Reconstructing spatially extended brain sources via enforcing multiple transform sparseness

Source imaging method based on diagonal covariance bases and its applications to OPM-MEG

Magnetoencephalography (MEG) is a noninvasive imaging technique used in neuroscience and clinical research. The source estimation of MEG involves solving a highly underdetermined inverse problem, which requires additional constraints to restrict the solution space. Traditional methods tend to obscure the extent of the sources. However, an accurate estimation of the source extent is important for studying brain activity or preoperatively estimating pathogenic regions. To improve the estimation accuracy of the extended source extent, the spatial constraint of sources is employed in the Bayesian framework. For example, the source is decomposed into a linear combination of validated spatial basis functions, which is proved to improve the source imaging accuracy. In this work, we further construct the spatial properties of the source using the diagonal covariance bases (DCB), which we summarize as the source imaging method SI-DCB. In this approach, specifically, the covariance matrix of the spatial coefficients is modeled as a weighted combination of diagonal covariance basis functions. The convex analysis is used to estimate noise and model parameters under the Bayesian framework. Extensive numerical simulations showed that SI-DCB outperformed five benchmark methods in accurately estimating the location and extent of patch sources. The effectiveness of SI-DCB was verified through somatosensory stimulation experiments performed on a 31-channel OPM-MEG system. The SI-DCB correctly identified the source area where each brain response occurred. The superior performance of SI-DCB suggests that it can provide a template approach for improving the accuracy of source extent estimations under a sparse Bayesian framework.

EEG dynamic source imaging using a regularized optimization with spatio-temporal constraints

One of the most important needs in neuroimaging is brain dynamic source imaging with high spatial and temporal resolution. EEG source imaging estimates the underlying sources from EEG recordings, which provides enhanced spatial resolution with intrinsically high temporal resolution. To ensure identifiability in the underdetermined source reconstruction problem, constraints on EEG sources are essential. This paper introduces a novel method for estimating source activities based on spatio-temporal constraints and a dynamic source imaging algorithm. The method enhances time resolution by incorporating temporal evolution of neural activity into a regularization function. Additionally, two spatial regularization constraints based on L 1 and L 2 norms are applied in the transformed domain to address both focal and spread neural activities, achieved through spatial gradient and Laplacian transform. Performance evaluation, conducted quantitatively using synthetic datasets, discusses the influence of parameters such as source extent, number of sources, correlation level, and SNR level on temporal and spatial metrics. Results demonstrate that the proposed method provides superior spatial and temporal reconstructions compared to state-of-the-art inverse solutions including STRAPS, sLORETA, SBL, dSPM, and MxNE. This improvement is attributed to the simultaneous integration of transformed spatial and temporal constraints. When applied to a real auditory ERP dataset, our algorithm accurately reconstructs brain source time series and locations, effectively identifying the origins of auditory evoked potentials. In conclusion, our proposed method with spatio-temporal constraints outperforms the state-of-the-art algorithms in estimating source distribution and time courses.

Multi-Modal Electrophysiological Source Imaging With Attention Neural Networks Based on Deep Fusion of EEG and MEG

The process of reconstructing underlying cortical and subcortical electrical activities from Electroencephalography (EEG) or Magnetoencephalography (MEG) recordings is called Electrophysiological Source Imaging (ESI). Given the complementarity between EEG and MEG in measuring radial and tangential cortical sources, combined EEG/MEG is considered beneficial in improving the reconstruction performance of ESI algorithms. Traditional algorithms mainly emphasize incorporating predesigned neurophysiological priors to solve the ESI problem. Deep learning frameworks aim to directly learn the mapping from scalp EEG/MEG measurements to the underlying brain source activities in a data-driven manner, demonstrating superior performance compared to traditional methods. However, most of the existing deep learning approaches for the ESI problem are performed on a single modality of EEG or MEG, meaning the complementarity of these two modalities has not been fully utilized. How to fuse the EEG and MEG in a more principled manner under the deep learning paradigm remains a challenging question. This study develops a Multi-Modal Deep Fusion (MMDF) framework using Attention Neural Networks (ANN) to fully leverage the complementary information between EEG and MEG for solving the ESI inverse problem, which is termed as MMDF-ANN. Specifically, our proposed brain source imaging approach consists of four phases, including feature extraction, weight generation, deep feature fusion, and source mapping. Our experimental results on both synthetic dataset and real dataset demonstrated that using a fusion of EEG and MEG can significantly improve the source localization accuracy compared to using a single-modality of EEG or MEG. Compared to the benchmark algorithms, MMDF-ANN demonstrated good stability when reconstructing sources with extended activation areas and situations of EEG/MEG measurements with a low signal-to-noise ratio.

VSSI-GGD: A Variation Sparse EEG Source Imaging Approach Based on Generalized Gaussian Distribution

Electroencephalographic (EEG) source imaging (ESI) is a powerful method for studying brain functions and surgical resection of epileptic foci. However, accurately estimating the location and extent of brain sources remains challenging due to noise and background interference in EEG signals. To reconstruct extended brain sources, we propose a new ESI method called Variation Sparse Source Imaging based on Generalized Gaussian Distribution (VSSI-GGD). VSSI-GGD uses the generalized Gaussian prior as a sparse constraint on the spatial variation domain and embeds it into the Bayesian framework for source estimation. Using a variational technique, we approximate the intractable true posterior with a Gaussian density. Through convex analysis, the Bayesian inference problem is transformed entirely into a series of regularized L2p -norm ( ) optimization problems, which are efficiently solved with the ADMM algorithm. Imaging results of numerical simulations and human experimental dataset analysis reveal the superior performance of VSSI-GGD, which provides higher spatial resolution with clear boundaries compared to benchmark algorithms. VSSI-GGD can potentially serve as an effective and robust spatiotemporal EEG source imaging method. The source code of VSSI-GGD is available at https://github.com/Mashirops/VSSI-GGD.git.

