An alternative subspace approach to EEG dipole source localization

Mobile Electroencephalography for Studying Neural Control of Human Locomotion

Walking or running in real-world environments requires dynamic multisensory processing within the brain. Studying supraspinal neural pathways during human locomotion provides opportunities to better understand complex neural circuity that may become compromised due to aging, neurological disorder, or disease. Knowledge gained from studies examining human electrical brain dynamics during gait can also lay foundations for developing locomotor neurotechnologies for rehabilitation or human performance. Technical barriers have largely prohibited neuroimaging during gait, but the portability and precise temporal resolution of non-invasive electroencephalography (EEG) have expanded human neuromotor research into increasingly dynamic tasks. In this narrative mini-review, we provide a (1) brief introduction and overview of modern neuroimaging technologies and then identify considerations for (2) mobile EEG hardware, (3) and data processing, (4) including technical challenges and possible solutions. Finally, we summarize (5) knowledge gained from human locomotor control studies that have used mobile EEG, and (6) discuss future directions for real-world neuroimaging research.

Advanced Signal Processing Methods for Characterization of Schizophrenia

OBJECTIVE

Schizophrenia is a severe mental disorder associated with nerobiological deficits. Auditory oddball P300 have been found to be one of the most consistent markers of schizophrenia. The goal of this study is to find quantitative features that can objectively distinguish patients with schizophrenia (SCZs) from healthy controls (HCs) based on their recorded auditory odd-ball P300 electroencephalogram (EEG) data.

METHODS

Using EEG dataset, we develop a machine learning (ML) algorithm to distinguish 57 SCZs from 66 HCs. The proposed ML algorithm has three steps. In the first step, a brain source localization (BSL) procedure using the linearly constrained minimum variance (LCMV) beamforming approach is employed on EEG signals to extract source waveforms from 30 specified brain regions. In the second step, a method for estimating effective connectivity, referred to as symbolic transfer entropy (STE), is applied to the source waveforms. In the third step the ML algorithm is applied to the STE connectivity matrix to determine whether a set of features can be found that successfully discriminate SCZ from HC.

RESULTS

The findings revealed that the SCZs have significantly higher effective connectivity compared to HCs and the selected STE features could achieve an accuracy of 92.68%, with a sensitivity of 92.98% and specificity of 92.42%.

CONCLUSION

The findings imply that the extracted features are from the regions that are mainly affected by SCZ and can be used to distinguish SCZs from HCs.

SIGNIFICANCE

The proposed ML algorithm may prove to be a promising tool for the clinical diagnosis of schizophrenia.

A Machine Learning Approach Using Effective Connectivity to Predict Response to Clozapine Treatment

Clozapine is an anti-psychotic drug that is known to be effective in the treatment of patients with chronic treatment-resistant schizophrenia (TRS-SCZ), commonly estimated to be around one third of all cases. However, clinicians sometimes delay the initiation of this drug because of its adverse side-effects. Therefore, identification of predictive biological markers of clozapine response are extremely valuable to aid on-time initiation of treatment. In this study, we develop a machine learning (ML) algorithm based on pre-treatment electroencephalogram (EEG) data sets to predict response to clozapine treatment in 57 TRS-SCZs, where the treatment outcome, after at least one-year follow-up is determined using the positive and negative syndrome scale (PANSS). The ML algorithm has three steps: 1) a brain source localization (BSL) procedure using the linearly constrained minimum variance (LCMV) beamforming approach is employed on the EEG signals to extract source waveforms from 30 specified brain regions. 2) An effective connectivity measure named symbolic transfer entropy (STE) is applied to the source waveforms. 3) A ML algorithm is applied to the STE matrix to determine whether a set of features can be found to discriminate most-responder (MR) SCZ patients from least-responder (LR) ones. The findings of this study reveal that STE features can achieve an accuracy of 95.83%. This finding implies that analysis of pre-treatment EEG could contribute to our ability to distinguish MR from LR SCZs, and that the source STE matrix may prove to be a promising tool for the prediction of the clinical response to clozapine.

EEG Source Imaging (ESI) utility in clinical practice

Epilepsy surgery is an important treatment modality for medically refractory focal epilepsy. The outcome of surgery usually depends on the localization accuracy of the epileptogenic zone (EZ) during pre-surgical evaluation. Good localization can be achieved with various electrophysiological and neuroimaging approaches. However, each approach has its own merits and limitations. Electroencephalography (EEG) Source Imaging (ESI) is an emerging model-based computational technique to localize cortical sources of electrical activity within the brain volume, three-dimensionally. ESI based pre-surgical evaluation gives an overall clinical yield of 73-91%, depending on choice of head model, inverse solution and EEG electrode density. It is a cost effective, non-invasive method which provides valuable additional information in presurgical evaluation due to its high localizing value specifically in MRI-negative cases, extra or basal temporal lobe epilepsy, multifocal lesions such as tuberous sclerosis or cases with multiple hypotheses. Unfortunately, less than 1% of surgical centers in developing countries use this method as a part of pre-surgical evaluation. This review promotes ESI as a useful clinical tool especially for patients with lesion-negative MRI to determine EZ cost-effectively with high accuracy under the optimized conditions.

