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

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.

Spontaneous HFO Sequences Reveal Propagation Pathways for Precise Delineation of Epileptogenic Networks

Epilepsy, a neurological disorder affecting millions worldwide, poses great challenges in precisely delineating the epileptogenic zone - the brain region generating seizures - for effective treatment. High-frequency oscillations (HFOs) are emerging as promising biomarkers; however, the clinical utility is hindered by the difficulties in distinguishing pathological HFOs from non- epileptiform activities at single electrode and single patient resolution and understanding their dynamic role in epileptic networks. Here, we introduce an HFO-sequencing approach to analyze spontaneous HFOs traversing cortical regions in 40 drug-resistant epilepsy patients. This data- driven method automatically detected over 8.9 million HFOs, pinpointing pathological HFO- networks, and unveiled intricate millisecond-scale spatiotemporal dynamics, stability, and functional connectivity of HFOs in prolonged intracranial EEG recordings. These HFO sequences demonstrated a significant improvement in localization of epileptic tissue, with an 818.47% increase in concordance with seizure-onset zone (mean error: 2.92 mm), compared to conventional benchmarks. They also accurately predicted seizure outcomes for 90% AUC based on pre-surgical information using generalized linear models. Importantly, this mapping remained reliable even with short recordings (mean standard deviation: 3.23 mm for 30-minute segments). Furthermore, HFO sequences exhibited distinct yet highly repetitive spatiotemporal patterns, characterized by pronounced synchrony and predominant inward information flow from periphery towards areas involved in propagation, suggesting a crucial role for excitation-inhibition balance in HFO initiation and progression. Together, these findings shed light on the intricate organization of epileptic network and highlight the potential of HFO-sequencing as a translational tool for improved diagnosis, surgical targeting, and ultimately, better outcomes for vulnerable patients with drug-resistant epilepsy.

One Sentence Summary

Pathological fast brain oscillations travel like traffic along varied routes, outlining recurrently visited neural sites emerging as critical hotspots in epilepsy network.

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.

Rejuvenating classical brain electrophysiology source localization methods with spatial graph Fourier filters for source extents estimation

EEG/MEG source imaging (ESI) aims to find the underlying brain sources to explain the observed EEG or MEG measurement. Multiple classical approaches have been proposed to solve the ESI problem based on different neurophysiological assumptions. To support clinical decision-making, it is important to estimate not only the exact location of the source signal but also the extended source activation regions. Existing methods may render over-diffuse or sparse solutions, which limit the source extent estimation accuracy. In this work, we leverage the graph structures defined in the 3D mesh of the brain and the spatial graph Fourier transform (GFT) to decompose the spatial graph structure into sub-spaces of low-, medium-, and high-frequency basis. We propose to use the low-frequency basis of spatial graph filters to approximate the extended areas of brain activation and embed the GFT into the classical ESI methods. We validated the classical source localization methods with the corresponding improved version using GFT in both synthetic data and real data. We found the proposed method can effectively reconstruct focal source patterns and significantly improve the performance compared to the classical algorithms.

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.

Deep learning based source imaging provides strong sublobar localization of epileptogenic zone from MEG interictal spikes

Electromagnetic source imaging (ESI) offers unique capability of imaging brain dynamics for studying brain functions and aiding the clinical management of brain disorders. Challenges exist in ESI due to the ill-posedness of the inverse problem and thus the need of modeling the underlying brain dynamics for regularizations. Advances in generative models provide opportunities for more accurate and realistic source modeling that could offer an alternative approach to ESI for modeling the underlying brain dynamics beyond equivalent physical source models. However, it is not straightforward to explicitly formulate the knowledge arising from these generative models within the conventional ESI framework. Here we investigate a novel source imaging framework based on mesoscale neuronal modeling and deep learning (DL) that can learn the sensor-source mapping relationship directly from MEG data for ESI. Two DL-based ESI models were trained based on data generated by neural mass models and either generic or personalized head models. The robustness of the two DL models was evaluated by systematic computer simulations and clinical validation in a cohort of 29 drug-resistant focal epilepsy patients who underwent intracranial EEG (iEEG) evaluation or surgical resection. Results estimated from pre-operative MEG interictal spikes were quantified using the overlap with resection regions and the distance to the seizure-onset zone (SOZ) defined by iEEG recordings. The DL-based ESI provided robust results when no personalized head geometry is considered, reaching a spatial dispersion of 21.90 ± 19.03 mm, sublobar concordance of 83 %, and sublobar sensitivity and specificity of 66 and 97 % respectively. When using personalized head geometry derived from individual patients' MRI in the training data, personalized DL-based ESI model can further improve the performance and reached a spatial dispersion of 8.19 ± 8.14 mm, sublobar concordance of 93 %, and sublobar sensitivity and specificity of 77 and 99 % respectively. When compared to the SOZ, the localization error of the personalized approach is 15.78 ± 5.54 mm, outperforming the conventional benchmarks. This work demonstrates that combining generative models and deep learning enables an accurate and robust imaging of epileptogenic zone from MEG recordings with strong sublobar precision, suggesting its added value to enhancing MEG source localization and imaging, and to epilepsy source localization and other clinical 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.

