Identifying true cortical interactions in MEG using the nulling beamformer

Changes in Resting-State Brain Activity After Cognitive Behavioral Therapy for Chronic Pain: A Magnetoencephalography Study

Cognitive behavioral therapy (CBT) is believed to be an effective treatment for chronic pain due to its association with cognitive and emotional factors. Nevertheless, there is a paucity of magnetoencephalography (MEG) investigations elucidating its underlying mechanisms. This study investigated the neurophysiological effects of CBT employing MEG and analytical techniques. We administered resting-state MEG scans to 30 patients with chronic pain and 31 age-matched healthy controls. Patients engaged in a 12-session group CBT program. We conducted pretreatment (T1) and post-treatment (T2) MEG and clinical assessments. MEG data were examined within predefined regions of interest, guided by the authors' and others' prior magnetic resonance imaging studies. Initially, we selected regions displaying significant changes in power spectral density and multiscale entropy between patients at T1 and healthy controls. Then, we examined the changes within these regions after conducting CBT. Furthermore, we applied support vector machine analysis to MEG data to assess the potential for classifying treatment effects. We observed normalization of power in the gamma2 band (61-90 Hz) within the right inferior frontal gyrus (IFG) and multiscale entropy within the right dorsolateral prefrontal cortex (DLPFC) of patients with chronic pain after CBT. Notably, changes in pain intensity before and after CBT positively correlated with the alterations of multiscale entropy. Importantly, responders predicted by the support vector machine classifier had significantly higher treatment improvement rates than nonresponders. These findings underscore the pivotal role of the right IFG and DLPFC in ameliorating pain intensity through CBT. Further accumulation of evidence is essential for future applications. PERSPECTIVE: We conducted MEG scans on 30 patients with chronic pain before and after a CBT program, comparing results with 31 healthy individuals. There were CBT-related changes in the right IFG and DLPFC. These results highlight the importance of specific brain regions in pain reduction through CBT.

Localization of Brain Signals by Alternating Projection

A popular approach for modeling brain activity in MEG and EEG is based on a small set of current dipoles, where each dipole represents the combined activation of a local area of the brain. Here, we address the problem of multiple dipole localization with a novel solution called Alternating Projection (AP). The AP solution is based on minimizing the least-squares (LS) criterion by transforming the multi-dimensional optimization required for direct LS solution, to a sequential and iterative solution in which one source at a time is localized, while keeping the other sources fixed. Results from simulated, phantom, and human MEG data demonstrated the high accuracy of the AP method, with superior localization results than popular scanning methods from the multiple-signal classification (MUSIC) and beamformer families. In addition, the AP method was more robust to forward model errors resulting from head rotations and translations, as well as different cortex tessellation grids for the forward and inverse solutions, with consistently higher localization accuracy in low SNR and highly correlated sources.

Network modeling of dynamic brain interactions predicts emergence of neural information that supports human cognitive behavior

How cognitive task behavior is generated by brain network interactions is a central question in neuroscience. Answering this question calls for the development of novel analysis tools that can firstly capture neural signatures of task information with high spatial and temporal precision (the "where and when") and then allow for empirical testing of alternative network models of brain function that link information to behavior (the "how"). We outline a novel network modeling approach suited to this purpose that is applied to noninvasive functional neuroimaging data in humans. We first dynamically decoded the spatiotemporal signatures of task information in the human brain by combining MRI-individualized source electroencephalography (EEG) with multivariate pattern analysis (MVPA). A newly developed network modeling approach-dynamic activity flow modeling-then simulated the flow of task-evoked activity over more causally interpretable (relative to standard functional connectivity [FC] approaches) resting-state functional connections (dynamic, lagged, direct, and directional). We demonstrate the utility of this modeling approach by applying it to elucidate network processes underlying sensory-motor information flow in the brain, revealing accurate predictions of empirical response information dynamics underlying behavior. Extending the model toward simulating network lesions suggested a role for the cognitive control networks (CCNs) as primary drivers of response information flow, transitioning from early dorsal attention network-dominated sensory-to-response transformation to later collaborative CCN engagement during response selection. These results demonstrate the utility of the dynamic activity flow modeling approach in identifying the generative network processes underlying neurocognitive phenomena.

MEG Source Localization via Deep Learning

We present a deep learning solution to the problem of localization of magnetoencephalography (MEG) brain signals. The proposed deep model architectures are tuned to single and multiple time point MEG data, and can estimate varying numbers of dipole sources. Results from simulated MEG data on the cortical surface of a real human subject demonstrated improvements against the popular RAP-MUSIC localization algorithm in specific scenarios with varying SNR levels, inter-source correlation values, and number of sources. Importantly, the deep learning models had robust performance to forward model errors resulting from head translation and rotation and a significant reduction in computation time, to a fraction of 1 ms, paving the way to real-time MEG source localization.

Helium-4 magnetometers for room-temperature biomedical imaging: toward collective operation and photon-noise limited sensitivity

Optically-pumped magnetometers constitute a valuable tool for imaging biological magnetic signals without cryogenic cooling. Nowadays, numerous developments are being pursued using alkali-based magnetometers, which have demonstrated excellent sensitivities in the spin-exchange relaxation free (SERF) regime that requires heating to >100 °C. In contrast, metastable helium-4 based magnetometers work at any temperature, which allows a direct contact with the scalp, yielding larger signals and a better patient comfort. However former ⁴He magnetometers displayed large noises of >200 fT/Hz^1/2 with 300-Hz bandwidth. We describe here an improved magnetometer reaching a sensitivity better than 50 fT/Hz^1/2, nearly the photon shot noise limit, with a bandwidth of 2 kHz. Like other zero-field atomic magnetometers, these magnetometers can be operated in closed-loop architecture reaching several hundredths nT of dynamic range. A small array of 4 magnetometers operating in a closed loop has been tested with a successful correction of the cross-talks.

SUPFUNSIM: Spatial Filtering Toolbox for EEG

Brain activity pattern recognition from EEG or MEG signal analysis is one of the most important method in cognitive neuroscience. The supFunSim library is a new Matlab toolbox which generates accurate EEG forward model and implements a collection of spatial filters for EEG source reconstruction, including the linearly constrained minimum-variance (LCMV), eigenspace LCMV, nulling (NL), and minimum-variance pseudo-unbiased reduced-rank (MV-PURE) filters in various versions. It also enables source-level directed connectivity analysis using partial directed coherence (PDC) measure. The supFunSim library is based on the well-known FieldTrip toolbox for EEG and MEG analysis and is written using object-oriented programming paradigm. The resulting modularity of the toolbox enables its simple extensibility. This paper gives a complete overview of the toolbox from both developer and end-user perspectives, including description of the installation process and use cases.