Deep EEG source localization via EMD-based fMRI high spatial frequency

Brain imaging with a high-spatiotemporal resolution is crucial for accurate brain-function mapping. Electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI) are two popular neuroimaging modalities with complementary features that record brain function with high temporal and spatial resolution, respectively. One popular non-invasive way to obtain data with both high spatial and temporal resolutions is to combine the fMRI activation map and EEG data to improve the spatial resolution of the EEG source localization. However, using the whole fMRI map may cause spurious results for the EEG source localization, especially for deep brain regions. Considering the head's conductivity, deep regions' sources with low activity are unlikely to be detected by the EEG electrodes at the scalp. In this study, we use fMRI's high spatial-frequency component to identify the local high-intensity activations that are most likely to be captured by the EEG. The 3D Empirical Mode Decomposition (3D-EMD), a data-driven method, is used to decompose the fMRI map into its spatial-frequency components. Different validation measurements for EEG source localization show improved performance for the EEG inverse-modeling informed by the fMRI's high-frequency spatial component compared to the fMRI-informed EEG source-localization methods. The level of improvement varies depending on the voxels' intensity and their distribution. Our experimental results also support this conclusion.

μ-STAR: A novel framework for spatio-temporal M/EEG source imaging optimized by microstates

Source imaging of Electroencephalography (EEG) and Magnetoencephalography (MEG) provides a noninvasive way of monitoring brain activities with high spatial and temporal resolution. In order to address this highly ill-posed problem, conventional source imaging models adopted spatio-temporal constraints that assume spatial stability of the source activities, neglecting the transient characteristics of M/EEG. In this work, a novel source imaging method μ-STAR that includes a microstate analysis and a spatio-temporal Bayesian model was introduced to address this problem. Specifically, the microstate analysis was applied to achieve automatic determination of time window length with quasi-stable source activity pattern for optimal reconstruction of source dynamics. Then a user-specific spatial prior and data-driven temporal basis functions were utilized to characterize the spatio-temporal information of sources within each state. The solution of the source reconstruction was obtained through a computationally efficient algorithm based upon variational Bayesian and convex analysis. The performance of the μ-STAR was first assessed through numerical simulations, where we found that the determination and inclusion of optimal temporal length in the spatio-temporal prior significantly improved the performance of source reconstruction. More importantly, the μ-STAR model achieved robust performance under various settings (i.e., source numbers/areas, SNR levels, and source depth) with fast convergence speed compared with five widely-used benchmark models (including wMNE, STV, SBL, BESTIES, & SI-STBF). Additional validations on real data were then performed on two publicly-available datasets (including block-design face-processing ERP and continuous resting-state EEG). The reconstructed source activities exhibited spatial and temporal neurophysiologically plausible results consistent with previously-revealed neural substrates, thereby further proving the feasibility of the μ-STAR model for source imaging in various applications.

WRA-MTSI: A Robust Extended Source Imaging Algorithm Based on Multi-Trial EEG

OBJECTIVE

Reconstructing brain activities from electroencephalography (EEG) signals is crucial for studying brain functions and their abnormalities. However, since EEG signals are nonstationary and vulnerable to noise, brain activities reconstructed from single-trial EEG data are often unstable, and significant variability may occur across different EEG trials even for the same cognitive task.

METHODS

In an effort to leverage the shared information across the EEG data of multiple trials, this paper proposes a multi-trial EEG source imaging method based on Wasserstein regularization, termed WRA-MTSI. In WRA-MTSI, Wasserstein regularization is employed to perform multi-trial source distribution similarity learning, and the structured sparsity constraint is enforced to enable accurate estimation of the source extents, locations and time series. The resulting optimization problem is solved by a computationally efficient algorithm based on the alternating direction method of multipliers (ADMM).

RESULTS

Both numerical simulations and real EEG data analysis demonstrate that WRA-MTSI outperforms existing single-trial ESI methods (e.g., wMNE, LORETA, SISSY, and SBL) in mitigating the influence of artifacts in EEG data. Moreover, WRA-MTSI yields superior performance compared to other state-of-the-art multi-trial ESI methods (e.g., group lasso, the dirty model, and MTW) in estimating source extents.

CONCLUSION AND SIGNIFICANCE

WRA-MTSI may serve as an effective robust EEG source imaging method in the presence of multi-trial noisy EEG data.

