Connectome spectral analysis to track EEG task dynamics on a subsecond scale

Connectome spectrum electromagnetic tomography: A method to reconstruct electrical brain source networks at high-spatial resolution

Connectome spectrum electromagnetic tomography (CSET) combines diffusion MRI-derived structural connectivity data with well-established graph signal processing tools to solve the M/EEG inverse problem. Using simulated EEG signals from fMRI responses, and two EEG datasets on visual-evoked potentials, we provide evidence supporting that (i) CSET captures realistic neurophysiological patterns with better accuracy than state-of-the-art methods, (ii) CSET can reconstruct brain responses more accurately and with more robustness to intrinsic noise in the EEG signal. These results demonstrate that CSET offers high spatio-temporal accuracy, enabling neuroscientists to extend their research beyond the current limitations of low sampling frequency in functional MRI and the poor spatial resolution of M/EEG.

Decomposing cortical activity through neuronal tracing connectome-eigenmodes in marmosets

Deciphering the complex relationship between neuroanatomical connections and functional activity in primate brains remains a daunting task, especially regarding the influence of monosynaptic connectivity on cortical activity. Here, we investigate the anatomical-functional relationship and decompose the neuronal-tracing connectome of marmoset brains into a series of eigenmodes using graph signal processing. These cellular connectome eigenmodes effectively constrain the cortical activity derived from resting-state functional MRI, and uncover a patterned cellular-functional decoupling. This pattern reveals a spatial gradient from coupled dorsal-posterior to decoupled ventral-anterior cortices, and recapitulates micro-structural profiles and macro-scale hierarchical cortical organization. Notably, these marmoset-derived eigenmodes may facilitate the inference of spontaneous cortical activity and functional connectivity of homologous areas in humans, highlighting the potential generalizing of the connectomic constraints across species. Collectively, our findings illuminate how neuronal-tracing connectome eigenmodes constrain cortical activity and improve our understanding of the brain's anatomical-functional relationship.

The coupling between the spatial and temporal scales of neural processes revealed by a joint time-vertex connectome spectral analysis

Brain oscillations are produced by the coordinated activity of large groups of neurons and different rhythms are thought to reflect different modes of information processing. These modes, in turn, are known to occur at different spatial scales. Nevertheless, how these rhythms support different spatial modes of information processing at the brain scale is not yet fully understood. Here we use "Joint Time-Vertex Spectral Analysis" to characterize the joint spectral content of brain activity both in time (temporal frequencies) and in space over the connectivity graph (spatial connectome harmonics). This method allows us to characterize the relationship between spatially localized or distributed neural processes on one side and their respective temporal frequency bands in source-reconstructed M/EEG signals. We explore this approach on two different datasets, an auditory steady-state response (ASSR) and a visual grating task. Our results suggest that different information processing mechanisms are carried out at different frequency bands: while spatially distributed activity (which may also be interpreted as integration) specifically occurs at low temporal frequencies (alpha and theta) and low graph spatial frequencies, localized electrical activity (i.e., segregation) is observed at high temporal frequencies (high and low gamma) over restricted high spatial graph frequencies. Crucially, the estimated contribution of the distributed and localized neural activity predicts performance in a behavioral task, demonstrating the neurophysiological relevance of the joint time-vertex spectral representation.

Structure-function coupling increases during interictal spikes in temporal lobe epilepsy: A graph signal processing study

OBJECTIVE

Structure-function coupling remains largely unknown in brain disorders. We studied this coupling during interictal epileptic discharges (IEDs), using graph signal processing in temporal lobe epilepsy (TLE).

METHODS

We decomposed IEDs of 17 patients on spatial maps, i.e. network harmonics, extracted from a structural connectome. Harmonics were split in smooth maps (long-range interactions reflecting integration) and coarse maps (short-range interactions reflecting segregation) and were used to reconstruct the part of the signal coupled (Xc) and decoupled (Xd) from the structure, respectively. We analysed how Xc and Xd embed the IED energy over time, at global and regional level.

