected more reliably as compared to other frequencies.

We applied attenuation correction of correlations (Spearman, 1904) to disambiguate these two scenarios (Fig. 6A; for other recent uses of this approach see: Hipp et al., 2015; Siems et al., 2016; Siems and Siegel, 2020). As a first step, we estimated the reliability of aperiodic and oscillatory correlation patterns as their inter-subject correlation. High reliability indicates consistent correlation patterns across subjects, whereas low reliability indicates strong variability across subjects. For both signal components, reliability peaked from about 8 to 16 Hz with stronger reliability for aperiodic correlation patterns and two peaks for oscillatory reliability around 10 and 23 Hz (Fig. 6C). Reliability of aperiodic correlation was broadly distributed across the cortex peaking in parietal, occipital and central regions (Fig. 6D). Reliability of oscillatory correlations showed a more distinct pattern with frequency-dependent peaks in frontal, central and occipital regions.

In the next step. we used these reliabilities to attenuation-correct the correlation between oscillatory and aperiodic correlation patterns (Fig. 6A). This had a marked effect. The corrected correlation coefficient between oscillatory and aperiodic correlation patterns was around 0.85 with little variability across frequencies (Fig. 6B; orange). This had two implications. First, the spectral specificity of the similarity between oscillatory and aperiodic correlation patterns (Fig. 6B; purple) was largely driven by different reliabilities across frequencies. Second, the fact that corrected correlation coefficients were high, but significantly smaller than 1 across a broad frequency range (p < 0.01 FDR corrected, one tailed t-test, n = 107; Fig. 6B), implied that cortical correlation patterns of oscillatory and aperiodic activity were similar but distinct.

Differences between aperiodic and oscillatory correlation patterns point to known oscillations

The previous results shown that aperiodic and oscillatory correlation patterns across all pairs of brain regions and frequencies are similar but show reliable differences. We next sought to further characterize nature of these differences in two ways. First, we compared aperiodic and oscillatory correlation pattern differences across frequencies, and second, we investigated for individual pairs of local cortical regions, whether their oscillatory and aperiodic correlation structures differed.

In the first approach, i.e. the comparison across frequencies, we first isolated the differences between aperiodic and oscillatory correlation patterns and then compared these differences across frequencies (Fig. 7). For each frequency and subject, we normalized and subtracted aperiodic and oscillatory correlation patterns, which removed their global similarities (see also Fig. S5A). We then correlated the differences between aperiodic and oscillatory correlation patterns across frequencies (Fig. 7A). In other words, we quantified if what made aperiodic and oscillatory correlation patterns different at one frequency, was similar to the difference at another frequency. Importantly, we again corrected for reliability confounds by applying attenuation correction (see also Fig. S5B).

Fig. 7

Correlation of pattern differences across frequencies. (A) Diagram of the attenuation correction procedure applied to the differences of connectivity matrices of aperiodic and oscillatory components across frequencies. (B) Corrected cross-frequency correlation of differences between aperiodic and oscillatory correlation patterns. Outlined areas show corrected correlation values < 1 (p-values < 10−5 and < 10−6 FDR corrected, n = 107, one tailed t-test). The cyan spectrum at the top shows the average negative log10 of p-values per frequency. The arrows indicate the natural spectral grouping of differences.

We found that, across the entire pair-wise frequency space, corrected correlation coefficients were broadly distributed between 0.2 to 1 (Fig. 7B). Attenuation correction allowed us to test which frequency combinations showed distinct differences between aperiodic and oscillatory correlations, i.e. correlation coefficients smaller than 1. If organized in columns, we can think of these frequencies as separators of distinct differences between aperiodic and oscillatory correlations. Indeed, testing for correlations smaller than 1 (p < 10−5 FDR corrected, one tailed t-test, n = 107) revealed a columnar structure separating the frequency ranges of characteristic brain rhythms. For example, 10 Hz showed correlations smaller than 1 with all lower frequencies (∼0.8 to ∼6.7 Hz) and frequencies higher than 16 Hz. This identifies 10 Hz as having consistent differences between oscillatory and aperiodic correlations that only occur at 10 Hz and neighboring frequencies. We found similar separations for frequencies around 4 Hz, 20 Hz and 40 Hz. Differences around 4 Hz were distinct from 10 to 45 Hz but not from other frequency ranges.