Electromagnetic Source Imaging via Bayesian Modeling with Smoothness in Spatial and Temporal Domains

Accurate reconstruction of cortical activation from electroencephalography and magnetoencephalography (E/MEG) is a long-standing challenge because of the inherently ill-posed inverse problem. In this paper, a novel algorithm under the empirical Bayesian framework, source imaging with smoothness in spatial and temporal domains (SI-SST), is proposed to address this issue. In SI-SST, current sources are decomposed into the product of spatial smoothing kernel, sparseness encoding coefficients, and temporal basis functions (TBFs). Further smoothness is integrated in the temporal domain with the employment of an underlying autoregressive model. Because sparseness encoding coefficients are constructed depending on overlapped clusters over cortex in this model, we derived a novel update rule based on fixed-point criterion instead of the convexity based approach which becomes invalid in this scenario. Entire variables and hyper parameters are updated alternatively in the variational inference procedure. SI-SST was assessed by multiple metrics with both simulated and experimental datasets. In practice, SI-SST had the superior reconstruction performance in both spatial extents and temporal profiles compared to the benchmarks.

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.

Exploring the extent of source imaging: Recent advances in noninvasive electromagnetic brain imaging

Electrophysiological source imaging (ESI) has been successfully employed in many brain imaging applications during the last 20 years. ESI estimates of underlying brain networks provide millisecond resolution of dynamic brain processes; yet, it remains to be a challenge to further improve the spatial resolution of ESI modality, in particular on its capability of imaging the extent of underlying brain sources. In this review, we discuss the recent developments in signal processing and machine learning that have made it possible to image the extent, i.e. size, of underlying brain sources noninvasively, using scalp electromagnetic measurements from electroencephalogram (EEG) and magnetoencephalogram (MEG) recordings.

Brain-wide functional diffuse optical tomography of resting state networks

Objective.Diffuse optical tomography (DOT) has the potential in reconstructing resting state networks (RSNs) in human brains with high spatio-temporal resolutions and multiple contrasts. While several RSNs have been reported and successfully reconstructed using DOT, its full potential in recovering a collective set of distributed brain-wide networks with the number of RSNs close to those reported using functional magnetic resonance imaging (fMRI) has not been demonstrated.Approach.The present study developed a novel brain-wide DOT (BW-DOT) framework that integrates a cap-based whole-head optode placement system with multiple computational approaches, i.e. finite-element modeling, inverse source reconstruction, data-driven pattern recognition, and statistical correlation tomography, to reconstruct RSNs in dual contrasts of oxygenated (HbO) and deoxygenated hemoglobins (HbR).Main results.Our results from the proposed framework revealed a comprehensive set of RSNs and their subnetworks, which collectively cover almost the entire neocortical surface of the human brain, both at the group level and individual participants. The spatial patterns of these DOT RSNs suggest statistically significant similarities to fMRI RSN templates. Our results also reported the networks involving the medial prefrontal cortex and precuneus that had been missed in previous DOT studies. Furthermore, RSNs obtained from HbO and HbR suggest similarity in terms of both the number of RSN types reconstructed and their corresponding spatial patterns, while HbR RSNs show statistically more similarity to fMRI RSN templates and HbO RSNs indicate more bilateral patterns over two hemispheres. In addition, the BW-DOT framework allowed consistent reconstructions of RSNs across individuals and across recording sessions, indicating its high robustness and reproducibility, respectively.Significance.Our present results suggest the feasibility of using the BW-DOT, as a neuroimaging tool, in simultaneously mapping multiple RSNs and its potential values in studying RSNs, particularly in patient populations under diverse conditions and needs, due to its advantages in accessibility over fMRI.

Probabilistic Structure Learning for EEG/MEG Source Imaging With Hierarchical Graph Priors

Brain source imaging is an important method for noninvasively characterizing brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG) recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume the source activities at different time points are unrelated, and do not utilize the temporal structure in the source activation, making the ESI analysis sensitive to noise. Some methods may encourage very similar activation patterns across the entire time course and may be incapable of accounting the variation along the time course. To effectively deal with noise while maintaining flexibility and continuity among brain activation patterns, we propose a novel probabilistic ESI model based on a hierarchical graph prior. Under our method, a spanning tree constraint ensures that activity patterns have spatiotemporal continuity. An efficient algorithm based on an alternating convex search is presented to solve the resulting problem of the proposed model with guaranteed convergence. Comprehensive numerical studies using synthetic data on a realistic brain model are conducted under different levels of signal-to-noise ratio (SNR) from both sensor and source spaces. We also examine the EEG/MEG datasets in two real applications, in which our ESI reconstructions are neurologically plausible. All the results demonstrate significant improvements of the proposed method over benchmark methods in terms of source localization performance, especially at high noise levels.

Accuracy and spatial properties of distributed magnetic source imaging techniques in the investigation of focal epilepsy patients

Source localization of interictal epileptiform discharges (IEDs) is clinically useful in the presurgical workup of epilepsy patients. We aimed to compare the performance of four different distributed magnetic source imaging (dMSI) approaches: Minimum norm estimate (MNE), dynamic statistical parametric mapping (dSPM), standardized low-resolution electromagnetic tomography (sLORETA), and coherent maximum entropy on the mean (cMEM). We also evaluated whether a simple average of maps obtained from multiple inverse solutions (Ave) can improve localization accuracy. We analyzed dMSI of 206 IEDs derived from magnetoencephalography recordings in 28 focal epilepsy patients who had a well-defined focus determined through intracranial EEG (iEEG), epileptogenic MRI lesions or surgical resection. dMSI accuracy and spatial properties were quantitatively estimated as: (a) distance from the epilepsy focus, (b) reproducibility, (c) spatial dispersion (SD), (d) map extension, and (e) effect of thresholding on map properties. Clinical performance was excellent for all methods (median distance from the focus MNE = 2.4 mm; sLORETA = 3.5 mm; cMEM = 3.5 mm; dSPM = 6.8 mm, Ave = 0 mm). Ave showed the lowest distance between the map maximum and epilepsy focus (Dmin lower than cMEM, MNE, and dSPM, p = .021, p = .008, p < .001, respectively). cMEM showed the best spatial features, with lowest SD outside the focus (SD lower than all other methods, p < .001 consistently) and high contrast between the generator and surrounding regions. The average map Ave provided the best localization accuracy, whereas cMEM exhibited the lowest amount of spurious distant activity. dMSI techniques have the potential to significantly improve identification of iEEG targets and to guide surgical planning, especially when multiple methods are combined.

