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

Source Imaging Method Based on Spatial Smoothing and Edge Sparsity (SISSES) and Its Application to OPM-MEG

Source estimation in magnetoencephalography (MEG) involves solving a highly ill-posed problem without a unique solution. Accurate estimation of the time course and spatial extent of the source is important for studying the mechanisms of brain activity and preoperative functional localization. Traditional methods tend to yield small-amplitude diffuse or large-amplitude focused source estimates. Recently, the structured sparsity-based source imaging algorithm has emerged as one of the most promising algorithms for improving source extent estimation. However, it suffers from a notable amplitude bias. To improve the spatiotemporal resolution of reconstructed sources, we propose a novel method called the source imaging method based on spatial smoothing and edge sparsity (SISSES). In this method, the temporal dynamics of sources are modeled using a set of temporal basis functions, and the spatial characteristics of the source are represented by a first-order Markov random field (MRF) model. In particular, sparse constraints are imposed on the MRF model residuals in the original and variation domains. Numerical simulations were conducted to validate the SISSES. The results demonstrate that SISSES outperforms benchmark methods for estimating the time course, location, and extent of patch sources. Additionally, auditory and median nerve stimulation experiments were performed using a 31-channel optically pumped magnetometer MEG system, and the SISSES was applied to the source imaging of these data. The results demonstrate that SISSES correctly identified the source regions in which brain responses occurred at different times, demonstrating its feasibility for various practical applications.

Source Extent Estimation in OPM-MEG: A Two-Stage Champagne Approach

The accurate estimation of source extent using magnetoencephalography (MEG) is important for the study of preoperative functional localization in epilepsy. Conventional source imaging techniques tend to produce diffuse or focused source estimates that fail to capture the source extent accurately. To address this issue, we propose a novel method called the two-stage Champagne approach (TS-Champagne). TS-Champagne divides source extent estimation into two stages. In the first stage, the Champagne algorithm with noise learning (Champagne-NL) is employed to obtain an initial source estimate. In the second stage, spatial basis functions are constructed from the initial source estimate. These spatial basis functions consist of potential activation source centers and their neighbors, and serve as spatial priors, which are incorporated into Champagne-NL to obtain a final source estimate. We evaluated the performance of TS-Champagne through numerical simulations. TS-Champagne achieved more robust performance under various conditions (i.e., varying source extent, number of sources, signal-to-noise level, and correlation coefficients between sources) than Champagne-NL and several benchmark methods. Furthermore, auditory and median nerve stimulation experiments were conducted using a 31-channel optically pumped magnetometer (OPM)-MEG system. The validation results indicated that the reconstructed source activity was spatially and temporally consistent with the neurophysiological results of previous OPM-MEG studies, further demonstrating the feasibility of TS-Champagne for practical applications.

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.

EEG changes induced by meditative practices: State and trait effects in healthy subjects and in patients with epilepsy

The effect of meditation on brain activity has been the topic of many studies in healthy subjects and in patients suffering from chronic diseases. These effects are either explored during meditation practice (state effects) or as a longer-term result of meditation training during the resting-state (trait). The topic of this article is to first review these findings by focusing on electroencephalography (EEG) changes in healthy subjects with or without experience in meditation. Modifications in EEG baseline rhythms, functional connectivity and advanced nonlinear parameters are discussed in regard to feasibility in clinical applications. Secondly, we provide a state-of-the-art of studies that proposed meditative practices as a complementary therapy in patients with epilepsy, in whom anxiety and depressive symptoms are prevalent. In these studies, the effects of standardized meditation programs including elements of traditional meditation practices such as mindfulness, loving-kindness and compassion are explored both at the level of psychological functioning and on the occurrence of seizures. Lastly, preliminary results are given regarding our ongoing study, the aim of which is to quantify the effects of a mindfulness self-compassion (MSC) practice on interictal and ictal epileptic activity. Feasibility, difficulties, and prospects of this study are discussed.

Localization of Brain Signals by Alternating Projection

A popular approach for modeling brain activity in MEG and EEG is based on a small set of current dipoles, where each dipole represents the combined activation of a local area of the brain. Here, we address the problem of multiple dipole localization with a novel solution called Alternating Projection (AP). The AP solution is based on minimizing the least-squares (LS) criterion by transforming the multi-dimensional optimization required for direct LS solution, to a sequential and iterative solution in which one source at a time is localized, while keeping the other sources fixed. Results from simulated, phantom, and human MEG data demonstrated the high accuracy of the AP method, with superior localization results than popular scanning methods from the multiple-signal classification (MUSIC) and beamformer families. In addition, the AP method was more robust to forward model errors resulting from head rotations and translations, as well as different cortex tessellation grids for the forward and inverse solutions, with consistently higher localization accuracy in low SNR and highly correlated sources.