Minimum variance based fusion of fundamental and second harmonic ultrasound imaging: Simulation and experimental study

Harmonic imaging is widely used in clinical ultrasound due to its higher resolution in comparison with fundamental mode. However, the low amplitude of harmonic components in this imaging method is a crucial problem, resulting in a high sensitivity to noise, while the fundamental imaging is more robust against noise. To exploit the benefits of both the fundamental and harmonic imaging, we propose a minimum variance (MV)-based adaptive combination of fundamental and harmonic images. The performance of the proposed mixing-together MV (MTMV) beamformer is evaluated on simulated and experimental RF data. The results of the simulated point targets show that in the regions near of point targets, where the desire signals exist, the proposed MTMV beamformer mostly follows the MV-beamformed harmonic image to retain a better resolution. In the regions far from the point targets, where there is just noise, it follows the MV-beamformed fundamental image to benefit from more robustness. Also, the results of the simulated and experimental cyst phantoms indicate that MTMV reduces the background noise level and improves the contrast without compromising the high resolution of the MV-beamformed harmonic image. In the simulated cyst phantom, in comparison to DAS (fundamental), DAS (harmonic), MV (fundamental), MV (harmonic), and wavelet fusion, the image contrast ratio (CR) is increased, in average, about 5.2 dB, 3.5 dB, 1.5 dB, 3.6 dB, and 2.8 dB, respectively. The contrast-to-noise ratio (CNR) is significantly improved; about 59%, 53%, 41%, 37%, and 24%, respectively. In the experimental cyst phantom, these relative improvements are about 6.6 dB, 3.5 dB, 4.2 dB, 2.1 dB, and 3.8 dB for CR, and about 64%, 52%, 25%, 33%, and 33%, for CNR, respectively.

Electrophysiological Brain Connectivity: Theory and Implementation

We review the theory and algorithms of electrophysiological brain connectivity analysis. This tutorial is aimed at providing an introduction to brain functional connectivity from electrophysiological signals, including electroencephalography (EEG), magnetoencephalography (MEG), electrocorticography (ECoG), stereoelectroencephalography (SEEG). Various connectivity estimators are discussed, and algorithms introduced. Important issues for estimating and mapping brain functional connectivity with electrophysiology are discussed.

Modified Dominant Mode Rejection Beamformer for Localizing Brain Activities When Data Covariance Matrix Is Rank Deficient

OBJECTIVE

Minimum variance beamformer (MVB) and its extensions fail in localizing short time brain activities particularly evoked potentials because of rank deficiency or inaccurate estimation of a data covariance matrix. In this paper, the conventional dominant mode rejection (DMR) adaptive beamformer is modified to localize brain short time activities.

METHODS

In the modified DMR, it is attempted to obtain a well-conditioned covariance matrix by dividing the eigenvalues of the data covariance matrix into dominant, medium, and small eigenvalues and then modifying medium and small parts. The performance of the proposed approach is compared with diagonal loading MVB (DL_MVB) and fast fully adaptive (FFA) beamformer by using simulated event-related potentials and real event-related field data. Eigenspace versions of DL_MVB and modified DMR are also implemented.

RESULTS

In all simulations, the modified DMR obtains the least localization error (0-5 mm) and spread radius (0-8 mm) when the signal-to-noise ratio (SNR) varies from 0 to 10 dB with step 1 dB. In real data, the new approach in comparison to two other ones attains the most concentrated power spectrum. Eigenspace projection of DL_MVB presents better results than DL_MVB but worse results than the modified DMR. Applying eigenspace projection on the proposed method improves its performance at high SNR levels.

CONCLUSION

Empirical results illustrate the superiority of the proposed DMR method to the DL_MVB and FFA in localizing brain short time activities.

SIGNIFICANCE

The proposed method can be utilized in source localization of epilepsy for presurgical clinical evaluation purpose and also in applications dealing with the localization of evoked potentials and fields.

Fused multivariate empirical mode decomposition (MEMD) and inverse solution method for EEG source localization

EEG source localization is determining possible cortical sources of brain activities with scalp EEG. Generally, every step of the data processing sequence affects the accuracy of EEG source localization. In this paper, we introduce a fused multivariate empirical mode decomposing (MEMD) and inverse solution algorithm with an embedded unsupervised eye blink remover in order to localize the epileptogenic zone accurately. For this purpose, we constructed realistic forward models using MRI and boundary element method (BEM) for each patient to obtain results that are more realistic. We also developed an unsupervised algorithm utilizing a wavelet method to remove eye blink artifacts. Additionally, we applied MEMD, which is one of the recent and suitable feature extraction methods for non-linear, non-stationary, and multivariate signals such as EEG, to extract the signal of interest. We examined the localization results using the two most reliable linear distributed inverse methods in the literature: weighted minimum norm estimation (wMN) and standardized low resolution tomography (sLORETA). Results affirm the success of the proposed algorithm with the highest agreement compared to MRI reference by a specialist. Fusion of MEMD and sLORETA results in approximately zero localization error in terms of spatial difference with the validated MRI reference. High accuracy results of proposed algorithm using non-invasive and low-resolution EEG provide the potential of using this work for pre-surgical evaluation towards epileptogenic zone localization in clinics.

