Estimation of neural dynamics from MEG/EEG cortical current density maps: application to the reconstruction of large-scale cortical synchrony

There is a growing interest in elucidating the role of specific patterns of neural dynamics--such as transient synchronization between distant cell assemblies--in brain functions. Magnetoencephalography (MEG)/electroencephalography (EEG) recordings consist in the spatial integration of the activity from large and multiple remotely located populations of neurons. Massive diffusive effects and poor signal-to-noise ratio (SNR) preclude the proper estimation of indices related to cortical dynamics from nonaveraged MEG/EEG surface recordings. Source localization from MEG/EEG surface recordings with its excellent time resolution could contribute to a better understanding of the working brain. We propose a robust and original approach to the MEG/EEG distributed inverse problem to better estimate neural dynamics of cortical sources. For this, the surrogate data method is introduced in the MEG/EEG inverse problem framework. We apply this approach on nonaveraged data with poor SNR using the minimum norm estimator and find source localization results weakly sensitive to noise. Surrogates allow the reduction of the source space in order to reconstruct MEG/EEG data with reduced biases in both source localization and time-series dynamics. Monte Carlo simulations and results obtained from real MEG data indicate it is possible to estimate non invasively an important part of cortical source locations and dynamic and, therefore, to reveal brain functional networks.     

A Bayesian approach to introducing anatomo-functional priors in theEEG/MEG inverse problem

We present a new approach to the recovering of dipole magnitudes in a distributed source model for magnetoencephalographic (MEG) and electroencephalographic (EEG) imaging. This method consists in introducing spatial and temporal a priori information as a cure to this ill-posed inverse problem. A nonlinear spatial regularization scheme allows the preservation of dipole moment discontinuities between some a priori noncorrelated sources, for instance, when considering dipoles located on both sides of a sulcus. Moreover, we introduce temporal smoothness constraints on dipole magnitude evolution at time scales smaller than those of cognitive processes. These priors are easily integrated into a Bayesian formalism, yielding a maximum a posteriori (MAP) estimator of brain electrical activity. Results from EEG simulations of our method are presented and compared with those of classical quadratic regularization and a now popular generalized minimum-norm technique called low-resolution electromagnetic tomography (LORETA)     

Evaluating the Performance of Kalman-Filter-Based EEG Source Localization

Electroencephalographic (EEG) source localization is an important tool for noninvasive study of brain dynamics, due to its ability to probe neural activity more directly, with better temporal resolution than other imaging modalities. One promising technique for solving the EEG inverse problem is Kalman filtering, because it provides a natural framework for incorporating dynamic EEG generation models in source localization. Here, a recently developed inverse solution is introduced, which uses spatiotemporal Kalman filtering tuned through likelihood maximization. Standard diagnostic tests for objectively evaluating Kalman filter performance are then described and applied to inverse solutions for simulated and clinical EEG data. These tests, employed for the first time in Kalman-filter-based source localization, check the statistical properties of the innovation and validate the use of likelihood maximization for filter tuning. However, this analysis also reveals that the filter's existing space- and time-invariant process model, which contains a single fixed-frequency resonance, is unable to completely model the complex spatiotemporal dynamics of EEG data. This finding indicates that the algorithm could be improved by allowing the process model parameters to vary in space.      

A multiresolution framework to MEG/EEG source imaging

A new method based on a multiresolution approach for solving the ill-posed problem of brain electrical activity reconstruction from electroencephaloram (EEG)/magnetoencephalogram (MEG) signals is proposed in a distributed source model. At each step of the algorithm, a regularized solution to the inverse problem is used to constrain the source space on the cortical surface to be scanned at higher spatial resolution. We present the iterative procedure together with an extension of the ST-maximum a posteriori method [1] that integrates spatial and temporal a priori information in an estimator of the brain electrical activity. Results from EEG in a phantom head experiment with a real human skull and from real MEG data on a healthy human subject are presented. The performances of the multiresolution method combined with a nonquadratic estimator are compared with commonly used dipolar methods, and to minimum-norm method with and without multiresolution. In all cases, the proposed approach proved to be more efficient both in terms of computational load and result quality, for the identification of sparse focal patterns of cortical current density, than the fixed scale imaging approach.     

