A state-space modeling approach for localization of focal current sources from MEG

Bridging M/EEG Source Imaging and Independent Component Analysis Frameworks Using Biologically Inspired Sparsity Priors

Electromagnetic source imaging (ESI) and independent component analysis (ICA) are two popular and apparently dissimilar frameworks for M/EEG analysis. This letter shows that the two frameworks can be linked by choosing biologically inspired source sparsity priors. We demonstrate that ESI carried out by the sparse Bayesian learning (SBL) algorithm yields source configurations composed of a few active regions that are also maximally independent from one another. In addition, we extend the standard SBL approach to source imaging in two important directions. First, we augment the generative model of M/EEG to include artifactual sources. Second, we modify SBL to allow for efficient model inversion with sequential data. We refer to this new algorithm as recursive SBL (RSBL), a source estimation filter with potential for online and offline imaging applications. We use simulated data to verify that RSBL can accurately estimate and demix cortical and artifactual sources under different noise conditions. Finally, we show that on real error-related EEG data, RSBL can yield single-trial source estimates in agreement with the experimental literature. Overall, by demonstrating that ESI can produce maximally independent sources while simultaneously localizing them in cortical space, we bridge the gap between the ESI and ICA frameworks for M/EEG analysis.

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a certain amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention.

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.

Estimates of cortical column orientation improve MEG source inversion

Determining the anatomical source of brain activity non-invasively measured from EEG or MEG sensors is challenging. In order to simplify the source localization problem, many techniques introduce the assumption that current sources lie on the cortical surface. Another common assumption is that this current flow is orthogonal to the cortical surface, thereby approximating the orientation of cortical columns. However, it is not clear which cortical surface to use to define the current source locations, and normal vectors computed from a single cortical surface may not be the best approximation to the orientation of cortical columns. We compared three different surface location priors and five different approaches for estimating dipole vector orientation, both in simulations and visual and motor evoked MEG responses. We show that models with source locations on the white matter surface and using methods based on establishing correspondences between white matter and pial cortical surfaces dramatically outperform models with source locations on the pial or combined pial/white surfaces and which use methods based on the geometry of a single cortical surface in fitting evoked visual and motor responses. These methods can be easily implemented and adopted in most M/EEG analysis pipelines, with the potential to significantly improve source localization of evoked responses.

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.

Tracking of dynamic functional connectivity from MEG data with Kalman filtering

Owing to their millisecond-scale temporal resolution, magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools to study dynamic functional connectivity between regions in the human brain. However, current techniques to estimate functional connectivity from MEG/EEG are based on a two-step approach; first, the MEG/EEG inverse problem is solved to estimate the source activity, and second, connectivity is estimated between the sources. In this work, we propose a method for simultaneous estimation of source activities and their dynamic functional connectivity using a Kalman filter. Based on simulations, our approach can reliably estimate source activities and resolve their time-varying interactions even at low SNR (< 1). When applied on empirical MEG responses to simple visual stimuli, our approach could capture the dynamic patterns of the underlying functional connectivity changes between the lower (pericalcarine) and higher (fusiform and parahippocampal) visual areas. In conclusion, we demonstrate that our approach is capable of tracking changes in functional connectivity at the millisecond resolution of MEG/EEG and thus making it suitable for real-time tracking of functional connectivity, which none of the current techniques are capable of.

Reconstruction of Neural Activity from EEG Data Using Dynamic Spatiotemporal Constraints

We present a novel iterative regularized algorithm (IRA) for neural activity reconstruction that explicitly includes spatiotemporal constraints, performing a trade-off between space and time resolutions. For improving the spatial accuracy provided by electroencephalography (EEG) signals, we explore a basis set that describes the smooth, localized areas of potentially active brain regions. In turn, we enhance the time resolution by adding the Markovian assumption for brain activity estimation at each time period. Moreover, to deal with applications that have either distributed or localized neural activity, the spatiotemporal constraints are expressed through [Formula: see text] and [Formula: see text] norms, respectively. For the purpose of validation, we estimate the neural reconstruction performance in time and space separately. Experimental testing is carried out on artificial data, simulating stationary and non-stationary EEG signals. Also, validation is accomplished on two real-world databases, one holding Evoked Potentials and another with EEG data of focal epilepsy. Moreover, responses of functional magnetic resonance imaging for the former EEG data have been measured in advance, allowing to contrast our findings. Obtained results show that the [Formula: see text]-based IRA produces a spatial resolution that is comparable to the one achieved by some widely used sparse-based estimators of brain activity. At the same time, the [Formula: see text]-based IRA outperforms other similar smooth solutions, providing a spatial resolution that is lower than the sparse [Formula: see text]-based solution. As a result, the proposed IRA is a promising method for improving the accuracy of brain activity reconstruction.