Electromagnetic Brain Source Imaging by Means of a Robust Minimum Variance Beamformer

OBJECTIVE

Adaptive beamformer methods that have been extensively used for functional brain imaging using EEG/MEG (magnetoencephalography) signals are sensitive to model mismatches. We propose a robust minimum variance beamformer (RMVB) technique, which explicitly incorporates the uncertainty of the lead field matrix into the estimation of spatial-filter weights that are subsequently used to perform the imaging.

METHODS

The uncertainty of the lead field is modeled by ellipsoids in the RMVB method; these hyperellipsoids (ellipsoids in higher dimensions) define regions of uncertainty for a given nominal lead field vector. These ellipsoids are estimated empirically by sampling lead field vectors surrounding each point of the source space, or more generally by building several forward models for the source space. Once these uncertainty regions (ellipsoids) are estimated, they are used to perform the source-imaging task. Computer simulations are conducted to evaluate the performance of the proposed RMVB technique.

RESULTS

Our results show that robust beamformers can outperform conventional beamformers in terms of localization error, recovering source dynamics, and estimation of the underlying source extents when uncertainty in the lead field matrix is properly determined and modeled.

CONCLUSION

The RMVB can be substituted for conventional beamformers, especially in applications where source imaging is performed off-line, and computational speed and complexity are not of major concern.

SIGNIFICANCE

A high-quality source imaging can be utilized in various applications, such as determining the epileptogenic zone in medically intractable epilepsy patients or estimating the time course of activity, which is a required step for computing the functional connectivity of brain networks.

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.

Spatio-temporal Reconstruction of Neural Sources Using Indirect Dominant Mode Rejection

Adaptive minimum variance based beamformers (MVB) have been successfully applied to magnetoencephalogram (MEG) and electroencephalogram (EEG) data to localize brain activities. However, the performance of these beamformers falls down in situations where correlated or interference sources exist. To overcome this problem, we propose indirect dominant mode rejection (iDMR) beamformer application in brain source localization. This method by modifying measurement covariance matrix makes MVB applicable in source localization in the presence of correlated and interference sources. Numerical results on both EEG and MEG data demonstrate that presented approach accurately reconstructs time courses of active sources and localizes those sources with high spatial resolution. In addition, the results of real AEF data show the good performance of iDMR in empirical situations. Hence, iDMR can be reliably used for brain source localization especially when there are correlated and interference sources.

An Adaptive Synthetic Aperture Method Applied to Ultrasound Tissue Harmonic Imaging

In recent years, the minimum variance (MV) beamformer has been highly regarded since it provides high resolution and contrast in B-mode ultrasound imaging compared with nonadaptive delay-and-sum (DAS) beamformer. However, the performance of MV beamformer is degraded in the presence of the noise due to inaccurate estimation of the covariance matrix resulting in low-quality images. The conventional tissue harmonic imaging (THI) offers multiple advantages over conventional pulse-echo ultrasound imaging, including enhanced contrast resolution and improved axial and lateral resolutions, but low signal-to-noise ratio (SNR) is a major problem facing this imaging method, which uses a fixed transmit focus and dynamic receive focusing (DRF). In this paper, a synthetic aperture method based on the virtual source, namely, bidirectional pixel-based focusing (BiPBF), has been combined with the MV beamformer and then applied to second-harmonic ultrasound imaging. The main objective is suppressing the noise level to enhance the performance of the MV beamformer in the harmonic imaging, especially in lower and deeper depths where the SNR is low. In addition, combining the BiPBF and MV weighting results in simultaneous improvement in imaging resolution and contrast, in comparison with the conventional methods: DRF (DAS), BiPBF (DAS), and DRF (MV). The performance of the proposed method is evaluated on simulated and experimental RF data. The THI is achieved using the pulse-inversion technique. The results of the simulated wire phantom demonstrate that the proposed beamformer can achieve the best lateral resolution, along different depths, compared with DRF (DAS), BiPBF (DAS), and DRF (MV) methods. The results of the simulated and experimental cyst phantoms show that the new beamformer improves the contrast ratio (CR) and contrast-to-noise ratio (CNR) of the resulting images. In results of simulated cyst phantom, in average, the new beamformer improves the CR and CNR of the cyst about (7.4 dB, 49%), (3.2 dB, 16%), and (5 dB, 26%) compared with DRF (DAS), BiPBF (DAS), and DRF (MV), respectively. In results of experimental cyst phantom, these relative improvements are about (4.2 dB, 22%), (1.7 dB, 7%), and (2.6 dB, 15%). In addition, BiPBF (MV) method offers improved edge definition of cysts in comparison with the other methods.

