Selective minimum-norm solution of the biomagnetic inverse problem

Structured noise champagne: an empirical Bayesian algorithm for electromagnetic brain imaging with structured noise

Introduction

Electromagnetic brain imaging is the reconstruction of brain activity from non-invasive recordings of electroencephalography (EEG), magnetoencephalography (MEG), and also from invasive ones such as the intracranial recording of electrocorticography (ECoG), intracranial electroencephalography (iEEG), and stereo electroencephalography EEG (sEEG). These modalities are widely used techniques to study the function of the human brain. Efficient reconstruction of electrophysiological activity of neurons in the brain from EEG/MEG measurements is important for neuroscience research and clinical applications. An enduring challenge in this field is the accurate inference of brain signals of interest while accounting for all sources of noise that contribute to the sensor measurements. The statistical characteristic of the noise plays a crucial role in the success of the brain source recovery process, which can be formulated as a sparse regression problem.

Method

In this study, we assume that the dominant environment and biological sources of noise that have high spatial correlations in the sensors can be expressed as a structured noise model based on the variational Bayesian factor analysis. To the best of our knowledge, no existing algorithm has addressed the brain source estimation problem with such structured noise. We propose to apply a robust empirical Bayesian framework for iteratively estimating the brain source activity and the statistics of the structured noise. In particular, we perform inference of the variational Bayesian factor analysis (VBFA) noise model iteratively in conjunction with source reconstruction.

Results

To demonstrate the effectiveness of the proposed algorithm, we perform experiments on both simulated and real datasets. Our algorithm achieves superior performance as compared to several existing benchmark algorithms.

Discussion

A key aspect of our algorithm is that we do not require any additional baseline measurements to estimate the noise covariance from the sensor data under scenarios such as resting state analysis, and other use cases wherein a noise or artifactual source occurs only in the active period but not in the baseline period (e.g., neuro-modulatory stimulation artifacts and speech movements).

Accuracy of SEEG Source Localization: A Pilot Study Using Corticocortical Evoked Potentials

INTRODUCTION

EEG source localization is an established technique for localizing scalp EEG in medically refractory epilepsy but has not been adequately studied with intracranial EEG (iEEG). Differences in sensor location and spatial sampling may affect the accuracy of EEG source localization with iEEG. Corticocortical evoked potentials can be used to evaluate EEG source localization algorithms for iEEG given the known source location.

METHODS

We recorded 205 sets of corticocortical evoked potentials using low-frequency single-pulse electrical stimulation in four patients with iEEG. Averaged corticocortical evoked potentials were analyzed using 11 distributed source algorithms and compared using the Wilcoxon signed-rank test ( P < 0.05). We measured the localization error from stimulated electrodes and the spatial dispersion of each solution.

RESULTS

Minimum norm, standard low-resolution electromagnetic tomography (sLORETA), LP Norm, sLORETA-weighted accurate minimum norm (SWARM), exact LORETA (eLORETA), standardized weighted LORETA (swLORETA), and standardized shrinking LORETA-FOCUSS (ssLOFO) had the least localization error (13.3-15.7 mm) and were superior to focal underdetermined system solver (FOCUSS), logistic autoregressive average (LAURA, and LORETA, 17.9-21.7, P < 0.001). The FOCUSS solution had the smallest spatial dispersion (7.4 mm), followed by minimum norm, L1 norm, LP norm, and SWARM (20.8-28.3 mm). Gray matter stimulations had less localization error than white matter (median differences 3.1-6.1 mm) across all algorithms except SWARM, LORETA, and logistic autoregressive average. A multivariate linear regression showed that distance from the source to sensors and gray/white matter stimulation had a significant effect on localization error for some algorithms but not SWARM, minimum norm, focal underdetermined system solver, logistic autoregressive average, and LORETA.

CONCLUSIONS

Our study demonstrated that minimum norm, L1 norm, LP norm, and SWARM localize iEEG corticocortical evoked potentials well with lower localization error and spatial dispersion. Larger studies are needed to confirm these findings.

The maturation of infant and toddler visual cortex neural activity and associations with fine motor performance

Our understanding of how visual cortex neural processes mature during infancy and toddlerhood is limited. Using magnetoencephalography (MEG), the present study investigated the development of visual evoked responses (VERs) in cross-sectional and longitudinal samples of infants and toddlers 2 months to 3 years. Brain space analyses focused on N1m and P1m latency, as well as N1m-to-P1m amplitude. Associations between VER measures and developmental quotient (DQ) scores in the cognitive/visual and fine motor domains were also examined. Results showed a nonlinear decrease in N1m and P1m latency as a function of age, characterized by rapid changes followed by slower progression, with the N1m latency plateauing at 6-7 months and the P1m latency plateauing at 8-9 months. The N1m-to-P1m amplitude also exhibited a non-linear decrease, with strong responses observed in younger infants (∼2-3 months) and then a gradual decline. Associations between N1m and P1m latency and fine motor DQ scores were observed, suggesting that infants with faster visual processing may be better equipped to perform fine motor tasks. The present findings advance our understanding of the maturation of the infant visual system and highlight the relationship between the maturation of the visual system and fine motor skills.

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.

Functional and structural maturation of auditory cortex from 2 months to 2 years old

BACKGROUND

In school-age children, the myelination of the auditory radiation thalamocortical pathway is associated with the latency of auditory evoked responses, with the myelination of thalamocortical axons facilitating the rapid propagation of acoustic information. Little is known regarding this auditory system function-structure association in infants and toddlers.