In sum, the comparison across frequencies identified cortical delta, alpha, beta, and low gamma frequency bands and showed that the correlation structure of oscillatory activity in these bands had distinct differences to the correlation of aperiodic neuronal activity.

Connection-level differences between oscillatory and aperiodic correlations

We next compared oscillatory and aperiodic correlations at the connection level to identify which specific connections were distinct. For this, we employed local attenuation corrected correlation (Hipp et al., 2015). In this approach, not the entire cortex-wide correlation patterns were correlated between signal components, but instead we analyzed for each connection, i.e. each pair of cortical locations, the correlation pattern of their local neighborhoods. E.g., Fig. 8A exemplifies the connection between a location in left prefrontal cortex and a location in right parietal cortex with their local neighborhoods. This approach discounts coarse global correlation patterns and allows to resolve the similarity of correlation patterns between two specific regions.

Fig. 8

Differences of correlation at the connection level. (A) Schematic of local attenuation correction showing the neighborhood of two example seed locations. (B) Mean corrected and non-corrected correlation of connection-level oscillatory and aperiodic correlation patterns. Shaded regions show SEM across the medians of connection-level correlations per subject. The gray bar indicates frequencies with corrected correlations significantly smaller than 1 (p < 0.01 FDR-corrected, n = 107, one tailed t-test). (C) Average reliabilities and proportion of reliable connections (p < 0.01) of oscillatory and aperiodic correlations. (D) Circle plots show a random sample (800 connections) of the 10% lowest average corrected correlations across frequency-bands and subjects. The topographies show the marginal mean of the corrected correlations that are in the 10% lowest correlations per frequency band. Minimum and maximum marginal correlations are in parentheses. (E) Mean corrected correlation of local oscillatory and aperiodic correlation patterns grouped into anterior-anterior, posterior-posterior and anterior-posterior connections. Bars indicate pair-wise differences (p < 0.05 FDR corrected; shaded areas denote SEM across subjects’ median connection-level correlations, n = 107, one tailed t-test). (F) Same as (E) but for connections separated into left-left, left-right and right-right groups (p < 0.05 FDR corrected).

In accordance with the global correlation analysis, the connection-level attenuation corrected correlations showed again that oscillatory and aperiodic correlation patterns were similar, but still significantly distinct (correlation < 1) across broad frequency ranges (Fig. 8B; p < 0.01 FDR corrected, one tailed t-test, n = 107). Connection-level patterns were most similar in the alpha frequency range around 10 Hz, where the average correlation was indeed not significantly smaller than 1. Again, local reliabilities peaked from about 8 to 16 Hz and were stronger for aperiodic than for oscillatory correlations (Fig. 8C).

To characterize which connections underlie the differences between oscillatory and aperiodic correlations, we identified from all the reliable connections, the 10% least similar connections for each frequency (Fig. 8D). From 6 to 23 Hz, where at least 15% of connections were reliable, dissimilar connections were mostly found within frontal and between frontal and temporal cortices (see Fig. S6 for all individual frequencies and the average across all frequencies). This suggested that specifically anterior cortical regions showed distinct oscillatory and aperiodic correlation patterns.

To quantitively assess this, we divided cortical connections into three groups: anterior-anterior, posterior-posterior and anterior-posterior. We then compared the correlation between oscillatory and aperiodic correlation patterns between these three groups (Fig. 8E). Indeed, we found that anterior-anterior connections were most dissimilar, followed by anterior-posterior connections, and posterior-posterior connections. Furthermore, this analysis revealed a marked dissimilarity between oscillatory and aperiodic correlations specifically for anterior-anterior connections around 6 Hz. A control analysis separating connections according to left and right hemisphere (Fig. 8F) did not reveal a similar pattern.

