The use of anatomical constraints with MEG beamformers

Synthetic Aperture Magnetometry (SAM) is a beamformer approach for the localisation of neuronal activity from EEG/MEG data. SAM estimates the optimum orientation of each source in a predefined source space by a nonlinear search for the orientation that maximises the beamformer output. However, MEG is most sensitive to cortical sources and these sources are generally oriented perpendicular to the surface. The reconstructed neuronal activity can therefore reasonably be constrained to the cortical surface, orientated perpendicular to it, therefore removing the search for the optimum orientation for the computation of the beamformer weights. This paper sets out to compare the performance of a constrained and unconstrained beamformer (SAM), with respect to the localisation accuracy of the source reconstructions and the spatial resolution. Fifty sources were randomly placed on a cortical surface estimated from an MRI, and we simulated data over a range of different signal-to-noise ratios (SNRs) for each source. These datasets were analysed using both an unconstrained beamformer (SAM) and a constrained beamformer (with the sources orientated perpendicular to the cortical surface). The influence of errors in the estimation of the surface location and surface normals on the performance of the constrained beamformer, representing MEG/MRI coregistration and segmentation errors, were also examined. The spatial resolution of the beamformer improves, typically by a factor of four by applying anatomical constraints, and the localisation accuracy improves marginally. However, the advantage in spatial resolution disappears when errors are introduced into the orientation and location constraints, and, moreover, the localisation accuracy of the inaccurately constrained beamformer degrades rapidly. We conclude that the use of anatomical constraints is only advantageous if the MEG/MRI coregistration error is smaller than 2 mm and the error in the estimation of the cortical surface orientation is smaller than 10 degrees.     

Simultaneous EEG source localisation and artifact rejection during concurrent fMRI by means of spatial filtering

The simultaneous application of functional MRI and EEG represents an attractive, non-invasive technique for the combined measurement of electrical and haemodynamic activity in the human brain. Simultaneous EEG/fMRI provides a brain imaging modality with millimeter spatial accuracy, and millisecond temporal resolution. However, simultaneously acquired measurements are difficult due to the artifacts that are induced in the EEG by both the temporally varying field gradients used in MRI, and also blood flow effects. In this paper we apply an EEG beamformer spatial filter to EEG data recorded simultaneously with fMRI. We show, using this technique, that it is possible to localise accurately electrical effects in the brain, and that the localisation of driven oscillatory responses in the human visual cortex are spatially co-incident with the fMRI BOLD response. We also show how the beamformer can be used to extract timecourses of electrical activity from areas of interest in the brain. Such timecourses have millisecond time resolution. Finally, we show that in addition to source localisation, the beamformer spatial filter acts to reject interference in EEG signals, thus increasing the effective signal to noise ratio of electrical measurements. We show that the EEG-beamformer can eliminate effectively the ballistocardiogram artifact as well as residual gradient artifacts that remain in EEG data following correction using averaged artifact subtraction techniques.     

Optimising experimental design for MEG beamformer imaging

In recent years, the use of beamformers for source localisation has significantly improved the spatial accuracy of magnetoencephalography. In this paper, we examine techniques by which to optimise experimental design, and ensure that the application of beamformers yields accurate results. We show that variation in the experimental duration, or variation in the bandwidth of a signal of interest, can significantly affect the accuracy of a beamformer reconstruction of source power. Specifically, power will usually be underestimated if covariance windows are made too short, or bandwidths too narrow. The accuracy of spatial localisation may also be reduced. We conclude that for optimum accuracy, experimenters should aim to collect as much data as possible, and use a bandwidth spanning the entire frequency distribution of the signal of interest. This minimises distortion to reconstructed source images, time courses and power estimation. In the case where experimental duration is short, and small covariance windows are therefore used, we show that accurate power estimation can be achieved by matrix regularisation. However, large amounts of regularisation cause a loss in the spatial resolution of the MEG beamformer, hence regularisation should be used carefully, particularly if multiple sources in close proximity are expected.     

