Truncated RAP-MUSIC (TRAP-MUSIC) for MEG and EEG source localization

Representational dissimilarity component analysis (ReDisCA)

The principle of Representational Similarity Analysis (RSA) posits that neural representations reflect the structure of encoded information, allowing exploration of spatial and temporal organization of brain information processing. Traditional RSA when applied to EEG or MEG data faces challenges in accessing activation time series at the brain source level due to modeling complexities and insufficient geometric/anatomical data. To overcome this, we introduce Representational Dissimilarity Component Analysis (ReDisCA), a method for estimating spatial-temporal components in EEG or MEG responses aligned with a target representational dissimilarity matrix (RDM). ReDisCA yields informative spatial filters and associated topographies, offering insights into the location of "representationally relevant" sources. Applied to evoked response time series, ReDisCA produces temporal source activation profiles with the desired RDM. Importantly, while ReDisCA does not require inverse modeling its output is consistent with EEG and MEG observation equation and can be used as an input to rigorous source localization procedures. Demonstrating ReDisCA's efficacy through simulations and comparison with conventional methods, we show superior source localization accuracy and apply the method to real EEG and MEG datasets, revealing physiologically plausible representational structures without inverse modeling. ReDisCA adds to the family of inverse modeling free methods such as independent component analysis (Makeig, 1995), Spatial spectral decomposition (Nikulin, 2011), and Source power comodulation (Dähne, 2014) designed for extraction sources with desired properties from EEG or MEG data. Extending its utility beyond EEG and MEG analysis, ReDisCA is likely to find application in fMRI data analysis and exploration of representational structures emerging in multilayered artificial neural networks.

From bench to bedside: Overview of magnetoencephalography in basic principle, signal processing, source localization and clinical applications

Magnetoencephalography (MEG) is a non-invasive technique that can precisely capture the dynamic spatiotemporal patterns of the brain by measuring the magnetic fields arising from neuronal activity along the order of milliseconds. Observations of brain dynamics have been used in cognitive neuroscience, the diagnosis of neurological diseases, and the brain-computer interface (BCI). In this study, we outline the basic principle, signal processing, and source localization of MEG, and describe its clinical applications for cognitive assessment, the diagnoses of neurological diseases and mental disorders, preoperative evaluation, and the BCI. This review not only provides an overall perspective of MEG, ranging from practical techniques to clinical applications, but also enhances the prevalent understanding of neural mechanisms. The use of MEG is expected to lead to significant breakthroughs in neuroscience.

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.

An F-ratio-based method for estimating the number of active sources in MEG

Introduction

Magnetoencephalography (MEG) is a powerful technique for studying the human brain function. However, accurately estimating the number of sources that contribute to the MEG recordings remains a challenging problem due to the low signal-to-noise ratio (SNR), the presence of correlated sources, inaccuracies in head modeling, and variations in individual anatomy.

Methods

To address these issues, our study introduces a robust method for accurately estimating the number of active sources in the brain based on the F-ratio statistical approach, which allows for a comparison between a full model with a higher number of sources and a reduced model with fewer sources. Using this approach, we developed a formal statistical procedure that sequentially increases the number of sources in the multiple dipole localization problem until all sources are found.

Results

Our results revealed that the selection of thresholds plays a critical role in determining the method's overall performance, and appropriate thresholds needed to be adjusted for the number of sources and SNR levels, while they remained largely invariant to different inter-source correlations, translational modeling inaccuracies, and different cortical anatomies. By identifying optimal thresholds and validating our F-ratio-based method in simulated, real phantom, and human MEG data, we demonstrated the superiority of our F-ratio-based method over existing state-of-the-art statistical approaches, such as the Akaike Information Criterion (AIC) and Minimum Description Length (MDL).

Discussion

Overall, when tuned for optimal selection of thresholds, our method offers researchers a precise tool to estimate the true number of active brain sources and accurately model brain function.