Bayesian Adaptive Beamformer for Robust Electromagnetic Brain Imaging of Correlated Sources in High Spatial Resolution

Reconstructing complex brain source activity at a high spatiotemporal resolution from magnetoencephalography (MEG) or electroencephalography (EEG) remains a challenging problem. Adaptive beamformers are routinely deployed for this imaging domain using the sample data covariance. However adaptive beamformers have long been hindered by 1) high degree of correlation between multiple brain sources, and 2) interference and noise embedded in sensor measurements. This study develops a novel framework for minimum variance adaptive beamformers that uses a model data covariance learned from data using a sparse Bayesian learning algorithm (SBL-BF). The learned model data covariance effectively removes influence from correlated brain sources and is robust to noise and interference without the need for baseline measurements. A multiresolution framework for model data covariance computation and parallelization of the beamformer implementation enables efficient high-resolution reconstruction images. Results with both simulations and real datasets indicate that multiple highly correlated sources can be accurately reconstructed, and that interference and noise can be sufficiently suppressed. Reconstructions at 2-2.5mm resolution (  ∼  150K voxels) are possible with efficient run times of 1-3 minutes. This novel adaptive beamforming algorithm significantly outperforms the state-of-the-art benchmarks. Therefore, SBL-BF provides an effective framework for efficiently reconstructing multiple correlated brain sources with high resolution and robustness to interference and noise.

Repairing Artifacts in Neural Activity Recordings Using Low-Rank Matrix Estimation

Electrophysiology recordings are frequently affected by artifacts (e.g., subject motion or eye movements), which reduces the number of available trials and affects the statistical power. When artifacts are unavoidable and data are scarce, signal reconstruction algorithms that allow for the retention of sufficient trials become crucial. Here, we present one such algorithm that makes use of large spatiotemporal correlations in neural signals and solves the low-rank matrix completion problem, to fix artifactual entries. The method uses a gradient descent algorithm in lower dimensions to learn the missing entries and provide faithful reconstruction of signals. We carried out numerical simulations to benchmark the method and estimate optimal hyperparameters for actual EEG data. The fidelity of reconstruction was assessed by detecting event-related potentials (ERP) from a highly artifacted EEG time series from human infants. The proposed method significantly improved the standardized error of the mean in ERP group analysis and a between-trial variability analysis compared to a state-of-the-art interpolation technique. This improvement increased the statistical power and revealed significant effects that would have been deemed insignificant without reconstruction. The method can be applied to any time-continuous neural signal where artifacts are sparse and spread out across epochs and channels, increasing data retention and statistical power.

Ideal current dipoles are appropriate source representations for simulating neurons for intracranial recordings

OBJECTIVE

To determine whether dipoles are an appropriate simplified representation of neural sources for stereo-EEG (sEEG).

METHODS

We compared the distributions of voltages generated by a dipole, biophysically realistic cortical neuron models, and extended regions of cortex to determine how well a dipole represented neural sources at different spatial scales and at electrode to neuron distances relevant for sEEG. We also quantified errors introduced by the dipole approximation of neural sources in sEEG source localization using standardized low-resolution electrotomography (sLORETA).

