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

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.

EEGProgress: A fast and lightweight progressive convolution architecture for EEG classification

Because of the intricate topological structure and connection of the human brain, extracting deep spatial features from electroencephalograph (EEG) signals is a challenging and time-consuming task. The extraction of topological spatial information plays a crucial role in EEG classification, and the architecture of the spatial convolution greatly affects the performance and complexity of convolutional neural network (CNN) based EEG classification models. In this study, a progressive convolution CNN architecture named EEGProgress is proposed, aiming to efficiently extract the topological spatial information of EEG signals from multi-scale levels (electrode, brain region, hemisphere, global) with superior speed. To achieve this, the raw EEG data is permuted using the empirical topological permutation rule, integrating the EEG data with numerous topological properties. Subsequently, the spatial features are extracted by a progressive feature extractor including prior, electrode, region, and hemisphere convolution blocks, progressively extracting the deep spatial features with reduced parameters and speed. Finally, the comparison and ablation experiments under both cross-subject and within-subject scenarios are conducted on a public dataset to verify the performance of the proposed EEGProgress and the effectiveness of the topological permutation. The results demonstrate the superior feature extraction ability of the proposed EEGProgress, with an average increase of 4.02% compared to other CNN-based EEG classification models under both cross-subject and within-subject scenarios. Furthermore, with the obtained average testing time, FLOPs, and parameters, the proposed EEGProgress outperforms other comparison models in terms of model complexity.

Solving large-scale MEG/EEG source localisation and functional connectivity problems simultaneously using state-space models

State-space models are widely employed across various research disciplines to study unobserved dynamics. Conventional estimation techniques, such as Kalman filtering and expectation maximisation, offer valuable insights but incur high computational costs in large-scale analyses. Sparse inverse covariance estimators can mitigate these costs, but at the expense of a trade-off between enforced sparsity and increased estimation bias, necessitating careful assessment in low signal-to-noise ratio (SNR) situations. To address these challenges, we propose a three-fold solution: (1) Introducing multiple penalised state-space (MPSS) models that leverage data-driven regularisation; (2) Developing novel algorithms derived from backpropagation, gradient descent, and alternating least squares to solve MPSS models; (3) Presenting a K-fold cross-validation extension for evaluating regularisation parameters. We validate this MPSS regularisation framework through lower and more complex simulations under varying SNR conditions, including a large-scale synthetic magneto- and electro-encephalography (MEG/EEG) data analysis. In addition, we apply MPSS models to concurrently solve brain source localisation and functional connectivity problems for real event-related MEG/EEG data, encompassing thousands of sources on the cortical surface. The proposed methodology overcomes the limitations of existing approaches, such as constraints to small-scale and region-of-interest analyses. Thus, it may enable a more accurate and detailed exploration of cognitive brain functions.

NLGC: Network Localized Granger Causality with Application to MEG Directional Functional Connectivity Analysis

Identifying the directed connectivity that underlie networked activity between different cortical areas is critical for understanding the neural mechanisms behind sensory processing. Granger causality (GC) is widely used for this purpose in functional magnetic resonance imaging analysis, but there the temporal resolution is low, making it difficult to capture the millisecond-scale interactions underlying sensory processing. Magnetoencephalography (MEG) has millisecond resolution, but only provides low-dimensional sensor-level linear mixtures of neural sources, which makes GC inference challenging. Conventional methods proceed in two stages: First, cortical sources are estimated from MEG using a source localization technique, followed by GC inference among the estimated sources. However, the spatiotemporal biases in estimating sources propagate into the subsequent GC analysis stage, may result in both false alarms and missing true GC links. Here, we introduce the Network Localized Granger Causality (NLGC) inference paradigm, which models the source dynamics as latent sparse multivariate autoregressive processes and estimates their parameters directly from the MEG measurements, integrated with source localization, and employs the resulting parameter estimates to produce a precise statistical characterization of the detected GC links. We offer several theoretical and algorithmic innovations within NLGC and further examine its utility via comprehensive simulations and application to MEG data from an auditory task involving tone processing from both younger and older participants. Our simulation studies reveal that NLGC is markedly robust with respect to model mismatch, network size, and low signal-to-noise ratio, whereas the conventional two-stage methods result in high false alarms and mis-detections. We also demonstrate the advantages of NLGC in revealing the cortical network-level characterization of neural activity during tone processing and resting state by delineating task- and age-related connectivity changes.

