Spectral graph theory of brain oscillations - revisited and improved

Structure-function coupling in macroscale human brain networks

Precisely how the anatomical structure of the brain gives rise to a repertoire of complex functions remains incompletely understood. A promising manifestation of this mapping from structure to function is the dependency of the functional activity of a brain region on the underlying white matter architecture. Here, we review the literature examining the macroscale coupling between structural and functional connectivity, and we establish how this structure-function coupling (SFC) can provide more information about the underlying workings of the brain than either feature alone. We begin by defining SFC and describing the computational methods used to quantify it. We then review empirical studies that examine the heterogeneous expression of SFC across different brain regions, among individuals, in the context of the cognitive task being performed, and over time, as well as its role in fostering flexible cognition. Last, we investigate how the coupling between structure and function is affected in neurological and psychiatric conditions, and we report how aberrant SFC is associated with disease duration and disease-specific cognitive impairment. By elucidating how the dynamic relationship between the structure and function of the brain is altered in the presence of neurological and psychiatric conditions, we aim to not only further our understanding of their aetiology but also establish SFC as a new and sensitive marker of disease symptomatology and cognitive performance. Overall, this Review collates the current knowledge regarding the regional interdependency between the macroscale structure and function of the human brain in both neurotypical and neuroatypical individuals.

Integrative, segregative, and degenerate harmonics of the structural connectome

Unifying integration and segregation in the brain has been a fundamental puzzle in neuroscience ever since the conception of the "binding problem." Here, we introduce a framework that places integration and segregation within a continuum based on a fundamental property of the brain-its structural connectivity graph Laplacian harmonics and a new feature we term the gap-spectrum. This framework organizes harmonics into three regimes-integrative, segregative, and degenerate-that together account for various group-level properties. Integrative and segregative harmonics occupy the ends of the continuum, and they share properties such as reproducibility across individuals, stability to perturbation, and involve "bottom-up" sensory networks. Degenerate harmonics are in the middle of the continuum, and they are subject-specific, flexible, and involve "top-down" networks. The proposed framework accommodates inter-subject variation, sensitivity to changes, and structure-function coupling in ways that offer promising avenues for studying cognition and consciousness in the brain.

Spectral graph model for fMRI: a biophysical, connectivity-based generative model for the analysis of frequency-resolved resting state fMRI

Resting state functional MRI (rs-fMRI) is a popular and widely used technique to explore the brain's functional organization and to examine if it is altered in neurological or mental disorders. The most common approach for its analysis targets the measurement of the synchronized fluctuations between brain regions, characterized as functional connectivity (FC), typically relying on pairwise correlations in activity across different brain regions. While hugely successful in exploring state- and disease-dependent network alterations, these statistical graph theory tools suffer from two key limitations. First, they discard useful information about the rich frequency content of the fMRI signal. The rich spectral information now achievable from advances in fast multiband acquisitions is consequently being under-utilized. Second, the analyzed FCs are phenomenological without a direct neurobiological underpinning in the underlying structures and processes in the brain. There does not currently exist a complete generative model framework for whole brain resting fMRI that is informed by its underlying biological basis in the structural connectome. Here we propose that a different approach can solve both challenges at once: the use of an appropriately realistic yet parsimonious biophysical signal generation model followed by graph spectral (i.e. eigen) decomposition. We call this model a Spectral Graph Model (SGM) for fMRI, using which we can not only quantify the structure-function relationship in individual subjects, but also condense the variable and individual-specific repertoire of fMRI signal's spectral and spatial features into a small number of biophysically-interpretable parameters. We expect this model-based inference of rs-fMRI that seamlessly integrates with structure can be used to examine state and trait characteristics of structure-function relations in a variety of brain disorders.

Impaired long-range excitatory time scale predicts abnormal neural oscillations and cognitive deficits in Alzheimer's disease

BACKGROUND

Alzheimer's disease (AD) is the most common form of dementia, progressively impairing cognitive abilities. While neuroimaging studies have revealed functional abnormalities in AD, how these relate to aberrant neuronal circuit mechanisms remains unclear. Using magnetoencephalography imaging we documented abnormal local neural synchrony patterns in patients with AD. To identify global abnormal biophysical mechanisms underlying the spatial and spectral electrophysiological patterns in AD, we estimated the parameters of a biophysical spectral graph model (SGM).