METHODS AND PARTICIPANTS

The present study tested the hypothesis that maturation of auditory radiation white-matter microstructure (e.g., fractional anisotropy (FA); measured using diffusion-weighted MRI) is associated with the latency of the infant auditory response (the P2m response, measured using magnetoencephalography, MEG) in a cross-sectional (N = 47, 2 to 24 months, 19 females) as well as longitudinal cohort (N = 18, 2 to 29 months, 8 females) of typically developing infants and toddlers. Of 18 longitudinal infants, 2 infants had data from 3 timepoints and 16 infants had data from 2 timepoints.

RESULTS

In the cross-sectional sample, non-linear maturation of P2m latency and auditory radiation diffusion measures were observed. Auditory radiation diffusion accounted for significant variance in P2m latency, even after removing the variance associated with age in both P2m latency and auditory radiation diffusion measures. In the longitudinal sample, latency and FA associations could be observed at the level of a single child.

CONCLUSIONS

Findings provide strong support for the hypothesis that an increase in thalamocortical neural conduction velocity, due to increased axon diameter and/or myelin maturation, contributes to a decrease in the infant P2m auditory evoked response latency.

SIGNIFICANCE

Infant multimodal brain imaging identifies brain mechanisms contributing to the rapid changes in neural circuit activity during the first two years of life.

Improving source estimation of retinotopic MEG responses by combining data from multiple subjects

Magnetoencephalography (MEG) is a functional brain imaging modality, which measures the weak magnetic field arising from neuronal activity. The source amplitudes and locations are estimated from the sensor data by solving an ill-posed inverse problem. Commonly used solutions for these problems operate on data from individual subjects. Combining the measurements of multiple subjects has been suggested to increase the spatial resolution of MEG by leveraging the intersubject differences for increased information. In this article, we compare 3 multisubject analysis methods on a retinotopic mapping dataset recorded from 20 subjects. The compared methods are eLORETA with source-space averaging, minimum Wasserstein estimates (MWE), and MWE with source-space averaging. The results were quantified by the geodesic distances between early (60-100 ms) MEG peak activations and fMRI-based retinotopic target points in the primary visual cortex (V1). By increasing the subject count from 1 to 10, the median distances decreased by 6.6-9.4 mm (33-46%) compared with the single-subject median distances of around 20 mm. The observed peak activation locations with multisubject analysis also comply better with the established retinotopic maps of the primary visual cortex. Our results suggest that higher spatial accuracy can be achieved by pooling data from multiple subjects. The strength of MWE lies in individualized and sparse source estimates, but in our data, averaging eLORETA estimates across individuals in source space outperformed MWE in spatial accuracy.

The maturation of infant and toddler visual cortex neural activity and associations with fine motor performance

Our understanding of how visual cortex neural processes mature during infancy and toddlerhood is limited. Using magnetoencephalography (MEG), the present study investigated the development of visual evoked responses (VERs) in both cross-sectional and longitudinal samples of infants and toddlers 2 months to 3 years. Brain space analyses focused on N1m and P1m latency, as well as the N1m-to-P1m amplitude. Associations between VER measures and developmental quotient (DQ) scores in the cognitive/visual and fine motor domains were also examined. Results showed a nonlinear decrease in N1m and P1m latency as a function of age, characterized by rapid changes followed by slower progression, with the N1m latency plateauing at 6-7 months and the P1m latency plateauing at 8-9 months. The N1m-to-P1m amplitude also exhibited a non-linear decrease, with strong responses observed in younger infants (∼2-3 months) and then a gradual decline. Associations between N1m and P1m latency and fine motor DQ scores were observed, suggesting that infants with faster visual processing may be better equipped to perform fine motor tasks. The present findings advance our understanding of the maturation of the infant visual system and highlight the relationship between the maturation of visual system and fine motor skills.

Highlights

The infant N1m and P1m latency shows a nonlinear decrease.N1m latency decreases precede P1m latency decreases.N1m-to-P1m amplitude shows a nonlinear decrease, with stronger responses in younger than older infants.N1m and P1m latency are associated with fine motor DQ.

Functional and structural maturation of auditory cortex from 2 months to 2 years old

In school-age children, the myelination of the auditory radiation thalamocortical pathway is associated with the latency of auditory evoked responses, with the myelination of thalamocortical axons facilitating the rapid propagation of acoustic information. Little is known regarding this auditory system function-structure association in infants and toddlers. The present study tested the hypothesis that maturation of auditory radiation white-matter microstructure (e.g., fractional anisotropy (FA); measured using diffusion-weighted MRI) is associated with the latency of the infant auditory response (P2m measured using magnetoencephalography, MEG) in a cross-sectional (2 to 24 months) as well as longitudinal cohort (2 to 29 months) of typically developing infants and toddlers. In the cross-sectional sample, non-linear maturation of P2m latency and auditory radiation diffusion measures were observed. After removing the variance associated with age in both P2m latency and auditory radiation diffusion measures, auditory radiation still accounted for significant variance in P2m latency. In the longitudinal sample, latency and FA associations could be observed at the level of a single child. Findings provide strong support for a contribution of auditory radiation white matter to rapid cortical auditory encoding processes in infants.