Practical constraints on estimation of source extent with MEG beamformers

We aimed to determine practical constraints on the estimation of the spatial extent of neuronal activation using MEG beamformers. Correct estimation of spatial extent is a pre-requisite for accurate models of electrical activity, allows one to estimate current density, and enables non-invasive monitoring of functional recovery following stroke. The output of an MEG beamformer is maximum when the correct source model is used, so that the spatial extent of a source can in principal be determined through evaluation of different source models with the beamformer. Here, we simulated 275-channel MEG data using sources of varying spatial extents that followed the cortical geometry. These data were subsequently used to estimate the spatial extent of generic disc elements without knowledge of the underlying surface, and we compared these results to estimates based on cortical surface geometry (with and without error in surface location). We found that disc-shaped source models are too simplistic, particularly for areas with high curvature. For areas with low curvature spatial extent was underestimated, although on average there was a linear relationship between the true and estimated extent. In contrast, cortical surface models gave accurate predictions of spatial extent. However, adding small errors (>2 mm) to the estimated location of the cortical surface abolished this relationship between true and estimated extent, implying that accurate co-registration is needed with such models. Our results show that models exploiting surface information are necessary in order to model spatial extent and in turn current density, but in order to render such models applicable in practical situations, the accuracy of the cortical surface model itself needs to improve.     

Geometrical interpretation of fMRI-guided MEG/EEG inverse estimates

Magneto- and electroencephalography (MEG/EEG) and functional magnetic resonance imaging (fMRI) provide complementary information about the functional organization of the human brain. An important advantage of MEG/EEG is the millisecond time resolution in detecting electrical activity in the cerebral cortex. The interpretation of MEG/EEG signals, however, is limited by the difficulty of determining the spatial distribution of the neural activity. Functional MRI can help in the MEG/EEG source analysis by suggesting likely locations of activity. We present a geometric interpretation of fMRI-guided inverse solutions in which the MEG/EEG source estimate minimizes a distance to a subspace defined by the fMRI data. In this subspace regularization (SSR) approach, the fMRI bias does not assume preferred amplitudes for MEG/EEG sources, only locations. Characteristic dependence of the source estimates on the regularization parameters is illustrated with simulations. When the fMRI locations match the true MEG/EEG source locations, they serve to bias the underdetermined MEG/EEG inverse solution toward the fMRI loci. Importantly, when the fMRI loci do not match the true MEG/EEG loci, the solution is insensitive to those fMRI loci.     

MEG imaging of sensorimotor areas using inter-trial coherence in vibrotactile steady-state responses

We utilized a novel analysis technique to identify brain areas that activate synchronously during the steady-state interval of responses to vibrotactile stimulation of the right index finger. The inter-trial coherence at the stimulation rate (23 Hz) was determined for whole-brain neural activity estimates based on a linearly-constrained minimum variance beamformer applied to the MEG data. Neural activity coherent with the stimulus occurred in the contralateral primary somatosensory cortex in all subjects, and matched well with equivalent dipole modeling of the same data. Subsets of subjects exhibited additional loci of strongly coherent activity in the contralateral primary motor cortex, posterior parietal cortex, and supplementary motor area, as well as in deeper brain structures above the brainstem. An activation delay of 7 ms from deep structures to cortical areas was estimated based on the mean phase at each coherent neural source within a single subject. This new approach - volumetric mapping of the statistical parameter of inter-trial coherence in steady-state oscillations - broadens the range of MEG beamformer applications specifically for identifying brain areas that are synchronized to repetitive stimuli.     