METHODS

SGM is an analytic neural mass model that describes how long-range fiber projections in the brain mediate the excitatory and inhibitory activity of local neuronal subpopulations. Unlike other coupled neuronal mass models, the SGM is linear, available in closed-form, and parameterized by a small set of biophysical interpretable global parameters. This facilitates their rapid and unambiguous inference which we performed here on a well-characterized clinical population of patients with AD (N = 88, age = 62.73 +/- 8.64 years) and a cohort of age-matched controls (N = 88, age = 65.07 +/- 9.92 years).

RESULTS

Patients with AD showed significantly elevated long-range excitatory neuronal time scales, local excitatory neuronal time scales and local inhibitory neural synaptic strength. The long-range excitatory time scale had a larger effect size, compared to local excitatory time scale and inhibitory synaptic strength and contributed highest for the accurate classification of patients with AD from controls. Furthermore, increased long-range time scale was associated with greater deficits in global cognition.

CONCLUSIONS

These results demonstrate that long-range excitatory time scale of neuronal activity, despite being a global measure, is a key determinant in the local spectral signatures and cognition in the human brain, and how it might be a parsimonious factor underlying altered neuronal activity in AD. Our findings provide new insights into mechanistic links between abnormal local spectral signatures and global connectivity measures in AD.

Selective vulnerability and resilience to Alzheimer's disease tauopathy as a function of genes and the connectome

Brain regions in Alzheimer's (AD) exhibit distinct vulnerability to the disease's hallmark pathology, with the entorhinal cortex and hippocampus succumbing early to tau tangles while others like primary sensory cortices remain resilient. The quest to understand how local/regional genetic factors, pathogenesis, and network-mediated spread of pathology together govern this selective vulnerability (SV) or resilience (SR) is ongoing. Although many risk genes in AD are known from gene association and transgenic studies, it is still not known whether and how their baseline expression signatures confer SV or SR to brain structures. Prior analyses have yielded conflicting results, pointing to a disconnect between the location of genetic risk factors and downstream tau pathology. We hypothesize that a full accounting of genes' role in mediating SV/SR would require the modeling of network-based vulnerability, whereby tau misfolds, aggregates, and propagates along fiber projections. We therefore employed an extended network diffusion model (eNDM) and tested it on tau pathology PET data from 196 AD patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Thus the fitted eNDM model becomes a reference process from which to assess the role of innate genetic factors. Using the residual (observed - model-predicted) tau as a novel target outcome, we obtained its association with 100 top AD risk-genes, whose baseline spatial transcriptional profiles were obtained from the Allen Human Brain Atlas (AHBA). We found that while many risk genes at baseline showed a strong association with regional tau, many more showed a stronger association with residual tau. This suggests that both direct vulnerability, related to the network, as well as network-independent vulnerability, are conferred by risk genes. We then classified risk genes into four classes: network-related SV (SV-NR), network-independent SV (SV-NI), network-related SR (SR-NR), and network-independent SR (SR-NI). Each class has a distinct spatial signature and associated vulnerability to tau. Remarkably, we found from gene-ontology analyses, that genes in these classes were enriched in distinct functional processes and encompassed different functional networks. These findings offer new insights into the factors governing innate vulnerability or resilience in AD pathophysiology and may prove helpful in identifying potential intervention targets.

Cortical Synchrony and Information Flow during Transition from Wakefulness to Light Non-Rapid Eye Movement Sleep