High-resolution EEG source localization in personalized segmentation-free head model with multi-dipole fitting

Objective. Electroencephalograms (EEGs) are often used to monitor brain activity. Several source localization methods have been proposed to estimate the location of brain activity corresponding to EEG readings. However, only a few studies evaluated source localization accuracy from measured EEG using personalized head models in a millimeter resolution. In this study, based on a volume conductor analysis of a high-resolution personalized human head model constructed from magnetic resonance images, a finite difference method was used to solve the forward problem and to reconstruct the field distribution.Approach. We used a personalized segmentation-free head model developed using machine learning techniques, in which the abrupt change of electrical conductivity occurred at the tissue interface is suppressed. Using this model, a smooth field distribution was obtained to address the forward problem. Next, multi-dipole fitting was conducted using EEG measurements for each subject (N= 10 male subjects, age: 22.5 ± 0.5), and the source location and electric field distribution were estimated.Main results.For measured somatosensory evoked potential for electrostimulation to the wrist, a multi-dipole model with lead field matrix computed with the volume conductor model was found to be superior than a single dipole model when using personalized segmentation-free models (6/10). The correlation coefficient between measured and estimated scalp potentials was 0.89 for segmentation-free head models and 0.71 for conventional segmented models. The proposed method is straightforward model development and comparable localization difference of the maximum electric field from the target wrist reported using fMR (i.e. 16.4 ± 5.2 mm) in previous study. For comparison, DUNEuro based on sLORETA was (EEG: 17.0 ± 4.0 mm). In addition, somatosensory evoked magnetic fields obtained by Magnetoencephalography was 25.3 ± 8.5 mm using three-layer sphere and sLORETA.Significance. For measured EEG signals, our procedures using personalized head models demonstrated that effective localization of the somatosensory cortex, which is located in a non-shallower cortex region. This method may be potentially applied for imaging brain activity located in other non-shallow regions.

AB-PLS-DA: Pansharpening tailored for scanning electron microscopy and energy-dispersive X-ray spectrometry multimodal fusion

Pansharpening constitutes a category of data fusion techniques designed to enhance the spatial resolution of multispectral (MS) images by integrating spatial details from a high-resolution panchromatic (PAN) image. This process combines the high-spectral data of MS images with the rich spatial information of the PAN image, resulting in a pansharpened output ideal for more effective image analysis, such as object detection and environmental monitoring. Traditionally developed for satellite data, our paper introduces a novel pansharpening approach customized for the fusion of Scanning Electron Microscopy (SEM) and Energy-Dispersive X-ray Spectrometry (EDS) data. The proposed method, grounded in Partial Least Squares regression with Discriminant Analysis (PLS-DA), significantly boosts the spatial resolution of EDS data while preserving spectral details. A key feature of this approach involves partitioning the PAN image into intensity bins and dynamically adapting this division in cases of overlapping compounds with similar average atomic numbers. We evaluate the method's effectiveness using in-house EDS images obtained from both even and uneven sample surfaces. Comparative analysis against existing benchmarks and state-of-the-art pansharpening techniques demonstrates superior performance in both spectral and spatial quality indicators for our method.

Joint Learning of Full-Structure Noise in Hierarchical Bayesian Regression Models

We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

Maturation of auditory cortex neural responses during infancy and toddlerhood

The infant auditory system rapidly matures across the first years of life, with a primary goal of obtaining ever-more-accurate real-time representations of the external world. Our understanding of how left and right auditory cortex neural processes develop during infancy, however, is meager, with few studies having the statistical power to detect potential hemisphere and sex differences in primary/secondary auditory cortex maturation. Using infant magnetoencephalography (MEG) and a cross-sectional study design, left and right auditory cortex P2m responses to pure tones were examined in 114 typically developing infants and toddlers (66 males, 2 to 24 months). Non-linear maturation of P2m latency was observed, with P2m latencies decreasing rapidly as a function of age during the first year of life, followed by slower changes between 12 and 24 months. Whereas in younger infants auditory tones were encoded more slowly in the left than right hemisphere, similar left and right P2m latencies were observed by ∼21 months of age due to faster maturation rate in the left than right hemisphere. No sex differences in the maturation of the P2m responses were observed. Finally, an earlier left than right hemisphere P2m latency predicted better language performance in older infants (12 to 24 months). Findings indicate the need to consider hemisphere when examining the maturation of auditory cortex neural activity in infants and toddlers and show that the pattern of left-right hemisphere P2m maturation is associated with language performance.

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.

High-Resolution EEG Source Localization in Segmentation-Free Head Models Based on Finite-Difference Method and Matching Pursuit Algorithm

Electroencephalogram (EEG) is a method to monitor electrophysiological activity on the scalp, which represents the macroscopic activity of the brain. However, it is challenging to identify EEG source regions inside the brain based on data measured by a scalp-attached network of electrodes. The accuracy of EEG source localization significantly depends on the type of head modeling and inverse problem solver. In this study, we adopted different models with a resolution of 0.5 mm to account for thin tissues/fluids, such as the cerebrospinal fluid (CSF) and dura. In particular, a spatially dependent conductivity (segmentation-free) model created using deep learning was developed and used for more realist representation of electrical conductivity. We then adopted a multi-grid-based finite-difference method (FDM) for forward problem analysis and a sparse-based algorithm to solve the inverse problem. This enabled us to perform efficient source localization using high-resolution model with a reasonable computational cost. Results indicated that the abrupt spatial change in conductivity, inherent in conventional segmentation-based head models, may trigger source localization error accumulation. The accurate modeling of the CSF, whose conductivity is the highest in the head, was an important factor affecting localization accuracy. Moreover, computational experiments with different noise levels and electrode setups demonstrate the robustness of the proposed method with segmentation-free head model.

