Prior knowledge on cortex organization in the reconstruction of source current densities from EEG

Electromagnetic Source Imaging via a Data-Synthesis-Based Convolutional Encoder-Decoder Network

Electromagnetic source imaging (ESI) requires solving a highly ill-posed inverse problem. To seek a unique solution, traditional ESI methods impose various forms of priors that may not accurately reflect the actual source properties, which may hinder their broad applications. To overcome this limitation, in this article, a novel data-synthesized spatiotemporally convolutional encoder-decoder network (DST-CedNet) method is proposed for ESI. The DST-CedNet recasts ESI as a machine learning problem, where discriminative learning and latent-space representations are integrated in a CedNet to learn a robust mapping from the measured electroencephalography/magnetoencephalography (E/MEG) signals to the brain activity. In particular, by incorporating prior knowledge regarding dynamical brain activities, a novel data synthesis strategy is devised to generate large-scale samples for effectively training CedNet. This stands in contrast to traditional ESI methods where the prior information is often enforced via constraints primarily aimed for mathematical convenience. Extensive numerical experiments as well as analysis of a real MEG and epilepsy EEG dataset demonstrate that the DST-CedNet outperforms several state-of-the-art ESI methods in robustly estimating source signals under a variety of source configurations.

Optimizing EEG Source Reconstruction with Concurrent fMRI-Derived Spatial Priors

Reconstructing EEG sources involves a complex pipeline, with the inverse problem being the most challenging. Multiple inversion algorithms are being continuously developed, aiming to tackle the non-uniqueness of this problem, which has been shown to be partially circumvented by including prior information in the inverse models. Despite a few efforts, there are still current and persistent controversies regarding the inversion algorithm of choice and the optimal set of spatial priors to be included in the inversion models. The use of simultaneous EEG-fMRI data is one approach to tackle this problem. The spatial resolution of fMRI makes fMRI derived spatial priors very convenient for EEG reconstruction, however, only task activation maps and resting-state networks (RSNs) have been explored so far, overlooking the recent, but already accepted, notion that brain networks exhibit dynamic functional connectivity fluctuations. The lack of a systematic comparison between different source reconstruction algorithms, considering potentially more brain-informative priors such as fMRI, motivates the search for better reconstruction models. Using simultaneous EEG-fMRI data, here we compared four different inversion algorithms (minimum norm, MN; low resolution electromagnetic tomography, LORETA; empirical Bayes beamformer, EBB; and multiple sparse priors, MSP) under a Bayesian framework (as implemented in SPM), each with three different sets of priors consisting of: (1) those specific to the algorithm; (2) those specific to the algorithm plus fMRI task activation maps and RSNs; and (3) those specific to the algorithm plus fMRI task activation maps and RSNs and network modules of task-related dFC states estimated from the dFC fluctuations. The quality of the reconstructed EEG sources was quantified in terms of model-based metrics, namely the expectation of the posterior probability P(model|data) and variance explained of the inversion models, and the overlap/proportion of brain regions known to be involved in the visual perception tasks that the participants were submitted to, and RSN templates, with/within EEG source components. Model-based metrics suggested that model parsimony is preferred, with the combination MSP and priors specific to this algorithm exhibiting the best performance. However, optimal overlap/proportion values were found using EBB and priors specific to this algorithm and fMRI task activation maps and RSNs or MSP and considering all the priors (algorithm priors, fMRI task activation maps and RSNs and dFC state modules), respectively, indicating that fMRI spatial priors, including dFC state modules, might contain useful information to recover EEG source components reflecting neuronal activity of interest. Our main results show that providing fMRI spatial derived priors that reflect the dynamics of the brain might be useful to map neuronal activity more accurately from EEG-fMRI. Furthermore, this work paves the way towards a more informative selection of the optimal EEG source reconstruction approach, which may be critical in future studies.

Source imaging of deep-brain activity using the regional spatiotemporal Kalman filter

BACKGROUND AND OBJECTIVE

The human brain displays rich and complex patterns of interaction within and among brain networks that involve both cortical and subcortical brain regions. Due to the limited spatial resolution of surface electroencephalography (EEG), EEG source imaging is used to reconstruct brain sources and investigate their spatial and temporal dynamics. The majority of EEG source imaging methods fail to detect activity from subcortical brain structures. The reconstruction of subcortical sources is a challenging task because the signal from these sources is weakened and mixed with artifacts and other signals from cortical sources. In this proof-of-principle study we present a novel EEG source imaging method, the regional spatiotemporal Kalman filter (RSTKF), that can detect deep brain activity.