Modified Dominant Mode Rejection Beamformer for Localizing Brain Activities When Data Covariance Matrix Is Rank Deficient

OBJECTIVE

Minimum variance beamformer (MVB) and its extensions fail in localizing short time brain activities particularly evoked potentials because of rank deficiency or inaccurate estimation of a data covariance matrix. In this paper, the conventional dominant mode rejection (DMR) adaptive beamformer is modified to localize brain short time activities.

METHODS

In the modified DMR, it is attempted to obtain a well-conditioned covariance matrix by dividing the eigenvalues of the data covariance matrix into dominant, medium, and small eigenvalues and then modifying medium and small parts. The performance of the proposed approach is compared with diagonal loading MVB (DL_MVB) and fast fully adaptive (FFA) beamformer by using simulated event-related potentials and real event-related field data. Eigenspace versions of DL_MVB and modified DMR are also implemented.

RESULTS

In all simulations, the modified DMR obtains the least localization error (0-5 mm) and spread radius (0-8 mm) when the signal-to-noise ratio (SNR) varies from 0 to 10 dB with step 1 dB. In real data, the new approach in comparison to two other ones attains the most concentrated power spectrum. Eigenspace projection of DL_MVB presents better results than DL_MVB but worse results than the modified DMR. Applying eigenspace projection on the proposed method improves its performance at high SNR levels.

CONCLUSION

Empirical results illustrate the superiority of the proposed DMR method to the DL_MVB and FFA in localizing brain short time activities.

SIGNIFICANCE

The proposed method can be utilized in source localization of epilepsy for presurgical clinical evaluation purpose and also in applications dealing with the localization of evoked potentials and fields.

Assessing recurrent interactions in cortical networks: Modeling EEG response to transcranial magnetic stimulation

BACKGROUND

The basic mechanisms underlying the electroencephalograpy (EEG) response to transcranial magnetic stimulation (TMS) of the human cortex are not well understood.

NEW METHOD

A state-space modeling methodology is developed to gain insight into the network nature of the TMS/EEG response. Cortical activity is modeled using a multivariariate autoregressive model with exogenous stimulation parameters representing the effect of TMS. An observation equation models EEG measurement of cortical activity. An expectation-maximization algorithm is developed to estimate the model parameters.

RESULTS

The methodology is used to assess two different hypotheses for the mechanisms underlying TMS/EEG in wakefulness and sleep. The integrated model hypothesizes that recurrent interactions between cortical regions are the source of TMS/EEG, while the segregated model hypothesizes that the TMS/EEG results from excitation of independent cortical oscillators. The results show that the relatively simple EEG response to TMS recorded during non-rapid-eye-movement sleep is described equally well by either the integrated or segregated model. However, the integrated model fits the more complex TMS/EEG of wakefulness much better than the segregated model.

COMPARISON WITH EXISTING METHOD(S)

Existing methods are limited to small numbers of cortical regions of interest or do not represent the effect of TMS. Our results are consistent with previous studies contrasting the complexity of TMS/EEG in wakefulness and sleep.

CONCLUSION

The new method strongly suggests that effective feedback connections between cortical regions are required to produce the TMS/EEG in wakefulness.

Improving the Nulling Beamformer Using Subspace Suppression

Magnetoencephalography (MEG) captures the magnetic fields generated by neuronal current sources with sensors outside the head. In MEG analysis these current sources are estimated from the measured data to identify the locations and time courses of neural activity. Since there is no unique solution to this so-called inverse problem, multiple source estimation techniques have been developed. The nulling beamformer (NB), a modified form of the linearly constrained minimum variance (LCMV) beamformer, is specifically used in the process of inferring interregional interactions and is designed to eliminate shared signal contributions, or cross-talk, between regions of interest (ROIs) that would otherwise interfere with the connectivity analyses. The nulling beamformer applies the truncated singular value decomposition (TSVD) to remove small signal contributions from a ROI to the sensor signals. However, ROIs with strong crosstalk will have high separating power in the weaker components, which may be removed by the TSVD operation. To address this issue we propose a new method, the nulling beamformer with subspace suppression (NBSS). This method, controlled by a tuning parameter, reweights the singular values of the gain matrix mapping from source to sensor space such that components with high overlap are reduced. By doing so, we are able to measure signals between nearby source locations with limited cross-talk interference, allowing for reliable cortical connectivity analysis between them. In two simulations, we demonstrated that NBSS reduces cross-talk while retaining ROIs' signal power, and has higher separating power than both the minimum norm estimate (MNE) and the nulling beamformer without subspace suppression. We also showed that NBSS successfully localized the auditory M100 event-related field in primary auditory cortex, measured from a subject undergoing an auditory localizer task, and suppressed cross-talk in a nearby region in the superior temporal sulcus.

Spatio-temporal Reconstruction of Neural Sources Using Indirect Dominant Mode Rejection

Adaptive minimum variance based beamformers (MVB) have been successfully applied to magnetoencephalogram (MEG) and electroencephalogram (EEG) data to localize brain activities. However, the performance of these beamformers falls down in situations where correlated or interference sources exist. To overcome this problem, we propose indirect dominant mode rejection (iDMR) beamformer application in brain source localization. This method by modifying measurement covariance matrix makes MVB applicable in source localization in the presence of correlated and interference sources. Numerical results on both EEG and MEG data demonstrate that presented approach accurately reconstructs time courses of active sources and localizes those sources with high spatial resolution. In addition, the results of real AEF data show the good performance of iDMR in empirical situations. Hence, iDMR can be reliably used for brain source localization especially when there are correlated and interference sources.