Sleep is a highly stereotyped phenomenon, requiring robust spatiotemporal coordination of neural activity. Understanding how the brain coordinates neural activity with sleep onset can provide insights into the physiological functions subserved by sleep and the pathologic phenomena associated with sleep onset. We quantified whole-brain network changes in synchrony and information flow during the transition from wakefulness to light non-rapid eye movement (NREM) sleep, using MEG imaging in a convenient sample of 14 healthy human participants (11 female; mean 63.4 years [SD 11.8 years]). We furthermore performed computational modeling to infer excitatory and inhibitory properties of local neural activity. The transition from wakefulness to light NREM was identified to be encoded in spatially and temporally specific patterns of long-range synchrony. Within the delta band, there was a global increase in connectivity from wakefulness to light NREM, which was highest in frontoparietal regions. Within the theta band, there was an increase in connectivity in fronto-parieto-occipital regions and a decrease in temporal regions from wakefulness to Stage 1 sleep. Patterns of information flow revealed that mesial frontal regions receive hierarchically organized inputs from broad cortical regions upon sleep onset, including direct inflow from occipital regions and indirect inflow via parieto-temporal regions within the delta frequency band. Finally, biophysical neural mass modeling demonstrated changes in the anterior-to-posterior distribution of cortical excitation-to-inhibition with increased excitation-to-inhibition model parameters in anterior regions in light NREM compared with wakefulness. Together, these findings uncover whole-brain corticocortical structure and the orchestration of local and long-range, frequency-specific cortical interactions in the sleep-wake transition.SIGNIFICANCE STATEMENT Our work uncovers spatiotemporal cortical structure of neural synchrony and information flow upon the transition from wakefulness to light non-rapid eye movement sleep. Mesial frontal regions were identified to receive hierarchically organized inputs from broad cortical regions, including both direct inputs from occipital regions and indirect inputs via the parieto-temporal regions within the delta frequency range. Biophysical neural mass modeling revealed a spatially heterogeneous, anterior-posterior distribution of cortical excitation-to-inhibition. Our findings shed light on the orchestration of local and long-range cortical neural structure that is fundamental to sleep onset, and support an emerging view of cortically driven regulation of sleep homeostasis.

Impaired long-range excitatory time scale predicts abnormal neural oscillations and cognitive deficits in Alzheimer's disease

Alzheimer's disease (AD) is the most common form of dementia, progressively impairing memory and cognition. While neuroimaging studies have revealed functional abnormalities in AD, how these relate to aberrant neuronal circuit mechanisms remains unclear. Using magnetoencephalography imaging we documented abnormal local neural synchrony patterns in patients with AD. To identify abnormal biophysical mechanisms underlying these abnormal electrophysiological patterns, we estimated the parameters of a spectral graph-theory model (SGM). SGM is an analytic model that describes how long-range fiber projections in the brain mediate the excitatory and inhibitory activity of local neuronal subpopulations. The long-range excitatory time scale was associated with greater deficits in global cognition and was able to distinguish AD patients from controls with high accuracy. These results demonstrate that long-range excitatory time scale of neuronal activity, despite being a global measure, is a key determinant in the spatiospectral signatures and cognition in AD.

Impaired long-range excitatory time scale predicts abnormal neural oscillations and cognitive deficits in Alzheimer's disease

Alzheimer's disease (AD) is the most common form of dementia, progressively impairing memory and cognition. While neuroimaging studies have revealed functional abnormalities in AD, how these relate to aberrant neuronal circuit mechanisms remains unclear. Using magnetoencephalography imaging we documented abnormal local neural synchrony patterns in patients with AD. To identify abnormal biophysical mechanisms underlying these abnormal electrophysiological patterns, we estimated the parameters of a spectral graph-theory model (SGM). SGM is an analytic model that describes how long-range fiber projections in the brain mediate the excitatory and inhibitory activity of local neuronal subpopulations. The long-range excitatory time scale was associated with greater deficits in global cognition and was able to distinguish AD patients from controls with high accuracy. These results demonstrate that long-range excitatory time scale of neuronal activity, despite being a global measure, is a key determinant in the spatiospectral signatures and cognition in AD.

Enhanced brain structure-function tethering in transmodal cortex revealed by high-frequency eigenmodes

While the link between brain structure and function remains an ongoing challenge, the prevailing hypothesis is that the structure-function relationship may itself be gradually decoupling from unimodal to transmodal cortex. However, this hypothesis is constrained by the underlying models which may neglect requisite information. Here we relate structural and functional connectivity derived from diffusion and functional MRI through orthogonal eigenmodes governing frequency-specific diffusion patterns. We find that low-frequency eigenmodes contribute little to functional interactions in transmodal cortex, resulting in divergent structure-function relationships. Conversely, high-frequency eigenmodes predominantly support neuronal coactivation patterns in these areas, inducing structure-function convergence along a unimodal-transmodal hierarchy. High-frequency information, although weak and scattered, could enhance the structure-function tethering, especially in transmodal association cortices. Our findings suggest that the structure-function decoupling may not be an intrinsic property of brain organization, but can be narrowed through multiplexed and regionally specialized spatiotemporal propagation regimes.