Unification of sparse Bayesian learning algorithms for electromagnetic brain imaging with the majorization minimization framework

Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of SBL in three important ways. First, we reformulate three existing SBL algorithms under the majorization-minimization (MM) framework. This unification perspective not only provides a useful theoretical framework for comparing different algorithms in terms of their convergence behavior, but also provides a principled recipe for constructing novel algorithms with specific properties by designing appropriate bounds of the Bayesian marginal likelihood function. Second, building on the MM principle, we propose a novel method called LowSNR-BSI that achieves favorable source reconstruction performance in low signal-to-noise-ratio (SNR) settings. Third, precise knowledge of the noise level is a crucial requirement for accurate source reconstruction. Here we present a novel principled technique to accurately learn the noise variance from the data either jointly within the source reconstruction procedure or using one of two proposed cross-validation strategies. Empirically, we could show that the monotonous convergence behavior predicted from MM theory is confirmed in numerical experiments. Using simulations, we further demonstrate the advantage of LowSNR-BSI over conventional SBL in low-SNR regimes, and the advantage of learned noise levels over estimates derived from baseline data. To demonstrate the usefulness of our novel approach, we show neurophysiologically plausible source reconstructions on averaged auditory evoked potential data.

The Role of Spectral Complexity in Connectivity Estimation

The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity.

Enhanced Fast-VESTAL for Magnetoencephalography Source Imaging: From Theory to Clinical Application in Epilepsy

A novel magnetoencephalography source imaging approach called Fast Vector-based Spatio-Temporal Analysis (Fast-VESTAL) has been successfully applied in creating source images from evoked and resting-state data from both healthy subjects and individuals with neurological and/or psychiatric disorders, but its reconstructed source images may show false-positive activations, especially under low signal-to-noise ratio conditions. Here, to effectively reduce false-positive artifacts, we introduced an enhanced Fast-VESTAL (eFast-VESTAL) approach that adopts generalized second-order cone programming. We compared the spatiotemporal characteristics of the eFast-VESTAL approach to those of the popular distributed source approaches (e.g., the minimum L2-norm/ mixed-norm methods) using computer simulations and auditory experiments. More importantly, we applied eFast-VESTAL to the presurgical evaluation of epilepsy. Our results demonstrated that eFast-VESTAL exhibited a lower dipole localization error and/or a higher correlation coefficient (CC) between the estimated source time series and ground truth under various conditions of source waveforms. Experimentally, eFast-VESTAL displayed more focal activation maps and a higher CC between the raw and predicted sensor data in response to auditory stimulation. Notably, eFast-VESTAL was the most accurate method for noninvasively detecting the epileptic zones determined using more invasive stereo-electroencephalography in the comparison.

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.

Transcranial magnetic stimulation-evoked potentials after the stimulation of the right-hemispheric homologue of Broca's area

The combination of transcranial magnetic stimulation and electroencephalography can be applied to probe effective connectivity. Neurons are excited by magnetic pulses, which produce transcranial magnetic stimulation-evoked potentials that can be monitored with electroencephalography. Effective connectivity refers to causal connections in the brain; it describes how different brain areas communicate with each other. Broca's area is crucial for all phases of speech processing and is located in the frontotemporal region of the cortex. Only a few studies have investigated this region using transcranial magnetic stimulation-electroencephalography because of the large cranial muscles that are located over these areas, resulting in large artifacts covering the transcranial magnetic stimulation-evoked potentials. However, it is shown that this obstacle can be overcome with new artifact-removal tools. We used minimum-norm estimation to locate the sources of the neuronal signals in electroencephalography data after stimulating the right-hemispheric homologue of Broca's area in three right-handed subjects; it was shown that the spreading of brain activity might be different for different individuals and that the brain activity spread fast to the contralateral hemisphere.

MEG Source Imaging and Group Analysis Using VBMEG

Variational Bayesian Multimodal EncephaloGraphy (VBMEG) is a MATLAB toolbox that estimates distributed source currents from magnetoencephalography (MEG)/electroencephalography (EEG) data by integrating functional MRI (fMRI) (https://vbmeg.atr.jp/). VBMEG also estimates whole-brain connectome dynamics using anatomical connectivity derived from a diffusion MRI (dMRI). In this paper, we introduce the VBMEG toolbox and demonstrate its usefulness. By collaborating with VBMEG's tutorial page (https://vbmeg.atr.jp/docs/v2/static/vbmeg2_tutorial_neuromag.html), we show its full pipeline using an open dataset recorded by Wakeman and Henson (2015). We import the MEG data and preprocess them to estimate the source currents. From the estimated source currents, we perform a group analysis and examine the differences of current amplitudes between conditions by controlling the false discovery rate (FDR), which yields results consistent with previous studies. We highlight VBMEG's characteristics by comparing these results with those obtained by other source imaging methods: weighted minimum norm estimate (wMNE), dynamic statistical parametric mapping (dSPM), and linearly constrained minimum variance (LCMV) beamformer. We also estimate source currents from the EEG data and the whole-brain connectome dynamics from the MEG data and dMRI. The observed results indicate the reliability, characteristics, and usefulness of VBMEG.

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.

Requirements for Coregistration Accuracy in On-Scalp MEG

Recent advances in magnetic sensing has made on-scalp magnetoencephalography (MEG) possible. In particular, optically-pumped magnetometers (OPMs) have reached sensitivity levels that enable their use in MEG. In contrast to the SQUID sensors used in current MEG systems, OPMs do not require cryogenic cooling and can thus be placed within millimetres from the head, enabling the construction of sensor arrays that conform to the shape of an individual's head. To properly estimate the location of neural sources within the brain, one must accurately know the position and orientation of sensors in relation to the head. With the adaptable on-scalp MEG sensor arrays, this coregistration becomes more challenging than in current SQUID-based MEG systems that use rigid sensor arrays. Here, we used simulations to quantify how accurately one needs to know the position and orientation of sensors in an on-scalp MEG system. The effects that different types of localisation errors have on forward modelling and source estimates obtained by minimum-norm estimation, dipole fitting, and beamforming are detailed. We found that sensor position errors generally have a larger effect than orientation errors and that these errors affect the localisation accuracy of superficial sources the most. To obtain similar or higher accuracy than with current SQUID-based MEG systems, RMS sensor position and orientation errors should be [Formula: see text] and [Formula: see text], respectively.