Detection of Brain Network Communities During Natural Speech Comprehension From Functionally Aligned EEG Sources

In recent years, electroencephalograph (EEG) studies on speech comprehension have been extended from a controlled paradigm to a natural paradigm. Under the hypothesis that the brain can be approximated as a linear time-invariant system, the neural response to natural speech has been investigated extensively using temporal response functions (TRFs). However, most studies have modeled TRFs in the electrode space, which is a mixture of brain sources and thus cannot fully reveal the functional mechanism underlying speech comprehension. In this paper, we propose methods for investigating the brain networks of natural speech comprehension using TRFs on the basis of EEG source reconstruction. We first propose a functional hyper-alignment method with an additive average method to reduce EEG noise. Then, we reconstruct neural sources within the brain based on the EEG signals to estimate TRFs from speech stimuli to source areas, and then investigate the brain networks in the neural source space on the basis of the community detection method. To evaluate TRF-based brain networks, EEG data were recorded in story listening tasks with normal speech and time-reversed speech. To obtain reliable structures of brain networks, we detected TRF-based communities from multiple scales. As a result, the proposed functional hyper-alignment method could effectively reduce the noise caused by individual settings in an EEG experiment and thus improve the accuracy of source reconstruction. The detected brain networks for normal speech comprehension were clearly distinctive from those for non-semantically driven (time-reversed speech) audio processing. Our result indicates that the proposed source TRFs can reflect the cognitive processing of spoken language and that the multi-scale community detection method is powerful for investigating brain networks.

Biophysical Model: A Promising Method in the Study of the Mechanism of Propofol: A Narrative Review

The physiological and neuroregulatory mechanism of propofol is largely based on very limited knowledge. It is one of the important puzzling issues in anesthesiology and is of great value in both scientific and clinical fields. It is acknowledged that neural networks which are comprised of a number of neural circuits might be involved in the anesthetic mechanism. However, the mechanism of this hypothesis needs to be further elucidated. With the progress of artificial intelligence, it is more likely to solve this problem through using artificial neural networks to perform temporal waveform data analysis and to construct biophysical computational models. This review focuses on current knowledge regarding the anesthetic mechanism of propofol, an intravenous general anesthetic, by constructing biophysical computational models.

A Mixed Filtering Approach for Real-Time Seizure State Tracking Using Multi-Channel Electroencephalography Data

Real-time continuous tracking of seizure state is necessary to develop feedback neuromodulation therapy that can prevent or terminate a seizure early. Due to its high temporal resolution, high scalp coverage, and non-invasive applicability, electroencephalography (EEG) is a good candidate for seizure tracking. In this research, we make multiple seizure state estimations using a mixed-filter and multiple channels found over the entire sensor space; then by applying a Kalman filter, we produce a single seizure state estimation made up of these individual estimations. Using a modified wrapper feature selection, we determine two optimal features of mixed data type, one continuous and one binary analyzing all available channels. These features are used in a state-space framework to model the continuous hidden seizure state. Expectation maximization is performed offline on the training and validation data sets to estimate unknown parameters. The seizure state estimation process is performed for multiple channels, and the seizure state estimation is derived using a square-root Kalman filter. A second expectation maximization step is utilized to estimate the unknown square-root Kalman filter parameters. This method is tested in a real-time applicable way for seizure state estimation. Applying this approach, we obtain a single seizure state estimation with quantitative information about the likelihood of a seizure occurring, which we call seizure probability. Our results on the experimental data (CHB-MIT EEG database) validate the proposed estimation method and we achieve an average accuracy, sensitivity, and specificity of 92.7%, 92.8%, and 93.4%, respectively. The potential applications of this seizure estimation model are for closed-loop neuromodulation and long-term quantitative analysis of seizure treatment efficacy.

