State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an $L^2$ regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intracortical sources. In our model, the observation model is derived from the steady-state solution to Maxwell's equations while the latent model representing neural dynamics is given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Bayesian multi-modal model comparison: a case study on the generators of the spike and the wave in generalized spike–wave complexes

We present a novel approach to assess the networks involved in the generation of spontaneous pathological brain activity based on multi-modal imaging data. We propose to use probabilistic fMRI-constrained EEG source reconstruction as a complement to EEG-correlated fMRI analysis to disambiguate between networks that co-occur at the fMRI time resolution. The method is based on Bayesian model comparison, where the different models correspond to different combinations of fMRI-activated (or deactivated) cortical clusters. By computing the model evidence (or marginal likelihood) of each and every candidate source space partition, we can infer the most probable set of fMRI regions that has generated a given EEG scalp data window. We illustrate the method using EEG-correlated fMRI data acquired in a patient with ictal generalized spike–wave (GSW) discharges, to examine whether different networks are involved in the generation of the spike and the wave components, respectively. To this effect, we compared a family of 128 EEG source models, based on the combinations of seven regions haemodynamically involved (deactivated) during a prolonged ictal GSW discharge, namely: bilateral precuneus, bilateral medial frontal gyrus, bilateral middle temporal gyrus, and right cuneus. Bayesian model comparison has revealed the most likely model associated with the spike component to consist of a prefrontal region and bilateral temporal–parietal regions and the most likely model associated with the wave component to comprise the same temporal–parietal regions only. The result supports the hypothesis of different neurophysiological mechanisms underlying the generation of the spike versus wave components of GSW discharges

Sparse EEG Source Localization Using Bernoulli Laplacian Priors

International audienceSource 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 non zero 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

The Surface Laplacian Technique in EEG: Theory and Methods

This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for EEG researchers unfamiliar with the technique. The popular methods of finite difference and splines are reviewed in detail. The former has the advantage of simplicity and low computational cost, but its estimates are prone to a variety of errors due to discretization. The latter eliminates all issues related to discretization and incorporates a regularization mechanism to reduce spatial noise, but at the cost of increasing mathematical and computational complexity. These and several others issues deserving further development are highlighted, some of which we address to the extent possible. Here we develop a set of discrete approximations for Laplacian estimates at peripheral electrodes and a possible solution to the problem of multiple-frame regularization. We also provide the mathematical details of finite difference approximations that are missing in the literature, and discuss the problem of computational performance, which is particularly important in the context of EEG splines where data sets can be very large. Along this line, the matrix representation of the surface Laplacian operator is carefully discussed and some figures are given illustrating the advantages of this approach. In the final remarks, we briefly sketch a possible way to incorporate finite-size electrodes into Laplacian estimates that could guide further developments.Comment: 43 pages, 8 figure

International Federation of Clinical Neurophysiology (IFCN) – EEG research workgroup: Recommendations on frequency and topographic analysis of resting state EEG rhythms. Part 1: Applications in clinical research studies

In 1999, the International Federation of Clinical Neurophysiology (IFCN) published “IFCN Guidelines for topographic and frequency analysis of EEGs and EPs” (Nuwer et al., 1999). Here a Workgroup of IFCN experts presents unanimous recommendations on the following procedures relevant for the topographic and frequency analysis of resting state EEGs (rsEEGs) in clinical research defined as neurophysiological experimental studies carried out in neurological and psychiatric patients: (1) recording of rsEEGs (environmental conditions and instructions to participants; montage of the EEG electrodes; recording settings); (2) digital storage of rsEEG and control data; (3) computerized visualization of rsEEGs and control data (identification of artifacts and neuropathological rsEEG waveforms); (4) extraction of “synchronization” features based on frequency analysis (band-pass filtering and computation of rsEEG amplitude/power density spectrum); (5) extraction of “connectivity” features based on frequency analysis (linear and nonlinear measures); (6) extraction of “topographic” features (topographic mapping; cortical source mapping; estimation of scalp current density and dura surface potential; cortical connectivity mapping), and (7) statistical analysis and neurophysiological interpretation of those rsEEG features. As core outcomes, the IFCN Workgroup endorsed the use of the most promising “synchronization” and “connectivity” features for clinical research, carefully considering the limitations discussed in this paper. The Workgroup also encourages more experimental (i.e. simulation studies) and clinical research within international initiatives (i.e., shared software platforms and databases) facing the open controversies about electrode montages and linear vs. nonlinear and electrode vs. source levels of those analyses

Algorithmic procedures for Bayesian MEG/EEG source reconstruction in SPM

AbstractThe MEG/EEG inverse problem is ill-posed, giving different source reconstructions depending on the initial assumption sets. Parametric Empirical Bayes allows one to implement most popular MEG/EEG inversion schemes (Minimum Norm, LORETA, etc.) within the same generic Bayesian framework. It also provides a cost-function in terms of the variational Free energy—an approximation to the marginal likelihood or evidence of the solution. In this manuscript, we revisit the algorithm for MEG/EEG source reconstruction with a view to providing a didactic and practical guide. The aim is to promote and help standardise the development and consolidation of other schemes within the same framework. We describe the implementation in the Statistical Parametric Mapping (SPM) software package, carefully explaining each of its stages with the help of a simple simulated data example. We focus on the Multiple Sparse Priors (MSP) model, which we compare with the well-known Minimum Norm and LORETA models, using the negative variational Free energy for model comparison. The manuscript is accompanied by Matlab scripts to allow the reader to test and explore the underlying algorithm

Ultrahigh Field Functional Magnetic Resonance Electrical Impedance Tomography (fMREIT) in Neural Activity Imaging

abstract: A direct Magnetic Resonance (MR)-based neural activity mapping technique with high spatial and temporal resolution may accelerate studies of brain functional organization. The most widely used technique for brain functional imaging is functional Magnetic Resonance Image (fMRI). The spatial resolution of fMRI is high. However, fMRI signals are highly influenced by the vasculature in each voxel and can be affected by capillary orientation and vessel size. Functional MRI analysis may, therefore, produce misleading results when voxels are nearby large vessels. Another problem in fMRI is that hemodynamic responses are slower than the neuronal activity. Therefore, temporal resolution is limited in fMRI. Furthermore, the correlation between neural activity and the hemodynamic response is not fully understood. fMRI can only be considered an indirect method of functional brain imaging. Another MR-based method of functional brain mapping is neuronal current magnetic resonance imaging (ncMRI), which has been studied over several years. However, the amplitude of these neuronal current signals is an order of magnitude smaller than the physiological noise. Works on ncMRI include simulation, phantom experiments, and studies in tissue including isolated ganglia, optic nerves, and human brains. However, ncMRI development has been hampered due to the extremely small signal amplitude, as well as the presence of confounding signals from hemodynamic changes and other physiological noise. Magnetic Resonance Electrical Impedance Tomography (MREIT) methods could have the potential for the detection of neuronal activity. In this technique, small external currents are applied to a body during MR scans. This current flow produces a magnetic field as well as an electric field. The altered magnetic flux density along the main magnetic field direction caused by this current flow can be obtained from phase images. When there is neural activity, the conductivity of the neural cell membrane changes and the current paths around the neurons change consequently. Neural spiking activity during external current injection, therefore, causes differential phase accumulation in MR data. Statistical analysis methods can be used to identify neuronal-current-induced magnetic field changes.Dissertation/ThesisDoctoral Dissertation Biomedical Engineering 201