Information spreading by a combination of MEG source estimation and multivariate pattern classification

To understand information representation in human brain activity, it is important to investigate its fine spatial patterns at high temporal resolution. One possible approach is to use source estimation of magnetoencephalography (MEG) signals. Previous studies have mainly quantified accuracy of this technique according to positional deviations and dispersion of estimated sources, but it remains unclear how accurately MEG source estimation restores information content represented by spatial patterns of brain activity. In this study, using simulated MEG signals representing artificial experimental conditions, we performed MEG source estimation and multivariate pattern analysis to examine whether MEG source estimation can restore information content represented by patterns of cortical current in source brain areas. Classification analysis revealed that the corresponding artificial experimental conditions were predicted accurately from patterns of cortical current estimated in the source brain areas. However, accurate predictions were also possible from brain areas whose original sources were not defined. Searchlight decoding further revealed that this unexpected prediction was possible across wide brain areas beyond the original source locations, indicating that information contained in the original sources can spread through MEG source estimation. This phenomenon of “information spreading” may easily lead to false-positive interpretations when MEG source estimation and classification analysis are combined to identify brain areas that represent target information. Real MEG data analyses also showed that presented stimuli were able to be predicted in the higher visual cortex at the same latency as in the primary visual cortex, also suggesting that information spreading took place. These results indicate that careful inspection is necessary to avoid false-positive interpretations when MEG source estimation and multivariate pattern analysis are combined.

Electrophysiological Source Imaging: A Noninvasive Window to Brain Dynamics

Brain activity and connectivity are distributed in the three-dimensional space and evolve in time. It is important to image brain dynamics with high spatial and temporal resolution. Electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive measurements associated with complex neural activations and interactions that encode brain functions. Electrophysiological source imaging estimates the underlying brain electrical sources from EEG and MEG measurements. It offers increasingly improved spatial resolution and intrinsically high temporal resolution for imaging large-scale brain activity and connectivity on a wide range of timescales. Integration of electrophysiological source imaging and functional magnetic resonance imaging could further enhance spatiotemporal resolution and specificity to an extent that is not attainable with either technique alone. We review methodological developments in electrophysiological source imaging over the past three decades and envision its future advancement into a powerful functional neuroimaging technology for basic and clinical neuroscience applications.

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.

The impact of MEG source reconstruction method on source-space connectivity estimation: A comparison between minimum-norm solution and beamforming

Despite numerous important contributions, the investigation of brain connectivity with magnetoencephalography (MEG) still faces multiple challenges. One critical aspect of source-level connectivity, largely overlooked in the literature, is the putative effect of the choice of the inverse method on the subsequent cortico-cortical coupling analysis. We set out to investigate the impact of three inverse methods on source coherence detection using simulated MEG data. To this end, thousands of randomly located pairs of sources were created. Several parameters were manipulated, including inter- and intra-source correlation strength, source size and spatial configuration. The simulated pairs of sources were then used to generate sensor-level MEG measurements at varying signal-to-noise ratios (SNR). Next, the source level power and coherence maps were calculated using three methods (a) L2-Minimum-Norm Estimate (MNE), (b) Linearly Constrained Minimum Variance (LCMV) beamforming, and (c) Dynamic Imaging of Coherent Sources (DICS) beamforming. The performances of the methods were evaluated using Receiver Operating Characteristic (ROC) curves. The results indicate that beamformers perform better than MNE for coherence reconstructions if the interacting cortical sources consist of point-like sources. On the other hand, MNE provides better connectivity estimation than beamformers, if the interacting sources are simulated as extended cortical patches, where each patch consists of dipoles with identical time series (high intra-patch coherence). However, the performance of the beamformers for interacting patches improves substantially if each patch of active cortex is simulated with only partly coherent time series (partial intra-patch coherence). These results demonstrate that the choice of the inverse method impacts the results of MEG source-space coherence analysis, and that the optimal choice of the inverse solution depends on the spatial and synchronization profile of the interacting cortical sources. The insights revealed here can guide method selection and help improve data interpretation regarding MEG connectivity estimation.

Consistency of EEG source localization and connectivity estimates

As the EEG inverse problem does not have a unique solution, the sources reconstructed from EEG and their connectivity properties depend on forward and inverse modeling parameters such as the choice of an anatomical template and electrical model, prior assumptions on the sources, and further implementational details. In order to use source connectivity analysis as a reliable research tool, there is a need for stability across a wider range of standard estimation routines. Using resting state EEG recordings of N=65 participants acquired within two studies, we present the first comprehensive assessment of the consistency of EEG source localization and functional/effective connectivity metrics across two anatomical templates (ICBM152 and Colin27), three electrical models (BEM, FEM and spherical harmonics expansions), three inverse methods (WMNE, eLORETA and LCMV), and three software implementations (Brainstorm, Fieldtrip and our own toolbox). Source localizations were found to be more stable across reconstruction pipelines than subsequent estimations of functional connectivity, while effective connectivity estimates where the least consistent. All results were relatively unaffected by the choice of the electrical head model, while the choice of the inverse method and source imaging package induced a considerable variability. In particular, a relatively strong difference was found between LCMV beamformer solutions on one hand and eLORETA/WMNE distributed inverse solutions on the other hand. We also observed a gradual decrease of consistency when results are compared between studies, within individual participants, and between individual participants. In order to provide reliable findings in the face of the observed variability, additional simulations involving interacting brain sources are required. Meanwhile, we encourage verification of the obtained results using more than one source imaging procedure.