Quantification of the benefit from integrating MEG and EEG data in minimum l2-norm estimation

Source current estimation from electromagnetic (MEG and EEG) signals is an ill-posed problem that often produces blurry or inaccurately positioned estimates. The two modalities have distinct factors limiting the resolution, e.g., MEG cannot detect radially oriented sources, while EEG is sensitive to accuracy of the head model. This makes combined EEG + MEG estimation techniques desirable, but different acquisition noise statistics, complexity of the head models, and lack of pertinent metrics all complicate the assessment of the resulting improvements. We investigated analytically the effect of including EEG recordings in MEG studies versus the addition of new MEG channels when computing noise-normalized minimum ℓ₂-norm estimates. Three-compartment boundary-element forward models were constructed using structural MRI scans for four subjects. Singular value analysis of the resulting forward models predicted better performance of the EEG + MEG case in the form of higher matrix rank. MNE inverse operators for EEG, MEG and EEG + MEG were constructed using the sensor noise covariance estimated from data. Metrics derived from the resolution matrices predicted higher spatial resolution in EEG + MEG as compared to MEG due to decreased spread (lower spatial dispersion, higher resolution index) with no reduction in dipole localization error. The effect was apparent in all source locations, with increased magnitude for deep areas such as the cingulate cortex. We were also able to corroborate the results for the somatosensory cortex using median nerve responses.     

Combining fMRI and MEG increases the reliability of presurgical language localization: a clinical study on the difference between and congruence of both modalities

To avoid neurological impairment during surgery near language-related eloquent brain areas, we performed presurgical functional brain mapping with functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) in 172 patients using language tasks. For MEG localizations, we used either a moving equivalent-current dipole fit or a current-density reconstruction using a minimum variance beamformer with a spatial filter algorithm. We localized the Wernicke and Broca language areas for every patient. We integrated the results into a frameless stereotaxy system. To visualize the results in the navigation microscope during surgery, we superimposed the fMRI and MEG findings on the brain surface. MEG and fMRI results differed in 4% of cases, and in 19%, one modality showed activation but not the other. In the vicinity of large gliomas, the BOLD (blood oxygenation level-dependent) effect was suppressed in 53% of our patients. Of the 124 patients who had surgery, only 7 patients (5.6%) experienced a transient language deterioration, which resolved in all cases. We used MEG and fMRI to show different aspects of brain activity and to establish validation between MEG and fMRI. We conclude that measurement by both MEG and fMRI increases the degree of reliability of language area localization and that the combination of fMRI and MEG is useful for presurgical localization of language-related eloquent cortex.     

MEG beamforming using Bayesian PCA for adaptive data covariance matrix regularization

Beamformers are a commonly used method for doing source localization from magnetoencephalography (MEG) data. A key ingredient in a beamformer is the estimation of the data covariance matrix. When the noise levels are high, or when there is only a small amount of data available, the data covariance matrix is estimated poorly and the signal-to-noise ratio (SNR) of the beamformer output degrades. One solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre-specified amount. However, this provides improvements at the expense of a loss in spatial resolution, and the parameter controlling the amount of regularization must be chosen subjectively. In this paper, we introduce a method that provides an adaptive solution to this problem by using a Bayesian Principle Component Analysis (PCA). This provides an estimate of the data covariance matrix to give a data-driven, non-arbitrary solution to the trade-off between the spatial resolution and the SNR of the beamformer output. This also provides a method for determining when the quality of the data covariance estimate maybe under question. We apply the approach to simulated and real MEG data, and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels.     

A probabilistic algorithm integrating source localization and noise suppression for MEG and EEG data

We have developed a novel probabilistic model that estimates neural source activity measured by MEG and EEG data while suppressing the effect of interference and noise sources. The model estimates contributions to sensor data from evoked sources, interference sources and sensor noise using Bayesian methods and by exploiting knowledge about their timing and spatial covariance properties. Full posterior distributions are computed rather than just the MAP estimates. In simulation, the algorithm can accurately localize and estimate the time courses of several simultaneously active dipoles, with rotating or fixed orientation, at noise levels typical for averaged MEG data. The algorithm even performs reasonably at noise levels typical of an average of just a few trials. The algorithm is superior to beamforming techniques, which we show to be an approximation to our graphical model, in estimation of temporally correlated sources. Success of this algorithm using MEG data for localizing bilateral auditory cortex, low-SNR somatosensory activations, and for localizing an epileptic spike source are also demonstrated.     