Localizing Event-Related Potentials Using Multi-source Minimum Variance Beamformers: A Validation Study

Adaptive and non-adaptive beamformers have become a prominent neuroimaging tool for localizing neural sources of electroencephalographic (EEG) and magnetoencephalographic (MEG) data. In this study, we investigated single-source and multi-source scalar beamformers with respect to their performances in localizing and reconstructing source activity for simulated and real EEG data. We compared a new multi-source search approach (multi-step iterative approach; MIA) to our previous multi-source search approach (single-step iterative approach; SIA) and a single-source search approach (single-step peak approach; SPA). In order to compare performances across these beamformer approaches, we manipulated various simulated source parameters, such as the amount of signal-to-noise ratio (0.1-0.9), inter-source correlations (0.3-0.9), number of simultaneously active sources (2-8), and source locations. Results showed that localization performance followed the order of MIA > SIA > SPA regardless of the number of sources, source correlations, and single-to-noise ratios. In addition, SIA and MIA were significantly better than SPA at localizing four or more sources. Moreover, MIA was better than SIA and SPA at identifying the true source locations when signal characteristics were at their poorest. Source waveform reconstructions were similar between MIA and SIA but were significantly better than that for SPA. A similar trend was also found when applying these beamformer approaches to a real EEG dataset. Based on our findings, we conclude that multi-source beamformers (MIA and SIA) are an improvement over single-source beamformers for localizing EEG. Importantly, our new search method, MIA, had better localization performance, localization precision, and source waveform reconstruction as compared to SIA or SPA. We therefore recommend its use for improved source localization and waveform reconstruction of event-related potentials.

The impact of MEG source reconstruction method on source-space connectivity estimation: A comparison between minimum-norm solution and beamforming

Despite numerous important contributions, the investigation of brain connectivity with magnetoencephalography (MEG) still faces multiple challenges. One critical aspect of source-level connectivity, largely overlooked in the literature, is the putative effect of the choice of the inverse method on the subsequent cortico-cortical coupling analysis. We set out to investigate the impact of three inverse methods on source coherence detection using simulated MEG data. To this end, thousands of randomly located pairs of sources were created. Several parameters were manipulated, including inter- and intra-source correlation strength, source size and spatial configuration. The simulated pairs of sources were then used to generate sensor-level MEG measurements at varying signal-to-noise ratios (SNR). Next, the source level power and coherence maps were calculated using three methods (a) L2-Minimum-Norm Estimate (MNE), (b) Linearly Constrained Minimum Variance (LCMV) beamforming, and (c) Dynamic Imaging of Coherent Sources (DICS) beamforming. The performances of the methods were evaluated using Receiver Operating Characteristic (ROC) curves. The results indicate that beamformers perform better than MNE for coherence reconstructions if the interacting cortical sources consist of point-like sources. On the other hand, MNE provides better connectivity estimation than beamformers, if the interacting sources are simulated as extended cortical patches, where each patch consists of dipoles with identical time series (high intra-patch coherence). However, the performance of the beamformers for interacting patches improves substantially if each patch of active cortex is simulated with only partly coherent time series (partial intra-patch coherence). These results demonstrate that the choice of the inverse method impacts the results of MEG source-space coherence analysis, and that the optimal choice of the inverse solution depends on the spatial and synchronization profile of the interacting cortical sources. The insights revealed here can guide method selection and help improve data interpretation regarding MEG connectivity estimation.

The auditory evoked-gamma response and its relation with the N1m

This study explored the patterns of oscillatory activity that underpin the N1m auditory evoked response. Evoked gamma activity is a small and relatively rarely-reported component of the auditory evoked response, and the objective of this work was to determine how this component relates to the larger and more prolonged changes in lower frequency bands. An event-related beamformer analysis of MEG data from monaural click stimulation was used to reconstruct volumetric images and virtual electrode time series. Group analysis of localisations showed that activity in the gamma band originated from a source that was more medial than those for activity in the theta-to-beta band, and virtual-electrode analysis showed that the source of the gamma activity could be statistically dissociated from the lower-frequency response. These findings are in accordance with separate functional roles for the activity in each frequency band, and provide evidence that the oscillatory activity that underpins the auditory evoked response may contain important information about the physiological basis of the macroscopic signals recorded by MEG in response to auditory stimulation.

Noninvasive Electromagnetic Source Imaging and Granger Causality Analysis: An Electrophysiological Connectome (eConnectome) Approach

OBJECTIVE

Combined source-imaging techniques and directional connectivity analysis can provide useful information about the underlying brain networks in a noninvasive fashion. Source-imaging techniques have been used successfully to either determine the source of activity or to extract source time-courses for Granger causality analysis, previously. In this work, we utilize source-imaging algorithms to both find the network nodes [regions of interest (ROI)] and then extract the activation time series for further Granger causality analysis. The aim of this work is to find network nodes objectively from noninvasive electromagnetic signals, extract activation time-courses, and apply Granger analysis on the extracted series to study brain networks under realistic conditions.

METHODS

Source-imaging methods are used to identify network nodes and extract time-courses and then Granger causality analysis is applied to delineate the directional functional connectivity of underlying brain networks. Computer simulations studies where the underlying network (nodes and connectivity pattern) is known were performed; additionally, this approach has been evaluated in partial epilepsy patients to study epilepsy networks from interictal and ictal signals recorded by EEG and/or Magnetoencephalography (MEG).

RESULTS

Localization errors of network nodes are less than 5 mm and normalized connectivity errors of ∼20% in estimating underlying brain networks in simulation studies. Additionally, two focal epilepsy patients were studied and the identified nodes driving the epileptic network were concordant with clinical findings from intracranial recordings or surgical resection.

CONCLUSION

Our study indicates that combined source-imaging algorithms with Granger causality analysis can identify underlying networks precisely (both in terms of network nodes location and internodal connectivity).

SIGNIFICANCE

The combined source imaging and Granger analysis technique is an effective tool for studying normal or pathological brain conditions.

A multi-resolution approach to localize neural sources of P300 event-related brain potential

BACKGROUND AND OBJECTIVE

P300 is probably the most well-known component of event-related brain potentials (ERPs). Using an oddball paradigm, a P300 component can be identified, that is, elicited by the target stimuli recognition. Since P300 is associated with attention and memory operations of the brain, investigation of this component can improve our understanding of these mechanisms. The present study is aimed at identifying the P300 generators in 30 healthy subjects aged 18-30 years using time-reduction region-suppression linearly constrained minimum variance (TR-LCMV) beamformer.