Bayesian inference of a spectral graph model for brain oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which cannot be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Comparing individual and group-level simulated neurophysiological brain connectivity using the Jansen and Rit neural mass model

Computational models are often used to assess how functional connectivity (FC) patterns emerge from neuronal population dynamics and anatomical brain connections. It remains unclear whether the commonly used group-averaged data can predict individual FC patterns. The Jansen and Rit neural mass model was employed, where masses were coupled using individual structural connectivity (SC). Simulated FC was correlated to individual magnetoencephalography-derived empirical FC. FC was estimated using phase-based (phase lag index (PLI), phase locking value (PLV)), and amplitude-based (amplitude envelope correlation (AEC)) metrics to analyze their goodness of fit for individual predictions. Individual FC predictions were compared against group-averaged FC predictions, and we tested whether SC of a different participant could equally well predict participants' FC patterns. The AEC provided a better match between individually simulated and empirical FC than phase-based metrics. Correlations between simulated and empirical FC were higher using individual SC compared to group-averaged SC. Using SC from other participants resulted in similar correlations between simulated and empirical FC compared to using participants' own SC. This work underlines the added value of FC simulations using individual instead of group-averaged SC for this particular computational model and could aid in a better understanding of mechanisms underlying individual functional network trajectories.

Variation in functional networks between clinical and subclinical discharges in childhood absence epilepsy: A multi-frequency MEG study

OBJECTIVE

Two types of spike-and-wave discharges (SWDs) exist in childhood absence epilepsy (CAE): clinical discharges are prolonged and manifest primarily as impaired consciousness, whereas subclinical discharges are brief with few objectively visible symptoms. This study aimed to compare neural functional network and default mode network (DMN) activity between clinical and subclinical discharges to better understand the underlying mechanism of CAE.

METHODS

Using magnetoencephalography (MEG) data from 21 patients, we obtained 25 segments each of clinical discharges and subclinical discharges. Amplitude envelope correlation analysis was used to construct functional networks and graph theory was used to calculate network topological data. We then compared differences in functional connectivity within the DMN between clinical and subclinical discharges. All statistical comparisons were performed using paired-sample tests.

RESULTS

Compared to subclinical discharges, the functional network of clinical discharges exhibited higher synchronization - particularly in the parahippocampal gyrus - as early as 10 s before the seizure. Additionally, the functional network of clinical SWDs presented an anterior shift of key nodes in the alpha frequency band. Regarding clinical discharge progression, there were gradual increases in the parameter node strengths (S), clustering coefficients (C), and global efficiency (E) of the functional networks, while the path lengths (L) decreased. These changes were most prominent at the onset of discharges and followed by some recovery in the high-frequency bands, but no significant change in the low-frequency bands. Furthermore, connections within the DMN during the discharge period were significantly stronger for clinical discharge compared to subclinical discharges.

CONCLUSIONS

These findings suggest that a more regular network before abnormal discharges in clinical discharges contributes to SWD explosion and that the parahippocampal gyrus plays an important role in maintaining oscillations. An absence seizure is a gradual process and the emergence of SWDs may be accompanied by initiation of inhibitory mechanisms. Enhanced functional connectivity among DMN brain regions may indicate that patients have entered a state of introspection, and functional abnormalities in the parahippocampal gyrus may be associated with patients' transient memory loss.