Source localization using recursively applied and projected MUSIC with flexible extent estimation

Magneto- and electroencephalography (M/EEG) are widespread techniques to measure neural activity in-vivo at a high temporal resolution but low spatial resolution. Locating the neural sources underlying the M/EEG poses an inverse problem, which is ill-posed. We developed a new method based on Recursive Application of Multiple Signal Classification (MUSIC). Our proposed method is able to recover not only the locations but, in contrast to other inverse solutions, also the extent of active brain regions flexibly (FLEX-MUSIC). This is achieved by allowing it to search not only for single dipoles but also dipole clusters of increasing extent to find the best fit during each recursion. FLEX-MUSIC achieved the highest accuracy for both single dipole and extended sources compared to all other methods tested. Remarkably, FLEX-MUSIC was capable to accurately estimate the level of sparsity in the source space (r = 0.82), whereas all other approaches tested failed to do so (r ≤ 0.18). The average computation time of FLEX-MUSIC was considerably lower compared to a popular Bayesian approach and comparable to that of another recursive MUSIC approach and eLORETA. FLEX-MUSIC produces only few errors and was capable to reliably estimate the extent of sources. The accuracy and low computation time of FLEX-MUSIC renders it an improved technique to solve M/EEG inverse problems both in neuroscience research and potentially in pre-surgery diagnostic in epilepsy.

The association of magnetoencephalography high-frequency oscillations with epilepsy types and a ripple-based method with source-level connectivity for mapping epilepsy sources

OBJECTIVE

To explore the association between high-frequency oscillations (HFOs) and epilepsy types and to improve the accuracy of source localization.

METHODS

Magnetoencephalography (MEG) ripples of 63 drug-resistant epilepsy patients were detected. Ripple rates, distribution, spatial complexity, and the clustering coefficient of ripple channels were used for the preliminary classification of lateral temporal lobe epilepsy (LTLE), mesial temporal lobe epilepsy (MTLE), and nontemporal lobe epilepsy (NTLE), mainly frontal lobe epilepsy (FLE). Furthermore, the seizure site identification was improved using the Tucker LCMV method and source-level betweenness centrality.

RESULTS

Ripple rates were significantly higher in MTLE than in LTLE and NTLE (p < 0.05). The LTLE and MTLE were mainly distributed in the temporal lobe, followed by the parietal lobe, occipital lobe, and frontal lobe, whereas MTLE ripples were mainly distributed in the frontal lobe, then parietal lobe and occipital lobe. Nevertheless, the NTLE ripples were primarily in the frontal lobe and partially in the occipital lobe (p < 0.05). Meanwhile, the spatial complexity of NTLE was significantly higher than that of LTLE and MTLE and was lowest in MTLE (p < 0.01). However, an opposite trend was observed for the standardized clustering coefficient compared with spatial complexity (p < 0.01). Finally, the tucker algorithm showed a higher percentage of ripples at the surgical site when the betweenness centrality was added (p < 0.01).

CONCLUSION

This study demonstrated that HFO rates, distribution, spatial complexity, and clustering coefficient of ripple channels varied considerably among the three epilepsy types. Additionally, tucker MEG estimation combined with ripple rates based on the source-level functional connectivity is a promising approach for presurgical epilepsy evaluation.

Synthetic Epileptic Brain Activities with TripleGAN

Epilepsy is a chronic noninfectious disease caused by sudden abnormal discharge of brain neurons, which leads to intermittent brain dysfunction. It is also one of the most common neurological diseases in the world. The automatic detection of epilepsy based on electroencephalogram through machine learning, correlation analysis, and temporal-frequency analysis plays an important role in epilepsy early warning and automatic recognition. In this study, we propose a method to realize EEG epilepsy recognition by means of triple genetic antagonism network (GAN). TripleGAN is used for EEG temporal domain, frequency domain, and temporal-frequency domain, respectively. The experiment was conducted through CHB-MIT datasets, which operated at the latest level in the same industry in the world. In the CHB-MIT dataset, the classification accuracy, sensitivity, and specificity exceeded 1.19%, 1.36%, and 0.27%, respectively. The crossobject ratio exceeded 0.53%, 2.2%, and 0.37%, respectively. It shows that the established deep learning model of TripleGAN has a good effect on EEG epilepsy classification through simulation and classification optimization of real signals.

