Higher-order functional connectivity analysis of resting-state functional magnetic resonance imaging data using multivariate cumulants.

Blood-level oxygenation-dependent (BOLD) functional magnetic resonance imaging (fMRI) is the most common modality to study functional connectivity in the human brain. Most research to date has focused on connectivity between pairs of brain regions. However, attention has recently turned towards connectivity involving more than two regions, that is, higher-order connectivity. It is not yet clear how higher-order connectivity can best be quantified. The measures that are currently in use cannot distinguish between pairwise (i.e., second-order) and higher-order connectivity. We show that genuine higher-order connectivity can be quantified by using multivariate cumulants. We explore the use of multivariate cumulants for quantifying higher-order connectivity and the performance of block bootstrapping for statistical inference. In particular, we formulate a generative model for fMRI signals exhibiting higher-order connectivity and use it to assess bias, standard errors, and detection probabilities. Application to resting-state fMRI data from the Human Connectome Project demonstrates that spontaneous fMRI signals are organized into higher-order networks that are distinct from second-order resting-state networks. Application to a clinical cohort of patients with multiple sclerosis further demonstrates that cumulants can be used to classify disease groups and explain behavioral variability. Hence, we present a novel framework to reliably estimate genuine higher-order connectivity in fMRI data which can be used for constructing hyperedges, and finally, which can readily be applied to fMRI data from populations with neuropsychiatric disease or cognitive neuroscientific experiments.

Characterization of Second-Order Mixing Effects in Reconstructed Cross-Spectra of Random Neural Fields.

Functional connectivity in electroencephalography (EEG) and magnetoencephalography (MEG) data is commonly assessed by using measures that are insensitive to instantaneously interacting sources and as such would not give rise to false positive interactions caused by instantaneous mixing of true source signals (first-order mixing). Recent studies, however, have drawn attention to the fact that such measures are still susceptible to instantaneous mixing from lagged sources (i.e. second-order mixing) and that this can lead to a large number of false positive interactions. In this study we relate first- and second-order mixing effects on the cross-spectra of reconstructed source activity to the properties of the resolution operators that are used for the reconstruction. We derive two identities that relate first- and second-order mixing effects to the transformation properties of measurement and source configurations and exploit them to establish several basic properties of signal mixing. First, we provide a characterization of the configurations that are maximally and minimally sensitive to second-order mixing. It turns out that second-order mixing effects are maximal when the measurement locations are far apart and the sources coincide with the measurement locations. Second, we provide a description of second-order mixing effects in the vicinity of the measurement locations in terms of the local geometry of the point-spread functions of the resolution operator. Third, we derive a version of Lagrange's identity for cross-talk functions that establishes the existence of a trade-off between the magnitude of first- and second-order mixing effects. It also shows that, whereas the magnitude of first-order mixing is determined by the inner product of cross-talk functions, the magnitude of second-order mixing is determined by a generalized cross-product of cross-talk functions (the wedge product) which leads to an intuitive geometric understanding of the trade-off. All results are derived within the general framework of random neural fields on cortical manifolds.

Non-reversibility outperforms functional connectivity in characterisation of brain states in MEG data.

Characterising brain states during tasks is common practice for many neuroscientific experiments using electrophysiological modalities such as electroencephalography (EEG) and magnetoencephalography (MEG). Brain states are often described in terms of oscillatory power and correlated brain activity, i.e. functional connectivity. It is, however, not unusual to observe weak task induced functional connectivity alterations in the presence of strong task induced power modulations using classical time-frequency representation of the data. Here, we propose that non-reversibility, or the temporal asymmetry in functional interactions, may be more sensitive to characterise task induced brain states than functional connectivity. As a second step, we explore causal mechanisms of non-reversibility in MEG data using whole brain computational models. We include working memory, motor, language tasks and resting-state data from participants of the Human Connectome Project (HCP). Non-reversibility is derived from the lagged amplitude envelope correlation (LAEC), and is based on asymmetry of the forward and reversed cross-correlations of the amplitude envelopes. Using random forests, we find that non-reversibility outperforms functional connectivity in the identification of task induced brain states. Non-reversibility shows especially better sensitivity to capture bottom-up gamma induced brain states across all tasks, but also alpha band associated brain states. Using whole brain computational models we find that asymmetry in the effective connectivity and axonal conduction delays play a major role in shaping non-reversibility across the brain. Our work paves the way for better sensitivity in characterising brain states during both bottom-up as well as top-down modulation in future neuroscientific experiments.

