Probabilistic algorithms for MEG/EEG source reconstruction using temporal basis functions learned from data

We present two related probabilistic methods for neural source reconstruction from MEG/EEG data that reduce effects of interference, noise, and correlated sources. Both methods localize source activity using a linear mixture of temporal basis functions (TBFs) learned from the data. In contrast to existing methods that use predetermined TBFs, we compute TBFs from data using a graphical factor analysis based model [Nagarajan, S.S., Attias, H.T., Hild, K.E., Sekihara, K., 2007a. A probabilistic algorithm for robust interference suppression in bioelectromagnetic sensor data. Stat Med 26, 3886-3910], which separates evoked or event-related source activity from ongoing spontaneous background brain activity. Both algorithms compute an optimal weighting of these TBFs at each voxel to provide a spatiotemporal map of activity across the brain and a source image map from the likelihood of a dipole source at each voxel. We explicitly model, with two different robust parameterizations, the contribution from signals outside a voxel of interest. The two models differ in a trade-off of computational speed versus accuracy of learning the unknown interference contributions. Performance in simulations and real data, both with large noise and interference and/or correlated sources, demonstrates significant improvement over existing source localization methods.     

A graphical model for estimating stimulus-evoked brain responses from magnetoencephalography data with large background brain activity

This paper formulates a novel probabilistic graphical model for noisy stimulus-evoked MEG and EEG sensor data obtained in the presence of large background brain activity. The model describes the observed data in terms of unobserved evoked and background factors with additive sensor noise. We present an expectation maximization (EM) algorithm that estimates the model parameters from data. Using the model, the algorithm cleans the stimulus-evoked data by removing interference from background factors and noise artifacts and separates those data into contributions from independent factors. We demonstrate on real and simulated data that the algorithm outperforms benchmark methods for denoising and separation. We also show that the algorithm improves the performance of localization with beamforming algorithms.     

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.     

Spectral signal space projection algorithm for frequency domain MEG and EEG denoising, whitening, and source imaging

MEG and EEG data contain additive correlated noise generated by environmental and physiological sources. To suppress this type of spatially coloured noise, source estimation is often performed with spatial whitening based on a measured or estimated noise covariance matrix. However, artifacts that span relatively small noise subspaces, such as cardiac, ocular, and muscle artifacts, are often explicitly removed by a variety of denoising methods (e.g., signal space projection) before source imaging. Here, we introduce a new approach, the spectral signal space projection (S(3)P) algorithm, in which time-frequency (TF)-specific spatial projectors are designed and applied to the noisy TF-transformed data, and whitened source estimation is performed in the TF domain. The approach can be used to derive spectral variants of all linear time domain whitened source estimation algorithms. The denoised sensor and source time series are obtained by the corresponding inverse TF-transform. The method is evaluated and compared with existing subspace projection and signal separation techniques using experimental data. Altogether, S(3)P provides an expanded framework for MEG/EEG data denoising and whitened source imaging in both the time and frequency/scale domains.     

Localization of realistic cortical activity in MEG using current multipoles

We present a novel approach to MEG source estimation based on a regularized first-order multipole solution. The Gaussian regularizing prior is obtained by calculation of the sample mean and covariance matrix for the equivalent moments of realistic simulated cortical activity. We compare the regularized multipole localization framework to the classical dipole and general multipole source estimation methods by evaluating the ability of all three solutions to localize the centroids of physiologically plausible patches of activity simulated on the surface of a human cerebral cortex. The results, obtained with a realistic sensor configuration, a spherical head model, and given in terms of field and localization error, depict the performance of the dipolar and multipolar models as a function of variable source surface area (50-500 mm(2)), noise conditions (20, 10, and 5 dB SNR), source orientation (0-90 degrees ), and source depth (3-11 cm). We show that as the sources increase in size, they become less accurately modeled as current dipoles. The regularized multipole systematically outperforms the single dipole model, increasingly so as the spatial extent of the sources increases. In addition, our simulations demonstrate that as the orientation of the sources becomes more radial, dipole localization accuracy decreases substantially, while the performance of the regularized multipole model is far less sensitive to orientation and even succeeds in localizing quasi-radial source configurations. Furthermore, our results show that the multipole model is able to localize superficial sources with higher accuracy than the current dipole. These results indicate that the regularized multipole solution may be an attractive alternative to current-dipole-based source estimation methods in MEG.     