RESULTS

For pyramidal neurons, the coefficient of correlation between voltages generated by a dipole and neuron model were > 0.9 for distances > 1 mm. For small regions of cortex (∼0.1 cm2), the error in voltages between a dipole and region was < 100 µV for all distances. However, larger regions of active cortex (>5 cm2) yielded > 50 µV errors within 1.5 cm of an electrode when compared to single dipoles. Finally, source localization errors were < 5 mm when using dipoles to represent realistic neural sources.

CONCLUSIONS

Single dipoles are an appropriate source model to represent both single neurons and small regions of active cortex, while multiple dipoles are required to represent large regions of cortex.

SIGNIFICANCE

Dipoles are computationally tractable and valid source models for sEEG.

From theory to practical fundamentals of electroencephalographic source imaging in localizing the epileptogenic zone

With continued advancement in computational technologies, the analysis of electroencephalography (EEG) has shifted from pure visual analysis to a noninvasive computational technique called EEG source imaging (ESI), which involves mathematical modeling of dipolar and distributed sources of a given scalp EEG pattern. ESI is a noninvasive phase I test for presurgical localization of the seizure onset zone in focal epilepsy. It is a relatively inexpensive modality, as it leverages scalp EEG and magnetic resonance imaging (MRI) data already collected typically during presurgical evaluation. With an adequate number of electrodes and combined with patient-specific MRI-based head models, ESI has proven to be a valuable and accurate clinical diagnostic tool for localizing the epileptogenic zone. Despite its advantages, however, ESI is routinely used at only a minority of epilepsy centers. This paper reviews the current evidence and practical fundamentals for using ESI of interictal and ictal epileptic activity during the presurgical evaluation of drug-resistant patients. We identify common errors in processing and interpreting ESI studies, describe the differences in approach needed for localizing interictal and ictal EEG discharges through practical examples, and describe best practices for optimizing the diagnostic information available from these studies.

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.

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.

Noninvasive high-frequency oscillations riding spikes delineates epileptogenic sources

Millions of people affected by epilepsy may undergo surgical resection of the epileptic tissues to stop seizures if such epileptic foci can be accurately delineated. High-frequency oscillations (HFOs), existing in electroencephalography, are highly correlated with epileptic brain, which is promising for guiding successful neurosurgery. However, it is unclear whether and how pathological HFOs can be differentiated to localize the epileptogenic tissues given the presence of various nonepileptic high-frequency activities. Here, we show morphological and source imaging evidence that pathological HFOs can be identified by the concurrence of epileptiform spikes. We describe a framework to delineate the underlying epileptogenicity using this biomarker. Our work may offer translational tools to improve treatments by noninvasively demarking pathological activities and hence epileptic foci.

High-frequency oscillations (HFOs) are a promising biomarker for localizing epileptogenic brain and guiding successful neurosurgery. However, the utility and translation of noninvasive HFOs, although highly desirable, is impeded by the difficulty in differentiating pathological HFOs from nonepileptiform high-frequency activities and localizing the epileptic tissue using noninvasive scalp recordings, which are typically contaminated with high noise levels. Here, we show that the consistent concurrence of HFOs with epileptiform spikes (pHFOs) provides a tractable means to identify pathological HFOs automatically, and this in turn demarks an epileptiform spike subgroup with higher epileptic relevance than the other spikes in a cohort of 25 temporal epilepsy patients (including a total of 2,967 interictal spikes and 1,477 HFO events). We found significant morphological distinctions of HFOs and spikes in the presence/absence of this concurrent status. We also demonstrated that the proposed pHFO source imaging enhanced localization of epileptogenic tissue by 162% (∼5.36 mm) for concordance with surgical resection and by 186% (∼12.48 mm) with seizure-onset zone determined by invasive studies, compared to conventional spike imaging, and demonstrated superior congruence with the surgical outcomes. Strikingly, the performance of spike imaging was selectively boosted by the presence of spikes with pHFOs, especially in patients with multitype spikes. Our findings suggest that concurrent HFOs and spikes reciprocally discriminate pathological activities, providing a translational tool for noninvasive presurgical diagnosis and postsurgical evaluation in vulnerable patients.