Dissociation between phase and power correlation networks in the human brain is driven by co-occurrent bursts.

Well-known haemodynamic resting-state networks are better mirrored in power correlation networks than phase coupling networks in electrophysiological data. However, what do these power correlation networks reflect? We address this long-outstanding question in neuroscience using rigorous mathematical analysis, biophysical simulations with ground truth and application of these mathematical concepts to empirical magnetoencephalography (MEG) data. Our mathematical derivations show that for two non-Gaussian electrophysiological signals, their power correlation depends on their coherence, cokurtosis and conjugate-coherence. Only coherence and cokurtosis contribute to power correlation networks in MEG data, but cokurtosis is less affected by artefactual signal leakage and better mirrors haemodynamic resting-state networks. Simulations and MEG data show that cokurtosis may reflect co-occurrent bursting events. Our findings shed light on the origin of the complementary nature of power correlation networks to phase coupling networks and suggests that the origin of resting-state networks is partly reflected in co-occurent bursts in neuronal activity.

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

[This corrects the article DOI: 10.1371/journal.pcbi.1008310.].

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.

Lag-invariant detection of interactions in spatially-extended systems using linear inverse modeling.

Measurements on physical systems result from the systems' activity being converted into sensor measurements by a forward model. In a number of cases, inversion of the forward model is extremely sensitive to perturbations such as sensor noise or numerical errors in the forward model. Regularization is then required, which introduces bias in the reconstruction of the systems' activity. One domain in which this is particularly problematic is the reconstruction of interactions in spatially-extended complex systems such as the human brain. Brain interactions can be reconstructed from non-invasive measurements such as electroencephalography (EEG) or magnetoencephalography (MEG), whose forward models are linear and instantaneous, but have large null-spaces and high condition numbers. This leads to incomplete unmixing of the forward models and hence to spurious interactions. This motivated the development of interaction measures that are exclusively sensitive to lagged, i.e. delayed interactions. The drawback of such measures is that they only detect interactions that have sufficiently large lags and this introduces bias in reconstructed brain networks. We introduce three estimators for linear interactions in spatially-extended systems that are uniformly sensitive to all lags. We derive some basic properties of and relationships between the estimators and evaluate their performance using numerical simulations from a simple benchmark model.

A methodological framework for inverse-modeling of propagating cortical activity using MEG/EEG.

The prevailing view on the dynamics of large-scale electrical activity in the human cortex is that it constitutes a functional network of discrete and localized circuits. Within this view, a natural way to analyse magnetoencephalographic (MEG) and electroencephalographic (EEG) data is by adopting methods from network theory. Invasive recordings, however, demonstrate that cortical activity is spatially continuous, rather than discrete, and exhibits propagation behavior. Furthermore, human cortical activity is known to propagate under a variety of conditions such as non-REM sleep, general anesthesia, and coma. Although several MEG/EEG studies have investigated propagating cortical activity, not much is known about the conditions under which such activity can be successfully reconstructed from MEG/EEG sensor-data. This study provides a methodological framework for inverse-modeling of propagating cortical activity. Within this framework, cortical activity is represented in the spatial frequency domain, which is more natural than the dipole domain when dealing with spatially continuous activity. We define angular power spectra, which show how the power of cortical activity is distributed across spatial frequencies, angular gain/phase spectra, which characterize the spatial filtering properties of linear inverse operators, and angular resolution matrices, which summarize how linear inverse operators leak signal within and across spatial frequencies. We adopt the framework to provide insight into the performance of several linear inverse operators in reconstructing propagating cortical activity from MEG/EEG sensor-data. We also describe how prior spatial frequency information can be incorporated into the inverse-modeling to obtain better reconstructions.

Linear distributed source modeling of local field potentials recorded with intra-cortical electrode arrays.

Planar intra-cortical electrode (Utah) arrays provide a unique window into the spatial organization of cortical activity. Reconstruction of the current source density (CSD) underlying such recordings, however, requires "inverting" Poisson's equation. For inter-laminar recordings, this is commonly done by the CSD method, which consists in taking the second-order spatial derivative of the recorded local field potentials (LFPs). Although the CSD method has been tremendously successful in mapping the current generators underlying inter-laminar LFPs, its application to planar recordings is more challenging. While for inter-laminar recordings the CSD method seems reasonably robust against violations of its assumptions, is it unclear as to what extent this holds for planar recordings. One of the objectives of this study is to characterize the conditions under which the CSD method can be successfully applied to Utah array data. Using forward modeling, we find that for spatially coherent CSDs, the CSD method yields inaccurate reconstructions due to volume-conducted contamination from currents in deeper cortical layers. An alternative approach is to "invert" a constructed forward model. The advantage of this approach is that any a priori knowledge about the geometrical and electrical properties of the tissue can be taken into account. Although several inverse methods have been proposed for LFP data, the applicability of existing electroencephalographic (EEG) and magnetoencephalographic (MEG) inverse methods to LFP data is largely unexplored. Another objective of our study therefore, is to assess the applicability of the most commonly used EEG/MEG inverse methods to Utah array data. Our main conclusion is that these inverse methods provide more accurate CSD reconstructions than the CSD method. We illustrate the inverse methods using event-related potentials recorded from primary visual cortex of a macaque monkey during a motion discrimination task.