Multi-modal and multi-model interrogation of large-scale functional brain networks

Existing whole-brain models are generally tailored to the modelling of a particular data modality (e.g., fMRI or MEG/EEG). We propose that despite the differing aspects of neural activity each modality captures, they originate from shared network dynamics. Building on the universal principles of self-organising delay-coupled nonlinear systems, we aim to link distinct features of brain activity - captured across modalities - to the dynamics unfolding on a macroscopic structural connectome. To jointly predict connectivity, spatiotemporal and transient features of distinct signal modalities, we consider two large-scale models - the Stuart Landau and Wilson and Cowan models - which generate short-lived 40 Hz oscillations with varying levels of realism. To this end, we measure features of functional connectivity and metastable oscillatory modes (MOMs) in fMRI and MEG signals - and compare them against simulated data. We show that both models can represent MEG functional connectivity (FC), functional connectivity dynamics (FCD) and generate MOMs to a comparable degree. This is achieved by adjusting the global coupling and mean conduction time delay and, in the WC model, through the inclusion of balance between excitation and inhibition. For both models, the omission of delays dramatically decreased the performance. For fMRI, the SL model performed worse for FCD and MOMs, highlighting the importance of balanced dynamics for the emergence of spatiotemporal and transient patterns of ultra-slow dynamics. Notably, optimal working points varied across modalities and no model was able to achieve a correlation with empirical FC higher than 0.4 across modalities for the same set of parameters. Nonetheless, both displayed the emergence of FC patterns that extended beyond the constraints of the anatomical structure. Finally, we show that both models can generate MOMs with empirical-like properties such as size (number of brain regions engaging in a mode) and duration (continuous time interval during which a mode appears). Our results demonstrate the emergence of static and dynamic properties of neural activity at different timescales from networks of delay-coupled oscillators at 40 Hz. Given the higher dependence of simulated FC on the underlying structural connectivity, we suggest that mesoscale heterogeneities in neural circuitry may be critical for the emergence of parallel cross-modal functional networks and should be accounted for in future modelling endeavours.

A joint subspace mapping between structural and functional brain connectomes

Understanding the connection between the brain's structural connectivity and its functional connectivity is of immense interest in computational neuroscience. Although some studies have suggested that whole brain functional connectivity is shaped by the underlying structure, the rule by which anatomy constraints brain dynamics remains an open question. In this work, we introduce a computational framework that identifies a joint subspace of eigenmodes for both functional and structural connectomes. We found that a small number of those eigenmodes are sufficient to reconstruct functional connectivity from the structural connectome, thus serving as low-dimensional basis function set. We then develop an algorithm that can estimate the functional eigen spectrum in this joint space from the structural eigen spectrum. By concurrently estimating the joint eigenmodes and the functional eigen spectrum, we can reconstruct a given subject's functional connectivity from their structural connectome. We perform elaborate experiments and demonstrate that the proposed algorithm for estimating functional connectivity from the structural connectome using joint space eigenmodes gives competitive performance as compared to the existing benchmark methods with better interpretability.

Bayesian Inference of a Spectral Graph Model for Brain Oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which can not be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Distributed harmonic patterns of structure-function dependence orchestrate human consciousness

A central question in neuroscience is how consciousness arises from the dynamic interplay of brain structure and function. Here we decompose functional MRI signals from pathological and pharmacologically-induced perturbations of consciousness into distributed patterns of structure-function dependence across scales: the harmonic modes of the human structural connectome. We show that structure-function coupling is a generalisable indicator of consciousness that is under bi-directional neuromodulatory control. We find increased structure-function coupling across scales during loss of consciousness, whether due to anaesthesia or brain injury, capable of discriminating between behaviourally indistinguishable sub-categories of brain-injured patients, tracking the presence of covert consciousness. The opposite harmonic signature characterises the altered state induced by LSD or ketamine, reflecting psychedelic-induced decoupling of brain function from structure and correlating with physiological and subjective scores. Overall, connectome harmonic decomposition reveals how neuromodulation and the network architecture of the human connectome jointly shape consciousness and distributed functional activation across scales.

Structure-function models of temporal, spatial, and spectral characteristics of non-invasive whole brain functional imaging

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.

Altered excitatory and inhibitory neuronal subpopulation parameters are distinctly associated with tau and amyloid in Alzheimer's disease

Background

Neuronal- and circuit-level abnormalities of excitation and inhibition are shown to be associated with tau and amyloid-beta (Aβ) in preclinical models of Alzheimer's disease (AD). These relationships remain poorly understood in patients with AD.

