MEG and EEG Source Localization in Beamspace

Spatiotemporal signal space separation for regions of interest: Application for extracting neuromagnetic responses evoked by deep brain stimulation

Magnetoencephalography (MEG) recordings are often contaminated by interference that can exceed the amplitude of physiological brain activity by several orders of magnitude. Furthermore, the activity of interference sources may spatially extend (known as source leakage) into the activity of brain signals of interest, resulting in source estimation inaccuracies. This problem is particularly apparent when using MEG to interrogate the effects of brain stimulation on large-scale cortical networks. In this technical report, we develop a novel denoising approach for suppressing the leakage of interference source activity into the activity representing a brain region of interest. This approach leverages spatial and temporal domain projectors for signal arising from prespecified anatomical regions of interest. We apply this denoising approach to reconstruct simulated evoked response topographies to deep brain stimulation (DBS) in a phantom recording. We highlight the advantages of our approach compared to the benchmark-spatiotemporal signal space separation-and show that it can more accurately reveal brain stimulation-evoked response topographies. Finally, we apply our method to MEG recordings from a single patient with Parkinson's disease, to reveal early cortical-evoked responses to DBS of the subthalamic nucleus.

A new data covariance matrix estimation for improving minimum variance brain source localization

Data with finite samples results in accuracy and robustness reduction of data covariance matrix estimation, which in turn results in performance reduction of minimum variance beamformer (MVB) for brain source localization (BSL). General linear combination (GLC) and convex combination (CC) are methods of interest for data covariance matrix estimation and increasing its accuracy and robustness because their scalar coefficients are obtained automatically and adaptively. However, based on our best knowledge, the applicability of GLC and CC algorithms has not been investigated for BSL to inform us about their performance. In this paper, we have two goals: 1) Investigation of GLC and CC covariance matrices applications for BSL is carried out using various simulated MEG scenarios and real MEG and clinical epilepsy data; 2) Modified GLC and CC are developed for more accurate and robust estimation of data covariance matrix when data with finite samples is available. In the modified versions, the scalar coefficients are replaced by diagonal matrix form coefficients. These matrix form coefficients are computed using the Hadamard product and mean square error concept. The evaluations show that the CC and modified CC based MVBs are not robust for BSL due to very small values of coefficients. Based on the simulated, real, and clinical data results, it can be stated that the modified GLC is significantly superior to conventional GLC in terms of localization error, spatial resolution (all z < -2; all p-values < 0.001), and offering reliable results. Also, the proposed GLC offers fewer missed sources and less sensitivity to the depth biasing problem, particularly in a high signal-to-noise ratio. In conclusion, it can be said that the covariance matrix of modified GLC which is user-free and robust against the finite data samples can improve the MVB performance for BSL in terms of localization error and spatial resolution.

Frequency-Resolved Functional Connectivity: Role of Delay and the Strength of Connections

The brain functional network extracted from the BOLD signals reveals the correlated activity of the different brain regions, which is hypothesized to underlie the integration of the information across functionally specialized areas. Functional networks are not static and change over time and in different brain states, enabling the nervous system to engage and disengage different local areas in specific tasks on demand. Due to the low temporal resolution, however, BOLD signals do not allow the exploration of spectral properties of the brain dynamics over different frequency bands which are known to be important in cognitive processes. Recent studies using imaging tools with a high temporal resolution has made it possible to explore the correlation between the regions at multiple frequency bands. These studies introduce the frequency as a new dimension over which the functional networks change, enabling brain networks to transmit multiplex of information at any time. In this computational study, we explore the functional connectivity at different frequency ranges and highlight the role of the distance between the nodes in their correlation. We run the generalized Kuramoto model with delayed interactions on top of the brain's connectome and show that how the transmission delay and the strength of the connections, affect the correlation between the pair of nodes over different frequency bands.

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.

Beamspace dual signal space projection (bDSSP): a method for selective detection of deep sources in MEG measurements

OBJECTIVE

Magnetoencephalography (MEG) has a well-recognized weakness at detecting deeper brain activities. This paper proposes a novel algorithm for selective detection of deep sources by suppressing interference signals from superficial sources in MEG measurements.