Noninvasive electromagnetic source imaging of spatiotemporally distributed epileptogenic brain sources

Brain networks are spatiotemporal phenomena that dynamically vary over time. Functional imaging approaches strive to noninvasively estimate these underlying processes. Here, we propose a novel source imaging approach that uses high-density EEG recordings to map brain networks. This approach objectively addresses the long-standing limitations of conventional source imaging techniques, namely, difficulty in objectively estimating the spatial extent, as well as the temporal evolution of underlying brain sources. We validate our approach by directly comparing source imaging results with the intracranial EEG (iEEG) findings and surgical resection outcomes in a cohort of 36 patients with focal epilepsy. To this end, we analyzed a total of 1,027 spikes and 86 seizures. We demonstrate the capability of our approach in imaging both the location and spatial extent of brain networks from noninvasive electrophysiological measurements, specifically for ictal and interictal brain networks. Our approach is a powerful tool for noninvasively investigating large-scale dynamic brain networks.

Noninvasive electromagnetic measurements are utilized effectively to estimate large scale dynamic brain networks. Sohrabpour et al. propose a novel electrophysiological source imaging approach to estimate the location and size of epileptogenic tissues in patients with epilepsy.

Whole-brain electrophysiological functional connectivity dynamics in resting-state EEG

OBJECTIVE

Functional connectivity (FC) dynamics have been studied in functional magnetic resonance imaging (fMRI) data, while it is largely unknown in electrophysiological data, e.g. EEG.

APPROACH

The present study proposed a novel analytic framework to study spatiotemporal dynamics of FC (dFC) in resting-state human EEG data, including independent component analysis, cortical source imaging, sliding-window correlation analysis, and k-means clustering.

MAIN RESULTS

Our results confirm that major fMRI intrinsic connectivity networks (ICNs) can be successfully reconstructed from EEG using our analytic framework. Prominent spatial and temporal variability were revealed in these ICNs. The mean dFC spatial patterns of individual ICNs resemble their corresponding static FC (sFC) patterns but show fewer cross-talks among distinct ICNs. Our investigation unveils evidences of time-domain variations in individual ICNs comparable to their mean FC level in terms of magnitude. The major contributors to these variations are from the frequency below 0.0156 Hz, in the similar range of FC dynamics from fMRI data. Among different ICNs, larger temporal variabilities are observed in the frontal attention and auditory/visual ICNs, while sensorimotor, salience, and default model networks showed less. Our analytic framework for the first time revealed quasi-stable states within individual EEG ICNs, with various strengths or spatial patterns that were reliably detected at both group and individual levels. These states all together reveal a more complete picture of EEG ICNs: (1) quasi-stable state spatial patterns as a whole for each EEG ICN are more consistent with the corresponding fMRI ICN in terms of the bilateral distribution and multi-nodes structure; (2) EEG ICNs reveal more transient patterns about within-ICN between-node communications than fMRI ICNs.

SIGNIFICANCE

The present findings highlight the fact that rich temporal and spatial dynamics exist in ICN that can be detected from EEG data. Future studies might extend investigations towards spectral dynamics of EEG ICNs.

Robust Empirical Bayesian Reconstruction of Distributed Sources for Electromagnetic Brain Imaging

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of the magnetic fields and electric potentials. An enduring challenge in this imaging modality is estimating the number, location, and time course of sources, especially for the reconstruction of distributed brain sources with complex spatial extent. Here, we introduce a novel robust empirical Bayesian algorithm that enables better reconstruction of distributed brain source activity with two key ideas: kernel smoothing and hyperparameter tiling. Since the proposed algorithm builds upon many of the performance features of the sparse source reconstruction algorithm - Champagne and we refer to this algorithm as Smooth Champagne. Smooth Champagne is robust to the effects of high levels of noise, interference, and highly correlated brain source activity. Simulations demonstrate excellent performance of Smooth Champagne when compared to benchmark algorithms in accurately determining the spatial extent of distributed source activity. Smooth Champagne also accurately reconstructs real MEG and EEG data.

Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources Based on Matrix Factorization

Accurate estimation of the locations and extents of neural sources from electroencephalography and magnetoencephalography (E/MEG) is challenging, especially for deep and highly correlated neural activities. In this study, we proposed a new fully data-driven source imaging method, source imaging based on spatio-temporal basis function (SI-STBF), which is built upon a Bayesian framework, to address this issue. The SI-STBF is based on the factorization of a source matrix as a product of a sparse coding matrix and a temporal basis function (TBF) matrix, which includes a few TBFs. The prior of the TBF is set in the empirical Bayesian manner. Similarly, for the spatial constraint, the SI-STBF assumes the prior covariance of the coding matrix as a weighted sum of several spatial covariance components. Both the TBFs and the coding matrix are learned from E/MEG simultaneously through variational Bayesian inference. To enable inference on high-resolution source space, we derived a scalable algorithm using convex analysis. The performance of the SI-STBF was assessed using both simulated and experimental E/MEG recordings. Compared with L₂-norm constrained methods, the SI-STBF is superior in reconstructing extended sources with less spatial diffusion and less localization error. By virtue of the spatio-temporal factorization of source matrix, the SI-STBF also produces more accurate estimations than spatial-only constraint method for high correlated and deep sources.

Electrophysiological Signatures of Intrinsic Functional Connectivity Related to rTMS Treatment for Mal de Debarquement Syndrome

To determine intrinsic functional connectivity (IFC) related to symptom changes induced by rTMS in mal de debarquement syndrome (MdDS), a motion perceptual disorder induced by entrainment to oscillating motion. Twenty right-handed women (mean age: 52.9 ± 12.6 years; mean duration illness: 35.2 ± 24.2 months) with MdDS received five sessions of rTMS (1 Hz right DLPFC, 10 Hz left DLPFC) over consecutive days. High-density (128-channel) resting-state EEG were recorded prior to and following treatment sessions and analyzed using a group-level independent component (IC) analysis. IFC between 19 ICs was quantified by inter-IC phase coherence (ICPC) in six frequency bands (delta, theta, low alpha, high alpha, beta, gamma). Correlational analyses between IFCs and symptoms were performed. Symptom improvement after rTMS was significantly correlated with (1) an increase in low alpha band (8–10 Hz) IFC but a decrease of IFC in all other bands, and (2) high baseline IFC in the high alpha (11–13 Hz) and beta bands (14–30 Hz). Most treatment related IFC changes occurred between frontal and parietal regions with a linear association between the degree of symptom improvement and the number of coherent IFC changes. Frequency band and region specific IFC changes correlate with and can predict symptom changes induced by rTMS over DLPFC in MdDS. MdDS symptom response correlates with high baseline IFC in most frequency bands. Treatment induced increase in long-range low alpha IFC and decreases in IFC in other bands as well as the proportion of coherent IFC changes correlate with symptom reduction.

Improved Back-Projection Cortical Potential Imaging by Multi-resolution Optimization Technique

Electroencephalogram (EEG) has evolved to be a well-established tool for imaging brain activity. This progress is mainly due to the development of high-resolution (HR) EEG methods. One class of HR-EEG is the cortical potential imaging (CPI), which aims to estimate the potential distribution on the cortical surface, which is much more informative than EEG. Even though these methods exhibit good performance, most of them have inherent inaccuracies that originate from their operating principles that constrain the solution or require a complex calculation process. The back-projection CPI (BP-CPI) method is relatively new and has the advantage of being constraint-free and computation inexpensive. The method has shown relatively good accuracy, which is necessary to become a clinical tool. However, better performance must be achieved. In the present study, two improvements are proposed. Both are embedded as adjacent stages to the BP-CPI and are based on the multi-resolution optimization approach (MR-CPI). A series of Monte-Carlo simulations were performed to examine the characteristics of the proposed improvements. Additional tests were done, including different EEG noise levels and variation in electrode-numbers. The results showed highly accurate cortical potential estimations, with a reduction in estimation error by a factor of 3.75 relative to the simple BP-CPI estimation error. We also validated these results with true EEG data. Analyzing these EEGs, we have demonstrated the MR-CPI competence to correctly localize cortical activations in a real environment. The MR-CPI methods were shown to be reliable for estimating cortical potentials, enabling researchers to obtain fast and robust high-resolution EEGs.

Electrophysiological signatures of atypical intrinsic brain connectivity networks in autism

OBJECTIVE

Abnormal local and long-range brain connectivity have been widely reported in autism spectrum disorder (ASD), yet the nature of these abnormalities and their functional relevance at distinct cortical rhythms remains unknown. Investigations of intrinsic connectivity networks (ICNs) and their coherence across whole brain networks hold promise for determining whether patterns of functional connectivity abnormalities vary across frequencies and networks in ASD. In the present study, we aimed to probe atypical intrinsic brain connectivity networks in ASD from resting-state electroencephalography (EEG) data via characterizing the whole brain network.

APPROACH

Connectivity within individual ICNs (measured by spectral power) and between ICNs (measured by coherence) were examined at four canonical frequency bands via a time-frequency independent component analysis on high-density EEG, which were recorded from 20 ASD and 20 typical developing (TD) subjects during an eyes-closed resting state.

MAIN RESULTS

Among twelve identified electrophysiological ICNs, individuals with ASD showed hyper-connectivity in individual ICNs and hypo-connectivity between ICNs. Functional connectivity alterations in ASD were more severe in the frontal lobe and the default mode network (DMN) and at low frequency bands. These functional connectivity measures also showed abnormal age-related associations in ICNs related to frontal, temporal and motor regions in ASD.

SIGNIFICANCE

Our findings suggest that ASD is characterized by the opposite directions of abnormalities (i.e. hypo- and hyper-connectivity) in the hierarchical structure of the whole brain network, with more impairments in the frontal lobe and the DMN at low frequency bands, which are critical for top-down control of sensory systems, as well as for both cognition and social skills.