RESULTS

For Xc, the energy was smaller than for Xd before the IED onset (p < .001), but became larger around the first IED peak (p < .05, cluster 2, C2). Locally, the ipsilateral mesial regions were significantly coupled to the structure over the whole epoch. The ipsilateral hippocampus increased its coupling during C2 (p < .01).

CONCLUSIONS

At whole-brain level, segregation gives way to integrative processes during the IED. Locally, brain regions commonly involved in the TLE epileptogenic network increase their reliance on long-range couplings during IED (C2).

SIGNIFICANCE

In TLE, integration mechanisms prevail during the IED and are localized in the ipsilateral mesial temporal regions.

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.

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.

Mixtures of large-scale dynamic functional brain network modes

Accurate temporal modelling of functional brain networks is essential in the quest for understanding how such networks facilitate cognition. Researchers are beginning to adopt time-varying analyses for electrophysiological data that capture highly dynamic processes on the order of milliseconds. Typically, these approaches, such as clustering of functional connectivity profiles and Hidden Markov Modelling (HMM), assume mutual exclusivity of networks over time. Whilst a powerful constraint, this assumption may be compromising the ability of these approaches to describe the data effectively. Here, we propose a new generative model for functional connectivity as a time-varying linear mixture of spatially distributed statistical "modes". The temporal evolution of this mixture is governed by a recurrent neural network, which enables the model to generate data with a rich temporal structure. We use a Bayesian framework known as amortised variational inference to learn model parameters from observed data. We call the approach DyNeMo (for Dynamic Network Modes), and show using simulations it outperforms the HMM when the assumption of mutual exclusivity is violated. In resting-state MEG, DyNeMo reveals a mixture of modes that activate on fast time scales of 100-150 ms, which is similar to state lifetimes found using an HMM. In task MEG data, DyNeMo finds modes with plausible, task-dependent evoked responses without any knowledge of the task timings. Overall, DyNeMo provides decompositions that are an approximate remapping of the HMM's while showing improvements in overall explanatory power. However, the magnitude of the improvements suggests that the HMM's assumption of mutual exclusivity can be reasonable in practice. Nonetheless, DyNeMo provides a flexible framework for implementing and assessing future modelling developments.

High-density EEG sleep correlates of cognitive and affective impairment at 12-month follow-up after COVID-19

Objective

To disentangle the pathophysiology of cognitive/affective impairment in Coronavirus Disease-2019 (COVID-19), we studied long-term cognitive and affective sequelae and sleep high-density electroencephalography (EEG) at 12-month follow-up in people with a previous hospital admission for acute COVID-19.

Methods

People discharged from an intensive care unit (ICU) and a sub-intensive ward (nonICU) between March and May 2020 were contacted between March and June 2021. Participants underwent cognitive, psychological, and sleep assessment. High-density EEG recording was acquired during a nap. Slow and fast spindles density/amplitude/frequency and source reconstruction in brain gray matter were extracted. The relationship between psychological and cognitive findings was explored with Pearson correlation.

Results

We enrolled 33 participants ( 17 nonICU) and 12 controls. We observed a lower Physical Quality of Life index, higher post-traumatic stress disorder (PTSD) score, and a worse executive function performance in nonICU participants. Higher PTSD and Beck Depression Inventory scores correlated with lower executive performance. The same group showed a reorganization of spindle cortical generators.

Conclusions

Our results show executive and psycho-affective deficits and spindle alterations in COVID-19 survivors – especially in nonICU participants – after 12 months from discharge.

Significance

These findings may be suggestive of a crucial contribution of stress experienced during hospital admission on long-term cognitive functioning.