Electrophysiological brain imaging based on simulation-driven deep learning in the context of epilepsy

Identifying the location, the spatial extent and the electrical activity of distributed brain sources in the context of epilepsy through ElectroEncephaloGraphy (EEG) recordings is a challenging task because of the highly ill-posed nature of the underlying Electrophysiological Source Imaging (ESI) problem. To guarantee a unique solution, most existing ESI methods pay more attention to solve this inverse problem by imposing physiological constraints. This paper proposes an efficient ESI approach based on simulation-driven deep learning. Epileptic High-resolution 256-channels scalp EEG (Hr-EEG) signals are simulated in a realistic manner to train the proposed patient-specific model. More particularly, a computational neural mass model developed in our team is used to generate the temporal dynamics of the activity of each dipole while the forward problem is solved using a patient-specific three-shell realistic head model and the boundary element method. A Temporal Convolutional Network (TCN) is considered in the proposed model to capture local spatial patterns. To enable the model to observe the EEG signals from different scale levels, the multi-scale strategy is leveraged to capture the overall features and fine-grain features by adjusting the convolutional kernel size. Then, the Long Short-Term Memory (LSTM) is used to extract temporal dependencies among the computed spatial features. The performance of the proposed method is evaluated through three different scenarios of realistic synthetic interictal Hr-EEG data as well as on real interictal Hr-EEG data acquired in three patients with drug-resistant partial epilepsy, during their presurgical evaluation. A performance comparison study is also conducted with two other deep learning-based methods and four classical ESI techniques. The proposed model achieved a Dipole Localization Error (DLE) of 1.39 and Normalized Hamming Distance (NHD) of 0.28 in the case of one patch with SNR of 10 dB. In the case of two uncorrelated patches with an SNR of 10 dB, obtained DLE and NHD were respectively 1.50 and 0.28. Even in the more challenging scenario of two correlated patches with an SNR of 10 dB, the proposed approach still achieved a DLE of 3.74 and an NHD of 0.43. The results obtained on simulated data demonstrate that the proposed method outperforms the existing methods for different signal-to-noise and source configurations. The good behavior of the proposed method is also confirmed on real interictal EEG data. The robustness with respect to noise makes it a promising and alternative tool to localize epileptic brain areas and to reconstruct their electrical activities from EEG signals.

LOCALIZATION OF SPATIALLY EXTENDED BRAIN SOURCES BY FLEXIBLE ALTERNATING PROJECTION (FLEX-AP)

Magnetoencephalography (MEG) and electroencephalography (EEG) are widely employed techniques for the in-vivo measurement of neural activity with exceptional temporal resolution. Modeling the neural sources underlying these signals is of high interest for both neuroscience research and pathology. The method of Alternating Projection (AP) was recently shown to outperform the well-established recursively applied and projected multiple signal classification (RAP-MUSIC) algorithm. In this work, we further enhanced AP to allow for source extent estimation, a novel approach termed flexible extent AP (FLEX-AP). We found that FLEX-AP achieves significantly lower errors for spatially coherent sources compared to AP, RAP-MUSIC, and the corresponding extension, FLEX-RAP-MUSIC. We also found an advantage for discrete dipoles under forward modeling errors encountered in real-world scenarios. Together, our results indicate that the FLEX-AP method can unify dipole fitting and distributed source imaging into a single algorithm with promising accuracy.

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.

Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

This article addresses the problem of estimating brain effective connectivity from electroencephalogram (EEG) signals using a Granger causality (GC) characterized on state-space models, extended from the conventional vector autoregressive (VAR) process. The scheme involves two main steps: model estimation and model inference to estimate brain connectivity. The model estimation performs a subspace identification and active source selection based on group-norm regularized least-squares. The model inference relies on the concept of state-space GC that requires solving a Riccati equation for the covariance of estimation error. We verify the performance on simulated datasets that represent realistic human brain activities under several conditions, including percentages and location of active sources, and the number of EEG electrodes. Our model's accuracy in estimating connectivity is compared with a two-stage approach using source reconstructions and a VAR-based Granger analysis. Our method achieved better performances than the two-stage approach under the assumptions that the true source dynamics are sparse and generated from state-space models. When the method was applied to a real EEG SSVEP dataset, the temporal lobe was found to be a mediating connection between the temporal and occipital areas, which agreed with findings in previous studies.

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.

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.

On the identification of the blood vessel confounding effect in intravoxel incoherent motion (IVIM) Diffusion-Weighted (DW)-MRI in liver: An efficient sparsity based algorithm

IntraVoxel Incoherent Motion (IVIM) Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) is of great interest for evaluating tissue diffusion and perfusion and producing parametric maps in clinical applications for liver pathologies. However, the presence of macroscopic blood vessels (not capillaries) in a given Region of Interest (ROI) results in a confounding effect that bias the quantification of tissue perfusion. Therefore, it is necessary to identify those voxels affected by blood vessels. In this paper, an efficient algorithm for an automatic identification of blood vessels in a given ROI is proposed. It relies on the sparsity of the spatial distribution of blood vessels. This sparsity prior can be easily incorporated using the all-voxel IVIM-MRI model introduced in this paper. In addition to the identification of blood vessels, the proposed algorithm provides a quantification of blood vessels, tissue diffusion and tissue perfusion of all voxels in a given ROI, in one single step. Besides, two strategies are proposed in this paper to deal with the nonnegativity of the model parameters. The efficiency of the proposed algorithm compared to the Non-Negative Least Square (NNLS)-based method, recently introduced to deal with the confounding blood vessel effect in the IVIM-MRI model, is confirmed using both realistic and real DW-MR images.

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.