APPROACH

The proposed algorithm combines the beamspace preprocessing method with the dual signal space projection (DSSP) interference suppression method. A prerequisite of the proposed algorithm is prior knowledge of the location of the deep sources. The proposed algorithm first derives the basis vectors that span a local region just covering the locations of the deep sources. It then estimates the time-domain signal subspace of the superficial sources by using the projector composed of these basis vectors. Signals from the deep sources are extracted by projecting the row space of the data matrix onto the direction orthogonal to the signal subspace of the superficial sources.

MAIN RESULTS

Compared with the previously proposed beamspace signal space separation (SSS) method, the proposed algorithm is capable of suppressing much stronger interference from superficial sources. This capability is demonstrated in our computer simulation as well as experiments using phantom data.

SIGNIFICANCE

The proposed bDSSP algorithm can be a powerful tool in studies of physiological functions of midbrain and deep brain structures.

Decoding Brain States Based on Magnetoencephalography From Prespecified Cortical Regions

Brain state decoding based on whole-head MEG has been extensively studied over the past decade. Recent MEG applications pose an emerging need of decoding brain states based on MEG signals originating from prespecified cortical regions. Toward this goal, we propose a novel region-of-interest-constrained discriminant analysis algorithm (RDA) in this paper. RDA integrates linear classification and beamspace transformation into a unified framework by formulating a constrained optimization problem. Our experimental results based on human subjects demonstrate that RDA can efficiently extract the discriminant pattern from prespecified cortical regions to accurately distinguish different brain states.

Optimising beamformer regions of interest analysis

Beamforming is a spatial filtering based source reconstruction method for EEG and MEG that allows the estimation of neuronal activity at a particular location within the brain. The computation of the location specific filter depends solely on an estimate of the data covariance matrix and on the forward model. Increasing the number of M/EEG sensors, increases the quantity of data required for accurate covariance matrix estimation. Often however we have a prior hypothesis about the site of, or the signal of interest. Here we show how this prior specification, in combination with optimal estimations of data dimensionality, can give enhanced beamformer performance for relatively short data segments. Specifically we show how temporal (Bayesian Principal Component Analysis) and spatial (lead field projection) methods can be combined to produce improvements in source estimation over and above employing the approaches individually.

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This paper concerns optimising beamformer analysis for anatomical ROIs.

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Channel reduction is performed using an ROI projection and Bayesian PCA.

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This improves covariance matrix estimation for a given data length.

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The proposed approach results in improvements in source estimation.

Minimum variance brain source localization for short data sequences

In the electroencephalogram (EEG) or magnetoencephalogram (MEG) context, brain source localization methods that rely on estimating second-order statistics often fail when the number of samples of the recorded data sequences is small in comparison to the number of electrodes. This condition is particularly relevant when measuring evoked potentials. Due to the correlated background EEG/MEG signal, an adaptive approach to localization is desirable. Previous work has addressed these issues by reducing the adaptive degrees of freedom (DoFs). This reduction results in decreased resolution and accuracy of the estimated source configuration. This paper develops and tests a new multistage adaptive processing technique based on the minimum variance beamformer for brain source localization that has been previously used in the radar statistical signal processing context. This processing, referred to as the fast fully adaptive (FFA) approach, can significantly reduce the required sample support, while still preserving all available DoFs. To demonstrate the performance of the FFA approach in the limited data scenario, simulation and experimental results are compared with two previous beamforming approaches; i.e., the fully adaptive minimum variance beamforming method and the beamspace beamforming method. Both simulation and experimental results demonstrate that the FFA method can localize all types of brain activity more accurately than the other approaches with limited data.

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.

Brain source localization based on fast fully adaptive approach

In the electroencephalogram (EEG) or magnetoencephalogram (MEG) context, brain source localization (beamforming) methods often fail when the number of observations is small. This is particularly true when measuring evoked potentials, especially when the number of electrodes is large. Due to the nonstationarity of the EEG/MEG, an adaptive capability is desirable. Previous work has addressed these issues by reducing the adaptive degrees of freedom (DoFs). This paper develops and tests a new multistage adaptive processing for brain source localization that has been previously used for radar statistical signal processing application with uniform linear antenna array. This processing, referred to as the fast fully adaptive (FFA) approach, could significantly reduce the required sample support and computational complexity, while still processing all available DoFs. The performance improvement offered by the FFA approach in comparison to the fully adaptive minimum variance beamforming (MVB) with limited data is demonstrated by bootstrapping simulated data to evaluate the variability of the source location.