Effects of reconstructed magnetic field from sparse noisy boundary measurements on localization of active neural source

Localization of active neural source (ANS) from measurements on head surface is vital in magnetoencephalography. As neuron-generated magnetic fields are extremely weak, significant uncertainties caused by stochastic measurement interference complicate its localization. This paper presents a novel computational method based on reconstructed magnetic field from sparse noisy measurements for enhanced ANS localization by suppressing effects of unrelated noise. In this approach, the magnetic flux density (MFD) in the nearby current-free space outside the head is reconstructed from measurements through formulating the infinite series solution of the Laplace's equation, where boundary condition (BC) integrals over the entire measurements provide "smooth" reconstructed MFD with the decrease in unrelated noise. Using a gradient-based method, reconstructed MFDs with good fidelity are selected for enhanced ANS localization. The reconstruction model, spatial interpolation of BC, parametric equivalent current dipole-based inverse estimation algorithm using reconstruction, and gradient-based selection are detailed and validated. The influences of various source depths and measurement signal-to-noise ratio levels on the estimated ANS location are analyzed numerically and compared with a traditional method (where measurements are directly used), and it was demonstrated that gradient-selected high-fidelity reconstructed data can effectively improve the accuracy of ANS localization.

STRAPS: A Fully Data-Driven Spatio-Temporally Regularized Algorithm for M/EEG Patch Source Imaging

For M/EEG-based distributed source imaging, it has been established that the L2-norm-based methods are effective in imaging spatially extended sources, whereas the L1-norm-based methods are more suited for estimating focal and sparse sources. However, when the spatial extents of the sources are unknown a priori, the rationale for using either type of methods is not adequately supported. Bayesian inference by exploiting the spatio-temporal information of the patch sources holds great promise as a tool for adaptive source imaging, but both computational and methodological limitations remain to be overcome. In this paper, based on state-space modeling of the M/EEG data, we propose a fully data-driven and scalable algorithm, termed STRAPS, for M/EEG patch source imaging on high-resolution cortices. Unlike the existing algorithms, the recursive penalized least squares (RPLS) procedure is employed to efficiently estimate the source activities as opposed to the computationally demanding Kalman filtering/smoothing. Furthermore, the coefficients of the multivariate autoregressive (MVAR) model characterizing the spatial-temporal dynamics of the patch sources are estimated in a principled manner via empirical Bayes. Extensive numerical experiments demonstrate STRAPS's excellent performance in the estimation of locations, spatial extents and amplitudes of the patch sources with varying spatial extents.

Effect of EEG electrode number on epileptic source localization in pediatric patients

OBJECTIVE

To investigate the relationship between EEG source localization and the number of scalp EEG recording channels.

METHODS

128 EEG channel recordings of 5 pediatric patients with medically intractable partial epilepsy were used to perform source localization of interictal spikes. The results were compared with surgical resection and intracranial recordings. Various electrode configurations were tested and a series of computer simulations based on a realistic head boundary element model were also performed in order to further validate the clinical findings.

RESULTS

The improvement seen in source localization substantially decreases as the number of electrodes increases. This finding was evaluated using the surgical resection, intracranial recordings and computer simulation. It was also shown in the simulation that increasing the electrode numbers could remedy the localization error of deep sources. A plateauing effect was seen in deep and superficial sources with further increasing the electrode number.

CONCLUSION

The source localization is improved when electrode numbers increase, but the absolute improvement in accuracy decreases with increasing electrode number.

SIGNIFICANCE

Increasing the electrode number helps decrease localization error and thus can more ably assist the physician to better plan for surgical procedures.