Efficient high resolution sLORETA in brain source localization

Objective. Estimation of the source location within the brain from electroencephalography (EEG) and magnetoencephalography measures is a challenging task. Among the existing techniques in the field, which are known as brain imaging methods, standardized low-resolution brain electromagnetic tomography (sLORETA) is the most popular method due to its simplicity and high accuracy. However, in this work we illustrate that sLORETA is still noisy and the additive noise is causing the blurry image. The existing pre-fixed/manual thresholding process after sLORETA can partially take care of denoising. However, this ad-hoc theresholding can either remove so much of the desired data or leave much of the noise in the process. Manual correction to avoid such extreme cases can be time-consuming. The objective of this paper is to automate the denoising process in the form of adaptive thresholding. Approach. The proposed method, denoted by efficient high-resolution sLORETA (EHR-sLORETA), is based on minimizing the error between the desired denoised source and the source estimates. Main results. The approach is evaluated using synthetic EEG and real EEG data. spatial dispersion (SD), and mean square error (MSE) are used as metrics to provide the quantitative performance of the method. In addition, qualitative analysis of the method is provided for real EEG data. This proposed model demonstrates advantages over the existing methods in sense of accuracy and robustness with SD and MSE comparison. Significance. EHR-sLORETA could have a significant impact on clinical studies with source estimation task, as it improves the accuracy of source estimation and eliminates the need for manual thresholding.

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.

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.

Higher Resolution sLORETA (HR-sLORETA) in EEG Source Imaging

sLORETA is one of the well-established EEG source localization methods that is popular for its satisfactory estimation, simplicity, and fast computation. However, the method has a low-resolution and requires manual post-processing thresholding to provide a sparser solution with acceptable resolution in source detection. Here we propose a subspace based thresholding that results in a higher resolution brain imaging based on minimizing a desired least square source detection error. Simulation results show the proposed method, denoted by HR-sLORETA, provides stable and high resolution solution in terms of Percentage of Undetected Sources (PUS) and Spatial Dispersion (SD) compared to the existing manual thresholding approaches as well as Otsu thresholding approach. It is shown that HR-sLORETA outperforms Otsu, which is the only other available automatic thresholding method, in scenarios with three or more sources.

EEGSourceSim: A framework for realistic simulation of EEG scalp data using MRI-based forward models and biologically plausible signals and noise

BACKGROUND

Electroencephalography (EEG) is widely used to investigate human brain function. Simulation studies are essential for assessing the validity of EEG analysis methods and the interpretability of results.

NEW METHOD

Here we present a simulation environment for generating EEG data by embedding biologically plausible signal and noise into MRI-based forward models that incorporate individual-subject variability in structure and function.

RESULTS

The package includes pipelines for the evaluation and validation of EEG analysis tools for source estimation, functional connectivity, and spatial filtering. EEG dynamics can be simulated using realistic noise and signal models with user specifiable signal-to-noise ratio (SNR). We also provide a set of quantitative metrics tailored to source estimation, connectivity and spatial filtering applications.

COMPARISON WITH EXISTING METHOD(S)

We provide a larger set of forward solutions for individual MRI-based head models than has been available previously. These head models are surface-based and include two sets of regions-of-interest (ROIs) that have been brought into registration with the brain of each individual using surface-based alignment - one from a whole brain and the other from a visual cortex atlas. We derive a realistic model of noise by fitting different model components to measured resting state EEG. We also provide a set of quantitative metrics for evaluating source-localization, functional connectivity and spatial filtering methods.

CONCLUSIONS

The inclusion of a larger number of individual head-models, combined with surface-atlas based labeling of ROIs and plausible models of signal and noise, allows for simulation of EEG data with greater realism than previous packages.

Multi-Resolution Graph Based Volumetric Cortical Basis Functions From Local Anatomic Features

OBJECTIVE

Modern clinical MRI collects millimeter scale anatomic information, but scalp electroencephalography source localization is ill posed, and cannot resolve individual sources at that resolution. Dimensionality reduction in the space of cortical sources is needed to improve computational and storage complexity, yet volumetric methods still employ simplistic grid coarsening that eliminates fine scale anatomic structure. We present an approach to extend near-arbitrary spatial scaling to volumetric localization.