METHODS

In our study, TR-LCMV beamformer with multi-resolution approach is proposed, coarse-resolution space to find the approximated coherent source locations, fine-resolution space to estimate covariance matrix for dimension reduction of determined regions, and normal-resolution space to localize the P300 generators in the brain.

RESULTS

Our results over simulated and real data showed that this approach is a suitable tool to the analysis of ERP fields with localizing superior and inferior frontal lobe, middle temporal gyrus, parietal lobe, and cingulate gyrus as the most prominent sources of P300. The result of P300 localization was finally compared with the other localization methods and it is demonstrated that enhanced performance is achieved.

CONCLUSIONS

Our results showed that the P300 originates from a widespread neuronal network in the brain and not from a specific region. Our finding over simulated and real data demonstrated the ability of the TR-LCMV algorithm for P300 source localization.

How reliable are MEG resting-state connectivity metrics?

MEG offers dynamic and spectral resolution for resting-state connectivity which is unavailable in fMRI. However, there are a wide range of available network estimation methods for MEG, and little in the way of existing guidance on which ones to employ. In this technical note, we investigate the extent to which many popular measures of stationary connectivity are suitable for use in resting-state MEG, localising magnetic sources with a scalar beamformer. We use as empirical criteria that network measures for individual subjects should be repeatable, and that group-level connectivity estimation shows good reproducibility. Using publically-available data from the Human Connectome Project, we test the reliability of 12 network estimation techniques against these criteria. We find that the impact of magnetic field spread or spatial leakage artefact is profound, creates a major confound for many connectivity measures, and can artificially inflate measures of consistency. Among those robust to this effect, we find poor test-retest reliability in phase- or coherence-based metrics such as the phase lag index or the imaginary part of coherency. The most consistent methods for stationary connectivity estimation over all of our tests are simple amplitude envelope correlation and partial correlation measures.

Spectral and spatial changes of brain rhythmic activity in response to the sustained thermal pain stimulation

The aim of this study was to investigate the neurophysiological correlates of pain caused by sustained thermal stimulation. A group of 21 healthy volunteers was studied. Sixty-four channel continuous electroencephalography (EEG) was recorded while the subject received tonic thermal stimulation. Spectral changes extracted from EEG were quantified and correlated with pain scales reported by subjects, the stimulation intensity, and the time course. Network connectivity was assessed to study the changes in connectivity patterns and strengths among brain regions that have been previously implicated in pain processing. Spectrally, a global reduction in power was observed in the lower spectral range, from delta to alpha, with the most marked changes in the alpha band. Spatially, the contralateral region of the somatosensory cortex, identified using source localization, was most responsive to stimulation status. Maximal desynchrony was observed when stimulation was present. The degree of alpha power reduction was linearly correlated to the pain rating reported by the subjects. Contralateral alpha power changes appeared to be a robust correlate of pain intensity experienced by the subjects. Granger causality analysis showed changes in network level connectivity among pain-related brain regions due to high intensity of pain stimulation versus innocuous warm stimulation. These results imply the possibility of using noninvasive EEG to predict pain intensity and to study the underlying pain processing mechanism in coping with prolonged painful experiences. Once validated in a broader population, the present EEG-based approach may provide an objective measure for better pain management in clinical applications. Hum Brain Mapp 37:2976-2991, 2016. © 2016 Wiley Periodicals, Inc.

The LDA beamformer: Optimal estimation of ERP source time series using linear discriminant analysis

We introduce a novel beamforming approach for estimating event-related potential (ERP) source time series based on regularized linear discriminant analysis (LDA). The optimization problems in LDA and linearly-constrained minimum-variance (LCMV) beamformers are formally equivalent. The approaches differ in that, in LCMV beamformers, the spatial patterns are derived from a source model, whereas in an LDA beamformer the spatial patterns are derived directly from the data (i.e., the ERP peak). Using a formal proof and MEG simulations, we show that the LDA beamformer is robust to correlated sources and offers a higher signal-to-noise ratio than the LCMV beamformer and PCA. As an application, we use EEG data from an oddball experiment to show how the LDA beamformer can be harnessed to detect single-trial ERP latencies and estimate connectivity between ERP sources. Concluding, the LDA beamformer optimally reconstructs ERP sources by maximizing the ERP signal-to-noise ratio. Hence, it is a highly suited tool for analyzing ERP source time series, particularly in EEG/MEG studies wherein a source model is not available.

Thalamocortical relationship in epileptic patients with generalized spike and wave discharges--A multimodal neuroimaging study

Unlike focal or partial epilepsy, which has a confined range of influence, idiopathic generalized epilepsy (IGE) often affects the whole or a larger portion of the brain without obvious, known cause. It is important to understand the underlying network which generates epileptic activity and through which epileptic activity propagates. The aim of the present study was to investigate the thalamocortical relationship using non-invasive imaging modalities in a group of IGE patients. We specifically investigated the roles of the mediodorsal nuclei in the thalami and the medial frontal cortex in generating and spreading IGE activities. We hypothesized that the connectivity between these two structures is key in understanding the generation and propagation of epileptic activity in brains affected by IGE. Using three imaging techniques of EEG, fMRI and EEG-informed fMRI, we identified important players in generation and propagation of generalized spike-and-wave discharges (GSWDs). EEG-informed fMRI suggested multiple regions including the medial frontal area near to the anterior cingulate cortex, mediodorsal nuclei of the thalamus, caudate nucleus among others that related to the GSWDs. The subsequent seed-based fMRI analysis revealed a reciprocal cortical and bi-thalamic functional connection. Through EEG-based Granger Causality analysis using (DTF) and adaptive DTF, within the reciprocal thalamocortical circuitry, thalamus seems to serve as a stronger source in driving cortical activity from initiation to the propagation of a GSWD. Such connectivity change starts before the GSWDs and continues till the end of the slow wave discharge. Thalamus, especially the mediodorsal nuclei, may serve as potential targets for deep brain stimulation to provide more effective treatment options for patients with drug-resistant generalized epilepsy.