Seizure Onset Zone Localization from Ictal High-Density EEG in Refractory Focal Epilepsy

Epilepsy surgery is the most efficient treatment option for patients with refractory epilepsy. Before surgery, it is of utmost importance to accurately delineate the seizure onset zone (SOZ). Non-invasive EEG is the most used neuroimaging technique to diagnose epilepsy, but it is hard to localize the SOZ from EEG due to its low spatial resolution and because epilepsy is a network disease, with several brain regions becoming active during a seizure. In this work, we propose and validate an approach based on EEG source imaging (ESI) combined with functional connectivity analysis to overcome these problems. We considered both simulations and real data of patients. Ictal epochs of 204-channel EEG and subsets down to 32 channels were analyzed. ESI was done using realistic head models and LORETA was used as inverse technique. The connectivity pattern between the reconstructed sources was calculated, and the source with the highest number of outgoing connections was selected as SOZ. We compared this algorithm with a more straightforward approach, i.e. selecting the source with the highest power after ESI as the SOZ. We found that functional connectivity analysis estimated the SOZ consistently closer to the simulated EZ/RZ than localization based on maximal power. Performance, however, decreased when 128 electrodes or less were used, especially in the realistic data. The results show the added value of functional connectivity analysis for SOZ localization, when the EEG is obtained with a high-density setup. Next to this, the method can potentially be used as objective tool in clinical settings.

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.

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.

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.

Minimum variance brain source localization for short data sequences

In the electroencephalogram (EEG) or magnetoencephalogram (MEG) context, brain source localization methods that rely on estimating second-order statistics often fail when the number of samples of the recorded data sequences is small in comparison to the number of electrodes. This condition is particularly relevant when measuring evoked potentials. Due to the correlated background EEG/MEG signal, an adaptive approach to localization is desirable. Previous work has addressed these issues by reducing the adaptive degrees of freedom (DoFs). This reduction results in decreased resolution and accuracy of the estimated source configuration. This paper develops and tests a new multistage adaptive processing technique based on the minimum variance beamformer for brain source localization that has been previously used in the radar statistical signal processing context. This processing, referred to as the fast fully adaptive (FFA) approach, can significantly reduce the required sample support, while still preserving all available DoFs. To demonstrate the performance of the FFA approach in the limited data scenario, simulation and experimental results are compared with two previous beamforming approaches; i.e., the fully adaptive minimum variance beamforming method and the beamspace beamforming method. Both simulation and experimental results demonstrate that the FFA method can localize all types of brain activity more accurately than the other approaches with limited data.

High-resolution Functional Source and Impedance Imaging

Functional imaging has played a significant role in bettering our understanding of mechanisms of brain function and dysfunctions. We review recent research on electrophysiological neuroimaging, multimodal neuroimaging integrating functional MRI with EEG, and our development of magnetoacoustic tomography with magnetic induction for high resolution impedance imaging. Examples from research of our group will be shown to illustrate the concepts. The extensive work being pursued by a number of investigators suggests the promise of functional neuroimaging in imaging neural activity from noninvasive measurements.

Pitfalls in the dipolar model for the neocortical EEG sources

For about six decades, primary current sources of the electroencephalogram (EEG) have been assumed dipolar in nature. In this study, we used electrophysiological recordings from anesthetized Wistar rats undergoing repeated whisker deflections to revise the biophysical foundations of the EEG dipolar model. In a first experiment, we performed three-dimensional recordings of extracellular potentials from a large portion of the barrel field to estimate intracortical multipolar moments generated either by single spiking neurons (i.e., pyramidal cells, PC; spiny stellate cells, SS) or by populations of them while experiencing synchronized postsynaptic potentials. As expected, backpropagating spikes along PC dendrites caused dipolar field components larger in the direction perpendicular to the cortical surface (49.7 ± 22.0 nA·mm). In agreement with the fact that SS cells have “close-field” configurations, their dipolar moment at any direction was negligible. Surprisingly, monopolar field components were detectable both at the level of single units (i.e., −11.7 ± 3.4 nA for PC) and at the mesoscopic level of mixed neuronal populations receiving extended synaptic inputs within either a cortical column (−0.44 ± 0.20 μA) or a 2.5-m3-voxel volume (−3.32 ± 1.20 μA). To evaluate the relationship between the macroscopically defined EEG equivalent dipole and the mesoscopic intracortical multipolar moments, we performed concurrent recordings of high-resolution skull EEG and laminar local field potentials. From this second experiment, we estimated the time-varying EEG equivalent dipole for the entire barrel field using either a multiple dipole fitting or a distributed type of EEG inverse solution. We demonstrated that mesoscopic multipolar components are altogether absorbed by any equivalent dipole in both types of inverse solutions. We conclude that the primary current sources of the EEG in the neocortex of rodents are not precisely represented by a single equivalent dipole and that the existence of monopolar components must be also considered at the mesoscopic level.

EEG source imaging in epilepsy--practicalities and pitfalls

EEG source imaging (ESI) is a model-based imaging technique that integrates temporal and spatial components of EEG to identify the generating source of electrical potentials recorded on the scalp. Recent advances in computer technologies have made the analysis of ESI data less time-consuming, and have rekindled interest in this technique as a clinical diagnostic tool. On the basis of the available body of evidence, ESI seems to be a promising tool for epilepsy evaluation; however, the precise clinical value of ESI in presurgical evaluation of epilepsy and in localization of eloquent cortex remains to be investigated. In this Review, we describe two fundamental issues in ESI; namely, the forward and inverse problems, and their solutions. The clinical application of ESI in surgical planning for patients with medically refractory focal epilepsy, and its use in source reconstruction together with invasive recordings, is also discussed. As ESI can be used to map evoked responses, we discuss the clinical utility of this technique in cortical mapping-an essential process when planning resective surgery for brain regions that are in close proximity to eloquent cortex.