Identifying epileptic source location and extent: an iterative sparse electromagnetic source imaging algorithm

In this paper we have introduced a novel electromagnetic source imaging (ESI) technique and demonstrated its validity and excellent performance in imaging the location and extent of underlying epileptic sources in patients suffering from focal epilepsy. The proposed algorithm employs ideas from sparse signal processing literature and convex optimization theories to improve source imaging results obtained from scalp-recorded electroencephalogram (EEG). EEG source imaging results generally use subjective methods to determine the extent of the underlying brain activity. The proposed technique provides significant improvement in dealing with such shortcomings and eliminates the need for thresholding. The results of our computer simulations and clinical validation study demonstrate the excellent performance of the proposed algorithm and suggest it may become a useful tool for objectively determining the location and extent of focal epileptic activity in a noninvasive fashion.

Spatio-temporal reconstruction of brain dynamics from EEG with a Markov prior

Electroencephalography (EEG) can capture brain dynamics in high temporal resolution. By projecting the scalp EEG signal back to its origin in the brain also high spatial resolution can be achieved. Source localized EEG therefore has potential to be a very powerful tool for understanding the functional dynamics of the brain. Solving the inverse problem of EEG is however highly ill-posed as there are many more potential locations of the EEG generators than EEG measurement points. Several well-known properties of brain dynamics can be exploited to alleviate this problem. More short ranging connections exist in the brain than long ranging, arguing for spatially focal sources. Additionally, recent work (Delorme et al., 2012) argues that EEG can be decomposed into components having sparse source distributions. On the temporal side both short and long term stationarity of brain activation are seen. We summarize these insights in an inverse solver, the so-called "Variational Garrote" (Kappen and Gómez, 2013). Using a Markov prior we can incorporate flexible degrees of temporal stationarity. Through spatial basis functions spatially smooth distributions are obtained. Sparsity of these are inherent to the Variational Garrote solver. We name our method the MarkoVG and demonstrate its ability to adapt to the temporal smoothness and spatial sparsity in simulated EEG data. Finally a benchmark EEG dataset is used to demonstrate MarkoVG's ability to recover non-stationary brain dynamics.

s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography

EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ1-2 regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ1-2 regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ1-2 regularization is able to enhance sparsity and accelerate computations than ℓ1 regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the advantages of the proposed method over other state-of-the-art methods in terms of total reconstruction accuracy, localization accuracy and focalization degree. The application to the source localization of event-related potential data further demonstrates the performance of the proposed method in real-world scenarios.

Imaging brain source extent from EEG/MEG by means of an iteratively reweighted edge sparsity minimization (IRES) strategy

Estimating extended brain sources using EEG/MEG source imaging techniques is challenging. EEG and MEG have excellent temporal resolution at millisecond scale but their spatial resolution is limited due to the volume conduction effect. We have exploited sparse signal processing techniques in this study to impose sparsity on the underlying source and its transformation in other domains (mathematical domains, like spatial gradient). Using an iterative reweighting strategy to penalize locations that are less likely to contain any source, it is shown that the proposed iteratively reweighted edge sparsity minimization (IRES) strategy can provide reasonable information regarding the location and extent of the underlying sources. This approach is unique in the sense that it estimates extended sources without the need of subjectively thresholding the solution. The performance of IRES was evaluated in a series of computer simulations. Different parameters such as source location and signal-to-noise ratio were varied and the estimated results were compared to the targets using metrics such as localization error (LE), area under curve (AUC) and overlap between the estimated and simulated sources. It is shown that IRES provides extended solutions which not only localize the source but also provide estimation for the source extent. The performance of IRES was further tested in epileptic patients undergoing intracranial EEG (iEEG) recording for pre-surgical evaluation. IRES was applied to scalp EEGs during interictal spikes, and results were compared with iEEG and surgical resection outcome in the patients. The pilot clinical study results are promising and demonstrate a good concordance between noninvasive IRES source estimation with iEEG and surgical resection outcomes in the same patients. The proposed algorithm, i.e. IRES, estimates extended source solutions from scalp electromagnetic signals which provide relatively accurate information about the location and extent of the underlying source.

The Iterative Reweighted Mixed-Norm Estimate for Spatio-Temporal MEG/EEG Source Reconstruction

Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is ill-posed, constraints are required. For the analysis of evoked brain activity, spatial sparsity of the neuronal activation is a common assumption. It is often taken into account using convex constraints based on the l1-norm. The resulting source estimates are however biased in amplitude and often suboptimal in terms of source selection due to high correlations in the forward model. In this work, we demonstrate that an inverse solver based on a block-separable penalty with a Frobenius norm per block and a l0.5-quasinorm over blocks addresses both of these issues. For solving the resulting non-convex optimization problem, we propose the iterative reweighted Mixed Norm Estimate (irMxNE), an optimization scheme based on iterative reweighted convex surrogate optimization problems, which are solved efficiently using a block coordinate descent scheme and an active set strategy. We compare the proposed sparse imaging method to the dSPM and the RAP-MUSIC approach based on two MEG data sets. We provide empirical evidence based on simulations and analysis of MEG data that the proposed method improves on the standard Mixed Norm Estimate (MxNE) in terms of amplitude bias, support recovery, and stability.