Effect of Field Spread on Resting-State Magneto Encephalography Functional Network Analysis: A Computational Modeling Study.

A popular way to analyze resting-state electroencephalography (EEG) and magneto encephalography (MEG) data is to treat them as a functional network in which sensors are identified with nodes and the interaction between channel time series and the network connections. Although conceptually appealing, the network-theoretical approach to sensor-level EEG and MEG data is challenged by the fact that EEG and MEG time series are mixtures of source activity. It is, therefore, of interest to assess the relationship between functional networks of source activity and the ensuing sensor-level networks. Since these topological features are of high interest in experimental studies, we address the question of to what extent the network topology can be reconstructed from sensor-level functional connectivity (FC) measures in case of MEG data. Simple simulations that consider only a small number of regions do not allow to assess network properties; therefore, we use a diffusion magnetic resonance imaging-constrained whole-brain computational model of resting-state activity. Our motivation lies behind the fact that still many contributions found in the literature perform network analysis at sensor level, and we aim at showing the discrepancies between source- and sensor-level network topologies by using realistic simulations of resting-state cortical activity. Our main findings are that the effect of field spread on network topology depends on the type of interaction (instantaneous or lagged) and leads to an underestimation of lagged FC at sensor level due to instantaneous mixing of cortical signals, instantaneous interaction is more sensitive to field spread than lagged interaction, and discrepancies are reduced when using planar gradiometers rather than axial gradiometers. We, therefore, recommend using lagged interaction measures on planar gradiometer data when investigating network properties of resting-state sensor-level MEG data.

Increased Stability and Breakdown of Brain Effective Connectivity During Slow-Wave Sleep: Mechanistic Insights from Whole-Brain Computational Modelling.

Recent research has found that the human sleep cycle is characterised by changes in spatiotemporal patterns of brain activity. Yet, we are still missing a mechanistic explanation of the local neuronal dynamics underlying these changes. We used whole-brain computational modelling to study the differences in global brain functional connectivity and synchrony of fMRI activity in healthy humans during wakefulness and slow-wave sleep. We applied a whole-brain model based on the normal form of a supercritical Hopf bifurcation and studied the dynamical changes when adapting the bifurcation parameter for all brain nodes to best match wakefulness and slow-wave sleep. Furthermore, we analysed differences in effective connectivity between the two states. In addition to significant changes in functional connectivity, synchrony and metastability, this analysis revealed a significant shift of the global dynamic working point of brain dynamics, from the edge of the transition between damped to sustained oscillations during wakefulness, to a stable focus during slow-wave sleep. Moreover, we identified a significant global decrease in effective interactions during slow-wave sleep. These results suggest a mechanism for the empirical functional changes observed during slow-wave sleep, namely a global shift of the brain's dynamic working point leading to increased stability and decreased effective connectivity.

Resting-state fMRI correlations: From link-wise unreliability to whole brain stability.

The functional architecture of spontaneous BOLD fluctuations has been characterized in detail by numerous studies, demonstrating its potential relevance as a biomarker. However, the systematic investigation of its consistency is still in its infancy. Here, we analyze within- and between-subject variability and test-retest reliability of resting-state functional connectivity (FC) in a unique data set comprising multiple fMRI scans (42) from 5 subjects, and 50 single scans from 50 subjects. We adopt a statistical framework that enables us to identify different sources of variability in FC. We show that the low reliability of single links can be significantly improved by using multiple scans per subject. Moreover, in contrast to earlier studies, we show that spatial heterogeneity in FC reliability is not significant. Finally, we demonstrate that despite the low reliability of individual links, the information carried by the whole-brain FC matrix is robust and can be used as a functional fingerprint to identify individual subjects from the population.

Discrepancies between Multi-Electrode LFP and CSD Phase-Patterns: A Forward Modeling Study.