METHODS

Starting from a voxelwise brain parcellation, sub-parcels are identified from local cortical connectivity with an iterated graph cut approach. Spatial basis functions in each parcel are constructed using either a decomposition of the local leadfield matrix or spectral basis functions of local cortical connectivity graphs.

RESULTS

We present quantitative evaluation with extensive simulations and use multiple sets of real data to highlight how parameter changes impact computed reconstructions. Our results show that volumetric basis functions can improve accuracy by as much as 30%, while reducing computational complexity by over two orders of magnitude. In real data from epilepsy surgical candidates, accurate localization of seizure onset regions is demonstrated.

CONCLUSION

Spatial dimensionality reduction with volumetric basis functions improves reconstruction accuracy while reducing computational complexity.

SIGNIFICANCE

Near-arbitrary spatial dimensionality reduction will enable volumetric reconstruction with modern computationally intensive algorithms and anatomically driven multi-resolution methods.

Electrophysiological Brain Connectivity: Theory and Implementation

We review the theory and algorithms of electrophysiological brain connectivity analysis. This tutorial is aimed at providing an introduction to brain functional connectivity from electrophysiological signals, including electroencephalography (EEG), magnetoencephalography (MEG), electrocorticography (ECoG), stereoelectroencephalography (SEEG). Various connectivity estimators are discussed, and algorithms introduced. Important issues for estimating and mapping brain functional connectivity with electrophysiology are discussed.

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.

Mapping electrical properties heterogeneity of tumor using boundary informed electrical properties tomography (BIEPT) at 7T

PURPOSES

To develop and evaluate a boundary informed electrical properties tomography (BIEPT) technique for high-resolution imaging of tumor electrical properties (EPs) heterogeneity on a rodent tumor xenograft model.

METHODS

Tumor EP distributions were inferred from a reference area external to the tumor, as well as internal EP spatial variations derived from a plurality of relative transmit B1 measurements at 7T. Edge sparsity constraint was enforced to enhance numerical stability. Phantom experiments were performed to determine the imaging accuracy and sensitivity for structures of various EP values, as well as geometrical sizes down to 1.5 mm. Numerical simulation of a realistic rodent model was used to quantify the algorithm performance in the presence of noise. Eleven athymic rats with human breast cancer xenograft were imaged in vivo, and representative pathological samples were acquired for comparison.

RESULTS

Reconstructed EPs of the phantoms correspond well to the ground truth acquired from dielectric probe measurements, with the smallest structure reliably detectable being 3 mm. EPs heterogeneity inside a tumor is successfully retrieved in both simulated and experimental cases. In vivo tumor imaging results demonstrate similar local features and spatial patterns to anatomical MRI and pathological slides. The imaged conductivity of necrotic tissue is higher than that of viable tissues, which agrees with our expectation.

CONCLUSION

BIEPT enables robust detection of tumor EPs heterogeneity with high accuracy and sensitivity to small structures. The retrieved quantitative EPs reflect tumor pathological features (e.g., necrosis). These results provide strong rationale to further expand BIEPT studies toward pathological conditions where EPs may yield valuable, non-invasive biomarkers.

EEG electrode digitization with commercial virtual reality hardware

Accurate spatial co-registration of EEG electrode positions with individual head models is an important component for EEG source localization and imaging. Due to variations in head shape between individuals, this requires measurements of electrode locations in each individual. Existing hardware for digitization can be accurate, but also relatively expensive. With the goal of making digitization more accessible for a range of research laboratories, we have developed an open-source software tool that can make use of less expensive consumer virtual reality hardware for EEG electrode digitization. Here we describe our developed VRDigitizer system and compare it to existing digitization solutions. Experimental evaluations were performed in a phantom head model and in 12 human subjects. In our comparison experiments, VRDigitizer was able to measure electrode positions with a mean error of 3.74 mm, compared to 1.73 mm and 2.98 mm for the commercial systems tested.

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.

Reducing the Computational Complexity of EEG Source Localization With Cortical Patch Decomposition and Optimal Electrode Selection

OBJECTIVE

Real-time implementation of EEG source localization can be employed in a broad area of applications such as clinical diagnosis of neurologic diseases and brain-computer interface. However, a power-efficient, low-complexity, and real-time implementation of EEG source localization is still challenging due to extensive iterations in the solutions. In this study, two techniques are introduced to reduce the computational burden of the subspace-based MUltiple SIgnal Classification (MUSIC) algorithm.