Assessing dynamic spectral causality by lagged adaptive directed transfer function and instantaneous effect factor

It is of significance to assess the dynamic spectral causality among physiological signals. Several practical estimators adapted from spectral Granger causality have been exploited to track dynamic causality based on the framework of time-varying multivariate autoregressive (tvMVAR) models. The nonzero covariance of the model's residuals has been used to describe the instantaneous effect phenomenon in some causality estimators. However, for the situations with Gaussian residuals in some autoregressive models, it is challenging to distinguish the directed instantaneous causality if the sufficient prior information about the "causal ordering" is missing. Here, we propose a new algorithm to assess the time-varying causal ordering of tvMVAR model under the assumption that the signals follow the same acyclic causal ordering for all time lags and to estimate the instantaneous effect factor (IEF) value in order to track the dynamic directed instantaneous connectivity. The time-lagged adaptive directed transfer function (ADTF) is also estimated to assess the lagged causality after removing the instantaneous effect. In this study, we first investigated the performance of the causal-ordering estimation algorithm and the accuracy of IEF value. Then, we presented the results of IEF and time-lagged ADTF method by comparing with the conventional ADTF method through simulations of various propagation models. Statistical analysis results suggest that the new algorithm could accurately estimate the causal ordering and give a good estimation of the IEF values in the Gaussian residual conditions. Meanwhile, the time-lagged ADTF approach is also more accurate in estimating the time-lagged dynamic interactions in a complex nervous system after extracting the instantaneous effect. In addition to the simulation studies, we applied the proposed method to estimate the dynamic spectral causality on real visual evoked potential (VEP) data in a human subject. Its usefulness in time-variant spectral causality assessment was demonstrated through the mutual causality investigation of brain activity during the VEP experiments.

Noninvasive imaging of the high frequency brain activity in focal epilepsy patients

High-frequency (HF) activity represents a potential biomarker of the epileptogenic zone in epilepsy patients, the removal of which is considered to be crucial for seizure-free surgical outcome. We proposed a high frequency source imaging (HFSI) approach to noninvasively image the brain sources of the scalp-recorded HF EEG activity. Both computer simulation and clinical patient data analysis were performed to investigate the feasibility of using the HFSI approach to image the sources of HF activity from noninvasive scalp EEG recordings. The HF activity was identified from high-density scalp recordings after high-pass filtering the EEG data and the EEG segments with HF activity were concatenated together to form repetitive HF activity. Independent component analysis was utilized to extract the components corresponding to the HF activity. Noninvasive EEG source imaging using realistic geometric boundary element head modeling was then applied to image the sources of the pathological HF brain activity. Five medically intractable focal epilepsy patients were studied and the estimated sources were found to be concordant with the surgical resection or intracranial recordings of the patients. The present study demonstrates, for the first time, that source imaging from the scalp HF activity could help to localize the seizure onset zone and provide a novel noninvasive way of studying the epileptic brain in humans. This study also indicates the potential application of studying HF activity in the presurgical planning of medically intractable epilepsy patients.

Lateralization and localization of epilepsy related hemodynamic foci using presurgical fMRI

OBJECTIVE

The aim was to develop a method for the purpose of localizing epilepsy related hemodynamic foci for patients suffering intractable focal epilepsy using task-free fMRI alone.

METHODS

We studied three groups of subjects: patients with intractable focal epilepsy, healthy volunteers performing motor tasks, and healthy volunteers in resting state. We performed spatial independent component analysis (ICA) on the fMRI alone data and developed a set of IC selection criteria to identify epilepsy related ICs. The method was then tested in the two healthy groups.

RESULTS

In seven out of the nine surgery patients, identified ICs were concordant with surgical resection. Our results were also consistent with presurgical evaluation of the remaining one patient without surgery and may explain why she was not suitable for resection treatment. In the motor task study of ten healthy subjects, our method revealed components with concordant spatial and temporal features as expected from the unilateral motor tasks. In the resting state study of seven healthy subjects, the method successfully rejected all components in four out of seven subjects as non-epilepsy related components.

CONCLUSION

These results suggest the lateralization and localization value of fMRI alone in presurgical evaluation for patients with intractable unilateral focal epilepsy.

SIGNIFICANCE

The proposed method is noninvasive in nature and easy to implement. It has the potential to be incorporated in current presurgical workup for treating intractable focal epilepsy patients.