Robust Bayesian estimation of the location, orientation, and time course of multiple correlated neural sources using MEG

The synchronous brain activity measured via MEG (or EEG) can be interpreted as arising from a collection (possibly large) of current dipoles or sources located throughout the cortex. Estimating the number, location, and time course of these sources remains a challenging task, one that is significantly compounded by the effects of source correlations and unknown orientations and by the presence of interference from spontaneous brain activity, sensor noise, and other artifacts. This paper derives an empirical Bayesian method for addressing each of these issues in a principled fashion. The resulting algorithm guarantees descent of a cost function uniquely designed to handle unknown orientations and arbitrary correlations. Robust interference suppression is also easily incorporated. In a restricted setting, the proposed method is shown to produce theoretically zero reconstruction error estimating multiple dipoles even in the presence of strong correlations and unknown orientations, unlike a variety of existing Bayesian localization methods or common signal processing techniques such as beamforming and sLORETA. Empirical results on both simulated and real data sets verify the efficacy of this approach.     

Bayesian analysis of the neuromagnetic inverse problem with l(p)-norm priors

Magnetoencephalography (MEG) allows millisecond-scale non-invasive measurement of magnetic fields generated by neural currents in the brain. However, localization of the underlying current sources is ambiguous due to the so-called inverse problem. The most widely used source localization methods (i.e., minimum-norm and minimum-current estimates (MNE and MCE) and equivalent current dipole (ECD) fitting) require ad hoc determination of the cortical current distribution (l(2)-, l(1)-norm priors and point-sized dipolar, respectively). In this article, we perform a Bayesian analysis of the MEG inverse problem with l(p)-norm priors for the current sources. This way, we circumvent the arbitrary choice between l(1)- and l(2)-norm prior, which is instead rendered automatically based on the data. By obtaining numerical samples from the joint posterior probability distribution of the source current parameters and model hyperparameters (such as the l(p)-norm order p) using Markov chain Monte Carlo (MCMC) methods, we calculated the spatial inverse estimates as expectation values of the source current parameters integrated over the hyperparameters. Real MEG data and simulated (known) source currents with realistic MRI-based cortical geometry and 306-channel MEG sensor array were used. While the proposed model is sensitive to source space discretization size and computationally rather heavy, it is mathematically straightforward, thus allowing incorporation of, for instance, a priori functional magnetic resonance imaging (fMRI) information.     

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.     

A new method to identify multiple sources of oscillatory activity from magnetoencephalographic data

Identifying the sources of oscillatory activity in the human brain is a challenging problem in current magnetoencephalography (MEG) and electroencephalography (EEG) research. The fluctuations in phase and amplitude of cortical oscillations preclude signal averaging over successive sections of the data without a priori assumptions. In addition, several sources at different locations often produce oscillatory activity at similar frequencies. For example, spontaneous oscillatory activity in the 8- to 13-Hz band is produced simultaneously at least in the posterior parts of the brain and bilaterally in the sensorimotor cortices. The previous approaches of identifying sources of oscillatory activity by dipole modeling of bandpass filtered data are quite laborious and require that multiple criteria are defined by an experienced user. In this work we introduce a convenient method for source localization using minimum current estimates in the frequency domain. Individual current estimates are calculated for the Fourier transforms of successive sections of continuous data. These current estimates are then averaged. The algorithm was tested on simulated and measured MEG data and compared with conventional dipole modeling. The main advantage of the proposed method is that it provides an efficient approach for simultaneous estimation of multiple sources of oscillatory activity in the same frequency band.     