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

State-space modeling is a promising approach for current source reconstruction from magnetoencephalography (MEG) because it constrains the spatiotemporal behavior of inverse solutions in a flexible manner. However, state-space model-based source localization research remains underdeveloped; extraction of spatially focal current sources and handling of the high dimensionality of the distributed source model remain problematic. In this study, we propose a novel state-space model-based method that resolves these problems, extending our previous source localization method to include a temporal constraint by state-space modeling. To enable focal current reconstruction, we account for spatially inhomogeneous temporal dynamics by introducing dynamics model parameters that differ for each cortical position. The model parameters and the intensity of the current sources are jointly estimated according to a bayesian framework. We circumvent the high dimensionality of the problem by assuming prior distributions of the model parameters to reduce the sensitivity to unmodeled components, and by adopting variational bayesian inference to reduce the computational cost. Through simulation experiments and application to real MEG data, we have confirmed that our proposed method successfully reconstructs focal current activities, which evolve with their temporal dynamics.

Projection versus prewhitening for EEG interference suppression

Suppression of strong, spatially correlated background interference is a challenge associated with electroencephalography (EEG) source localization problems. The most common way of dealing with such interference is through the use of a prewhitening transformation based on an estimate of the covariance of the interference plus noise. This approach is based on strong assumptions regarding temporal stationarity of the data, which do not commonly hold in EEG applications. In addition, prewhitening cannot typically be implemented directly due to ill conditioning of the covariance matrix, and ad hoc regularization is often necessary. Using both simulation examples and experiments involving real EEG data with auditory evoked responses, we demonstrate that a straightforward interference projection method is significantly more robust than prewhitening for EEG source localization.

Efficient dipole parameter estimation in EEG systems with near-ML performance

Source signals that have strong temporal correlation can pose a challenge for high-resolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other high-resolution methods such as multiple signal classification and linearly constrained minimum variance beamforming fail. These methods are based on approximations to the optimal maximum likelihood (ML) approach, but offer significant computational advantages over ML when estimates of the equivalent EEG dipole orientation and moment are required in addition to the source location. The first method uses a two-stage approach in which localization is performed assuming an unstructured dipole moment model, and then the dipole orientation is obtained by using these estimates in a second step. The second method is based on the use of the noise subspace fitting concept, and has been shown to provide performance that is asymptotically equivalent to the direct ML method. Both techniques lead to a considerably simpler optimization than ML since the estimation of the source locations and dipole moments is decoupled. Examples using data from simulations and auditory experiments are presented to illustrate the performance of the algorithms.

Seizure source imaging by means of FINE spatio-temporal dipole localization and directed transfer function in partial epilepsy patients

OBJECTIVE

To investigate the usage of a high-density EEG recording system and source imaging technique for localizing seizure activity in patients with medically intractable partial epilepsy.

METHODS

High-density, 76-channel scalp EEG signals were recorded in 10 patients with partial epilepsy. The patients underwent routine clinical pre-surgical evaluation and all had resective surgery with seizure free outcome. After applying a FINE (first principle vectors) spatio-temporal source localization and DTF (directed transfer function) connectivity analysis approach, ictal sources were imaged. Effects of number of scalp EEG electrodes on the seizure localization were also assessed using 76, 64, 48, 32, and 21 electrodes, respectively.

RESULTS

Surgical resections were used to assess the source imaging results. Results from the 76-channel EEG in the 10 patients showed high correlation with the surgically resected brain regions. The localization of seizure onset zone from 76-channel EEG showed improved source detection accuracy compared to other EEG configurations with fewer electrodes.

CONCLUSIONS

FINE together with DTF was able to localize seizure onset zones of partial epilepsy patients. High-density EEG recording can help achieve improved seizure source imaging.

SIGNIFICANCE

The present results suggest the promise of high-density EEG and electrical source imaging for noninvasively localizing seizure onset zones.

Electrophysiological imaging of brain activity and connectivity-challenges and opportunities

Unlocking the dynamic inner workings of the brain continues to remain a grand challenge of the 21st century. To this end, functional neuroimaging modalities represent an outstanding approach to better understand the mechanisms of both normal and abnormal brain functions. The ability to image brain function with ever increasing spatial and temporal resolution has made a significant leap over the past several decades. Further delineation of functional networks could lead to improved understanding of brain function in both normal and diseased states. This paper reviews recent advancements and current challenges in dynamic functional neuroimaging techniques, including electrophysiological source imaging, multimodal neuroimaging integrating fMRI with EEG/MEG, and functional connectivity imaging.

Region-based current-source reconstruction for the inverse EEG problem

This paper presents a new method for the reconstruction of current sources for the electroencephalography (EEG) inverse problem, which produces reconstructed sources, which are confined to a few anatomical regions. The method is based on a partition of the gray matter into a set of regions, and in the construction of a simple linear model for the potential produced by feasible source configurations inside each one of these regions. The proposed method computes the solution in two stages: in the first one, a subset of active regions is found so that the combined potentials produced by sources inside them approximate the measured potential data. In the second stage, a detailed reconstruction of the current sources inside each active region is performed. Experimental results with synthetic data are presented, which show that the proposed scheme is fast, computationally efficient and robust to noise, producing results that are competitive with other published methods, especially when the current sources are effectively distributed in few anatomical regions. The proposed method is also validated with real data from an experiment with visual evoked potentials.