Pursuing the flow of information: connectivity between bilateral premotor cortices predicts better accuracy in the phonological working memory task

Using Magnetoencephalography (MEG) we studied functional connectivity of cortical areas during phonological working memory task. Six subjects participated in the experiment and their neuronal activity was measured by a 306-channel MEG system. We used a modified version of the visual Sternberg paradigm, which required subjects to memorize 8 alphabet letters in 2s for a late recall period. We estimated functional connectivity of oscillatory regional brain activities during the encoding session for each trial of each subject using beamformer source reconstruction and Granger causality analysis. Regional brain activities were mostly found in the bilateral premotor cortex (Brodmann area (BA) 6: PMC), the right dorsolateral prefrontal cortex (BA 9: DLPFC), and the right frontal eye field (BA 8). Considering that the left and right PMCs participate in the functions of phonological loop (PL) and the visuospatial sketchpad (VS) in the Baddeley's model of working memory, respectively, our result suggests that subjects utilized either single function or both functions of working memory circuitry to execute the task. Interestingly, the accuracy of the task was significantly higher in the trials where the alpha band oscillatory activities in the bilateral PMCs established functional connectivity compared to those where the PMC was not working in conjunction with its counterpart. Similar relationship was found in the theta band oscillatory activities between the right PMC and the right DLPFC, however in this case the establishment of functional connectivity significantly decreased the accuracy of the task. These results suggest that sharing the memory load with both PL- and VS- type memory storage circuitries contributed to better performance in the highly-demanding cognitive task.

Overcoming the effects of false positives and threshold bias in graph theoretical analyses of neuroimaging data

Graph theory (GT) is a powerful framework for quantifying topological features of neuroimaging-derived functional and structural networks. However, false positive (FP) connections arise frequently and influence the inferred topology of networks. Thresholding is often used to overcome this problem, but an appropriate threshold often relies on a priori assumptions, which will alter inferred network topologies. Four common network metrics (global efficiency, mean clustering coefficient, mean betweenness and smallworldness) were tested using a model tractography dataset. It was found that all four network metrics were significantly affected even by just one FP. Results also show that thresholding effectively dampens the impact of FPs, but at the expense of adding significant bias to network metrics. In a larger number (n=248) of tractography datasets, statistics were computed across random group permutations for a range of thresholds, revealing that statistics for network metrics varied significantly more than for non-network metrics (i.e., number of streamlines and number of edges). Varying degrees of network atrophy were introduced artificially to half the datasets, to test sensitivity to genuine group differences. For some network metrics, this atrophy was detected as significant (p<0.05, determined using permutation testing) only across a limited range of thresholds. We propose a multi-threshold permutation correction (MTPC) method, based on the cluster-enhanced permutation correction approach, to identify sustained significant effects across clusters of thresholds. This approach minimises requirements to determine a single threshold a priori. We demonstrate improved sensitivity of MTPC-corrected metrics to genuine group effects compared to an existing approach and demonstrate the use of MTPC on a previously published network analysis of tractography data derived from a clinical population. In conclusion, we show that there are large biases and instability induced by thresholding, making statistical comparisons of network metrics difficult. However, by testing for effects across multiple thresholds using MTPC, true group differences can be robustly identified.

Influence of the head model on EEG and MEG source connectivity analyses

The results of brain connectivity analysis using reconstructed source time courses derived from EEG and MEG data depend on a number of algorithmic choices. While previous studies have investigated the influence of the choice of source estimation method or connectivity measure, the effects of the head modeling errors or simplifications have not been studied sufficiently. In the present simulation study, we investigated the influence of particular properties of the head model on the reconstructed source time courses as well as on source connectivity analysis in EEG and MEG. Therefore, we constructed a realistic head model and applied the finite element method to solve the EEG and MEG forward problems. We considered the distinction between white and gray matter, the distinction between compact and spongy bone, the inclusion of a cerebrospinal fluid (CSF) compartment, and the reduction to a simple 3-layer model comprising only the skin, skull, and brain. Source time courses were reconstructed using a beamforming approach and the source connectivity was estimated by the imaginary coherence (ICoh) and the generalized partial directed coherence (GPDC). Our results show that in both EEG and MEG, neglecting the white and gray matter distinction or the CSF causes considerable errors in reconstructed source time courses and connectivity analysis, while the distinction between spongy and compact bone is just of minor relevance, provided that an adequate skull conductivity value is used. Large inverse and connectivity errors are found in the same regions that show large topography errors in the forward solution. Moreover, we demonstrate that the very conservative ICoh is relatively safe from the crosstalk effects caused by imperfect head models, as opposed to the GPDC.

Altered Network Oscillations and Functional Connectivity Dynamics in Children Born Very Preterm

Structural brain connections develop atypically in very preterm children, and altered functional connectivity is also evident in fMRI studies. Such alterations in brain network connectivity are associated with cognitive difficulties in this population. Little is known, however, about electrophysiological interactions among specific brain networks in children born very preterm. In the present study, we recorded magnetoencephalography while very preterm children and full-term controls performed a visual short-term memory task. Regions expressing task-dependent activity changes were identified using beamformer analysis, and inter-regional phase synchrony was calculated. Very preterm children expressed altered regional recruitment in distributed networks of brain areas, across standard physiological frequency ranges including the theta, alpha, beta and gamma bands. Reduced oscillatory synchrony was observed among task-activated brain regions in very preterm children, particularly for connections involving areas critical for executive abilities, including middle frontal gyrus. These findings suggest that inability to recruit neurophysiological activity and interactions in distributed networks including frontal regions may contribute to difficulties in cognitive development in children born very preterm.

Cognitive and clinical dysfunction, altered MEG resting-state networks and thalamic atrophy in multiple sclerosis

The relation between pathological findings and clinical and cognitive decline in Multiple Sclerosis remains unclear. Here, we tested the hypothesis that altered functional connectivity could provide a missing link between structural findings, such as thalamic atrophy and white matter lesion load, and clinical and cognitive dysfunction. Resting-state magnetoencephalography recordings from 21 MS patients and 17 gender- and age matched controls were projected onto atlas-based regions-of-interest using beamforming. Average functional connectivity was computed for each ROI and literature-based resting-state networks using the phase-lag index. Structural measures of whole brain and thalamic atrophy and lesion load were estimated from MRI scans. Global analyses showed lower functional connectivity in the alpha2 band and higher functional connectivity in the beta band in patients with Multiple Sclerosis. Additionally, alpha2 band functional connectivity was lower for the patients in two resting-state networks, namely the default mode network and the visual network. Higher beta band functional connectivity was found in the default mode network and in the temporo-parietal network. Lower alpha2 band functional connectivity in the visual network was related to lower thalamic volumes. Beta band functional connectivity correlated positively with disability scores, most prominently in the default mode network, and correlated negatively with cognitive performance in this network. These findings illustrate the relationship between thalamic atrophy, altered functional connectivity and clinical and cognitive dysfunction in MS, which could serve as a bridge to understand how neurodegeneration is associated with altered functional connectivity and subsequently clinical and cognitive decline.