Validation of SOBI components from high-density EEG

Second-order blind identification (SOBI) is a blind source separation (BSS) algorithm that can be used to decompose mixtures of signals into a set of components or putative recovered sources. Previously, SOBI, as well as other BSS algorithms, has been applied to magnetoencephalography (MEG) and electroencephalography (EEG) data. These BSS algorithms have been shown to recover components that appear to be physiologically and neuroanatomically interpretable. While some proponents of these algorithms suggest that fundamental discoveries about the human brain might be made through the application of these techniques, validation of BSS components has not yet received sufficient attention. Here we present two experiments for validating SOBI-recovered components. The first takes advantage of the fact that noise sources associated with individual sensors can be objectively validated independently from the SOBI process. The second utilizes the fact that the time course and location of primary somatosensory (SI) cortex activation by median nerve stimulation have been extensively characterized using converging imaging methods. In this paper, using both known noise sources and highly constrained and well-characterized neuronal sources, we provide validation for SOBI decomposition of high-density EEG data. We show that SOBI is able to (1) recover known noise sources that were either spontaneously occurring or artificially induced; (2) recover neuronal sources activated by median nerve stimulation that were spatially and temporally consistent with estimates obtained from previous EEG, MEG, and fMRI studies; (3) improve the signal-to-noise ratio (SNR) of somatosensory-evoked potentials (SEPs); and (4) reduce the level of subjectivity involved in the source localization process.     

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.     

Source reconstruction of brain electromagnetic fields — Source iteration of minimum norm (SIMN)

A recursive scheme aiming at obtaining sparse and focal brain electromagnetic source distribution is proposed based on the interpretation that the weighted minimum norm is the minimum norm estimates of amplitudes on grid points for the source distribution specified by the diagonal elements of the weight matrix. The source distribution is updated so that, at each grid point, the number of current dipoles equals the total source strength estimate of the pre-specified current dipoles. The source strength of a pre-specified current dipole is estimated by projecting the vector of minimum norm estimate to the space spanned by the three column vectors, corresponding to the three amplitudes of the current dipole, of the resolution matrix. The norm of the projected vector yields the source strength estimate of the current dipole. Exact inverse solutions are obtained by this source iteration of minimum norm (SIMN) algorithm for noiseless MEG signals from multi-point sources provided the sources are sufficiently sparse and there are no substantial cancellations among the signals of the sources. For noisy data, a set of “noise sources” is introduced. The diagonal matrix formed by the “noise source numbers” plays the role of regularization matrix and Tikhonov regularization is applied to initialize the “noise source numbers”. Application to the source localization of real EEG data is also presented.     

Performance evaluation of the Champagne source reconstruction algorithm on simulated and real M/EEG data

In this paper, we present an extensive performance evaluation of a novel source localization algorithm, Champagne. It is derived in an empirical Bayesian framework that yields sparse solutions to the inverse problem. It is robust to correlated sources and learns the statistics of non-stimulus-evoked activity to suppress the effect of noise and interfering brain activity. We tested Champagne on both simulated and real M/EEG data. The source locations used for the simulated data were chosen to test the performance on challenging source configurations. In simulations, we found that Champagne outperforms the benchmark algorithms in terms of both the accuracy of the source localizations and the correct estimation of source time courses. We also demonstrate that Champagne is more robust to correlated brain activity present in real MEG data and is able to resolve many distinct and functionally relevant brain areas with real MEG and EEG data.     

Understanding brain connectivity from EEG data by identifying systems composed of interacting sources