Head movements of children in MEG: quantification, effects on source estimation, and compensation

Head movements during magnetoencephalography (MEG) recordings may lead to inaccurate localization of brain activity. This can be particularly problematic for studies with children. We quantified head movements in 8- to 12-year-old children performing a cognitive task and examined how the movements affected source estimation. Each child was presented auditory word stimuli in five 4-min runs. The mean change in the MEG sensor locations during the experiment ranged from 3 to 26mm across subjects. The variation in the head position was largest in the up-down direction. The mean localization error in equivalent current dipole (ECD) simulations was 12mm for runs with the most head movement, with the frontal cortex appearing to be most prone to errors due to head movements. In addition, we examined the effect of head movements on two types of source estimates, ECDs and minimum-norm estimates (MNE), for an auditory evoked response. Application of a recently introduced signal space separation (SSS) method to compensate for the head movements was found to increase the goodness-of-fit of the ECDs, reduce the spatial confidence intervals of the ECDs, and enhance the peak amplitude in the MNE. These results are indicative of the SSS method being able to compensate for the spatial smoothing of the signals caused by head movements. Overall, the results suggest that MEG source estimates are relatively robust against head movements in children, and that confounds due to head movements can be successfully dealt with in MEG studies of developmental cognition.     

Application of multi-source minimum variance beamformers for reconstruction of correlated neural activity

Linearly constrained minimum variance beamformers are highly effective for analysis of weakly correlated brain activity, but their performance degrades when correlations become significant. Multiple constrained minimum variance (MCMV) beamformers are insensitive to source correlations but require a priori information about the source locations. Besides the question whether unbiased estimates of source positions and orientations can be obtained remained unanswered. In this work, we derive MCMV-based source localizers that can be applied to both induced and evoked brain activity. They may be regarded as a generalization of scalar minimum-variance beamformers for the case of multiple correlated sources. We show that for arbitrary noise covariance these beamformers provide simultaneous unbiased estimates of multiple source positions and orientations and remain bounded at singular points. We also propose an iterative search algorithm that makes it possible to find sources approximately without a priori assumptions about their locations and orientations. Simulations and analyses of real MEG data demonstrate that presented approach is superior to traditional single-source beamformers in situations where correlations between the sources are significant.     

Spectral spatiotemporal imaging of cortical oscillations and interactions in the human brain

This paper presents a computationally efficient source estimation algorithm that localizes cortical oscillations and their phase relationships. The proposed method employs wavelet-transformed magnetoencephalography (MEG) data and uses anatomical MRI to constrain the current locations to the cortical mantle. In addition, the locations of the sources can be further confined with the help of functional MRI (fMRI) data. As a result, we obtain spatiotemporal maps of spectral power and phase relationships. As an example, we show how the phase locking value (PLV), that is, the trial-by-trial phase relationship between the stimulus and response, can be imaged on the cortex. We apply the method to spontaneous, evoked, and driven cortical oscillations measured with MEG. We test the method of combining MEG, structural MRI, and fMRI using simulated cortical oscillations along Heschl's gyrus (HG). We also analyze sustained auditory gamma-band neuromagnetic fields from MEG and fMRI measurements. Our results show that combining the MEG recording with fMRI improves source localization for the non-noise-normalized wavelet power. In contrast, noise-normalized spectral power or PLV localization may not benefit from the fMRI constraint. We show that if the thresholds are not properly chosen, noise-normalized spectral power or PLV estimates may contain false (phantom) sources, independent of the inclusion of the fMRI prior information. The proposed algorithm can be used for evoked MEG/EEG and block-designed or event-related fMRI paradigms, or for spontaneous MEG data sets. Spectral spatiotemporal imaging of cortical oscillations and interactions in the human brain can provide further understanding of large-scale neural activity and communication between different brain regions.     