METHODS

To shrink the exhaustive search inherent in MUSIC, the cortex is parsed into cortical regions. A novel nomination procedure involving a dictionary learning step will pick a number of regions to be searched for the active sources. In addition, a new electrode selection algorithm based on the Cramer-Rao bound of the errors is introduced to pick the best set of an arbitrary number of electrodes out of the total.

RESULTS

The performance of the proposed techniques were evaluated using simulated EEG signal under variation of different parameters such as the number of nominated regions, the signal to noise ratio, and the number of electrodes. The proposed techniques can reduce the computational complexity by up to $90\%$. Furthermore, the proposed techniques were tested on EEG data from an auditory oddball experiment.

CONCLUSION

A good concordance was observed in the comparison of the topographies and the localization errors derived from the proposed technique and regular MUSIC.

SIGNIFICANCE

Such reduction can be exploited in the real-time, long-run, and mobile monitoring of cortical activity for clinical diagnosis and research purposes.

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.

Categorization for Faces and Tools-Two Classes of Objects Shaped by Different Experience-Differs in Processing Timing, Brain Areas Involved, and Repetition Effects

The brain mechanisms that integrate the separate features of sensory input into a meaningful percept depend upon the prior experience of interaction with the object and differ between categories of objects. Recent studies using representational similarity analysis (RSA) have characterized either the spatial patterns of brain activity for different categories of objects or described how category structure in neuronal representations emerges in time, but never simultaneously. Here we applied a novel, region-based, multivariate pattern classification approach in combination with RSA to magnetoencephalography data to extract activity associated with qualitatively distinct processing stages of visual perception. We asked participants to name what they see whilst viewing bitonal visual stimuli of two categories predominantly shaped by either value-dependent or sensorimotor experience, namely faces and tools, and meaningless images. We aimed to disambiguate the spatiotemporal patterns of brain activity between the meaningful categories and determine which differences in their processing were attributable to either perceptual categorization per se, or later-stage mentalizing-related processes. We have extracted three stages of cortical activity corresponding to low-level processing, category-specific feature binding, and supra-categorical processing. All face-specific spatiotemporal patterns were associated with bilateral activation of ventral occipito-temporal areas during the feature binding stage at 140–170 ms. The tool-specific activity was found both within the categorization stage and in a later period not thought to be associated with binding processes. The tool-specific binding-related activity was detected within a 210–220 ms window and was located to the intraparietal sulcus of the left hemisphere. Brain activity common for both meaningful categories started at 250 ms and included widely distributed assemblies within parietal, temporal, and prefrontal regions. Furthermore, we hypothesized and tested whether activity within face and tool-specific binding-related patterns would demonstrate oppositely acting effects following procedural perceptual learning. We found that activity in the ventral, face-specific network increased following the stimuli repetition. In contrast, tool processing in the dorsal network adapted by reducing its activity over the repetition period. Altogether, we have demonstrated that activity associated with visual processing of faces and tools during the categorization stage differ in processing timing, brain areas involved, and in their dynamics underlying stimuli learning.

Electromagnetic source imaging using simultaneous scalp EEG and intracranial EEG: An emerging tool for interacting with pathological brain networks

OBJECTIVE

The goal of this study is to investigate the performance, merits and limitations of source imaging using intracranial EEG (iEEG) recordings and to compare its accuracy to the results of EEG source imaging. Accuracy in this study, is measured both by determining the location and inter-nodal connectivity of underlying brain networks.

METHODS

Systematic computer simulation studies are conducted to evaluate iEEG-based source imaging vs. EEG-based source imaging, and source imaging using both EEG and iEEG. To test the source imaging models, networks of inter-connected nodes (in terms of activity) are simulated. The location of the network nodes is randomly selected within a realistic geometry head model and a connectivity link is created among these nodes based on a multi-variate auto-regressive (MVAR) model. Then the forward problem is solved to calculate the potentials at the electrodes and noise (white and correlated) is added to these simulated potentials to simulate realistic measurements. Subsequently, the inverse problem is solved and an algorithm based on principle component analysis is performed on the estimated source activities to determine the location of the simulated network nodes. The activity of these nodes (over time), is then extracted, and used to estimate the connectivity links among the mentioned nodes using Granger causality analysis.