Graph theoretical analysis of resting magnetoencephalographic functional connectivity networks

Complex networks have been observed to comprise small-world properties, believed to represent an optimal organization of local specialization and global integration of information processing at reduced wiring cost. Here, we applied magnitude squared coherence to resting magnetoencephalographic time series in reconstructed source space, acquired from controls and patients with schizophrenia, and generated frequency-dependent adjacency matrices modeling functional connectivity between virtual channels. After configuring undirected binary and weighted graphs, we found that all human networks demonstrated highly localized clustering and short characteristic path lengths. The most conservatively thresholded networks showed efficient wiring, with topographical distance between connected vertices amounting to one-third as observed in surrogate randomized topologies. Nodal degrees of the human networks conformed to a heavy-tailed exponentially truncated power-law, compatible with the existence of hubs, which included theta and alpha bilateral cerebellar tonsil, beta and gamma bilateral posterior cingulate, and bilateral thalamus across all frequencies. We conclude that all networks showed small-worldness, minimal physical connection distance, and skewed degree distributions characteristic of physically-embedded networks, and that these calculations derived from graph theoretical mathematics did not quantifiably distinguish between subject populations, independent of bandwidth. However, post-hoc measurements of edge computations at the scale of the individual vertex revealed trends of reduced gamma connectivity across the posterior medial parietal cortex in patients, an observation consistent with our prior resting activation study that found significant reduction of synthetic aperture magnetometry gamma power across similar regions. The basis of these small differences remains unclear.

Canonical Granger causality between regions of interest

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors, voxels, or vertices despite the fact that a single region of interest will often include multiple such recordings. In this paper, we present a novel measure of interaction between regions of interest rather than individual signals. The proposed measure, termed canonical Granger causality, combines ideas from canonical correlation and Granger causality analysis to yield a measure that reflects directed causality between two regions of interest. In particular, canonical Granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario. The optimized linear combinations are obtained using a variation of a technique developed for optimization on the Stiefel manifold. We demonstrate the advantages of canonical Granger causality in comparison to alternative causality measures for a range of different simulated datasets. We also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task. Results demonstrate that canonical Granger causality can be used to identify causal relationships between striate and prestriate cortexes in cases where standard Granger causality is unable to identify statistically significant interactions.

Detection of correlated sources in EEG using combination of beamforming and surface Laplacian methods

Beamforming offers a way to estimate the solution to the inverse problem in EEG and MEG but is also known to perform poorly in the presence of highly correlated sources, e.g. during binaural auditory stimulation, when both left and right primary auditory cortices are activated simultaneously. Surface Laplacian, or the second spatial derivative calculated from the electric potential, allows for deblurring of EEG potential recordings reducing the effects of low skull conductivity and is independent of the reference electrode location. We show that anatomically constrained beamforming in conjunction with the surface Laplacian allows for detection of both locations and dynamics of temporally correlated sources in EEG. Whole-head 122 channel binaural stimulus EEG data were simulated using a boundary element method (BEM) and realistic geometry forward model. We demonstrate that in contrast to conventional potential-based EEG beamforming, Laplacian beamforming allows to determine locations of correlated source dipoles without any a priori assumption about the number of sources. We also show (by providing simulations of auditory evoked potentials) that the dynamics at the detected source locations can be derived from subsets of electrodes. Deblurring auditory evoked potential maps subdivides EEG signals from each hemisphere and allows for the beamformer to be applied separately for left and right hemispheres.

Disrupted directed connectivity along the cingulate cortex determines vigilance after sleep deprivation

The cingulate cortex is regarded as the backbone of structural and functional connectivity of the brain. While its functional connectivity has been intensively studied, little is known about its effective connectivity, its modulation by behavioral states, and its involvement in cognitive performance. Given the previously reported effects on cingulate functional connectivity, we investigated how eye-closure and sleep deprivation changed cingulate effective connectivity, estimated from resting-state high-density electroencephalography (EEG) using a novel method to calculate Granger Causality directly in source space. Effective connectivity along the cingulate cortex was dominant in the forward direction. Eyes-open connectivity in the forward direction was greater compared to eyes-closed, in well-rested participants. The difference between eyes-open and eyes-closed connectivity was attenuated and no longer significant after sleep deprivation. Individual variability in the forward connectivity after sleep deprivation predicted subsequent task performance, such that those subjects who showed a greater increase in forward connectivity between the eyes-open and the eyes-closed periods also performed better on a sustained attention task. Effective connectivity in the opposite, backward, direction was not affected by whether the eyes were open or closed or by sleep deprivation. These findings indicate that the effective connectivity from posterior to anterior cingulate regions is enhanced when a well-rested subject has his eyes open compared to when they are closed. Sleep deprivation impairs this directed information flow, proportional to its deleterious effect on vigilance. Therefore, sleep may play a role in the maintenance of waking effective connectivity.

A fast statistical significance test for baseline correction and comparative analysis in phase locking

Human perception, cognition, and action are supported by a complex network of interconnected brain regions. There is an increasing interest in measuring and characterizing these networks as a function of time and frequency, and inter-areal phase locking is often used to reveal these networks. This measure assesses the consistency of phase angles between the electrophysiological activity in two areas at a specific time and frequency. Non-invasively, the signals from which phase locking is computed can be measured with magnetoencephalography (MEG) and electroencephalography (EEG). However, due to the lack of spatial specificity of reconstructed source signals in MEG and EEG, inter-areal phase locking may be confounded by false positives resulting from crosstalk. Traditional phase locking estimates assume that no phase locking exists when the distribution of phase angles is uniform. However, this conjecture is not true when crosstalk is present. We propose a novel method to improve the reliability of the phase-locking measure by sampling phase angles from a baseline, such as from a prestimulus period or from resting-state data, and by contrasting this distribution against one observed during the time period of interest.