Multi-electrode recordings of local field potentials (LFPs) provide the opportunity to investigate the spatiotemporal organization of neural activity on the scale of several millimeters. In particular, the phases of oscillatory LFPs allow studying the coordination of neural oscillations in time and space and to tie it to cognitive processing. Given the computational roles of LFP phases, it is important to know how they relate to the phases of the underlying current source densities (CSDs) that generate them. Although CSDs and LFPs are distinct physical quantities, they are often (implicitly) identified when interpreting experimental observations. That this identification is problematic is clear from the fact that LFP phases change when switching to different electrode montages, while the underlying CSD phases remain unchanged. In this study we use a volume-conductor model to characterize discrepancies between LFP and CSD phase-patterns, to identify the contributing factors, and to assess the effect of different electrode montages. Although we focus on cortical LFPs recorded with two-dimensional (Utah) arrays, our findings are also relevant for other electrode configurations. We found that the main factors that determine the discrepancy between CSD and LFP phase-patterns are the frequency of the neural oscillations and the extent to which the laminar CSD profile is balanced. Furthermore, the presence of laminar phase-differences in cortical oscillations, as commonly observed in experiments, precludes identifying LFP phases with those of the CSD oscillations at a given cortical depth. This observation potentially complicates the interpretation of spike-LFP coherence and spike-triggered LFP averages. With respect to reference strategies, we found that the average-reference montage leads to larger discrepancies between LFP and CSD phases as compared with the referential montage, while the Laplacian montage reduces these discrepancies. We therefore advice to conduct analysis of two-dimensional LFP recordings using the Laplacian montage.

Hippocampal Sharp-Wave Ripples Influence Selective Activation of the Default Mode Network.

The default mode network (DMN) is a commonly observed resting-state network (RSN) that includes medial temporal, parietal, and prefrontal regions involved in episodic memory [1-3]. The behavioral relevance of endogenous DMN activity remains elusive, despite an emerging literature correlating resting fMRI fluctuations with memory performance [4, 5]-particularly in DMN regions [6-8]. Mechanistic support for the DMN's role in memory consolidation might come from investigation of large deflections (sharp-waves) in the hippocampal local field potential that co-occur with high-frequency (>80 Hz) oscillations called ripples-both during sleep [9, 10] and awake deliberative periods [11-13]. Ripples are ideally suited for memory consolidation [14, 15], since the reactivation of hippocampal place cell ensembles occurs during ripples [16-19]. Moreover, the number of ripples after learning predicts subsequent memory performance in rodents [20-22] and humans [23], whereas electrical stimulation of the hippocampus after learning interferes with memory consolidation [24-26]. A recent study in macaques showed diffuse fMRI neocortical activation and subcortical deactivation specifically after ripples [27]. Yet it is unclear whether ripples and other hippocampal neural events influence endogenous fluctuations in specific RSNs-like the DMN-unitarily. Here, we examine fMRI datasets from anesthetized monkeys with simultaneous hippocampal electrophysiology recordings, where we observe a dramatic increase in the DMN fMRI signal following ripples, but not following other hippocampal electrophysiological events. Crucially, we find increases in ongoing DMN activity after ripples, but not in other RSNs. Our results relate endogenous DMN fluctuations to hippocampal ripples, thereby linking network-level resting fMRI fluctuations with behaviorally relevant circuit-level neural dynamics.

Intra-cortical propagation of EEG alpha oscillations.

The most salient feature of spontaneous human brain activity as recorded with electroencephalography (EEG) are rhythmic fluctuations around 10Hz. These alpha oscillations have been reported to propagate over the scalp with velocities in the range of 5-15m/s. Since these velocities are in the range of action potential velocities through cortico-cortical axons, it has been hypothesized that the observed scalp waves reflect cortico-cortically mediated propagation of cortical oscillations. The reported scalp velocities however, appear to be inconsistent with those estimated from local field potential recordings in dogs, which are <1m/s and agree with the propagation velocity of action potentials in intra-cortical axons. In this study, we resolve these diverging findings using a combination of EEG data-analysis and biophysical modeling. In particular, we demonstrate that the observed scalp velocities can be accounted for by slow traveling oscillations, which provides support for the claim that spatial propagation of alpha oscillations is mediated by intra-cortical axons.

Generalized periodic discharges after acute cerebral ischemia: reflection of selective synaptic failure?