Predicting time-resolved electrophysiological brain networks from structural eigenmodes

How temporal modulations in functional interactions are shaped by the underlying anatomical connections remains an open question. Here, we analyse the role of structural eigenmodes, in the formation and dissolution of temporally evolving functional brain networks using resting-state magnetoencephalography and diffusion magnetic resonance imaging data at the individual subject level. Our results show that even at short timescales, phase and amplitude connectivity can partly be expressed by structural eigenmodes, but hardly by direct structural connections. Albeit a stronger relationship was found between structural eigenmodes and time-resolved amplitude connectivity. Time-resolved connectivity for both phase and amplitude was mostly characterised by a stationary process, superimposed with very brief periods that showed deviations from this stationary process. For these brief periods, dynamic network states were extracted that showed different expressions of eigenmodes. Furthermore, the eigenmode expression was related to overall cognitive performance and co-occurred with fluctuations in community structure of functional networks. These results implicate that ongoing time-resolved resting-state networks, even at short timescales, can to some extent be understood in terms of activation and deactivation of structural eigenmodes and that these eigenmodes play a role in the dynamic integration and segregation of information across the cortex, subserving cognitive functions.

Source imaging of high-density visual evoked potentials with multi-scale brain parcellations and connectomes

We describe the multimodal neuroimaging dataset VEPCON (OpenNeuro Dataset ds003505). It includes raw data and derivatives of high-density EEG, structural MRI, diffusion weighted images (DWI) and single-trial behavior (accuracy, reaction time). Visual evoked potentials (VEPs) were recorded while participants (n = 20) discriminated briefly presented faces from scrambled faces, or coherently moving stimuli from incoherent ones. EEG and MRI were recorded separately from the same participants. The dataset contains raw EEG and behavioral data, pre-processed EEG of single trials in each condition, structural MRIs, individual brain parcellations at 5 spatial resolutions (83 to 1015 regions), and the corresponding structural connectomes computed from fiber count, fiber density, average fractional anisotropy and mean diffusivity maps. For source imaging, VEPCON provides EEG inverse solutions based on individual anatomy, with Python and Matlab scripts to derive activity time-series in each brain region, for each parcellation level. The BIDS-compatible dataset can contribute to multimodal methods development, studying structure-function relations, and to unimodal optimization of source imaging and graph analyses, among many other possibilities.

Spectral graph theory of brain oscillations - revisited and improved

Mathematical modeling of the relationship between the functional activity and the structural wiring of the brain has largely been undertaken using non-linear and biophysically detailed mathematical models with regionally varying parameters. While this approach provides us a rich repertoire of multistable dynamics that can be displayed by the brain, it is computationally demanding. Moreover, although neuronal dynamics at the microscopic level are nonlinear and chaotic, it is unclear if such detailed nonlinear models are required to capture the emergent meso-(regional population ensemble) and macro-scale (whole brain) behavior, which is largely deterministic and reproducible across individuals. Indeed, recent modeling effort based on spectral graph theory has shown that an analytical model without regionally varying parameters and without multistable dynamics can capture the empirical magnetoencephalography frequency spectra and the spatial patterns of the alpha and beta frequency bands accurately.

In this work, we demonstrate an improved hierarchical, linearized, and analytic spectral graph theory-based model that can capture the frequency spectra obtained from magnetoencephalography recordings of resting healthy subjects. We reformulated the spectral graph theory model in line with classical neural mass models, therefore providing more biologically interpretable parameters, especially at the local scale. We demonstrated that this model performs better than the original model when comparing the spectral correlation of modeled frequency spectra and that obtained from the magnetoencephalography recordings. This model also performs equally well in predicting the spatial patterns of the empirical alpha and beta frequency bands.