Anatomical harmonics basis based brain source localization with application to epilepsy

Brain Source Localization (BSL) using Electroencephalogram (EEG) has been a useful noninvasive modality for the diagnosis of epileptogenic zones, study of evoked related potentials, and brain disorders. The inverse solution of BSL is limited by high computational cost and localization error. The performance is additionally limited by head shape assumption and the corresponding harmonics basis function. In this work, an anatomical harmonics basis (Spherical Harmonics (SH), and more particularly Head Harmonics (H²)) based BSL is presented. The spatio-temporal four shell head model is formulated in SH and H² domain. The anatomical harmonics domain formulation leads to dimensionality reduction and increased contribution of source eigenvalues, resulting in decreased computation and increased accuracy respectively. The performance of spatial subspace based Multiple Signal Classification (MUSIC) and Recursively Applied and Projected (RAP)-MUSIC method is compared with the proposed SH and H² counterparts on simulated data. SH and H² domain processing effectively resolves the problem of high computational cost without sacrificing the inverse source localization accuracy. The proposed H² MUSIC was additionally validated for epileptogenic zone localization on clinical EEG data. The proposed framework offers an effective solution to clinicians in automated and time efficient seizure localization.

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.

Multiple Source Detection based on Spatial Clustering and Its Applications on Wearable OPM-MEG

OBJECTIVE

Magnetoencephalography (MEG) is a non-invasive technique that measures the magnetic fields of brain activity. In particular, a new type of optically pumped magnetometer (OPM)-based wearable MEG system has been developed in recent years. Source localization in MEG can provide signals and locations of brain activity. However, conventional source localization methods face the difficulty of accurately estimating multiple sources. The present study presented a new parametric method to estimate the number of sources and localize multiple sources. In addition, we applied the proposed method to a constructed wearable OPM-MEG system.

METHODS

We used spatial clustering of the dipole spatial distribution to detect sources. The spatial distribution of dipoles was obtained by segmenting the MEG data temporally into slices and then estimating the parameters of the dipoles on each data slice using the particle swarm optimization algorithm. Spatial clustering was performed using the spatial-temporal density-based spatial clustering of applications with a noise algorithm. The performance of our approach for detecting multiple sources was compared with that of four typical benchmark algorithms using the OPM-MEG sensor configuration.

RESULTS

The simulation results showed that the proposed method had the best performance for detecting multiple sources. Moreover, the effectiveness of the method was verified by a multimodel sensory stimuli experiment on a real constructed 31-channel OPM-MEG.

CONCLUSION

Our study provides an effective method for the detection of multiple sources.

SIGNIFICANCE

With the improvement of the source localization methods, MEG may have a wider range of applications in neuroscience and clinical research.

Imaging the extent and location of spatiotemporally distributed epileptiform sources from MEG measurements

Non-invasive MEG/EEG source imaging provides valuable information about the epileptogenic brain areas which can be used to aid presurgical planning in focal epilepsy patients suffering from drug-resistant seizures. However, the source extent estimation for electrophysiological source imaging remains to be a challenge and is usually largely dependent on subjective choice. Our recently developed algorithm, fast spatiotemporal iteratively reweighted edge sparsity minimization (FAST-IRES) strategy, has been shown to objectively estimate extended sources from EEG recording, while it has not been applied to MEG recordings. In this work, through extensive numerical experiments and real data analysis in a group of focal drug-resistant epilepsy patients' interictal spikes, we demonstrated the ability of FAST-IRES algorithm to image the location and extent of underlying epilepsy sources from MEG measurements. Our results indicate the merits of FAST-IRES in imaging the location and extent of epilepsy sources for pre-surgical evaluation from MEG measurements.

Sparse algorithms for EEG source localization

Source localization using EEG is important in diagnosing various physiological and psychiatric diseases related to the brain. The high temporal resolution of EEG helps medical professionals assess the internal physiology of the brain in a more informative way. The internal sources are obtained from EEG by an inversion process. The number of sources in the brain outnumbers the number of measurements. In this article, a comprehensive review of the state-of-the-art sparse source localization methods in this field is presented. A recently developed method, certainty-based-reduced-sparse-solution (CARSS), is implemented and is examined. A vast comparative study is performed using a sixty-four-channel setup involving two source spaces. The first source space has 5004 sources and the other has 2004 sources. Four test cases with one, three, five, and seven simulated active sources are considered. Two noise levels are also being added to the noiseless data. The CARSS is also evaluated. The results are examined. A real EEG study is also attempted. Graphical Abstract.

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.