OBJECTIVES: Generalized periodic discharges (GPDs) can be observed in the electroencephalogram (EEG) of patients after acute cerebral ischemia and reflect pathological neuronal synchronization. Whether GPDs represent ictal activity, which can be treated with anti-epileptic drugs, or severe ischemic damage, in which treatment is futile, is unknown. We hypothesize that GPDs result from selective ischemic damage of glutamatergic synapses, which are known to be relatively vulnerable to effects of ischemia. METHODS: We employed a macroscopic model of cortical dynamics in which we increasingly eliminated glutamatergic synapses. We compared the output of the model with clinical EEG recordings in patients showing GPDs after cardiac arrest. RESULTS: Selective elimination of glutamatergic synapses from pyramidal cells to inhibitory interneurons led to simulated GPDs whose waveshape and frequency matched those of patients showing GPDs after cardiac arrest. Mere reduction of glutamatergic synapses between pyramidal cells themselves did not result in GPDs. CONCLUSIONS: Selective ischemic damage of glutamatergic synapses on inhibitory cortical interneurons leads to the generation of ischemia induced GPDs. Disinhibition of cortical pyramidal neurons is a candidate mechanism. SIGNIFICANCE: This study increases the insight in the pathophysiological mechanisms underlying the generation GPDS after acute cerebral ischemia.

Thalamo-cortical mechanisms underlying changes in amplitude and frequency of human alpha oscillations.

Although a large number of studies have been devoted to establishing correlations between changes in amplitude and frequency of EEG alpha oscillations and cognitive processes, it is currently unclear through which physiological mechanisms such changes are brought about. In this study we use a biophysical model of EEG generation to gain a fundamental understanding of the functional changes within the thalamo-cortical system that might underly such alpha responses. The main result of this study is that, although the physiology of the thalamo-cortical system is characterized by a large number of parameters, alpha responses effectively depend on only three variables. Physiologically, these variables determine the resonance properties of feedforward, cortico-thalamo-cortical, and intra-cortical circuits. By examining the effect of modulations of these resonances on the amplitude and frequency of EEG alpha oscillations, it is established that the model can reproduce the variety of experimentally observed alpha responses, as well as the experimental finding that changes in alpha amplitude are typically an order of magnitude larger than changes in alpha frequency. The modeling results are also in line with the fact that alpha responses often correlate linearly with indices characterizing cognitive processes. By investigating the effect of synaptic and intrinsic neuronal parameters, we find that alpha responses reflect changes in cortical activation, which is consistent with the hypothesis that alpha activity serves to selectively inhibit cortical regions during cognitive processing demands. As an example of how these analyses can be applied to specific experimental protocols, we reproduce benzodiazepine-induced alpha responses and clarify the putative underlying thalamo-cortical mechanisms. The findings reported in this study provide a fundamental physiological framework within which alpha responses observed in specific experimental protocols can be understood.

Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status epilepticus.

The EEG of patients in non-convulsive status epilepticus (NCSE) often displays delta oscillations or generalized spike-wave discharges. In some patients, these delta oscillations coexist with intermittent epileptic spikes. In this study we verify the prediction of a computational model of the thalamo-cortical system that these spikes are phase-locked to the delta oscillations. We subsequently describe the physiological mechanism underlying this observation as suggested by the model. It is suggested that the spikes reflect inhibitory stochastic fluctuations in the input to thalamo-cortical relay neurons and phase-locking is a consequence of differential excitability of relay neurons over the delta cycle. Further analysis shows that the observed phase-locking can be regarded as a stochastic precursor of generalized spike-wave discharges. This study thus provides an explanation of intermittent spikes during delta oscillations in NCSE and might be generalized to other encephathologies in which delta activity can be observed.

Meanfield modeling of propofol-induced changes in spontaneous EEG rhythms.

During the maintenance period of propofol-induced general anesthesia, specific changes in spontaneous EEG rhythms can be observed. These comprise increased delta and theta power and the emergence of alpha oscillations over frontal regions. In this study we use a meanfield model of the thalamo-cortical system to reproduce these changes and to elucidate the underlying mechanisms. The model is able to reproduce the most dominant changes in the EEG and suggests that they are caused by the amplification of resonances within the thalamo-cortical system. Specifically, while observed increases in delta and alpha power are reflections of amplified resonances in the respective frequency bands, increases in theta power are caused indirectly by spectral power leakage from delta and alpha bands. The model suggests that these changes are brought about through increased inhibition within local cortical interneuron circuits. These results are encouraging and motivate more extensive use of neural meanfield models in elucidating the physiological mechanisms underlying the effects of pharmacological agents on macroscopic brain dynamics.