In sum, the comparison on the connection level identified cortical correlations involving the frontal cortex as most dissimilar between oscillatory and aperiodic neuronal activity.

Discussion

We combined source-analysis, signal orthogonalization and IRASA to systematically characterize the cortical distribution and correlation of aperiodic neuronal activity in resting-state MEG. We found that aperiodic population activity is robustly correlated across the cortex, that this correlation is spatially well structured, and that the cortical correlation structure of aperiodic activity is similar but distinct from the correlation structure of oscillatory population activity.

Spectral profile of aperiodic activity

Our findings add to previous studies that have characterized the spectral profile of aperiodic cortical activity as multi-fractal (He et al., 2010; Miller et al., 2009; Muthukumaraswamy and Liley, 2018; Wen and Liu, 2016a). Based on objective criteria (AIC) and systematic model comparison we identified an optimal model consisting of two continuous power laws with a knee at 15 Hz and additive noise. The continuous piece-wise linear model reduced the number of parameters and allowed to effectively reconstruct the aperiodic power spectrum with one offset and two slopes. Furthermore, modeling the noise (Bédard et al., 2010; Miller et al., 2009) did not only critically improve the model fit, but also allowed to reconstruct noise-free aperiodic power, which added an additional degree of independence between oscillatory and aperiodic activity.

The average slope coefficients that we identified were generally more extreme than those previously reported for MEG. Specifically, the average low- and high-frequency slopes (<15 Hz: 0.46; >15 Hz: 1.99) were smaller and larger than previously reported, respectively (Dehghani et al., 2010a; Muthukumaraswamy and Liley, 2018; Wen and Liu, 2016b). This could be explained by several factors: First, in contrast to most previous studies, we separated oscillatory and aperiodic components before quantifying aperiodic slopes. Second, the exact frequency range over which slopes are estimated differs between studies. Third, in contrast to previous studies (Muthukumaraswamy and Liley, 2018) we measured resting state with eyes open. Fourth, in contrast to previous studies (Muthukumaraswamy and Liley, 2018; Wen and Liu, 2016a) we modeled the noise component of the power spectrum. In particular at very low and high frequencies, modeling the noise component assigns power to the noise term. This leads to smaller and larger aperiodic slopes for low and high frequencies, respectively.

Intriguingly, the spectral profile of aperiodic power that we found is closer to the profile that has been reported for intra-cortical measurements, which are less affected by noise (Miller et al., 2009; Muthukumaraswamy and Liley, 2018). Thus, the combination of component separation (IRASA) and noise modeling may yield measurements of aperiodic activity closer to the underlying intracortical activity.

Cortical profile of aperiodic activity

In accordance with previous reports (Dehghani et al., 2010b; Donoghue et al., 2020; Mahjoory et al., 2020; Muthukumaraswamy and Liley, 2018; Wen and Liu, 2016b), source analysis and parametric modeling of aperiodic activity showed a robust and prominent anterior-posterior gradient of the cortical distribution of the aperiodic slopes. Specifically, we found steeper aperiodic slopes for frequencies below and above 15 Hz in anterior and posterior regions, respectively. Further large-scale invasive studies are required to link these findings to measures of local population activity (LFP) and spiking activity.

This study provides, to our knowledge, the first systematic characterization of the cortical correlation structure of aperiodic activity. Our results extend previous reports that linked correlations of aperiodic activity to fMRI signals (Wen and Liu, 2016a). Importantly, we combined source reconstruction (beamforming) and signal orthogonalization to discount spurious correlations generated by signal leakage and to directly characterize the correlation structure at the cortical level. We found that temporal fluctuations of aperiodic activity were robustly correlated across the cortex and that these correlations were spatially well structured. Average correlations were strongest in parietal cortex with prominent interhemispheric correlations of homologous sensory areas and frontoparietal cortices.