MEG Connectivity and Power Detections with Minimum Norm Estimates Require Different Regularization Parameters

Minimum Norm Estimation (MNE) is an inverse solution method widely used to reconstruct the source time series that underlie magnetoencephalography (MEG) data. MNE addresses the ill-posed nature of MEG source estimation through regularization (e.g., Tikhonov regularization). Selecting the best regularization parameter is a critical step. Generally, once set, it is common practice to keep the same coefficient throughout a study. However, it is yet to be known whether the optimal lambda for spectral power analysis of MEG source data coincides with the optimal regularization for source-level oscillatory coupling analysis. We addressed this question via extensive Monte-Carlo simulations of MEG data, where we generated 21,600 configurations of pairs of coupled sources with varying sizes, signal-to-noise ratio (SNR), and coupling strengths. Then, we searched for the Tikhonov regularization coefficients (lambda) that maximize detection performance for (a) power and (b) coherence. For coherence, the optimal lambda was two orders of magnitude smaller than the best lambda for power. Moreover, we found that the spatial extent of the interacting sources and SNR, but not the extent of coupling, were the main parameters affecting the best choice for lambda. Our findings suggest using less regularization when measuring oscillatory coupling compared to power estimation.

Estimating underlying neuronal activity from EEG using an iterative sparse technique

In this paper a novel technique for solving the bio-electromagnetic inverse problem is proposed. This method provides information about the location and extent of underlying neuronal activity. This is essential for the presurgical planning for partial epilepsy patients who are resistant to anti-epileptic drugs. The proposed algorithm takes advantage of the fact that neuronal activity transparent to EEG, arises from a spatially extended brain region. This spatial coherence is modeled within the framework of sparse signal processing techniques and makes better use of the limited number of EEG recordings. An iterative data-driven weighting is also introduced to better the extent estimation as well as eliminating the need to threshold estimated solutions.

Sparse EEG Source Localization Using Bernoulli Laplacian Priors

Source localization in electroencephalography has received an increasing amount of interest in the last decade. Solving the underlying ill-posed inverse problem usually requires choosing an appropriate regularization. The usual l2 norm has been considered and provides solutions with low computational complexity. However, in several situations, realistic brain activity is believed to be focused in a few focal areas. In these cases, the l2 norm is known to overestimate the activated spatial areas. One solution to this problem is to promote sparse solutions for instance based on the l1 norm that are easy to handle with optimization techniques. In this paper, we consider the use of an l0 + l1 norm to enforce sparse source activity (by ensuring the solution has few nonzero elements) while regularizing the nonzero amplitudes of the solution. More precisely, the l0 pseudonorm handles the position of the nonzero elements while the l1 norm constrains the values of their amplitudes. We use a Bernoulli-Laplace prior to introduce this combined l0 + l1 norm in a Bayesian framework. The proposed Bayesian model is shown to favor sparsity while jointly estimating the model hyperparameters using a Markov chain Monte Carlo sampling technique. We apply the model to both simulated and real EEG data, showing that the proposed method provides better results than the l2 and l1  norms regularizations in the presence of pointwise sources. A comparison with a recent method based on multiple sparse priors is also conducted.

Spatially Sparse, Temporally Smooth MEG Via Vector ℓ0

In this paper, we describe a new method for solving the magnetoencephalography inverse problem: temporal vector ℓ0-penalized least squares (TV-L0LS). The method calculates maximally sparse current dipole magnitudes and directions via spatial ℓ0 regularization on a cortically-distributed source grid, while constraining the solution to be smooth with respect to time. We demonstrate the utility of this method on real and simulated data by comparison to existing methods.

Brain activities of visual thinkers and verbal thinkers: A MEG study

In this study we measured activation patterns in the primary visual cortex and the frontal language areas and compared them in individuals with strong and weak capacities to mentally visualize information during spontaneous thinking. Subjects were first administered a 5-item questionnaire to assess their ability to create mental pictures, and were divided into two groups (strong and weak visualizers) on this basis. They then performed tasks requiring visual imagery and verbal recollection, and their local neural activities were measured, using magnetoencephalography (MEG). Notably in the high beta-band (25Hz), the visual area (BA 17) was more strongly activated in strong visualizers, whereas, the frontal language areas were more strongly activated in weak visualizers. Strong visualizers are considered to be visual thinkers, and weak visualizers are verbal thinkers.

Optimizing the regularization for image reconstruction of cerebral diffuse optical tomography

Functional near-infrared spectroscopy (fNIRS) is an optical method for noninvasively determining brain activation by estimating changes in the absorption of near-infrared light. Diffuse optical tomography (DOT) extends fNIRS by applying overlapping “high density” measurements, and thus providing a three-dimensional imaging with an improved spatial resolution. Reconstructing brain activation images with DOT requires solving an underdetermined inverse problem with far more unknowns in the volume than in the surface measurements. All methods of solving this type of inverse problem rely on regularization and the choice of corresponding regularization or convergence criteria. While several regularization methods are available, it is unclear how well suited they are for cerebral functional DOT in a semi-infinite geometry. Furthermore, the regularization parameter is often chosen without an independent evaluation, and it may be tempting to choose the solution that matches a hypothesis and rejects the other. In this simulation study, we start out by demonstrating how the quality of cerebral DOT reconstructions is altered with the choice of the regularization parameter for different methods. To independently select the regularization parameter, we propose a cross-validation procedure which achieves a reconstruction quality close to the optimum. Additionally, we compare the outcome of seven different image reconstruction methods for cerebral functional DOT. The methods selected include reconstruction procedures that are already widely used for cerebral DOT [minimum l2-norm estimate (l2MNE) and truncated singular value decomposition], recently proposed sparse reconstruction algorithms [minimum l1- and a smooth minimum l0-norm estimate (l1MNE, l0MNE, respectively)] and a depth- and noise-weighted minimum norm (wMNE). Furthermore, we expand the range of algorithms for DOT by adapting two EEG-source localization algorithms [sparse basis field expansions and linearly constrained minimum variance (LCMV) beamforming]. Independent of the applied noise level, we find that the LCMV beamformer is best for single spot activations with perfect location and focality of the results, whereas the minimum l1-norm estimate succeeds with multiple targets.