Multi-core beamformers: derivation, limitations and improvements

Minimum variance beamformers are popular tools used in EEG and MEG for analysis of brain activity. In recent years new multi-source beamformer methods were developed, including the Dual-Core Beamformer (DCBF) and its enhanced version (eDCBF). Both techniques should allow modeling of correlated brain activity under a wide range of conditions. However, the mathematical justification given is based on single-source results and computer simulations, which do not provide an insight into the assumptions involved and the limits of their applicability. Current work addresses this problem. Analytical expressions relating actual source parameters to those obtained with the DCBF and eDCBF are derived, and rigorous conclusions regarding the accuracy of the DCBF/eDCBF reconstructions are made. In particular, it is shown that DCBF accurately identifies source coordinates, but amplitudes and orientations are only correct for high SNRs and fully correlated sources. In contrast, eDCBF source localization is inaccurate, but if the source positions are found precisely, eDCBF allows perfect reconstruction for arbitrary SNRs. If the source positions are approximate, the reconstruction errors are generally larger for higher SNR values. The eDCBF results can be improved by using global unbiased localizer functions and an alternative way of estimating source orientations.

Source reconstruction accuracy of MEG and EEG Bayesian inversion approaches

Electro- and magnetoencephalography allow for non-invasive investigation of human brain activation and corresponding networks with high temporal resolution. Still, no correct network detection is possible without reliable source localization. In this paper, we examine four different source localization schemes under a common Variational Bayesian framework. A Bayesian approach to the Minimum Norm Model (MNM), an Empirical Bayesian Beamformer (EBB) and two iterative Bayesian schemes (Automatic Relevance Determination (ARD) and Greedy Search (GS)) are quantitatively compared. While EBB and MNM each use a single empirical prior, ARD and GS employ a library of anatomical priors that define possible source configurations. The localization performance was investigated as a function of (i) the number of sources (one vs. two vs. three), (ii) the signal to noise ratio (SNR; 5 levels) and (iii) the temporal correlation of source time courses (for the cases of two or three sources). We also tested whether the use of additional bilateral priors specifying source covariance for ARD and GS algorithms improved performance. Our results show that MNM proves effective only with single source configurations. EBB shows a spatial accuracy of few millimeters with high SNRs and low correlation between sources. In contrast, ARD and GS are more robust to noise and less affected by temporal correlations between sources. However, the spatial accuracy of ARD and GS is generally limited to the order of one centimeter. We found that the use of correlated covariance priors made no difference to ARD/GS performance.

MEG-SIM: a web portal for testing MEG analysis methods using realistic simulated and empirical data

MEG and EEG measure electrophysiological activity in the brain with exquisite temporal resolution. Because of this unique strength relative to noninvasive hemodynamic-based measures (fMRI, PET), the complementary nature of hemodynamic and electrophysiological techniques is becoming more widely recognized (e.g., Human Connectome Project). However, the available analysis methods for solving the inverse problem for MEG and EEG have not been compared and standardized to the extent that they have for fMRI/PET. A number of factors, including the non-uniqueness of the solution to the inverse problem for MEG/EEG, have led to multiple analysis techniques which have not been tested on consistent datasets, making direct comparisons of techniques challenging (or impossible). Since each of the methods is known to have their own set of strengths and weaknesses, it would be beneficial to quantify them. Toward this end, we are announcing the establishment of a website containing an extensive series of realistic simulated data for testing purposes ( http://cobre.mrn.org/megsim/ ). Here, we present: 1) a brief overview of the basic types of inverse procedures; 2) the rationale and description of the testbed created; and 3) cases emphasizing functional connectivity (e.g., oscillatory activity) suitable for a wide assortment of analyses including independent component analysis (ICA), Granger Causality/Directed transfer function, and single-trial analysis.

Interhemispheric effective and functional cortical connectivity signatures of spina bifida are consistent with callosal anomaly

The impact of the posterior callosal anomalies associated with spina bifida on interhemispheric cortical connectivity is studied using a method for estimating cortical multivariable autoregressive models from scalp magnetoencephalography data. Interhemispheric effective and functional connectivity, measured using conditional Granger causality and coherence, respectively, is determined for the anterior and posterior cortical regions in a population of five spina bifida and five control subjects during a resting eyes-closed state. The estimated connectivity is shown to be consistent over the randomly selected subsets of the data for each subject. The posterior interhemispheric effective and functional connectivity and cortical power are significantly lower in the spina bifida group, a result that is consistent with posterior callosal anomalies. The anterior interhemispheric effective and functional connectivity are elevated in the spina bifida group, a result that may reflect compensatory mechanisms. In contrast, the intrahemispheric effective connectivity is comparable in the two groups. The differences between the spina bifida and control groups are most significant in the θ and α bands.

Localizing true brain interactions from EEG and MEG data with subspace methods and modified beamformers

To address the problem of mixing in EEG or MEG connectivity analysis we exploit that noninteracting brain sources do not contribute systematically to the imaginary part of the cross-spectrum. Firstly, we propose to apply the existing subspace method “RAP-MUSIC” to the subspace found from the dominant singular vectors of the imaginary part of the cross-spectrum rather than to the conventionally used covariance matrix. Secondly, to estimate the specific sources interacting with each other, we use a modified LCMV-beamformer approach in which the source direction for each voxel was determined by maximizing the imaginary coherence with respect to a given reference. These two methods are applicable in this form only if the number of interacting sources is even, because odd-dimensional subspaces collapse to even-dimensional ones. Simulations show that (a) RAP-MUSIC based on the imaginary part of the cross-spectrum accurately finds the correct source locations, that (b) conventional RAP-MUSIC fails to do so since it is highly influenced by noninteracting sources, and that (c) the second method correctly identifies those sources which are interacting with the reference. The methods are also applied to real data for a motor paradigm, resulting in the localization of four interacting sources presumably in sensory-motor areas.

Enhancing the signal of corticomuscular coherence

The availability of multichannel neuroimaging techniques, such as MEG and EEG, provides us with detailed topographical information of the recorded magnetic and electric signals and therefore gives us a good overview on the concomitant signals generated in the brain. To assess the location and the temporal dynamics of neuronal sources with noninvasive recordings, reconstruction tools such as beamformers have been shown to be useful. In the current study, we are in particular interested in cortical motor control involved in the isometric contraction of finger muscles. To this end we are measuring the interaction between the dynamics of brain signals and the electrical activity of hand muscles. We were interested to find out whether in addition to the well-known correlated activity between contralateral primary motor cortex and the hand muscles, additional functional connections can be demonstrated. We adopted coherence as a functional index and propose a so-called nulling beamformer method which is computationally efficient and addresses the localization of multiple correlated sources. In simulations of cortico-motor coherence, the proposed method was able to correctly localize secondary sources. The application of the approach on real electromyographic and magnetoencephalographic data collected during an isometric contraction and rest revealed an additional activity in the hemisphere ipsilateral to the hand involved in the task.