These results suggest that correlations of aperiodic population activity serve as robust markers of large-scale cortical network interactions. It remains open for further investigation to what extend correlations of aperiodic activity do not only reflect, but are also causally relevant for the communication between different cortical areas.

Comparison of oscillatory and aperiodic component correlations

Our results provide a systematic comparison of the correlation structure of oscillatory and aperiodic activity across the cortex and a broad frequency range. This extends previous studies reporting correlations between oscillatory and aperiodic components mostly in the alpha band (Muthukumaraswamy and Liley, 2018; Wen and Liu, 2016a). Importantly, we employed attenuation correction of correlations to quantify unbiased correlations independent of reliability confounds. This approach revealed both, a high similarity as well as significant differences between oscillatory and aperiodic correlation structures. In the following, we discuss both aspects.

Similarity of oscillatory and aperiodic correlation patterns

The present finding of strong similarities between the correlation structures of oscillatory and aperiodic cortical population activity with MEG stands in contrast to results from intracortical recordings (Miller et al., 2014; Ray et al., 2008), which suggest a substantial dissociation between oscillatory and aperiodic components. The different signal modalities may explain this discrepancy.

First, MEG may only weakly reflect the underlying aperiodic neuronal activity. For ECoG, it has been suggested that, compared to oscillatory spiking, aperiodic spiking has a smaller influence on the population signal (Ray et al., 2008), and that this difference is further accentuated with distance to electrode. Thus, the aperiodic signal picked up by MEG sensors may only to a small extent reflect underlying aperiodic spiking activity. Second, along a similar line, aperiodic activity may indeed be correlated with oscillatory activity, but at a spatial scale coarser than assessed with LFP or ECoG recordings. MEG may be particularly sensitive to these coarser correlations. Finally, the employed behavioral task may have an important effect. We studied resting state activity, while invasive studies focused on correlates of motor behavior (Miller et al., 2014) and sensory stimulation (Ray et al., 2008). Visual stimulation can robustly drive high-frequency MEG activity above 100 Hz (Kupers et al., 2018; Siegel et al., 2007), which may reflect broad-band spiking that is in turn dissociated from oscillatory activity.

Differences of oscillatory and aperiodic correlation patterns

Our results uncover significant differences between the correlation structure of oscillatory and aperiodic activity. We characterized these differences on three levels, starting from average brain-wide correlations, over seed-wise correlation patterns to correlation patterns at the level of individual connections and their local neighborhoods.

Brain wide correlations showed on average higher correlations for aperiodic activity as compared to oscillatory activity (Fig. 5.A). Aperiodic correlations had a unimodal spectral distribution peaking around 8 Hz. In contrast, oscillatory correlations had a bimodal spectral distribution with maxima close to 10 Hz and 20 Hz, which well corresponds to cortical alpha and beta rhythms.

Seed-wise correlation patterns were generally similar between both signal components (Fig. 5C). However, aperiodic correlations were more reliable than oscillatory correlations (Figs. 6C and D). Furthermore, aperiodic and oscillatory correlation patterns were significantly different across a broad frequency range with strongest dissimilarities outside of the 8 to 16 Hz band (Fig. 5C).

This was consistent with the results at the connection level (Fig. 8). Also at the connection level, oscillatory and aperiodic correlation patterns significantly differen over most of the frequency spectrum, with lowest dissimilarity around 8 to 16Hz. Furthermore, the connection-level analysis revealed that correlations between local neighborhoods in frontal cortex, as well as to temporal and central cortex were more distinct between oscillatory and aperiodic activity than between neighborhoods within posterior cortex (Fig. 8D). This was in particular the case around 6 Hz and in the alpha-frequency range. This suggests that there is no generic link between co-fluctuation of oscillatory and aperiodic neuronal activity, but that this relationship is specific for the cortical rhythm and region at hand.