Electromagnetic brain mapping

There has been tremendous advances in our ability to produce images of human brain function. Applications of functional brain imaging extend from improving our understanding of the basic mechanisms of cognitive processes to better characterization of pathologies that impair normal function. Magnetoencephalography (MEG) and electroencephalography (EEG) (MEG/EEG) localize neural electrical activity using noninvasive measurements of external electromagnetic signals. Among the available functional imaging techniques, MEG and EEG uniquely have temporal resolutions below 100 ms. This temporal precision allows us to explore the timing of basic neural processes at the level of cell assemblies. MEG/EEG source localization draws on a wide range of signal processing techniques including digital filtering, three-dimensional image analysis, array signal processing, image modeling and reconstruction, and, blind source separation and phase synchrony estimation. We describe the underlying models currently used in MEG/EEG source estimation and describe the various signal processing steps required to compute these sources. In particular we describe methods for computing the forward fields for known source distributions and parametric and imaging-based approaches to the inverse problem     

Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction

This paper presents a new algorithm called Standardized Shrinking LORETA-FOCUSS (SSLOFO) for solving the electroencephalogram (EEG) inverse problem. Multiple techniques are combined in a single procedure to robustly reconstruct the underlying source distribution with high spatial resolution. This algorithm uses a recursive process which takes the smooth estimate of sLORETA as initialization and then employs the re-weighted minimum norm introduced by FOCUSS. An important technique called standardization is involved in the recursive process to enhance the localization ability. The algorithm is further improved by automatically adjusting the source space according to the estimate of the previous step, and by the inclusion of temporal information. Simulation studies are carried out on both spherical and realistic head models. The algorithm achieves very good localization ability on noise-free data. It is capable of recovering complex source configurations with arbitrary shapes and can produce high quality images of extended source distributions. We also characterized the performance with noisy data in a realistic head model. An important feature of this algorithm is that the temporal waveforms are clearly reconstructed, even for closely spaced sources. This provides a convenient way to estimate neural dynamics directly from the cortical sources.     

Spatiotemporal EEG/MEG source analysis based on a parametric noise covariance model

A method is described to incorporate the spatiotemporal noise covariance matrix into a spatiotemporal source analysis. The essential feature is that the estimation problem is split into two parts. First, a model is fitted to the observed noise covariance matrix. This model is a Kronecker product of a spatial and a temporal matrix. The spatial matrix models the spatial covariances by a function dependent on sensor distance. The temporal matrix models the temporal covariances as lag dependent. In the second part, sources are estimated given this noise model, which can be done very efficiently due to the Kronecker formulation. An application to real electroencephalogram (EEG) data shows that the noise model fits the data very well. Simulation results show that the resulting source estimates are more precise than those obtained from a standard analysis neglecting the noise covariance. In addition, the estimated standard errors of the source parameter estimates are far more precise than those obtained from a standard analysis. Finally, the source parameter standard errors are used to investigate the effects of temporal sampling. It is shown that increasing the sampling by a factor x, decreases the standard errors of all source parameters with the square root of x.     

Principal-component localization of the sources of the backgroundEEG

A method, based on principal components for localizing the sources of the background EEG, is presented which overcomes the previous limitations of this approach. The spatiotemporal source model of the EEG is assumed to apply, and the method involves attempting to fit the spatial aspects of this general model with an optimal rotation of a subset of the principal components of a particular EEG. The method is shown to be equivalent to the subspace scanning method, a special case of the MUSIC algorithm, which enables multiple sources to be localized individually rather than all at once. The novel aspect of the new method is that it offers a way of selecting the relevant principal components for the localization problem. The relevant principal components are chosen by decomposing the EEG using spatial patterns common with a control EEG. These spatial patterns have the property that they account for maximally different proportions of the combined variances in the two EEG's. An example is given using a particular EEG from a neurologic patient. Components containing spike and sharp wave potentials are extracted, with respect to a standard EEG derived from 15 normal volunteers. Spike and sharp wave potentials are identified visually using the common spatial patterns decomposition and an EEG reconstructed from these components. Four dipole sources are fitted to the principal components of the reconstructed EEG and these source account for over 88% of the temporal variance present in that EEG     

基于变换数据空间的相干脑电源定位算法

不同脑区之间的相互协作对大脑完成认知任务具有重要意义.脑区电活动的相干性被认为是这种协作的表现形式.从头表脑电无创地三维定位相干源有助于了解大脑的内在机制.传统的MUSIC算法不能定位相干源.本文发展了一种在变换数据空间的MUSIC算法用于相干源定位.首先根据先验信息大致估计相干源区的范围,然后设计能压制相干源区的数据变换矩阵.最后在变换后的数据空间定位相干源.不同条件下的计算模拟实验表明,相比其它方法,这种方法具有更高的定位精度,运算速度也更快.     