Probability method for Cerenkov luminescence tomography based on conformance error minimization

Cerenkov luminescence tomography (CLT) was developed to reconstruct a three-dimensional (3D) distribution of radioactive probes inside a living animal. Reconstruction methods are generally performed within a unique framework by searching for the optimum solution. However, the ill-posed aspect of the inverse problem usually results in the reconstruction being non-robust. In addition, the reconstructed result may not match reality since the difference between the highest and lowest uptakes of the resulting radiotracers may be considerably large, therefore the biological significance is lost. In this paper, based on the minimization of a conformance error, a probability method is proposed that consists of qualitative and quantitative modules. The proposed method first pinpoints the organ that contains the light source. Next, we developed a 0-1 linear optimization subject to a space constraint to model the CLT inverse problem, which was transformed into a forward problem by employing a region growing method to solve the optimization. After running through all of the elements used to grow the sources, a source sequence was obtained. Finally, the probability of each discrete node being the light source inside the organ was reconstructed. One numerical study and two in vivo experiments were conducted to verify the performance of the proposed algorithm, and comparisons were carried out using the hp-finite element method (hp-FEM). The results suggested that our proposed probability method was more robust and reasonable than hp-FEM.

EEG/MEG source reconstruction with spatial-temporal two-way regularized regression

In this work, we propose a spatial-temporal two-way regularized regression method for reconstructing neural source signals from EEG/MEG time course measurements. The proposed method estimates the dipole locations and amplitudes simultaneously through minimizing a single penalized least squares criterion. The novelty of our methodology is the simultaneous consideration of three desirable properties of the reconstructed source signals, that is, spatial focality, spatial smoothness, and temporal smoothness. The desirable properties are achieved by using three separate penalty functions in the penalized regression framework. Specifically, we impose a roughness penalty in the temporal domain for temporal smoothness, and a sparsity-inducing penalty and a graph Laplacian penalty in the spatial domain for spatial focality and smoothness. We develop a computational efficient multilevel block coordinate descent algorithm to implement the method. Using a simulation study with several settings of different spatial complexity and two real MEG examples, we show that the proposed method outperforms existing methods that use only a subset of the three penalty functions.

Accuracy of estimating strengths of dipole moments from a small number of magnetoencephalographic trial data

The conventional analysis estimates both the locations and strengths of neural source activations from event-related magnetoencephalography data that are averaged across about a hundred trials. In the present report, we propose a new method based on a minimum modified-l 1-norm to obtain the dependence of strengths on the presented stimuli from a limited number of trial data. It estimates the strengths from 10-trial average data and the locations from 100-trial average data. The method can be applied to neural activations whose strengths, but not locations, depend on the presented stimuli. For instance, it can be used in experiments in which the activation in the anterior temporal area (aT) is measured by varying semantic relatedness between stimuli in linguistic experiments. We conducted a realistic simulation, following previous experiments on lexico-semantic processing, in which five neural sources were simultaneously activated. The results showed that when the signal-to-noise ratio was one for non-averaged data, the proposed method had standard deviations of 13 % for the normalized strengths in the aT. It is inferred on the basis of the general linear model in which the strength has a linear dependence on the stimulus parameters that the proposed method can detect the dependence at a significance level of 1 % if the peak-to-peak change in normalized strength is more than 49 %. It is smaller than 66 % for the conventional method, which estimated locations and strengths from 10-trial data for each point. Thus, the proposed method can plot an activation-strength versus stimulus-parameter curve with better sensitivity.

Potential Use of MEG to Understand Abnormalities in Auditory Function in Clinical Populations

Magnetoencephalography (MEG) provides a direct, non-invasive view of neural activity with millisecond temporal precision. Recent developments in MEG analysis allow for improved source localization and mapping of connectivity between brain regions, expanding the possibilities for using MEG as a diagnostic tool. In this paper, we first describe inverse imaging methods (e.g., minimum-norm estimation) and functional connectivity measures, and how they can provide insights into cortical processing. We then offer a perspective on how these techniques could be used to understand and evaluate auditory pathologies that often manifest during development. Here we focus specifically on how MEG inverse imaging, by providing anatomically based interpretation of neural activity, may allow us to test which aspects of cortical processing play a role in (central) auditory processing disorder [(C)APD]. Appropriately combining auditory paradigms with MEG analysis could eventually prove useful for a hypothesis-driven understanding and diagnosis of (C)APD or other disorders, as well as the evaluation of the effectiveness of intervention strategies.

MNE software for processing MEG and EEG data

Magnetoencephalography and electroencephalography (M/EEG) measure the weak electromagnetic signals originating from neural currents in the brain. Using these signals to characterize and locate brain activity is a challenging task, as evidenced by several decades of methodological contributions. MNE, whose name stems from its capability to compute cortically-constrained minimum-norm current estimates from M/EEG data, is a software package that provides comprehensive analysis tools and workflows including preprocessing, source estimation, time-frequency analysis, statistical analysis, and several methods to estimate functional connectivity between distributed brain regions. The present paper gives detailed information about the MNE package and describes typical use cases while also warning about potential caveats in analysis. The MNE package is a collaborative effort of multiple institutes striving to implement and share best methods and to facilitate distribution of analysis pipelines to advance reproducibility of research. Full documentation is available at http://martinos.org/mne.