Source activity correlation effects on LCMV beamformers in a realistic measurement environment

In EEG and MEG studies on brain functional connectivity and source interactions can be performed at sensor or source level. Beamformers are well-established source-localization tools for MEG/EEG signals, being employed in source connectivity studies both in time and frequency domain. However, it has been demonstrated that beamformers suffer from a localization bias due to correlation between source time courses. This phenomenon has been ascertained by means of theoretical proofs and simulations. Nonetheless, the impact of correlated sources on localization outputs with real data has been disputed for a long time. In this paper, by means of a phantom, we address the correlation issue in a realistic MEG environment. Localization performances in the presence of simultaneously active sources are studied as a function of correlation degree and distance between sources. A linear constrained minimum variance (LCMV) beamformer is applied to the oscillating signals generated by the current dipoles within the phantom. Results show that high correlation affects mostly dipoles placed at small distances (1, 5 centimeters). In this case the sources merge. If the dipoles lie 3 centimeters apart, the beamformer localization detects attenuated power amplitudes and blurred sources as the correlation level raises.

Projection versus prewhitening for EEG interference suppression

Suppression of strong, spatially correlated background interference is a challenge associated with electroencephalography (EEG) source localization problems. The most common way of dealing with such interference is through the use of a prewhitening transformation based on an estimate of the covariance of the interference plus noise. This approach is based on strong assumptions regarding temporal stationarity of the data, which do not commonly hold in EEG applications. In addition, prewhitening cannot typically be implemented directly due to ill conditioning of the covariance matrix, and ad hoc regularization is often necessary. Using both simulation examples and experiments involving real EEG data with auditory evoked responses, we demonstrate that a straightforward interference projection method is significantly more robust than prewhitening for EEG source localization.

Efficient dipole parameter estimation in EEG systems with near-ML performance

Source signals that have strong temporal correlation can pose a challenge for high-resolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other high-resolution methods such as multiple signal classification and linearly constrained minimum variance beamforming fail. These methods are based on approximations to the optimal maximum likelihood (ML) approach, but offer significant computational advantages over ML when estimates of the equivalent EEG dipole orientation and moment are required in addition to the source location. The first method uses a two-stage approach in which localization is performed assuming an unstructured dipole moment model, and then the dipole orientation is obtained by using these estimates in a second step. The second method is based on the use of the noise subspace fitting concept, and has been shown to provide performance that is asymptotically equivalent to the direct ML method. Both techniques lead to a considerably simpler optimization than ML since the estimation of the source locations and dipole moments is decoupled. Examples using data from simulations and auditory experiments are presented to illustrate the performance of the algorithms.

Cross validation for selection of cortical interaction models from scalp EEG or MEG

A cross-validation (CV) method based on state-space framework is introduced for comparing the fidelity of different cortical interaction models to the measured scalp electroencephalogram (EEG) or magnetoencephalography (MEG) data being modeled. A state equation models the cortical interaction dynamics and an observation equation represents the scalp measurement of cortical activity and noise. The measured data are partitioned into training and test sets. The training set is used to estimate model parameters and the model quality is evaluated by computing test data innovations for the estimated model. Two CV metrics normalized mean square error and log-likelihood are estimated by averaging over different training/test partitions of the data. The effectiveness of this method of model selection is illustrated by comparing two linear modeling methods and two nonlinear modeling methods on simulated EEG data derived using both known dynamic systems and measured electrocorticography data from an epilepsy patient.

Frequency-dependent functional connectivity within resting-state networks: an atlas-based MEG beamformer solution

The brain consists of functional units with more-or-less specific information processing capabilities, yet cognitive functions require the co-ordinated activity of these spatially separated units. Magnetoencephalography (MEG) has the temporal resolution to capture these frequency-dependent interactions, although, due to volume conduction and field spread, spurious estimates may be obtained when functional connectivity is estimated on the basis of the extra-cranial recordings directly. Connectivity estimates on the basis of reconstructed sources may similarly be affected by biases introduced by the source reconstruction approach.

Here we propose an analysis framework to reliably determine functional connectivity that is based around two main ideas: (i) functional connectivity is computed for a set of atlas-based ROIs in anatomical space that covers almost the entire brain, aiding the interpretation of MEG functional connectivity/network studies, as well as the comparison with other modalities; (ii) volume conduction and similar bias effects are removed by using a functional connectivity estimator that is insensitive to these effects, namely the Phase Lag Index (PLI).

Our analysis approach was applied to eyes-closed resting-state MEG data for thirteen healthy participants. We first demonstrate that functional connectivity estimates based on phase coherence, even at the source-level, are biased due to the effects of volume conduction and field spread. In contrast, functional connectivity estimates based on PLI are not affected by these biases. We then looked at mean PLI, or weighted degree, over areas and subjects and found significant mean connectivity in three (alpha, beta, gamma) of the five (including theta and delta) classical frequency bands tested. These frequency-band dependent patterns of resting-state functional connectivity were distinctive; with the alpha and beta band connectivity confined to posterior and sensorimotor areas respectively, and with a generally more dispersed pattern for the gamma band. Generally, these patterns corresponded closely to patterns of relative source power, suggesting that the most active brain regions are also the ones that are most-densely connected.

Our results reveal for the first time, using an analysis framework that enables the reliable characterisation of resting-state dynamics in the human brain, how resting-state networks of functionally connected regions vary in a frequency-dependent manner across the cortex.

Brainstorm: a user-friendly application for MEG/EEG analysis

Brainstorm is a collaborative open-source application dedicated to magnetoencephalography (MEG) and electroencephalography (EEG) data visualization and processing, with an emphasis on cortical source estimation techniques and their integration with anatomical magnetic resonance imaging (MRI) data. The primary objective of the software is to connect MEG/EEG neuroscience investigators with both the best-established and cutting-edge methods through a simple and intuitive graphical user interface (GUI).