The connectome spectrum as a canonical basis for a sparse representation of fast brain activity

The functional organization of neural processes is constrained by the brain's intrinsic structural connectivity, i.e., the connectome. Here, we explore how structural connectivity can improve the representation of brain activity signals and their dynamics. Using a multi-modal imaging dataset (electroencephalography, structural MRI, and diffusion MRI), we represent electrical brain activity at the cortical surface as a time-varying composition of harmonic modes of structural connectivity. These harmonic modes are known as connectome harmonics. Here we describe brain activity signal as a time-varying combination of connectome harmonics. We term this description as the connectome spectrum of the signal. We found that: first, the brain activity signal is represented more compactly by the connectome spectrum than by the traditional area-based representation; second, the connectome spectrum characterizes fast brain dynamics in terms of signal broadcasting profile, revealing different temporal regimes of integration and segregation that are consistent across participants. And last, the connectome spectrum characterizes fast brain dynamics with fewer degrees of freedom than area-based signal representations. Specifically, we show that a smaller number of dimensions capture the differences between low-level and high-level visual processing in the connectome spectrum. Also, we demonstrate that connectome harmonics capture more sensitively the topological properties of brain activity. In summary, this work provides statistical, functional, and topological evidence indicating that the description of brain activity in terms of structural connectivity fosters a more comprehensive understanding of large-scale dynamic neural functioning.

Functional harmonics reveal multi-dimensional basis functions underlying cortical organization

The human brain consists of specialized areas that flexibly interact to form a multitude of functional networks. Complementary to this notion of modular organization, brain function has been shown to vary along a smooth continuum across the whole cortex. We demonstrate a mathematical framework that accounts for both of these perspectives: harmonic modes. We calculate the harmonic modes of the brain's functional connectivity graph, called "functional harmonics," revealing a multi-dimensional, frequency-ordered set of basis functions. Functional harmonics link characteristics of cortical organization across several spatial scales, capturing aspects of intra-areal organizational features (retinotopy, somatotopy), delineating brain areas, and explaining macroscopic functional networks as well as global cortical gradients. Furthermore, we show how the activity patterns elicited by seven different tasks are reconstructed from a very small subset of functional harmonics. Our results suggest that the principle of harmonicity, ubiquitous in nature, also underlies functional cortical organization in the human brain.

Gradients of connectivity as graph Fourier bases of brain activity

The application of graph theory to model the complex structure and function of the brain has shed new light on its organization, prompting the emergence of network neuroscience. Despite the tremendous progress that has been achieved in this field, still relatively few methods exploit the topology of brain networks to analyze brain activity. Recent attempts in this direction have leveraged on the one hand graph spectral analysis (to decompose brain connectivity into eigenmodes or gradients) and the other graph signal processing (to decompose brain activity "coupled to" an underlying network in graph Fourier modes). These studies have used a variety of imaging techniques (e.g., fMRI, electroencephalography, diffusion-weighted and myelin-sensitive imaging) and connectivity estimators to model brain networks. Results are promising in terms of interpretability and functional relevance, but methodologies and terminology are variable. The goals of this paper are twofold. First, we summarize recent contributions related to connectivity gradients and graph signal processing, and attempt a clarification of the terminology and methods used in the field, while pointing out current methodological limitations. Second, we discuss the perspective that the functional relevance of connectivity gradients could be fruitfully exploited by considering them as graph Fourier bases of brain activity.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

The thermodynamics of cognition: A mathematical treatment

There is a general expectation that the laws of classical physics must apply to biology, particularly the neural system. The evoked cycle represents the brain's energy/information exchange with the physical environment through stimulus. Therefore, the thermodynamics of emotions might elucidate the neurological origin of intellectual evolution, and explain the psychological and health consequences of positive and negative emotional states based on their energy profiles. We utilized the Carnot cycle and Landauer's principle to analyze the energetic consequences of the brain's resting and evoked states during and after various cognitive states. Namely, positive emotional states can be represented by the reversed Carnot cycle, whereas negative emotional reactions trigger the Carnot cycle. The two conditions have contrasting energetic and entropic aftereffects with consequences for mental energy. The mathematics of the Carnot and reversed Carnot cycles, which can explain recent findings in human psychology, might be constructive in the scientific endeavor in turning psychology into hard science.

Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed "connectome harmonics", have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.