In understanding and modeling brain functioning by EEG/MEG, it is not only important to be able to identify active areas but also to understand interference among different areas. The EEG/MEG signals result from the superimposition of underlying brain source activities volume conducted through the head. The effects of volume conduction produce spurious interactions in the measured signals. It is fundamental to separate true source interactions from noise and to unmix the contribution of different systems composed by interacting sources in order to understand interference mechanisms. As a prerequisite, we consider the problem of unmixing the contribution of uncorrelated sources to a measured field. This problem is equivalent to the problem of unmixing the contribution of different uncorrelated compound systems composed by interacting sources. To this end, we develop a principal component analysis-based method, namely, the source principal component analysis (sPCA), which exploits the underlying assumption of orthogonality for sources, estimated from linear inverse methods, for the extraction of essential features in signal space. We then consider the problem of demixing the contribution of correlated sources that comprise each of the compound systems identified by using sPCA. While the sPCA orthogonality assumption is sufficient to separate uncorrelated systems, it cannot separate the individual components within each system. To address that problem, we introduce the Minimum Overlap Component Analysis (MOCA), employing a pure spatial criterion to unmix pairs of correlates (or coherent) sources. The proposed methods are tested in simulations and applied to EEG data from human micro and alpha rhythms.     

Investigations of dipole localization accuracy in MEG using the bootstrap

We describe the use of the nonparametric bootstrap to investigate the accuracy of current dipole localization from magnetoencephalography (MEG) studies of event-related neural activity. The bootstrap is well suited to the analysis of event-related MEG data since the experiments are repeated tens or even hundreds of times and averaged to achieve acceptable signal-to-noise ratios (SNRs). The set of repetitions or epochs can be viewed as a set of independent realizations of the brain's response to the experiment. Bootstrap resamples can be generated by sampling with replacement from these epochs and averaging. In this study, we applied the bootstrap resampling technique to MEG data from somatotopic experimental and simulated data. Four fingers of the right and left hand of a healthy subject were electrically stimulated, and about 400 trials per stimulation were recorded and averaged in order to measure the somatotopic mapping of the fingers in the S1 area of the brain. Based on single-trial recordings for each finger we performed 5000 bootstrap resamples. We reconstructed dipoles from these resampled averages using the Recursively Applied and Projected (RAP)-MUSIC source localization algorithm. We also performed a simulation for two dipolar sources with overlapping time courses embedded in realistic background brain activity generated using the prestimulus segments of the somatotopic data. To find correspondences between multiple sources in each bootstrap, sample dipoles with similar time series and forward fields were assumed to represent the same source. These dipoles were then clustered by a Gaussian Mixture Model (GMM) clustering algorithm using their combined normalized time series and topographies as feature vectors. The mean and standard deviation of the dipole position and the dipole time series in each cluster were computed to provide estimates of the accuracy of the reconstructed source locations and time series.     

A distributed spatio-temporal EEG/MEG inverse solver

We propose a novel l(1)l(2)-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard l(1)-norm inverse solvers, this sparse distributed inverse solver integrates the l(1)-norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and "spiky" reconstructed signals often produced by the currently used sparse solvers. The joint spatio-temporal model leads to a cost function with an l(1)l(2)-norm regularizer whose minimization can be reduced to a convex second-order cone programming (SOCP) problem and efficiently solved using the interior-point method. The efficient computation of the SOCP problem allows us to implement permutation tests for estimating statistical significance of the inverse solution. Validation with simulated and human MEG data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting, but without the need to specify the number of dipole sources in advance. Furthermore, the l(1)l(2)-norm solver achieves fewer false positives and a better representation of the source locations than the conventional l(2) minimum-norm estimates.     

Independent components of magnetoencephalography: single-trial response onset times

Werecently demonstrated that second-order blind identification (SOBI), an independent component analysis (ICA) method, can separate the mixture of neuronal and noise signals in magnetoencephalographic (MEG) data into neuroanatomically and neurophysiologically meaningful components. When the neuronal signals had relatively higher trial-to-trial variability, SOBI offered a particular advantage in identifying and localizing neuronal source activations with increased source detectability (A. C. Tang et al., 2002, Neural Comput. 14, 1827-1858). Here, we explore the utility of SOBI in the analysis of temporal aspects of neuromagnetic signals from MEG data. From SOBI components, we were able to measure single-trial response onset times of neuronal populations in visual, auditory, and somatosensory modalities during cognitive and sensory activation tasks, with a detection rate as high as 96% under optimal conditions. Comparing the SOBI-aided detection results with those obtained directly from the sensors, we found that with SOBI preprocessing, we were able to measure, among a greater proportion of trials, single-trial response onset times that are above background neuronal activity. We suggest that SOBI ICA can improve our current capability in measuring single-trial responses from human subjects using the noninvasive brain imaging method MEG.     