Electrophysiological Source Imaging: A Noninvasive Window to Brain Dynamics

Brain activity and connectivity are distributed in the three-dimensional space and evolve in time. It is important to image brain dynamics with high spatial and temporal resolution. Electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive measurements associated with complex neural activations and interactions that encode brain functions. Electrophysiological source imaging estimates the underlying brain electrical sources from EEG and MEG measurements. It offers increasingly improved spatial resolution and intrinsically high temporal resolution for imaging large-scale brain activity and connectivity on a wide range of timescales. Integration of electrophysiological source imaging and functional magnetic resonance imaging could further enhance spatiotemporal resolution and specificity to an extent that is not attainable with either technique alone. We review methodological developments in electrophysiological source imaging over the past three decades and envision its future advancement into a powerful functional neuroimaging technology for basic and clinical neuroscience applications.

Computationally Efficient Algorithms for Sparse, Dynamic Solutions to the EEG Source Localization Problem

OBJECTIVE

Electroencephalography (EEG) and magnetoencephalography noninvasively record scalp electromagnetic fields generated by cerebral currents, revealing millisecond-level brain dynamics useful for neuroscience and clinical applications. Estimating the currents that generate these fields, i.e., source localization, is an ill-conditioned inverse problem. Solutions to this problem have focused on spatial continuity constraints, dynamic modeling, or sparsity constraints. The combination of these key ideas could offer significant performance improvements, but substantial computational costs pose a challenge for practical application of such approaches. Here, we propose a new method for EEG source localization that combines: 1) covariance estimation for both source and measurement noises; 2) linear state-space dynamics; and 3) sparsity constraints, using 4) novel computationally efficient estimation algorithms.

METHODS

For source covariance estimation, we use a locally smooth basis alongside sparsity enforcing priors. For EEG measurement noise covariance estimation, we use an inverse Wishart prior density. We estimate these model parameters using an expectation-maximization algorithm that employs steady-state filtering and smoothing to expedite computations.

RESULTS

We characterized the performance of our method by analyzing simulated data and experimental recordings of eyes-closed alpha oscillations. Our sparsity enforcing priors significantly improved estimation of both the spatial distribution and time course of simulated data, while improving computational time by more than 12-fold over previous dynamic methods.

CONCLUSION

We developed and demonstrated a novel method for improved EEG source localization employing spatial covariance estimation, dynamics, and sparsity.

SIGNIFICANCE

Our approach provides substantial performance improvements over existing methods using computationally efficient algorithms that will facilitate practical applications in both neuroscience and medicine.

Cortical Statistical Correlation Tomography of EEG Resting State Networks

Resting state networks (RSNs) have been found in human brains during awake resting states. RSNs are composed of spatially distributed regions in which spontaneous activity fluctuations are temporally and dynamically correlated. A new computational framework for reconstructing RSNs with human EEG data has been developed in the present study. The proposed framework utilizes independent component analysis (ICA) on short-time Fourier transformed inverse source maps imaged from EEG data and statistical correlation analysis to generate cortical tomography of electrophysiological RSNs. The proposed framework was evaluated on three sets of resting-state EEG data obtained in the comparison of two conditions: (1) healthy controls with eyes closed and eyes open; (2) healthy controls and individuals with a balance disorder; (3) individuals with a balance disorder before and after receiving repetitive transcranial magnetic stimulation (rTMS) treatment. In these analyses, the same group of five RSNs with similar spatial and spectral patterns were successfully reconstructed by the proposed framework from each individual EEG dataset. These EEG RSN tomographic maps showed significant similarity with RSN templates derived from functional magnetic resonance imaging (fMRI). Furthermore, significant spatial and spectral differences of RSNs among compared conditions were observed in tomographic maps as well as their spectra, which were consistent with findings reported in the literature. Beyond the success of reconstructing EEG RSNs spatially on the cortical surface as in fMRI studies, this novel approach defines RSNs further with spectra, providing a new dimension in understanding and probing basic neural mechanisms of RSNs. The findings in patients' data further demonstrate its potential in identifying biomarkers for the diagnosis and treatment evaluation of neuropsychiatric disorders.

Clinical yield of magnetoencephalography distributed source imaging in epilepsy: A comparison with equivalent current dipole method

OBJECTIVE

Source localization of interictal epileptic discharges (IEDs) is clinically useful in the presurgical workup of epilepsy patients. It is usually obtained by equivalent current dipole (ECD) which localizes a point source and is the only inverse solution approved by clinical guidelines. In contrast, magnetic source imaging using distributed methods (dMSI) provides maps of the location and the extent of the generators, but its yield has not been clinically validated. We systematically compared ECD versus dMSI performed using coherent Maximum Entropy on the Mean (cMEM), a method sensitive to the spatial extent of the generators.

METHODS

340 source localizations of IEDs derived from 49 focal epilepsy patients with foci well-defined through intracranial EEG, MRI lesions, and surgery were analyzed. The comparison was based on the assessment of the sublobar concordance with the focus and of the distance between the source and the focus.

RESULTS

dMSI sublobar concordance was significantly higher than ECD (81% vs 69%, P < 0.001), especially for extratemporal lobe sources (dMSI = 84%; ECD = 67%, P < 0.001) and for seizure free patients (dMSI = 83%; ECD = 70%, P < 0.001). The median distance from the focus was 4.88 mm for ECD and 3.44 mm for dMSI (P < 0.001). ECD dipoles were often wrongly localized in deep brain regions.