Improvement in EEG Source Imaging Accuracy by Means of Wavelet Packet Transform and Subspace Component Selection

The electroencephalograph (EEG) source imaging (ESI) method is a non-invasive method that provides high temporal resolution imaging of brain electrical activity on the cortex. However, because the accuracy of EEG source imaging is often affected by unwanted signals such as noise or other source-irrelevant signals, the results of ESI are often incongruous with the real sources of brain activities. This study presents a novel ESI method (WPESI) that is based on wavelet packet transform (WPT) and subspace component selection to image the cerebral activities of EEG signals on the cortex. First, the original EEG signals are decomposed into several subspace components by WPT. Second, the subspaces associated with brain sources are selected and the relevant signals are reconstructed by WPT. Finally, the current density distribution in the cerebral cortex is obtained by establishing a boundary element model (BEM) from head MRI and applying the appropriate inverse calculation. In this study, the localization results obtained by this proposed approach were better than those of the original sLORETA approach (OESI) in the computer simulations and visual evoked potential (VEP) experiments. For epilepsy patients, the activity sources estimated by this proposed algorithm conformed to the seizure onset zones. The WPESI approach is easy to implement achieved favorable accuracy in terms of EEG source imaging. This demonstrates the potential for use of the WPESI algorithm to localize epileptogenic foci from scalp EEG signals.

Modified covariance beamformer for solving MEG inverse problem in the environment with correlated sources

Magnetoencephalography (MEG) is a neuroimaging method ideally suited for non-invasive studies of brain dynamics. MEG's spatial resolution critically depends on the approach used to solve the ill-posed inverse problem in order to transform sensor signals into cortical activation maps. Over recent years non-globally optimized solutions based on the use of adaptive beamformers (BF) gained popularity. When operating in the environment with a small number of uncorrelated sources the BFs perform optimally and yield high spatial resolution. However, the BFs are known to fail when dealing with correlated sources acting like poorly tuned spatial filters with low signal-to-noise ratio (SNR) of the output timeseries and often meaningless cortical maps of power distribution. This fact poses a serious limitation on the broader use of this promising technique especially since fundamental mechanisms of brain functioning, its inherent symmetry and task-based experimental paradigms result into a great deal of correlation in the activity of cortical sources. To cope with this problem, we developed a novel data covariance modification approach that allows for building beamformers that maintain high spatial resolution when operating in the environments with correlated sources. At the core of our method is a projection operation applied to the vectorized sensor-space covariance matrix. This projection does not remove the activity of the correlated sources from the sensor-space covariance matrix but rather selectively handles their contributions to the covariance matrix and creates a sufficiently accurate approximation of an ideal data covariance that could hypothetically be observed should these sources be uncorrelated. Since the projection operation is reciprocal to the PSIICOS method developed by us earlier (Ossadtchi et al., 2018) we refer to the family of algorithms presented here as ReciPSIICOS. We assess the performance of the novel approach using realistically simulated MEG data and show its superior performance in comparison to the classical BF approaches and well established MNE as a method immune to source synchrony by design. We have also applied our approach to the MEG datasets from the two experiments involving two different auditory tasks. The analysis of experimental MEG datasets showed that beamformers from ReciPSIICOS family, but not the classical BF, discovered the expected bilateral focal sources in the primary auditory cortex and detected motor cortex activity associated with the audio-motor task. In most cases MNE managed well but as expected produced more spatially diffuse source distributions. Notably, ReciPSIICOS beamformers yielded cortical activity estimates with SNR several times higher than that obtained with the classical BF, which may indirectly indicate the severeness of the signal cancellation problem when applying classical beamformers to MEG signals generated by synchronous sources.

A systematic review of EEG source localization techniques and their applications on diagnosis of brain abnormalities

In recent years, multiple noninvasive imaging modalities have been used to develop a better understanding of the human brain functionality, including positron emission tomography, single-photon emission computed tomography, and functional magnetic resonance imaging, all of which provide brain images with millimeter spatial resolutions. Despite good spatial resolution, time resolution of these methods are poor and values are about seconds. Scalp electroencephalography recordings can be used to perform the inverse problem in order to specify the location of the dominant sources of the brain activity. In this paper, EEG source localization method, diagnosis of brain abnormalities using common EEG source localization methods, investigating the effect of the head model on EEG source imaging results have been studied. In this review we present enough evidence that provides motivation for consideration in the future research using EEG source localization methods.