Functional neuroimaging of dynamic brain activation

Brain activation is distributed in 3-dimensional brain and evolves in time. This paper reviews our recent work on developing high resolution spatio-temporal functional neuroimaging methods.

Review on solving the inverse problem in EEG source analysis

In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided. This paper starts off with a mathematical description of the inverse problem and proceeds to discuss the two main categories of methods which were developed to solve the EEG inverse problem, mainly the non parametric and parametric methods. The main difference between the two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling within these categories are described including minimum norm estimates and their generalizations, LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA FOCUSS (SLF), SSLOFO and ALF for non parametric methods and beamforming techniques, BESA, subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and computational intelligence algorithms for parametric methods. From a review of the performance of these techniques as documented in the literature, one could conclude that in most cases the LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable biophysical and psychological constraints, as done by LAURA has given superior results. The Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF, for different noise levels and different simulated source depths has shown that for single source localization, regularized sLORETA gives the best solution in terms of both localization error and ghost sources. Furthermore the computationally intensive solution given by SLF was not found to give any additional benefits under such simulated conditions.

Multimodal functional neuroimaging: integrating functional MRI and EEG/MEG

Noninvasive functional neuroimaging, as an important tool for basic neuroscience research and clinical diagnosis, continues to face the need of improving the spatial and temporal resolution. While existing neuroimaging modalities might approach their limits in imaging capability mostly due to fundamental as well as technical reasons, it becomes increasingly attractive to integrate multiple complementary modalities in an attempt to significantly enhance the spatiotemporal resolution that cannot be achieved by any modality individually. Electrophysiological and hemodynamic/metabolic signals reflect distinct but closely coupled aspects of the underlying neural activity. Combining fMRI and EEG/MEG data allows us to study brain function from different perspectives. In this review, we start with an overview of the physiological origins of EEG/MEG and fMRI, as well as their fundamental biophysics and imaging principles, we proceed with a review of the major advances in the understanding and modeling of neurovascular coupling and in the methodologies for the fMRI-EEG/MEG simultaneous recording. Finally, we summarize important remaining issues and perspectives concerning multimodal functional neuroimaging, including brain connectivity imaging.

Three-dimensional brain current source reconstruction from intra-cranial ECoG recordings

We have investigated 3-dimensional brain current density reconstruction (CDR) from intracranial electrocorticogram (ECoG) recordings by means of finite element method (FEM). The brain electrical sources are modeled by a current density distribution and estimated from the ECoG signals with the aid of a weighted minimum norm estimation algorithm. A series of computer simulations were conducted to evaluate the performance of ECoG-CDR by comparing with the scalp EEG based CDR results. The present computer simulation results indicate that the ECoG-CDR provides enhanced performance in localizing single dipole sources which are located in regions underneath the implanted subdural ECoG grids, and in distinguishing and imaging multiple separate dipole sources, in comparison to the CDR results as obtained from the scalp EEG under the same conditions. We have also demonstrated the applicability of the present ECoG-CDR method to estimate 3-dimensional current density distribution from the subdural ECoG recordings in a human epilepsy patient. Eleven interictal epileptiform spikes (seven from the frontal region and four from parietal region) in an epilepsy patient undergoing surgical evaluation were analyzed. The present promising results indicate the feasibility and applicability of the developed ECoG-CDR method of estimating brain sources from intracranial electrical recordings, with detailed forward modeling using FEM.

Spatio-temporal source localization and Granger causality in ictal source analysis

We have proposed a new ictal source analysis approach by combining a spatio-temporal source localization approach, and causal interaction estimation technique. The FINE approach is used to identify neural electrical sources from spatio-temporal scalp-EEGs. The Granger causality estimation uses source waveforms estimated by FINE to characterize the causal interaction between the neural electrical sources in order to distinguish primary sources, which initiate ictal events, from secondary sources, which are caused by propagation. In the present study, we applied the proposed analysis approach to an epilepsy patient with symptomatic MRI lesions. It is found that the primary ictal source is within the visible lesion, which gave the consistent presurgical evaluation as MRI for this patient.

EEG source imaging: correlating source locations and extents with electrocorticography and surgical resections in epilepsy patients

SUMMARY

It is desirable to estimate epileptogenic zones with both location and extent information from noninvasive EEG. In the present study, the authors use a subspace source localization method (FINE), combined with a local thresholding technique, to achieve such tasks. The performance of this method was evaluated in interictal spikes from three pediatric patients with medically intractable partial epilepsy. The thresholded subspace correlation, which is obtained from FINE scanning, is a favorable marker, which implies the extents of current sources associated with epileptic activities. The findings were validated by comparing the results with invasive electrocorticographic (ECoG) recordings of interictal spike activity. The surgical resections in these three patients correlated well with the epileptogenic zones identified from both EEG sources and ECoG potential distributions. The value of the proposed noninvasive technique for estimating epileptiform activity was supported by satisfactory surgery outcomes.