Recent Developments in Spatio-Temporal EEG Source Reconstruction Techniques

EEG is gaining recognition in the field of real-time applications. However, the EEG inverse problem leads to poor spatial resolution in brain source localization. This paper presents an overview of the existing EEG inverse solution methods. Further, a comparative analysis of recent techniques has been presented. This work discusses the challenges associated with the existing source reconstruction algorithms. The main focus is on the recent reports in this field that have combined the EEG denoising in the pre-processing phase along with the inverse localization approaches. Out of various existing techniques, SLORETA offers better localization results but its noise sensitivity is very high. It has been validated in a comparative analysis for simulated dipole sources with no noise. To illustrate the advantage of using pre-processed data with inverse localization, the classification accuracy of conventional methods has been compared. The accuracy has been analyzed for depression signals using the Naïve Bayes, RF, and SVM classifiers. The VMD- SLORETA method shows better accuracy as compared to EMD-SLORETA and SLORETA only. The existing EEG localization methods are efficient but the spatial resolution is still to be improved in the presence of various noise sources in raw EEG. More accurate localization is achieved by implementing denoising in combination with the source localization framework. There is a need to investigate further stages of EEG signal processing along with optimal feature selection. Further, additional studies should be conducted to improve the noise sensitivity of other existing localization systems using pre-processing approaches.

Graphic Abstract

     

Estimating stationary dipoles from MEG/EEG data contaminated withspatially and temporally correlated background noise

The stationary dipole model for the inverse problem of magnetoencephalographic (MEG) and electroencephalographic (EEG) data is extended by including spatio-temporal correlations of the background noise. For that purpose, the spatio-temporal covariances are described as a Kronkecker product of a spatial and a temporal covariance matrix. The maximum likelihood method is used to estimate this Kronecker product from a series of trials of MEG/EEG data. A simulation study shows that the inclusion of the background noise generally improves the dipole estimate substantially. When the frequency of the source time functions, however, coincides with the frequency contents of the covariance function, the dipole estimate worsens when the temporal correlations are included. The inclusion of spatial correlations always improves the estimates     

Estimating parametric line-source models with electroencephalography

We develop three parametric models for electroencephalography (EEG) to estimate current sources that are spatially distributed on a line. We assume a realistic head model and solve the EEG forward problem using the boundary element method (BEM). We present the models with increasing degrees of freedom, provide the forward solutions, and derive the maximum-likelihood estimates as well as Cramér-Rao bounds of the unknown source parameters. A series of experiments are conducted to evaluate the applicability of the proposed models. We use numerical examples to demonstrate the usefulness of our line-source models in estimating extended sources. We also apply our models to the real EEG data of N20 response that is known to have an extended source. We observe that the line-source models explain the N20 measurements better than the dipole model.     

基于fMRI功能网络和贝叶斯矩阵分解的脑电源成像方法

脑电(EEG)是一种重要的脑功能成像技术,根据头皮记录的EEG信号重构皮层脑活动称为EEG源成像。然而脑源活动位置和尺寸的准确重构依然是一个挑战。为充分利用EEG和功能磁共振(fMRI)信号在时空分辨率上的互补信息,该文提出一个新的源成像方法——基于fMRI脑网络和时空约束的EEG源重构算法(FN-STCSI)。该方法在参数贝叶斯框架下,基于矩阵分解思想将源信号分解为若干时间基函数的线性组合。此外,为融合fMRI的高空间分辨率信息,FN-STCSI利用独立成分分析提取fMRI信号的功能网络,构建EEG源成像的空间协方差基,通过变分贝叶斯推断技术确定每个空间协方差基的相对贡献,实现EEG-fMRI融合。通过蒙特卡罗数值仿真和实验数据分析比较了FN-STCSI与现有算法在不同信噪比和不同先验条件下的性能,结果表明FN-STCSI能有效融合EEG-fMRI在时空上的互补信息,提高EEG弥散源成像的性能。     

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.     

Simultaneous EEG Source and Forward Model Reconstruction (SOFOMORE) Using a Hierarchical Bayesian Approach

We present an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model representation is motivated by the many random contributions to the path from sources to measurements including the tissue conductivity distribution, the geometry of the cortical surface, and electrode positions. We first present a hierarchical Bayesian framework for EEG source localization that jointly performs source and forward model reconstruction (SOFOMORE). Secondly, we evaluate the SOFOMORE approach by comparison with source reconstruction methods that use fixed forward models. Analysis of simulated and real EEG data provide evidence that reconstruction of the forward model leads to improved source estimates.     

Subspace projection filters for real-time brain electromagnetic imaging

An increasing number of neuroimaging laboratories are becoming interested in real-time investigations of the human brain. The opportunities offered by real-time applications are inversely proportional to the latency of the brain activity response and to the computational delay of brain activity estimation. Electromagnetic tomographies, based on electroencephalography (EEG) or magnetoencephalography (MEG), feature immediacy of brain activity response and excellent time resolution, hence they are natural candidates. However their spatial resolution and signal-to-noise ratio are poor. In this paper, we develop data-independent and data-dependent subspace projection filters for the standardized low-resolution electromagnetic tomography (sLORETA), a weighted minimum norm inverse solution for EEG/MEG. The filters are designed for extracting time-series of source activity in any given region of interest. The data-independent filter is shown to reduce interference of sources originating in neighboring regions, whereas the data-dependent filter is shown to suppress sensor measurement noise. An effective and straightforward way to combine them is demonstrated. The result is a dual subspace projection allowing both noise suppression and interference reduction.     

