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.</p

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 all 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. We find using random forests 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 induced brain states. Using whole brain computational models we find that especially 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

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

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

Relation between the phase-lag index and lagged coherence for assessing interactions in EEG and MEG data

Over the last two decades, a large number of estimators have been proposed to assess brain connectivity from electroencephalography (EEG) and magnetoencephalography (MEG) data. The statistical theory underlying these estimators, however, is relatively underdeveloped. In particular, the theoretical relationships between different estimators were unknown until very recently. In a recent preprint, Nolte et al. derived formulas for such relationships under the assumption that the data are Gaussian. One of the results was that the phase-lag index and the lagged coherence concentrate around identical values for large sample sizes, i.e. have identical asymptotic limits. A proof of this statement, however, was only sketched, the model assumptions were not checked in experimental data, and sampling properties of the estimators were not considered. We derive the probability density of the relative-phase in the Gaussian model and use it to provide an alternative proof of the asymptotic equality of the phase-lag index and the lagged coherence. The proof is based on power series expansions of the Fourier coefficients of the phase-lag index and the lagged coherence, which are demonstrated to be hypergeometric functions. We also assess the sampling properties of the phase-lag index and the lagged coherence through numerical simulations from the Gaussian model. These demonstrate that throughout the entire parameter space of the model and for all sample sizes, the standard error of the phase-lag index is higher than that of the lagged coherence and thus establish that the lagged coherence is a uniformly better estimator than the phase-lag index. We use experimental EEG and MEG data to verify to what extent the Gaussian assumption is appropriate. Deviations from normality were observed precisely at frequencies for which EEG/MEG power spectra had local maxima, i.e. at oscillatory resonances. Depending on the data-set, the resonances were located in the delta, alpha, and beta frequency bands and correspond to the respective brain rhythms. Based on these observations, we propose to model EEG/MEG data with exponential power densities, which include the Gaussian and Laplace densities as special cases. Lastly, we demonstrate that the asymptotic equality of the phase-lag index and the lagged coherence, as well as the large relative standard errors of the phase lag index, also hold in experimental EEG/MEG data. This establishes that the lagged coherence is not only a better estimator for Gaussian data, but for experimental EEG/MEG data as well

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

Neural Mass Modeling of the EEG

This chapter discusses neural mass models and EEG rhythms. We start with a simple model, adding additional components step-by-step, eventually resulting in coupled neural masses that simulate a physiological EEG rhythm with a peak frequency in the 8–13 Hz ( α ) frequency range. While this chapter focuses on physiology, we will learn in later chapters that neural mass models also find applications in furthering our understanding of pathological EEG patterns as present during seizures or anoxia

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 10 Hz. These alpha oscillations have been reported to propagate over the scalp with velocities in the range of 5–15 m/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 < 1 m/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.GD was supported by the ERC Advanced Grant: DYSTRUCTURE (no. 295129), by the Spanish Research Project SAF2010-16085 and by the CONSOLIDER-INGENIO 2010 Program CSD2007-00012, and the FP7-ICT BrainScales. The authors declare no competing financial interest