CONCLUSIONS

dMSI using cMEM exhibited better accuracy. dMSI also offered the advantage of recovering more realistic maps of the generator, which could be exploited for neuronavigation aimed at targeting invasive EEG and surgical resection. Therefore, dMSI may be preferred to ECD in clinical practice. Hum Brain Mapp 39:218-231, 2018. © 2017 Wiley Periodicals, Inc.

Strategies for statistical thresholding of source localization maps in magnetoencephalography and estimating source extent

BACKGROUND

Magnetoencephalography allows defining non-invasively the spatio-temporal activation of brain networks thanks to source localization algorithms. A major difficulty of MNE and beamforming methods, two classically used techniques, is the definition of proper thresholds that allow deciding the extent of activated cortex.

NEW METHOD

We investigated two strategies for computing a threshold, taking into account the difficult multiple comparison issue. The strategies were based either on parametric statistics (Bonferroni, FDR correction) or on empirical estimates (local FDR and a custom measure based on the survival function).

RESULTS

We found thanks to the simulations that parametric methods based on the sole estimation of H₀ (Bonferroni, FDR) performed poorly, in particular in high SNR situations. This is due to the spatial leakage originating from the source localization methods, which give a 'blurred' reconstruction of the patch extension: the higher the SNR, the more this effect is visible.

COMPARISON WITH EXISTING METHODS

Adaptive methods such as local FDR or our proposed 'concavity threshold' performed better than Bonferroni or classical FDR. We present an application to real data originating from auditory stimulation in MEG.

CONCLUSION

In order to estimate source extent, adaptive strategies should be preferred to parametric statistics when dealing with 'leaking' source reconstruction algorithms.

SISSY: An efficient and automatic algorithm for the analysis of EEG sources based on structured sparsity

Over the past decades, a multitude of different brain source imaging algorithms have been developed to identify the neural generators underlying the surface electroencephalography measurements. While most of these techniques focus on determining the source positions, only a small number of recently developed algorithms provides an indication of the spatial extent of the distributed sources. In a recent comparison of brain source imaging approaches, the VB-SCCD algorithm has been shown to be one of the most promising algorithms among these methods. However, this technique suffers from several problems: it leads to amplitude-biased source estimates, it has difficulties in separating close sources, and it has a high computational complexity due to its implementation using second order cone programming. To overcome these problems, we propose to include an additional regularization term that imposes sparsity in the original source domain and to solve the resulting optimization problem using the alternating direction method of multipliers. Furthermore, we show that the algorithm yields more robust solutions by taking into account the temporal structure of the data. We also propose a new method to automatically threshold the estimated source distribution, which permits to delineate the active brain regions. The new algorithm, called Source Imaging based on Structured Sparsity (SISSY), is analyzed by means of realistic computer simulations and is validated on the clinical data of four patients.

ICA-Derived EEG Correlates to Mental Fatigue, Effort, and Workload in a Realistically Simulated Air Traffic Control Task

Electroencephalograph (EEG) has been increasingly studied to identify distinct mental factors when persons perform cognitively demanding tasks. However, most of these studies examined EEG correlates at channel domain, which suffers the limitation that EEG signals are the mixture of multiple underlying neuronal sources due to the volume conduction effect. Moreover, few studies have been conducted in real-world tasks. To precisely probe EEG correlates with specific neural substrates to mental factors in real-world tasks, the present study examined EEG correlates to three mental factors, i.e., mental fatigue [also known as time-on-task (TOT) effect], workload and effort, in EEG component signals, which were obtained using an independent component analysis (ICA) on high-density EEG data. EEG data were recorded when subjects performed a realistically simulated air traffic control (ATC) task for 2 h. Five EEG independent component (IC) signals that were associated with specific neural substrates (i.e., the frontal, central medial, motor, parietal, occipital areas) were identified. Their spectral powers at their corresponding dominant bands, i.e., the theta power of the frontal IC and the alpha power of the other four ICs, were detected to be correlated to mental workload and effort levels, measured by behavioral metrics. Meanwhile, a linear regression analysis indicated that spectral powers at five ICs significantly increased with TOT. These findings indicated that different levels of mental factors can be sensitively reflected in EEG signals associated with various brain functions, including visual perception, cognitive processing, and motor outputs, in real-world tasks. These results can potentially aid in the development of efficient operational interfaces to ensure productivity and safety in ATC and beyond.

Identifying epileptic source location and extent: an iterative sparse electromagnetic source imaging algorithm

In this paper we have introduced a novel electromagnetic source imaging (ESI) technique and demonstrated its validity and excellent performance in imaging the location and extent of underlying epileptic sources in patients suffering from focal epilepsy. The proposed algorithm employs ideas from sparse signal processing literature and convex optimization theories to improve source imaging results obtained from scalp-recorded electroencephalogram (EEG). EEG source imaging results generally use subjective methods to determine the extent of the underlying brain activity. The proposed technique provides significant improvement in dealing with such shortcomings and eliminates the need for thresholding. The results of our computer simulations and clinical validation study demonstrate the excellent performance of the proposed algorithm and suggest it may become a useful tool for objectively determining the location and extent of focal epileptic activity in a noninvasive fashion.

s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography

EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ1-2 regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ1-2 regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ1-2 regularization is able to enhance sparsity and accelerate computations than ℓ1 regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios.