RESULTS

Source imaging based on iEEG recordings may or may not improve the accuracy in localization, depending on the number and location of active nodes relative to iEEG electrodes and to other nodes within the network. However, our simulation results suggest that combining EEG and iEEG modalities (simultaneous scalp and intracranial recordings) can improve the imaging accuracy significantly.

CONCLUSIONS

While iEEG source imaging is useful in estimating the exact location of sources near the iEEG electrodes, combining EEG and iEEG recordings can achieve a more accurate imaging due to the high spatial coverage of the scalp electrodes and the added near field information provided by the iEEG electrodes.

SIGNIFICANCE

The present results suggest the feasibility of localizing brain electrical sources from iEEG recordings and improving EEG source localization using simultaneous EEG and iEEG recordings to cover the whole brain. The hybrid EEG and iEEG source imaging can assist the clinicians when unequivocal decisions about determining the epileptogenic zone cannot be reached using a single modality.

Increased theta band EEG power in sickle cell disease patients

Objective

Pain is a major issue in the care of patients with sickle cell disease (SCD). The mechanisms behind pain and the best way to treat it are not well understood. We studied how electroencephalography (EEG) is altered in SCD patients.

Methods

We recruited 20 SCD patients and compared their resting state EEG to that of 14 healthy controls. EEG power was found across frequency bands using Welch's method. Electrophysiological source imaging was assessed for each frequency band using the eLORETA algorithm.

Results

SCD patients had increased theta power and decreased beta2 power compared to controls. Source localization revealed that areas of greater theta band activity were in areas related to pain processing. Imaging parameters were significantly correlated to emergency department visits, which indicate disease severity and chronic pain intensity.

Conclusion

The present results support the pain mechanism referred to as thalamocortical dysrhythmia. This mechanism causes increased theta power in patients.

Significance

Our findings show that EEG can be used to quantitatively evaluate differences between controls and SCD patients. Our results show the potential of EEG to differentiate between different levels of pain in an unbiased setting, where specific frequency bands could be used as biomarkers for chronic pain.

Reproducibility of EEG-MEG fusion source analysis of interictal spikes: Relevance in presurgical evaluation of epilepsy

Fusion of electroencephalography (EEG) and magnetoencephalography (MEG) data using maximum entropy on the mean method (MEM-fusion) takes advantage of the complementarities between EEG and MEG to improve localization accuracy. Simulation studies demonstrated MEM-fusion to be robust especially in noisy conditions such as single spike source localizations (SSSL). Our objective was to assess the reliability of SSSL using MEM-fusion on clinical data. We proposed to cluster SSSL results to find the most reliable and consistent source map from the reconstructed sources, the so-called consensus map. Thirty-four types of interictal epileptic discharges (IEDs) were analyzed from 26 patients with well-defined epileptogenic focus. SSSLs were performed on EEG, MEG, and fusion data and consensus maps were estimated using hierarchical clustering. Qualitative (spike-to-spike reproducibility rate, SSR) and quantitative (localization error and spatial dispersion) assessments were performed using the epileptogenic focus as clinical reference. Fusion SSSL provided significantly better results than EEG or MEG alone. Fusion found at least one cluster concordant with the clinical reference in all cases. This concordant cluster was always the one involving the highest number of spikes. Fusion yielded highest reproducibility (SSR EEG = 55%, MEG = 71%, fusion = 90%) and lowest localization error. Also, using only few channels from either modality (21EEG + 272MEG or 54EEG + 25MEG) was sufficient to reach accurate fusion. MEM-fusion with consensus map approach provides an objective way of finding the most reliable and concordant generators of IEDs. We, therefore, suggest the pertinence of SSSL using MEM-fusion as a valuable clinical tool for presurgical evaluation of epilepsy.

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.