Methods

Using empirical spectra from magnetoencephalography and computational modeling (neural mass model), we examined excitatory and inhibitory parameters of neuronal subpopulations and investigated their specific associations to regional tau and Aβ, measured by positron emission tomography, in patients with AD.

Results

Patients with AD showed abnormal excitatory and inhibitory time-constants and neural gains compared to age-matched controls. Increased excitatory time-constants distinctly correlated with higher tau depositions while increased inhibitory time-constants distinctly correlated with higher Aβ depositions.

Conclusions

Our results provide critical insights about potential mechanistic links between abnormal neural oscillations and cellular correlates of impaired excitatory and inhibitory synaptic functions associated with tau and Aβ in patients with AD.

Funding

This study was supported by the National Institutes of Health grants: K08AG058749 (KGR), F32AG050434-01A1 (KGR), K23 AG038357 (KAV), P50 AG023501, P01 AG19724 (BLM), P50-AG023501 (BLM and GDR), R01 AG045611 (GDR); AG034570, AG062542 (WJ); NS100440 (SSN), DC176960 (SSN), DC017091 (SSN), AG062196 (SSN); a grant from John Douglas French Alzheimer's Foundation (KAV); grants from Larry L. Hillblom Foundation: 2015-A-034-FEL (KGR), 2019-A-013-SUP (KGR); grants from the Alzheimer's Association: AARG-21-849773 (KGR); PCTRB-13-288476 (KAV), and made possible by Part the CloudTM (ETAC-09-133596); a grant from Tau Consortium (GDR and WJJ), and a gift from the S. D. Bechtel Jr. Foundation.

Alpha blocking and 1/fβ spectral scaling in resting EEG can be accounted for by a sum of damped alpha band oscillatory processes

The dynamical and physiological basis of alpha band activity and 1/f^β noise in the EEG are the subject of continued speculation. Here we conjecture, on the basis of empirical data analysis, that both of these features may be economically accounted for through a single process if the resting EEG is conceived of being the sum of multiple stochastically perturbed alpha band damped linear oscillators with a distribution of dampings (relaxation rates). The modulation of alpha-band and 1/f^β noise activity by changes in damping is explored in eyes closed (EC) and eyes open (EO) resting state EEG. We aim to estimate the distribution of dampings by solving an inverse problem applied to EEG power spectra. The characteristics of the damping distribution are examined across subjects, sensors and recording condition (EC/EO). We find that there are robust changes in the damping distribution between EC and EO recording conditions across participants. The estimated damping distributions are found to be predominantly bimodal, with the number and position of the modes related to the sharpness of the alpha resonance and the scaling (β) of the power spectrum (1/f^β). The results suggest that there exists an intimate relationship between resting state alpha activity and 1/f^β noise with changes in both governed by changes to the damping of the underlying alpha oscillatory processes. In particular, alpha-blocking is observed to be the result of the most weakly damped distribution mode becoming more heavily damped. The results suggest a novel way of characterizing resting EEG power spectra and provides new insight into the central role that damped alpha-band activity may play in characterising the spatio-temporal features of resting state EEG.

The resting human electroencephalogram (EEG) exhibits two dominant spectral features: the alpha rhythm (8–13 Hz) and its associated attenuation between eyes-closed and eyes-open resting state (alpha blocking), and the 1/f^β scaling of the power spectrum. While these phenomena are well studied a thorough understanding of their respective generative processes remains elusive. By employing a theoretical approach that follows from neural population models of EEG we demonstrate that it is possible to economically account for both of these phenomena using a singular mechanistic framework: resting EEG is assumed to arise from the summed activity of multiple uncorrelated, stochastically driven, damped alpha band linear oscillatory processes having a distribution of relaxation rates or dampings. By numerically estimating these damping distributions from eyes-closed and eyes-open EEG data, in a total of 136 participants, it is found that such damping distributions are predominantly bimodal in shape. The most weakly damped mode is found to account for alpha band power, with alpha blocking being driven by an increase in the damping of this weakly damped mode, whereas the second, and more heavily damped mode, is able to explain 1/f^β scaling present in the resting state EEG spectra.