Comparison of minimum current estimate and dipole modeling in the analysis of simulated activity in the human visual cortices

Magnetoencephalographic(MEG) data are typically interpreted using source models because of the nonunique inverse problem. Although single current dipoles, adequately representing local active areas, can be identified accurately, multiple and overlapping sources form a challenge for MEG modeling. We tested the performances of multidipole modeling and minimum current estimate (MCE) in the analysis of complicated source configurations. Simulated current sources were placed to physiologically meaningful areas of the human visual cortices. Ten volunteers from the laboratory staff analyzed four different simulations with both dipole modeling and MCE without prior information of the sources. In general, the same sources were found using both modeling methods. The subjects tended to report more false sources with MCE than with dipole model, in part due to their inexperience with the method. Dipole model was more accurate than MCE both in time and space for nonsimultaneous sources but both methods performed similarly when sources overlapped in time. For all source configurations, considerably smaller source amplitudes were reported with MCE than with dipole model.     

Reconstruction of correlated brain activity with adaptive spatial filters in MEG

Adaptive spatial filters (beamformers) have gained popularity as an effective method for the localization of brain activity from magnetoencephalography (MEG) data. Among the attractive features of some beamforming methods are high spatial resolution and no localization bias even in the presence of random noise. A drawback common to all beamforming methods, however, is significant degradation in performance in the presence of sources with high temporal correlations. Using numerical simulations and examples of auditory and visual evoked field responses, we demonstrate that, at typical signal-to-noise levels, the complete attenuation of fully correlated brain activity is less likely to occur, although significant localization and amplitude biases may occur. We compared various methods for correcting these biases and found the coherent source suppression model (CSSM) (Dalal et al., 2006) to be the most effective, with small biases for widely separated sources (e.g., bilateral auditory areas), however, amplitude biases increased systematically as distance between the sources was decreased. We assessed the performance and systematic biases that may result from the use of this model, and confirmed our findings with real examples of correlated brain activity in bilateral occipital and inferior temporal areas evoked by visually presented faces in a group of 21 adults. We demonstrated the ability to localize source activity in both regions, including correlated sources that are in close proximity (～ 3 cm) in bilateral primary visual cortex when using a priori information regarding source location. We conclude that CSSM, when carefully applied, can significantly improve localization accuracy, although amplitude biases may remain.     

Simultaneous MEG and intracranial EEG recordings during attentive reading

The relationship between neural oscillations recorded at various spatial scales remains poorly understood partly due to an overall dearth of studies utilizing simultaneous measurements. In an effort to study quantitative markers of attention during reading, we performed simultaneous magnetoencephalography (MEG) and intracranial electroencephalography (iEEG) recordings in four epileptic patients. Patients were asked to attend to a specific color when presented with an intermixed series of red words and green words, with words of a given color forming a cohesive story. We analyzed alpha, beta, and gamma band oscillatory responses to the word presentation and compared the strength and spatial organization of those responses in both electrophysiological recordings. Time-frequency analysis of iEEG revealed a network of clear attention-modulated high gamma band (50–150 Hz) power increases and alpha/beta (9–25 Hz) suppressions in response to the words. In addition to analyses at the sensor level, MEG time-frequency analysis was performed at the source level using a sliding window beamformer technique. Strong alpha/beta suppressions were observed in MEG reconstructions, in tandem with iEEG effects. While the MEG counterpart of high gamma band enhancement was difficult to interpret at the sensor level in two patients, MEG time-frequency source reconstruction revealed additional activation patterns in accordance with iEEG results. Importantly, iEEG allowed us to confirm that several sources of gamma band modulation observed with MEG were indeed of cortical origin rather than EMG muscular or ocular artifact.