Functional connectivity analysis in EEG source space: The choice of method

Functional connectivity (FC) is among the most informative features derived from EEG. However, the most straightforward sensor-space analysis of FC is unreliable owing to volume conductance effects. An alternative-source-space analysis of FC-is optimal for high- and mid-density EEG (hdEEG, mdEEG); however, it is questionable for widely used low-density EEG (ldEEG) because of inadequate surface sampling. Here, using simulations, we investigate the performance of the two source FC methods, the inverse-based source FC (ISFC) and the cortical partial coherence (CPC). To examine the effects of localization errors of the inverse method on the FC estimation, we simulated an oscillatory source with varying locations and SNRs. To compare the FC estimations by the two methods, we simulated two synchronized sources with varying between-source distance and SNR. The simulations were implemented for hdEEG, mdEEG, and ldEEG. We showed that the performance of both methods deteriorates for deep sources owing to their inaccurate localization and smoothing. The accuracy of both methods improves with the increasing between-source distance. The best ISFC performance was achieved using hd/mdEEG, while the best CPC performance was observed with ldEEG. In conclusion, with hdEEG, ISFC outperforms CPC and therefore should be the preferred method. In the studies based on ldEEG, the CPC is a method of choice.

Consistency of EEG source localization and connectivity estimates

As the EEG inverse problem does not have a unique solution, the sources reconstructed from EEG and their connectivity properties depend on forward and inverse modeling parameters such as the choice of an anatomical template and electrical model, prior assumptions on the sources, and further implementational details. In order to use source connectivity analysis as a reliable research tool, there is a need for stability across a wider range of standard estimation routines. Using resting state EEG recordings of N=65 participants acquired within two studies, we present the first comprehensive assessment of the consistency of EEG source localization and functional/effective connectivity metrics across two anatomical templates (ICBM152 and Colin27), three electrical models (BEM, FEM and spherical harmonics expansions), three inverse methods (WMNE, eLORETA and LCMV), and three software implementations (Brainstorm, Fieldtrip and our own toolbox). Source localizations were found to be more stable across reconstruction pipelines than subsequent estimations of functional connectivity, while effective connectivity estimates where the least consistent. All results were relatively unaffected by the choice of the electrical head model, while the choice of the inverse method and source imaging package induced a considerable variability. In particular, a relatively strong difference was found between LCMV beamformer solutions on one hand and eLORETA/WMNE distributed inverse solutions on the other hand. We also observed a gradual decrease of consistency when results are compared between studies, within individual participants, and between individual participants. In order to provide reliable findings in the face of the observed variability, additional simulations involving interacting brain sources are required. Meanwhile, we encourage verification of the obtained results using more than one source imaging procedure.

Noninvasive Electromagnetic Source Imaging and Granger Causality Analysis: An Electrophysiological Connectome (eConnectome) Approach

OBJECTIVE

Combined source-imaging techniques and directional connectivity analysis can provide useful information about the underlying brain networks in a noninvasive fashion. Source-imaging techniques have been used successfully to either determine the source of activity or to extract source time-courses for Granger causality analysis, previously. In this work, we utilize source-imaging algorithms to both find the network nodes [regions of interest (ROI)] and then extract the activation time series for further Granger causality analysis. The aim of this work is to find network nodes objectively from noninvasive electromagnetic signals, extract activation time-courses, and apply Granger analysis on the extracted series to study brain networks under realistic conditions.

METHODS

Source-imaging methods are used to identify network nodes and extract time-courses and then Granger causality analysis is applied to delineate the directional functional connectivity of underlying brain networks. Computer simulations studies where the underlying network (nodes and connectivity pattern) is known were performed; additionally, this approach has been evaluated in partial epilepsy patients to study epilepsy networks from interictal and ictal signals recorded by EEG and/or Magnetoencephalography (MEG).

RESULTS

Localization errors of network nodes are less than 5 mm and normalized connectivity errors of ∼20% in estimating underlying brain networks in simulation studies. Additionally, two focal epilepsy patients were studied and the identified nodes driving the epileptic network were concordant with clinical findings from intracranial recordings or surgical resection.

CONCLUSION

Our study indicates that combined source-imaging algorithms with Granger causality analysis can identify underlying networks precisely (both in terms of network nodes location and internodal connectivity).

SIGNIFICANCE

The combined source imaging and Granger analysis technique is an effective tool for studying normal or pathological brain conditions.

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.