METHODS

The regional spatiotemporal Kalman filter (RSTKF) is a generalization of the spatiotemporal Kalman filter (STKF), which allows for the characterization of different regional dynamics in the brain. It is based on state-space modeling with spatially heterogeneous dynamical noise variances, since models with spatial and temporal homogeneity fail to describe the dynamical complexity of brain activity. First, RSTKF is tested using simulated EEG data from sources in the frontal lobe, putamen, and thalamus. After that, it is applied to non-averaged interictal epileptic spikes from a presurgical epilepsy patient with focal epileptic activity in the amygdalo-hippocampal complex. The results of RSTKF are compared to those of low-resolution brain electromagnetic tomography (LORETA) and of standard STKF.

RESULTS

Only RSTKF is successful in consistently and accurately localizing the sources in deep brain regions. Additionally, RSTKF shows improved spatial resolution compared to LORETA and STKF.

CONCLUSIONS

RSTKF is a generalization of STKF that allows for accurate, focal, and consistent localization of sources, especially in the deeper brain areas. In contrast to standard source imaging methods, RSTKF may find application in the localization of the epileptogenic zone in deeper brain structures, such as mesial frontal and temporal lobe epilepsies, especially in EEG recordings for which no reliable averaged spike shape can be obtained due to lack of the necessary number of spikes required to reach a certain signal-to-noise ratio level after averaging.

Structural connectivity to reconstruct brain activation and effective connectivity between brain regions

OBJECTIVE

Understanding how brain regions interact to perform a specific task is very challenging. EEG and MEG are two non-invasive imaging modalities that allow the measurement of brain activation with high temporal resolution. Several works in EEG/MEG source reconstruction show that estimating brain activation can be improved by considering spatio-temporal constraints but only few of them use structural information to do so.

APPROACH

In this work, we present a source reconstruction algorithm that uses brain structural connectivity, estimated from diffusion MRI (dMRI), to constrain the EEG/MEG source reconstruction. Contrarily to most source reconstruction methods which reconstruct activation for each time instant, the proposed method estimates an initial reconstruction for the first time instants and a multivariate autoregressive model that explains the data in further time instants. This autoregressive model can be thought as an estimation of the effective connectivity between brain regions. We called this algorithm iterative Source and Dynamics reconstruction (iSDR).

MAIN RESULTS

This paper presents the overall iSDR approach and how the proposed model is optimized to obtain both brain activation and brain region interactions. The accuracy of our method is demonstrated using synthetic data in which it shows a good capability to reconstruct both activation and connectivity. iSDR is also tested with real data obtained from (Wakeman D and Henson R 2015 A multi-subject, multi-modal human neuroimaging dataset Scientific Data 2 15001) (face recognition task). The results are in phase with other works published with the same data and others that used different imaging modalities with the same task showing that the choice of using an autoregressive model gives relevant results.

SIGNIFICANCE

This work shows that complex EEG/MEG datasets can be explained by an initial state and a MAR model for effective connectivity. This is a compact way to describe brain dynamics and offers a direct access to effective connectivity.

Neuro-current response functions: A unified approach to MEG source analysis under the continuous stimuli paradigm

Characterizing the neural dynamics underlying sensory processing is one of the central areas of investigation in systems and cognitive neuroscience. Neuroimaging techniques such as magnetoencephalography (MEG) and Electroencephalography (EEG) have provided significant insights into the neural processing of continuous stimuli, such as speech, thanks to their high temporal resolution. Existing work in the context of auditory processing suggests that certain features of speech, such as the acoustic envelope, can be used as reliable linear predictors of the neural response manifested in M/EEG. The corresponding linear filters are referred to as temporal response functions (TRFs). While the functional roles of specific components of the TRF are well-studied and linked to behavioral attributes such as attention, the cortical origins of the underlying neural processes are not as well understood. In this work, we address this issue by estimating a linear filter representation of cortical sources directly from neuroimaging data in the context of continuous speech processing. To this end, we introduce Neuro-Current Response Functions (NCRFs), a set of linear filters, spatially distributed throughout the cortex, that predict the cortical currents giving rise to the observed ongoing MEG (or EEG) data in response to continuous speech. NCRF estimation is cast within a Bayesian framework, which allows unification of the TRF and source estimation problems, and also facilitates the incorporation of prior information on the structural properties of the NCRFs. To generalize this analysis to M/EEG recordings which lack individual structural magnetic resonance (MR) scans, NCRFs are extended to free-orientation dipoles and a novel regularizing scheme is put forward to lessen reliance on fine-tuned coordinate co-registration. We present a fast estimation algorithm, which we refer to as the Champ-Lasso algorithm, by leveraging recent advances in optimization, and demonstrate its utility through application to simulated and experimentally recorded MEG data under auditory experiments. Our simulation studies reveal significant improvements over existing methods that typically operate in a two-stage fashion, in terms of spatial resolution, response function reconstruction, and recovering dipole orientations. The analysis of experimentally-recorded MEG data without MR scans corroborates existing findings, but also delineates the distinct cortical distribution of the underlying neural processes at high spatiotemporal resolution. In summary, we provide a principled modeling and estimation paradigm for MEG source analysis tailored to extracting the cortical origin of electrophysiological responses to continuous stimuli.