Decomposition of magnetoencephalographic data into components corresponding to deep and superficial sources

We extend the signal space separation (SSS) method to decompose multichannel magnetoencephalographic (MEG) data into regions of interest inside the head. It has been shown that the SSS method can transform MEG data into a signal component generated by neurobiological sources and a noise component generated by external sources outside the head. In this paper, we show that the signal component obtained by the SSS method can be further decomposed by a simple operation into signals originating from deep and superficial sources within the brain. This is achieved by using a scheme that exploits the beamspace methodology that relies on a linear transformation that maximizes the power of the source space of interest. The efficiency and accuracy of the algorithm are demonstrated by experiments utilizing both simulated and real MEG data.

Cortical patch basis model for spatially extended neural activity

A new source model for representing spatially distributed neural activity is presented. The signal of interest is modeled as originating from a patch of cortex and is represented using a set of basis functions. Each cortical patch has its own set of bases, which allows representation of arbitrary source activity within the patch. This is in contrast to previously proposed cortical patch models which assume a specific distribution of activity within the patch. We present a procedure for designing bases that minimize the normalized mean squared representation error, averaged over different activity distributions within the patch. Extension of existing algorithms to the basis function framework is straightforward and is illustrated using linearly constrained minimum variance (LCMV) spatial filtering and maximum-likelihood signal estimation/generalized likelihood ratio test (ML/GLRT). The number of bases chosen for each patch determines a tradeoff between representation accuracy and the ability to differentiate between distinct patches. We propose choosing the minimum number of bases that satisfy a constraint on the normalized mean squared representation accuracy. A mismatch analysis for LCMV and ML/GLRT is presented to show that this is an appropriate strategy for choosing the number of bases. The effectiveness of the patch basis model is demonstrated using real and simulated evoked response data. We show that significant changes in performance occur as the number of basis functions varies, and that very good results are obtained by allowing modest representation error.

Subspace Projection Filters for Real-Time Brain Electromagnetic Imaging

An increasing number of neuroimaging laboratories are becoming interested in real-time investigations of the human brain. The opportunities offered by real-time applications are inversely proportional to the latency of the brain activity response and to the computational delay of brain activity estimation. Electromagnetic tomographies, based on electroencephalography (EEG) or magnetoencephalography (MEG), feature immediacy of brain activity response and excellent time resolution, hence they are natural candidates. However their spatial resolution and signal-to-noise ratio are poor. In this paper, we develop data-independent and data-dependent subspace projection filters for the standardized low-resolution electromagnetic tomography (sLORETA), a weighted minimum norm inverse solution for EEG/MEG. The filters are designed for extracting time-series of source activity in any given region of interest. The data-independent filter is shown to reduce interference of sources originating in neighboring regions, whereas the data-dependent filter is shown to suppress sensor measurement noise. An effective and straightforward way to combine them is demonstrated. The result is a dual subspace projection allowing both noise suppression and interference reduction.

Classification of movement intention by spatially filtered electromagnetic inverse solutions

We couple standardized low-resolution electromagnetic tomography, an inverse solution for electroencephalography (EEG) and the common spatial pattern, which is here conceived as a data-driven beamformer, to classify the benchmark BCI (brain-computer interface) competition 2003, data set IV. The data set is from an experiment where a subject performed a self-paced left and right finger tapping task. Available for analysis are 314 training trials whereas 100 unlabelled test trials have to be classified. The EEG data from 28 electrodes comprise the recording of the 500 ms before the actual finger movements, hence represent uniquely the left and right finger movement intention. Despite our use of an untrained classifier, and our extraction of only one attribute per class, our method yields accuracy similar to the winners of the competition for this data set. The distinct advantages of the approach presented here are the use of an untrained classifier and the processing speed, which make the method suitable for actual BCI applications. The proposed method is favourable over existing classification methods based on an EEG inverse solution, which rely either on iterative algorithms for single-trial independent component analysis or on trained classifiers.