A physiologically plausible spatio-temporal model for EEG signals recorded with intracerebral electrodes in human partial epilepsy

Stereoelectroencephalography (depth-EEG signals) is a presurgical investigation technique of drug-resistant partial epilepsy, in which multiple sensor intracerebral electrodes are used to directly record brain electrical activity. In order to interpret depth-EEG signals, we developed an extended source model which connects two levels of representation: (1) a distributed current dipole model which describes the spatial distribution of neuronal sources; (2) a model of coupled neuronal populations which describes their temporal dynamics. From this extended source model, depth-EEG signals were simulated from the forward solution at each electrode sensor located inside the brain. Results showed that realistic transient epileptiform activities (spikes) are obtained under specific conditions in the model in terms of degree of coupling between neuronal populations and spatial extent of the source. In particular, the cortical area involved in the generation of epileptic spikes was estimated to vary from 18 to 25 cm2, for brain conductivity values ranging from 30 to 35 x 10(-5) S/mm, for high coupling degree between neuronal populations and for a volume conductor model that accounts for the three main tissues of the head (brain, skull, and scalp). This study provides insight into the relationship between spatio-temporal properties of cortical neuronal sources and depth-EEG signals.     

Combined MEG and EEG source imaging by minimization of mutual information

Though very frequently assumed, the necessity to operate a joint processing of simultaneous magnetoencephalography (MEG) and electroencephalography (EEG) recordings for functional brain imaging has never been clearly demonstrated. However, the very last generation of MEG instruments allows the simultaneous recording of brain magnetic fields and electrical potentials on the scalp. But the general fear regarding the fusion between MEG and EEG data is that the drawbacks from one modality will systematically spoil the performances of the other one without any consequent improvement. This is the case for instance for the estimation of deeper or radial sources with MEG. In this paper, we propose a method for a cooperative processing of MEG and EEG in a distributed source model. First, the evaluation of the respective performances of each modality for the estimation of every dipole in the source pattern is made using a conditional entropy criterion. Then, the algorithm operates a preprocessing of the MEG and EEG gain matrices which minimizes the mutual information between these two transfer functions, by a selective weighting of the MEG and EEG lead fields. This new combined EEG/MEG modality brings major improvements to the localization of active sources, together with reduced sensitivity to perturbations on data.     

Assessing the Relevance of fMRI-Based Prior in the EEG Inverse Problem: A Bayesian Model Comparison Approach

Characterizing the cortical activity from electro- and magneto-encephalography (EEG/MEG) data requires solving an ill-posed inverse problem that does not admit a unique solution. As a consequence, the use of functional neuroimaging, for instance, functional Magnetic Resonance Imaging (fMRI), constitutes an appealing way of constraining the solution. However, the match between bioelectric and metabolic activities is desirable but not assured. Therefore, the introduction of spatial priors derived from other functional modalities in the EEG/MEG inverse problem should be considered with caution. In this paper, we propose a Bayesian characterization of the relevance of fMRI-derived prior information regarding the EEG/MEG data. This is done by quantifying the adequacy of this prior to the data, compared with that obtained using an noninformative prior instead. This quantitative comparison, using the so-called Bayes factor, allows us to decide whether the informative prior should (or not) be included in the inverse solution. We validate our approach using extensive simulations, where fMRI-derived priors are built as perturbed versions of the simulated EEG sources. Moreover, we show how this inference framework can be generalized to optimize the way we should incorporate the informative prior.     

Simultaneous Estimation and Testing of Sources in Multiple MEG Data Sets

The proposed Extended Couple Dipole Model (ECDM) is a trilinear component model that can be used to analyze multiple, related MEG data sets simultaneously. Related MEG data sets are data sets that contain activity of the same sources or activity of sources that have proportional source amplitudes. The simultaneous model uses a set of common sources and a set of common source time functions (wave shapes) to model the measured data in each data set. The set of common sources contains all sources that are active in at least one of the data sets to be analyzed. The number of common spatial and temporal components is specified by the user. The model for each data set is a linear combination of these common spatial and temporal components. This linear combination is estimated in a coupling matrix. Unlike the Coupled Dipole Model, where the user selects certain entries of the coupling matrix to be zero, the entire coupling matrix is estimated in the ECDM. This yields a more objective and statistically transparent estimation method, of which the identifiability constraints do not depend on the user's chosen design as in the CDM. CramÈr–Rao Bounds are derived for the ECDM, and the significance of the estimated source activity is computed and illustrated by confidence regions around estimated source time functions.