Beamformer reconstruction of correlated sources using a modified source model

This paper introduces a lead field formulation for use in beamformer analysis of MEG data. This 'dual source beamformer' is a technique to image two temporally correlated sources using beamformer methodology. We show that while the standard, single source beamformer suppresses the reconstructed power of two spatially separate but temporally correlated sources, the dual source beamformer allows for their accurate reconstruction. The technique is proven to be accurate using simulations. We also show that it can be used to image accurately the auditory steady state response, which is correlated between the left and right auditory cortices. We suggest that this technique represents a useful way of locating correlated sources, particularly if a seed location can be defined a priori for one of the two sources. Such a priori information could be based on previous studies using similar paradigms, or from other functional neuroimaging techniques.     

Spatiotemporal frequency tuning of BOLD and gamma band MEG responses compared in primary visual cortex

In this study, the spatial and temporal frequency tuning characteristics of the MEG gamma (40-60 Hz) rhythm and the BOLD response in primary visual cortex were measured and compared. In an identical MEG/fMRI paradigm, 10 participants viewed reversing square wave gratings at 2 spatial frequencies [0.5 and 3 cycles per degree (cpd)] reversing at 5 temporal frequencies (0, 1 6, 10, 15 Hz). Three-dimensional images of MEG source power were generated with synthetic aperture magnetometry (SAM) and showed a high degree of spatial correspondence with BOLD responses in primary visual cortex with a mean spatial separation of 6.5 mm, but the two modalities showed different tuning characteristics. The gamma rhythm showed a clear increase in induced power for the high spatial frequency stimulus while BOLD showed no difference in activity for the two spatial frequencies used. Both imaging modalities showed a general increase of activity with temporal frequency, however, BOLD plateaued around 6-10 Hz while the MEG generally increased with a dip exhibited at 6 Hz. These results demonstrate that the two modalities may show activation in similar spatial locations but that the functional pattern of these activations may differ in a complex manner, suggesting that they may be tuned to different aspects of neuronal activity.     

A multitrial analysis for revealing significant corticocortical networks in magnetoencephalography and electroencephalography

We present an MEG/EEG framework to reveal statistically significant brain areas engaged in the same cognitive process across trials without resort to averaging procedures. The variability of neuronal responses is assumed to take place only in the reconstructed time series of cortical sources and not in their positions. This hypothesis allows the use of the surrogate data method to detect recurrently active brain areas across trials adjusted with any cortically constrained focal MEEG inverse solution. Results obtained from synthetic data show that considering several trials enhances the accuracy of the source localisation. We apply this approach on MEG data recorded during a simple visual stimulation. The considered stimulus is frequency tagged in order to reveal the neural network correlated to its perception using phase synchronisation analysis. The results show consistent patterns of distributed synchronous networks centred on occipital areas.     

A method for spatiotemporal mapping of event-related modulation of cortical rhythmic activity

Cortical rhythmic activity can be systematically modulated by stimuli or tasks and may thus provide relevant information about brain function. Meaningful use of those phenomena requires characterization of both locations and time courses of event-related suppressions and increases of oscillatory activity. However, localization of the neural sources of cortical rhythms during intervals of very low levels of activity, and within short time intervals, is not a trivial matter. Hence, event-related modulation of rhythmic activity has typically been described at the level of magnetoencephalography (MEG) sensors or electroencephalography (EEG) electrodes, without reaching into the brain. Here, we introduce erDICS, an event-related version of Dynamic Imaging of Coherent Sources that allows spatial mapping of the level of oscillatory activity in the brain as a function of time, with respect to stimulus or task timing. By utilizing a time-resolved frequency-domain beamformer, erDICS yields the spatial distribution of both power suppressions and power increases. Permutation tests further reveal areas and time windows in which the modulations of oscillatory power are statistically significant, in individual subjects. We demonstrate the usability of erDICS on simulated and real MEG data. From the erDICS maps we identify areas showing salient event-related changes of rhythmic activity, represent them with equivalent current dipoles and calculate their contribution to the measured signal. Comparison of this multidipole model with the original signal yields a quantitative measure of goodness for the identified source areas and the analysis approach in general.     