Multiple Dipole Sources Localization from the Scalp EEG Using a High-resolution Subspace Approach

We have developed a new algorithm, FINE, to enhance the spatial resolution and localization accuracy for closely-spaced sources, in the framework of the subspace source localization. Computer simulations were conducted in the present study to evaluate the performance of FINE, as compared with classic subspace source localization algorithms, i.e. MUSIC and RAP-MUSIC, in a realistic geometry head model by means of boundary element method (BEM). The results show that FINE could distinguish superficial simulated sources, with distance as low as 8.5 mm and deep simulated sources, with distance as low as 16.3 mm. Our results also show that the accuracy of source orientation estimates from FINE is better than MUSIC and RAP-MUSIC for closely-spaced sources. Motor potentials, obtained during finger movements in a human subject, were analyzed using FINE. The detailed neural activity distribution within the contralateral premotor areas and supplemental motor areas (SMA) is revealed by FINE as compared with MUSIC. The present study suggests that FINE has excellent spatial resolution in imaging neural sources.

Reduced spatially correlated noise influence using subspace source localization method FINES

We have developed a high resolution subspace approach for EEG source localization within a realistic geometry inhomogeneous head model. The present study aims to reduce the influence caused by spatially correlated noise from background activities using FINES. Computer simulations were conducted on the realistic geometry head volume conductor model and compared with the classic MUSIC algorithm. The FINES approach was also applied to source localization of motor potentials induced by the execution of finger movement in a human subject. The present results suggest that FINES is insensitive to spatially correlated noise, and has enhanced performance as compared with MUSIC.

Ictal source analysis: localization and imaging of causal interactions in humans

We propose a new integrative approach to characterize the structure of seizures in the space, time, and frequency domains. Such characterization leads to a new technical development of ictal source analysis for the presurgical evaluation of epilepsy patients. The present new ictal source analysis method consists of three parts. First, a three-dimensional source scanning procedure is performed by a spatio-temporal FINE source localization method to locate the multiple sources responsible for the time evolving ictal rhythms at their onsets. Next, the dynamic behavior of the sources is modeled by a multivariate autoregressive process (MVAR). Lastly, the causal interaction patterns among the sources as a function of frequency are estimated from the MVAR modeling of the source temporal dynamics. The causal interaction patterns indicate the dynamic communications between sources, which are useful in distinguishing the primary sources responsible for the ictal onset from the secondary sources caused by the ictal propagation. The present ictal analysis strategy has been applied to a number of seizures from five epilepsy patients, and their results are consistent with observations from either MRI lesions or SPECT scans, which indicate its effectiveness. Each step of the ictal source analysis is statistically evaluated in order to guarantee the confidence in the results.

Spatio-temporal EEG source localization using a three-dimensional subspace FINE approach in a realistic geometry inhomogeneous head model

The subspace source localization approach, i.e., first principle vectors (FINE), is able to enhance the spatial resolvability and localization accuracy for closely-spaced neural sources from EEG and MEG measurements. Computer simulations were conducted to evaluate the performance of the FINE algorithm in an inhomogeneous realistic geometry head model under a variety of conditions. The source localization abilities of FINE were examined at different cortical regions and at different depths. The present computer simulation results indicate that FINE has enhanced source localization capability, as compared with MUSIC and RAP-MUSIC, when sources are closely spaced, highly noise-contaminated, or inter-correlated. The source localization accuracy of FINE is better, for closely-spaced sources, than MUSIC at various noise levels, i.e., signal-to-noise ratio (SNR) from 6 dB to 16 dB, and RAP-MUSIC at relatively low noise levels, i.e., 6 dB to 12 dB. The FINE approach has been further applied to localize brain sources of motor potentials, obtained during the finger tapping tasks in a human subject. The experimental results suggest that the detailed neural activity distribution could be revealed by FINE. The present study suggests that FINE provides enhanced performance in localizing multiple closely spaced, and inter-correlated sources under low SNR, and may become an important alternative to brain source localization from EEG or MEG.

Estimation of number of independent brain electric sources from the scalp EEGs

In electromagnetic source analysis, many source localization strategies require the number of sources as an input parameter (e.g., spatio-temporal dipole fitting and the multiple signal classification). In the present study, an information criterion method, in which the penalty functions are selected based on the spatio-temporal source model, has been developed to estimate the number of independent dipole sources from electromagnetic measurements such as the electroencephalogram (EEG). Computer simulations were conducted to evaluate the effects of various parameters on the estimation of the source number. A three-concentric-spheres head model was used to approximate the head volume conductor. Three kinds of typical signal sources, i.e., the damped sinusoid sources, sinusoid sources with one frequency band and sinusoid sources with two separated frequency bands, were used to simulate the oscillation characteristics of brain electric sources. The simulation results suggest that the present method can provide a good estimate of the number of independent dipole sources from the EEG measurements. In addition, the present simulation results suggest that choosing the optimal penalty function can successfully reduce the effect of noise on the estimation of number of independent sources. The present study suggests that the information criterion method may provide a useful means in estimating the number of independent brain electrical sources from EEG/MEG measurements.