Imaging brain source extent from EEG/MEG by means of an iteratively reweighted edge sparsity minimization (IRES) strategy

Estimating extended brain sources using EEG/MEG source imaging techniques is challenging. EEG and MEG have excellent temporal resolution at millisecond scale but their spatial resolution is limited due to the volume conduction effect. We have exploited sparse signal processing techniques in this study to impose sparsity on the underlying source and its transformation in other domains (mathematical domains, like spatial gradient). Using an iterative reweighting strategy to penalize locations that are less likely to contain any source, it is shown that the proposed iteratively reweighted edge sparsity minimization (IRES) strategy can provide reasonable information regarding the location and extent of the underlying sources. This approach is unique in the sense that it estimates extended sources without the need of subjectively thresholding the solution. The performance of IRES was evaluated in a series of computer simulations. Different parameters such as source location and signal-to-noise ratio were varied and the estimated results were compared to the targets using metrics such as localization error (LE), area under curve (AUC) and overlap between the estimated and simulated sources. It is shown that IRES provides extended solutions which not only localize the source but also provide estimation for the source extent. The performance of IRES was further tested in epileptic patients undergoing intracranial EEG (iEEG) recording for pre-surgical evaluation. IRES was applied to scalp EEGs during interictal spikes, and results were compared with iEEG and surgical resection outcome in the patients. The pilot clinical study results are promising and demonstrate a good concordance between noninvasive IRES source estimation with iEEG and surgical resection outcomes in the same patients. The proposed algorithm, i.e. IRES, estimates extended source solutions from scalp electromagnetic signals which provide relatively accurate information about the location and extent of the underlying source.

Bayesian electromagnetic spatio-temporal imaging of extended sources with Markov Random Field and temporal basis expansion

Estimating the locations and spatial extents of brain sources poses a long-standing challenge for electroencephalography and magnetoencephalography (E/MEG) source imaging. In the present work, a novel source imaging method, Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources (BESTIES), which is built upon a Bayesian framework that determines the spatio-temporal smoothness of source activities in a fully data-driven fashion, is proposed to address this challenge. In particular, a Markov Random Field (MRF), which can precisely capture local cortical interactions, is employed to characterize the spatial smoothness of source activities, the temporal dynamics of which are modeled by a set of temporal basis functions (TBFs). Crucially, all of the unknowns in the MRF and TBF models are learned from the data. To accomplish model inference efficiently on high-resolution source spaces, a scalable algorithm is developed to approximate the posterior distribution of the source activities, which is based on the variational Bayesian inference and convex analysis. The performance of BESTIES is assessed using both simulated and actual human E/MEG data. Compared with L₂-norm constrained methods, BESTIES is superior in reconstructing extended sources with less spatial diffusion and less localization error. By virtue of the MRF, BESTIES also overcomes the drawback of over-focal estimates in sparse constrained methods.

Estimating underlying neuronal activity from EEG using an iterative sparse technique

In this paper a novel technique for solving the bio-electromagnetic inverse problem is proposed. This method provides information about the location and extent of underlying neuronal activity. This is essential for the presurgical planning for partial epilepsy patients who are resistant to anti-epileptic drugs. The proposed algorithm takes advantage of the fact that neuronal activity transparent to EEG, arises from a spatially extended brain region. This spatial coherence is modeled within the framework of sparse signal processing techniques and makes better use of the limited number of EEG recordings. An iterative data-driven weighting is also introduced to better the extent estimation as well as eliminating the need to threshold estimated solutions.

Detection of EEG spatial-spectral-temporal signatures of errors: a comparative study of ICA-based and channel-based methods

The present study aimed to investigate the sensitivity of independent component analysis (ICA)- and channel-based methods in detecting electroencephalography (EEG) spatial-spectral-temporal signatures of performance errors. 128-channel EEG signals recorded from 18 subjects, who performed a color-word matching Stroop task, were analyzed. The spatial-spectral-temporal patterns in event-related potentials (ERPs) and oscillatory activities (i.e., power and phase) were measured at four selected channels, i.e., FCz, Pz, O1 and O2, from original EEG data after preprocessing, EEG data after additional current source density (CSD) transform, and back-projected EEG data from individual ICs after additional ICA analysis. Pair-wise correlation coefficient (CC) and mutual information (MI), calculated from three EEG data at four selected channels, were compared to examine mutual correlations in EEG signals obtained through three different means. Thereafter, EEG signatures of errors from these three means were statistically compared at multiple time windows in the contrast of error and correct responses. Significantly decreased CC and MI values were observed in CSD- and ICA-processed EEGs as compared with original EEG, with the smallest CC and MI in ICA EEG. Similar error patterns in ERPs and peri-response oscillatory activities were detected in all three EEGs, whereas the pre-stimulus and post-stimulus error-related oscillatory patterns identified in ICA EEG were either not or only partially detected in both original EEG and CSD EEGs in general. Both CSD and ICA processes can largely reduce signal correlations due to the volume conduction effect in original EEG, and EEG signatures of errors are better detected by ICA-based method than channel-based method (i.e., original and CSD EEGs). ICA provides the best sensitivity to detect EEG signatures linked to specific neural processes via disentangling superimposed channel-level EEG signals into distinct neurocognitive process-related component signals.