Multi-subject MEG/EEG source imaging with sparse multi-task regression

Magnetoencephalography and electroencephalography (M/EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Estimating the location and magnitude of the current sources that generated these electromagnetic fields is an inverse problem. Although it can be cast as a linear regression, this problem is severely ill-posed as the number of observations, which equals the number of sensors, is small. When considering a group study, a common approach consists in carrying out the regression tasks independently for each subject using techniques such as MNE or sLORETA. An alternative is to jointly localize sources for all subjects taken together, while enforcing some similarity between them. By pooling S subjects in a single joint regression, the number of observations is S times larger, potentially making the problem better posed and offering the ability to identify more sources with greater precision. Here we show how the coupling of the different regression problems can be done through a multi-task regularization that promotes focal source estimates. To take into account intersubject variabilities, we propose the Minimum Wasserstein Estimates (MWE). Thanks to a new joint regression method based on optimal transport (OT) metrics, MWE does not enforce perfect overlap of activation foci for all subjects but rather promotes spatial proximity on the cortical mantle. Besides, by estimating the noise level of each subject, MWE copes with the subject-specific signal-to-noise ratios with only one regularization parameter. On realistic simulations, MWE decreases the localization error by up to 4 ​mm per source compared to individual solutions. Experiments on the Cam-CAN dataset show improvements in spatial specificity in population imaging compared to individual models such as dSPM as well as a state-of-the-art Bayesian group level model. Our analysis of a multimodal dataset shows how multi-subject source localization reduces the gap between MEG and fMRI for brain mapping.

The impact of improved MEG-MRI co-registration on MEG connectivity analysis

Co-registration between structural head images and functional MEG data is needed for anatomically-informed MEG data analysis. Despite the efforts to minimize the co-registration error, conventional landmark- and surface-based strategies for co-registering head and MEG device coordinates achieve an accuracy of typically 5-10 mm. Recent advances in instrumentation and technical solutions, such as the development of hybrid ultra-low-field (ULF) MRI-MEG devices or the use of 3D-printed individualized foam head-casts, promise unprecedented co-registration accuracy, i.e., 2 mm or better. In the present study, we assess through simulations the impact of such an improved co-registration on MEG connectivity analysis. We generated synthetic MEG recordings for pairs of connected cortical sources with variable locations. We then assessed the capability to reconstruct source-level connectivity from these recordings for 0-15-mm co-registration error, three levels of head modeling detail (one-, three- and four-compartment models), two source estimation techniques (linearly constrained minimum-variance beamforming and minimum-norm estimation MNE) and five separate connectivity metrics (imaginary coherency, phase-locking value, amplitude-envelope correlation, phase-slope index and frequency-domain Granger causality). We found that beamforming can better take advantage of an accurate co-registration than MNE. Specifically, when the co-registration error was smaller than 3 mm, the relative error in connectivity estimates was down to one-third of that observed with typical co-registration errors. MNE provided stable results for a wide range of co-registration errors, while the performance of beamforming rapidly degraded as the co-registration error increased. Furthermore, we found that even moderate co-registration errors (>6 mm, on average) essentially decrease the difference of four- and three- or one-compartment models. Hence, a precise co-registration is important if one wants to take full advantage of highly accurate head models for connectivity analysis. We conclude that an improved co-registration will be beneficial for reliable connectivity analysis and effective use of highly accurate head models in future MEG connectivity studies.

Partial Least Square Aided Beamforming Algorithm in Magnetoencephalography Source Imaging

Beamforming techniques have played a prominent role in source imaging in neuroimaging and in locating epileptogenic zones. However, existing vector-beamformers are sensitive to noise on localization of epileptogenic zones. In this study, partial least square (PLS) was used to aid the minimum variance beamforming approach for source imaging with magnetoencephalography (MEG) arrays, and verified its effectiveness in simulated data and epilepsy data. First, PLS was employed to extract the components of the MEG arrays by maximizing the covariance between a linear combination of the predictors and the class variable. Noise was then removed by reconstructing the MEG arrays based on those components. The minimum variance beamforming method was used to estimate a source model. Simulations with a realistic head model and varying noise levels indicated that the proposed approach can provide higher spatial accuracy than other well-known beamforming methods. For real MEG recordings in 10 patients with temporal lobe epilepsy, the ratios of the number of spikes localized in the surgical excised region to the total number of spikes using the proposed method were higher than that of the dipole fitting method. These localization results using the proposed method are more consistent with the clinical evaluation. The proposed method may provide a new imaging marker for localization of epileptogenic zones.