Advances in Electrical Source Imaging: A Review of the Current Approaches, Applications and Challenges

Brain source localization has been consistently implemented over the recent years to elucidate complex brain operations, pairing the high temporal resolution of the EEG with the high spatial estimation of the estimated sources. This review paper aims to present the basic principles of Electrical source imaging (ESI) in the context of the recent progress for solving the forward and the inverse problems, and highlight the advantages and limitations of the different approaches. As such, a synthesis of the current state-of-the-art methodological aspects is provided, offering a complete overview of the present advances with regard to the ESI solutions. Moreover, the new dimensions for the analysis of the brain processes are indicated in terms of clinical and cognitive ESI applications, while the prevailing challenges and limitations are thoroughly discussed, providing insights for future approaches that could help to alleviate methodological and technical shortcomings.

Contextual MEG and EEG Source Estimates Using Spatiotemporal LSTM Networks

Most magneto- and electroencephalography (M/EEG) based source estimation techniques derive their estimates sample wise, independently across time. However, neuronal assemblies are intricately interconnected, constraining the temporal evolution of neural activity that is detected by MEG and EEG; the observed neural currents must thus be highly context dependent. Here, we use a network of Long Short-Term Memory (LSTM) cells where the input is a sequence of past source estimates and the output is a prediction of the following estimate. This prediction is then used to correct the estimate. In this study, we applied this technique on noise-normalized minimum norm estimates (MNE). Because the correction is found by using past activity (context), we call this implementation Contextual MNE (CMNE), although this technique can be used in conjunction with any source estimation method. We test CMNE on simulated epileptiform activity and recorded auditory steady state response (ASSR) data, showing that the CMNE estimates exhibit a higher degree of spatial fidelity than the unfiltered estimates in the tested cases.

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.

Spatial fidelity of MEG/EEG source estimates: A general evaluation approach

Low spatial resolution is often cited as the most critical limitation of magneto- and electroencephalography (MEG and EEG), but a unifying framework for quantifying the spatial fidelity of M/EEG source estimates has yet to be established; previous studies have focused on linear estimation methods under ideal scenarios without noise. Here we present an approach that quantifies the spatial fidelity of M/EEG estimates from simulated patch activations over the entire neocortex superposed on measured resting-state data. This approach grants more generalizability in the evaluation process that allows for, e.g., comparing linear and non-linear estimates in the whole brain for different signal-to-noise ratios (SNR), number of active sources and activation waveforms. Using this framework, we evaluated the MNE, dSPM, sLORETA, eLORETA, and MxNE methods and found that the spatial fidelity varies significantly with SNR, following a largely sigmoidal curve whose shape varies depending on which aspect of spatial fidelity that is being quantified and the source estimation method. We believe that these methods and results will be useful when interpreting M/EEG source estimates as well as in methods development.

A Novel Bayesian Approach for EEG Source Localization

We propose a new method for EEG source localization. An efficient solution to this problem requires choosing an appropriate regularization term in order to constraint the original problem. In our work, we adopt the Bayesian framework to place constraints; hence, the regularization term is closely connected to the prior distribution. More specifically, we propose a new sparse prior for the localization of EEG sources. The proposed prior distribution has sparse properties favoring focal EEG sources. In order to obtain an efficient algorithm, we use the variational Bayesian (VB) framework which provides us with a tractable iterative algorithm of closed-form equations. Additionally, we provide extensions of our method in cases where we observe group structures and spatially extended EEG sources. We have performed experiments using synthetic EEG data and real EEG data from three publicly available datasets. The real EEG data are produced due to the presentation of auditory and visual stimulus. We compare the proposed method with well-known approaches of EEG source localization and the results have shown that our method presents state-of-the-art performance, especially in cases where we expect few activated brain regions. The proposed method can effectively detect EEG sources in various circumstances. Overall, the proposed sparse prior for EEG source localization results in more accurate localization of EEG sources than state-of-the-art approaches.

Construction and validation of a database of head models for functional imaging of the neonatal brain

The neonatal brain undergoes dramatic structural and functional changes over the last trimester of gestation. The accuracy of source localisation of brain activity recorded from the scalp therefore relies on accurate age-specific head models. Although an age-appropriate population-level atlas could be used, detail is lost in the construction of such atlases, in particular with regard to the smoothing of the cortical surface, and so such a model is not representative of anatomy at an individual level. In this work, we describe the construction of a database of individual structural priors of the neonatal head using 215 individual-level datasets at ages 29-44 weeks postmenstrual age from the Developing Human Connectome Project. We have validated a method to segment the extra-cerebral tissue against manual segmentation. We have also conducted a leave-one-out analysis to quantify the expected spatial error incurred with regard to localising functional activation when using a best-matching individual from the database in place of a subject-specific model; the median error was calculated to be 8.3 mm (median absolute deviation 3.8 mm). The database can be applied for any functional neuroimaging modality which requires structural data whereby the physical parameters associated with that modality vary with tissue type and is freely available at www.ucl.ac.uk/dot-hub.

