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

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.

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.

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.

Optimization of patient-specific stereo-EEG recording sensitivity

Stereo-EEG is a minimally invasive technique used to localize the origin of epileptic activity (the epileptogenic zone) in patients with drug-resistant epilepsy. However, current stereo-EEG trajectory planning methods are agnostic to the spatial recording sensitivity of implanted electrodes. In this study, we used image-based patient-specific computational models to design optimized stereo-EEG electrode configurations. Patient-specific optimized electrode configurations exhibited substantially higher recording sensitivity than clinically implanted configurations, and this may lead to a more accurate delineation of the epileptogenic zone. The optimized configurations also achieved equally good or better recording sensitivity with fewer electrodes compared with clinically implanted configurations, and this may reduce the risk for complications, including intracranial haemorrhage. This approach improves localization of the epileptogenic zone by transforming the clinical use of stereo-EEG from a discrete ad hoc sampling to an intelligent mapping of the regions of interest.

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.

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

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

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.

L1-norm based time-varying brain neural network and its application to dynamic analysis for motor imagery

OBJECTIVE

EEG-based motor imagery (MI) brain-computer interface offers a promising way to improve the efficiency of motor rehabilitation and motor skill learning. In recent years, the power of dynamic network analysis for MI classification has been proved. In fact, its usability mainly depends on the accurate estimation of brain connection. However, traditional dynamic network estimation strategies such as adaptive directed transfer function (ADTF) are designed in the L2-norm. Usually, they estimate a series of pseudo connections caused by outliers, which results in biased features and further limits its online application. Thus, how to accurately infer dynamic causal relationship under outlier influence is urgent.

APPROACH

In this work, we proposed a novel ADTF, which solves the dynamic system in the L1-norm space (L1-ADTF), so as to restrict the outlier influence. To enhance its convergence, we designed an iteration strategy with the alternating direction method of multipliers (ADMM), which could be used for the solution of the dynamic state-space model restricted in the L1-norm space. Furthermore, we compared L1-ADTF to traditional ADTF and its dual extension across both simulation and real EEG experiments.

MAIN RESULTS

A quantitative comparison between L1-ADTF and other ADTFs in simulation studies demonstrates that fewer bias errors and more desirable dynamic state transformation patterns can be captured by the L1-ADTF. Application to real MI EEG datasets seriously noised by ocular artifacts also reveals the efficiency of the proposed L1-ADTF approach to extract the time-varying brain neural network patterns, even when more complex noises are involved.

SIGNIFICANCE

The L1-ADTF may not only be capable of tracking time-varying brain network state drifts robustly but may also be useful in solving a wide range of dynamic systems such as trajectory tracking problems and dynamic neural networks.

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.

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.