3D source localization of interictal spikes in epilepsy patients with MRI lesions

The present study aims to accurately localize epileptogenic regions which are responsible for epileptic activities in epilepsy patients by means of a new subspace source localization approach, i.e. first principle vectors (FINE), using scalp EEG recordings. Computer simulations were first performed to assess source localization accuracy of FINE in the clinical electrode set-up. The source localization results from FINE were compared with the results from a classic subspace source localization approach, i.e. MUSIC, and their differences were tested statistically using the paired t-test. Other factors influencing the source localization accuracy were assessed statistically by ANOVA. The interictal epileptiform spike data from three adult epilepsy patients with medically intractable partial epilepsy and well-defined symptomatic MRI lesions were then studied using both FINE and MUSIC. The comparison between the electrical sources estimated by the subspace source localization approaches and MRI lesions was made through the coregistration between the EEG recordings and MRI scans. The accuracy of estimations made by FINE and MUSIC was also evaluated and compared by R(2) statistic, which was used to indicate the goodness-of-fit of the estimated sources to the scalp EEG recordings. The three-concentric-spheres head volume conductor model was built for each patient with three spheres of different radii which takes the individual head size and skull thickness into consideration. The results from computer simulations indicate that the improvement of source spatial resolvability and localization accuracy of FINE as compared with MUSIC is significant when simulated sources are closely spaced, deep, or signal-to-noise ratio is low in a clinical electrode set-up. The interictal electrical generators estimated by FINE and MUSIC are in concordance with the patients' structural abnormality, i.e. MRI lesions, in all three patients. The higher R(2) values achieved by FINE than MUSIC indicate that FINE provides a more satisfactory fitting of the scalp potential measurements than MUSIC in all patients. The present results suggest that FINE provides a useful brain source imaging technique, from clinical EEG recordings, for identifying and localizing epileptogenic regions in epilepsy patients with focal partial seizures. The present study may lead to the establishment of a high-resolution source localization technique from scalp-recorded EEGs for aiding presurgical planning in epilepsy patients.

Estimation of cortical dipole sources by equivalent dipole layer imaging and independent component analysis

We explored suitable estimation method for equivalent dipole sources in the brain. In a previous study, we solved an inverse problem that estimated an equivalent dipole-layer distribution from the scalp electroencephalogram by a spatio-temporal inverse filters constructed with parametric projection filter. In the present study, we estimated equivalent dipole sources from dipole layer distributions. Moreover, to identify the number, position, and moment of equivalent dipole sources, we separated each dipole layer distribution using independent component analysis (ICA). The performance of the proposed estimation method was evaluated by computer simulation and human experimental studies in an inhomogeneous three-concentric sphere head model. The present simulation results indicated that the equivalent dipole sources was accurately estimated by ICA and dipole imaging. We also applied the proposed method to human visual evoked potential.

On the estimation of the number of dipole sources in EEG source localization

OBJECTIVE

The purpose of the present study was to determine the number of the equivalent dipole sources corresponding to the scalp EEG using the information criterion method based on the instantaneous-state modeling.

METHODS

A three-concentric-spheres head model was used to represent the head volume conductor. The Powell algorithm was used to solve the inverse problem of estimating the equivalent dipoles from the scalp EEG. The information criterion with different penalty functions was used to determine the dipole number. Computer simulations were conducted to evaluate effects of various parameters on the estimation of dipole number.

RESULTS

The present results suggest that the present method is able to estimate the number of equivalent current dipoles (ECDs) from instantaneous scalp EEG measurements, and that increase in the electrode number can improve the accuracy of estimation of the ECD number. For two ECDs, the best performance of estimation with 20% white noise were 85%, 92% and 94%, when 64, 128 and 256 electrodes are used, respectively. When there are 3 ECDs, the present results suggest that using 256 electrodes gave up to 82% estimation accuracy. The present simulation results also indicate that the accuracies of identification are similar when the minimum distance between dipoles is either 1 or 2 cm, which was used in the simulation. It was also found that the different penalty functions used in the information criterion method could have substantial influence on the estimation accuracy.

CONCLUSIONS

The present method can estimate the number of ECDs from instantaneous scalp EEG distribution for up to three dipoles.

SIGNIFICANCE

The successful estimation of the number of ECDs will play an important role in expanding the applicability of dipole source localization to multiple sources.

A second-order finite element algorithm for solving the three-dimensional EEG forward problem

A finite element algorithm has been developed to solve the electroencephalogram (EEG) forward problem. A new computationally efficient approach to calculate the stiffness matrix of second-order tetrahedral elements has been developed for second-order tetrahedral finite element models. The present algorithm has been evaluated by means of computer simulations, by comparing with analytic solutions in a multi-spheres concentric head model. The developed finite element method (FEM) algorithm has also been applied to address questions of interest in the EEG forward problem. The present simulation study indicates that the second-order FEM provides substantially enhanced numerical accuracy and computational efficiency, as compared with the first-order FEM for comparable numbers of tetrahedral elements. The anisotropic conductivity distribution of the head tissue can be taken into account in the present FEM algorithm. The effects of dipole eccentricity, size of finite elements and local mesh refinement on solution accuracy are also addressed in the present simulation study.