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.

Bayesian inverse methods for spatiotemporal characterization of gastric electrical activity from cutaneous multi-electrode recordings

Gastrointestinal (GI) problems give rise to 10 percent of initial patient visits to their physician. Although blockages and infections are easy to diagnose, more than half of GI disorders involve abnormal functioning of the GI tract, where diagnosis entails subjective symptom-based questionnaires or objective but invasive, intermittent procedures in specialized centers. Although common procedures capture motor aspects of gastric function, which do not correlate with symptoms or treatment response, recent findings with invasive electrical recordings show that spatiotemporal patterns of the gastric slow wave are associated with diagnosis, symptoms, and treatment response. We here consider developing non-invasive approaches to extract this information. Using CT scans from human subjects, we simulate normative and disordered gastric surface electrical activity along with associated abdominal activity. We employ Bayesian inference to solve the ill-posed inverse problem of estimating gastric surface activity from cutaneous recordings. We utilize a prior distribution on the spatiotemporal activity pertaining to sparsity in the number of wavefronts on the stomach surface, and smooth evolution of these wavefronts across time. We implement an efficient procedure to construct the Bayes optimal estimate and demonstrate its superiority compared to other commonly used inverse methods, for both normal and disordered gastric activity. Region-specific wave direction information is calculated and consistent with the simulated normative and disordered cases. We apply these methods to cutaneous multi-electrode recordings of two human subjects with the same clinical description of motor function, but different diagnosis of underlying cause. Our method finds statistically significant wave propagation in all stomach regions for both subjects, anterograde activity throughout for the subject with diabetic gastroparesis, and retrograde activity in some regions for the subject with idiopathic gastroparesis. These findings provide a further step towards towards non-invasive phenotyping of gastric function and indicate the long-term potential for enabling population health opportunities with objective GI assessment.

Investigating the vestibular system using modern imaging techniques-A review on the available stimulation and imaging methods

The vestibular organs, located in the inner ear, sense linear and rotational acceleration of the head and its position relative to the gravitational field of the earth. These signals are essential for many fundamental skills such as the coordination of eye and head movements in the three-dimensional space or the bipedal locomotion of humans. Furthermore, the vestibular signals have been shown to contribute to higher cognitive functions such as navigation. As the main aim of the vestibular system is the sensation of motion it is a challenging system to be studied in combination with modern imaging methods. Over the last years various different methods were used for stimulating the vestibular system. These methods range from artificial approaches like galvanic or caloric vestibular stimulation to passive full body accelerations using hexapod motion platforms, or rotatory chairs. In the first section of this review we provide an overview over all methods used in vestibular stimulation in combination with imaging methods (fMRI, PET, E/MEG, fNIRS). The advantages and disadvantages of every method are discussed, and we summarize typical settings and parameters used in previous studies. In the second section the role of the four imaging techniques are discussed in the context of vestibular research and their potential strengths and interactions with the presented stimulation methods are outlined.

Sparse Multi-task Inverse Covariance Estimation for Connectivity Analysis in EEG Source Space

Understanding how different brain areas interact to generate complex behavior is a primary goal of neuroscience research. One approach, functional connectivity analysis, aims to characterize the connectivity patterns within brain networks. In this paper, we address the problem of discriminative connectivity, i.e. determining the differences in network structure under different experimental conditions. We introduce a novel model called Sparse Multi-task Inverse Covariance Estimation (SMICE) which is capable of estimating a common connectivity network as well as discriminative networks across different tasks. We apply the method to EEG signals after solving the inverse problem of source localization, yielding networks defined on the cortical surface. We propose an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve SMICE. We apply our newly developed framework to find common and discriminative connectivity patterns for α-oscillations during the Sleep Onset Process (SOP) and during Rapid Eye Movement (REM) sleep. Even though both stages exhibit a similar α-oscillations, we show that the underlying networks are distinct.