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.

Hierarchical multiscale Bayesian algorithm for robust MEG/EEG source reconstruction

In this paper, we present a novel hierarchical multiscale Bayesian algorithm for electromagnetic brain imaging using magnetoencephalography (MEG) and electroencephalography (EEG). In particular, we present a solution to the source reconstruction problem for sources that vary in spatial extent. We define sensor data measurements using a generative probabilistic graphical model that is hierarchical across spatial scales of brain regions and voxels. We then derive a novel Bayesian algorithm for probabilistic inference with this graphical model. This algorithm enables robust reconstruction of sources that have different spatial extent, from spatially contiguous clusters of dipoles to isolated dipolar sources. We compare the new algorithm with several representative benchmarks on both simulated and real brain activities. The source locations and the correct estimation of source time courses used for the simulated data are chosen to test the performance on challenging source configurations. In simulations, performance of the novel algorithm shows superiority to several existing benchmark algorithms. We also demonstrate that the new algorithm is more robust to correlated brain activity present in real MEG and EEG data and is able to resolve distinct and functionally relevant brain areas with real MEG and EEG datasets.

Sparse EEG/MEG source estimation via a group lasso

Non-invasive recordings of human brain activity through electroencephalography (EEG) or magnetoencelphalography (MEG) are of value for both basic science and clinical applications in sensory, cognitive, and affective neuroscience. Here we introduce a new approach to estimating the intra-cranial sources of EEG/MEG activity measured from extra-cranial sensors. The approach is based on the group lasso, a sparse-prior inverse that has been adapted to take advantage of functionally-defined regions of interest for the definition of physiologically meaningful groups within a functionally-based common space. Detailed simulations using realistic source-geometries and data from a human Visual Evoked Potential experiment demonstrate that the group-lasso method has improved performance over traditional ℓ2 minimum-norm methods. In addition, we show that pooling source estimates across subjects over functionally defined regions of interest results in improvements in the accuracy of source estimates for both the group-lasso and minimum-norm approaches.

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

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

Incorporating priors for EEG source imaging and connectivity analysis

Electroencephalography source imaging (ESI) is a useful technique to localize the generators from a given scalp electric measurement and to investigate the temporal dynamics of the large-scale neural circuits. By introducing reasonable priors from other modalities, ESI reveals the most probable sources and communication structures at every moment in time. Here, we review the available priors from such techniques as magnetic resonance imaging (MRI), functional MRI (fMRI), and positron emission tomography (PET). The modality's specific contribution is analyzed from the perspective of source reconstruction. For spatial priors, EEG-correlated fMRI, temporally coherent networks (TCNs) and resting-state fMRI are systematically introduced in the ESI. Moreover, the fiber tracking (diffusion tensor imaging, DTI) and neuro-stimulation techniques (transcranial magnetic stimulation, TMS) are also introduced as the potential priors, which can help to draw inferences about the neuroelectric connectivity in the source space. We conclude that combining EEG source imaging with other complementary modalities is a promising approach toward the study of brain networks in cognitive and clinical neurosciences.

Methods for examining electrophysiological coherence in epileptic networks

Epilepsy may reflect a focal abnormality of cerebral tissue, but the generation of seizures typically involves propagation of abnormal activity through cerebral networks. We examined epileptiform discharges (spikes) with dense array electroencephalography (dEEG) in five patients to search for the possible engagement of pathological networks. Source analysis was conducted with individual electrical head models for each patient, including sensor position measurement for registration with MRI with geodesic photogrammetry; tissue segmentation and skull conductivity modeling with an atlas skull warped to each patient's MRI; cortical surface extraction and tessellation into 1 cm(2) equivalent dipole patches; inverse source estimation with either minimum norm or cortical surface Laplacian constraints; and spectral coherence computed among equivalent dipoles aggregated within Brodmann areas with 1 Hz resolution from 1 to 70 Hz. These analyses revealed characteristic source coherence patterns in each patient during the pre-spike, spike, and post-spike intervals. For one patient with both spikes and seizure onset localized to a single temporal lobe, we observed a cluster of apparently abnormal coherences over the involved temporal lobe. For the other patients, there were apparently characteristic coherence patterns associated with the discharges, and in some cases these appeared to reflect abnormal temporal lobe synchronization, but the coherence patterns for these patients were not easily related to an unequivocal epileptogenic zone. In contrast, simple localization of the site of onset of the spike discharge, and/or the site of onset of the seizure, with non-invasive 256 dEEG was useful in predicting the characteristic site of seizure onset for those cases that were verified by intracranial EEG and/or by surgical outcome.