GLM-beamformer method demonstrates stationary field, alpha ERD and gamma ERS co-localisation with fMRI BOLD response in visual cortex

Recently, we introduced a new 'GLM-beamformer' technique for MEG analysis that enables accurate localisation of both phase-locked and non-phase-locked neuromagnetic effects, and their representation as statistical parametric maps (SPMs). This provides a useful framework for comparison of the full range of MEG responses with fMRI BOLD results. This paper reports a 'proof of principle' study using a simple visual paradigm (static checkerboard). The five subjects each underwent both MEG and fMRI paradigms. We demonstrate, for the first time, the presence of a sustained (DC) field in the visual cortex, and its co-localisation with the visual BOLD response. The GLM-beamformer analysis method is also used to investigate the main non-phase-locked oscillatory effects: an event-related desynchronisation (ERD) in the alpha band (8-13 Hz) and an event-related synchronisation (ERS) in the gamma band (55-70 Hz). We show, using SPMs and virtual electrode traces, the spatio-temporal covariance of these effects with the visual BOLD response. Comparisons between MEG and fMRI data sets generally focus on the relationship between the BOLD response and the transient evoked response. Here, we show that the stationary field and changes in oscillatory power are also important contributors to the BOLD response, and should be included in future studies on the relationship between neuronal activation and the haemodynamic response.     

MRI-constrained spectral imaging of benzodiazepine modulation of spontaneous neuromagnetic activity in human cortex

Spontaneous electromagnetic brain rhythms have been widely used in human neuropharmacology, but their applicability is complicated by the difficulties to localize their origins in the human cortex. Here, we used a novel multi-modal non-invasive imaging approach to localize lorazepam (30 microg/kg i.v.) modulation of cortical generators of spontaneous brain rhythms. Eight healthy subjects were measured with 306-channel magnetoencephalography (MEG) in a double-blind, randomized, placebo-controlled (saline), crossover design. For anatomically realistic source modeling, wavelet-transformed MEG data were combined with high-resolution MRI to constrain the current locations to the cortical mantle, after which individual data were co-registered to surface-based coordinate system for the calculation of group statistical parametric maps of drug effects. The distributed MRI-constrained MEG source estimates demonstrated decreased alpha (10 Hz) activity in and around the parieto-occipital sulcus and in the calcarine sulcus of the occipital lobe, following from increased GABA(A)-inhibition by lorazepam. Anatomically constrained spectral imaging displays the cortical loci of drug effects on oscillatory brain activity, providing a novel tool for human pharmacological neuroimaging.     

A verifiable solution to the MEG inverse problem

Magnetoencephalography (MEG) is a non-invasive brain imaging technique with the potential for very high temporal and spatial resolution of neuronal activity. The main stumbling block for the technique has been that the estimation of a neuronal current distribution, based on sensor data outside the head, is an inverse problem with an infinity of possible solutions. Many inversion techniques exist, all using different a-priori assumptions in order to reduce the number of possible solutions. Although all techniques can be thoroughly tested in simulation, implicit in the simulations are the experimenter's own assumptions about realistic brain function. To date, the only way to test the validity of inversions based on real MEG data has been through direct surgical validation, or through comparison with invasive primate data. In this work, we constructed a null hypothesis that the reconstruction of neuronal activity contains no information on the distribution of the cortical grey matter. To test this, we repeatedly compared rotated sections of grey matter with a beamformer estimate of neuronal activity to generate a distribution of mutual information values. The significance of the comparison between the un-rotated anatomical information and the electrical estimate was subsequently assessed against this distribution. We found that there was significant (P < 0.05) anatomical information contained in the beamformer images across a number of frequency bands. Based on the limited data presented here, we can say that the assumptions behind the beamformer algorithm are not unreasonable for the visual-motor task investigated.