In addition to different spatial levels, we characterized how differences of oscillatory and aperiodic correlation structures compared across frequencies (Fig. 7). This revealed distinct differences of correlation structures in frequency ranges well matching characteristic oscillatory bands (delta, alpha, beta, and low gamma). This accords well with the spectral specificity of the cortical patterns of unseparated, broad-band power correlations (Hipp et al., 2012). Notably, differences of correlation structures were most distinct around 10 Hz. Thus, although on average oscillatory and aperiodic correlation patterns were least dissimilar in this frequency range, the differences around 10 Hz were most distinct from other frequency ranges.

Independent of the exact mechanisms underlying the aperiodic part of the M/EEG signal, the above differences between oscillatory and aperiodic correlation patterns may reflect distinct neurophysiological mechanisms underlying both signal components. Moreover, these findings imply that oscillatory and aperiodic signal components contain non-redundant information.

The observed differences between aperiodic and oscillatory activity point out several directions for future studies. On the one hand, aperiodic activity measured non-invasively with EEG and MEG has been linked to general brain-states such as sleep (Wen and Liu, 2016b), anesthesia (Colombo et al., 2019; Purdon et al., 2015; Zhang et al., 2018), meditation (Braboszcz et al., 2017), use of drugs (Muthukumaraswamy et al., 2013; Muthukumaraswamy and Liley, 2018), and aging (Waschke et al., 2017). On the other hand, oscillatory activity has been related to transient, task-dependent cognitive functions. Thus, decomposing broad-band population signals such as MEG into oscillatory and aperiodic components may allow to discount state-dependent variability of the aperiodic components, which may enhance the sensitivity and specificity of oscillatory analyses.

Furthermore, and independent of this approach, it remains to be determined how the similarities and differences between correlations of aperiodic and oscillatory activity reported here, generalize from the resting state to specific task contexts.

Correlations of neuronal oscillations have been used as biomarkers for various neuropsychiatric diseases (Hawellek et al., 2013; Hong et al., 2019; Kim et al., 2014; Nugent et al., 2015; Uhlhaas et al., 2008; Voytek and Knight, 2015). Given that aperiodic correlation patterns are non-redundant and more reliable compared to oscillatory correlation patterns, correlations of aperiodic activity may allow to further improve these biomarkers.

Relationship between aperiodic activity and alpha oscillations

As highlighted above, throughout our analyses, we noted close links between oscillatory and aperiodic activity in the alpha band. Several factors may explain these links. First, IRASA may not entirely separate oscillatory and aperiodic components which may drive correlations between both components. Second, the aperiodic part of the M/EEG spectrum may at least partially reflect the damped nature of alpha oscillators, which may cause correlations between alpha-band power and reconstructed aperiodic activity (Muthukumaraswamy and Liley, 2018). Third, spectral leakage of alpha oscillations into neighboring frequencies may result in correlations of oscillatory and aperiodic components.

Summary and conclusions

In summary, we found that aperiodic population activity shows robust and well-structured cortical correlation patterns. Thus, correlations of aperiodic activity may serve as robust markers of cortical network interactions. The correlation structure of aperiodic activity was similar but distinct from the correlation structure of oscillatory activity. This may reflect at least partly distinct neuronal mechanisms reflected by oscillatory and aperiodic neuronal population activity.

Data availability

The HCP data are available for download from https://www.humanconnectome.org/study/hcp-young-adult/document/900-subjects-data-release.

CRediT authorship contribution statement

Andrea Ibarra Chaoul: Conceptualization, Methodology, Formal analysis, Writing – original draft, Writing – review & editing. Markus Siegel: Conceptualization, Methodology, Formal analysis, Writing – original draft, Writing – review & editing, Funding acquisition, Resources, Supervision.