Zoltan J. Koles

Trends in EEG source localization

The concepts underlying the quantitative localization of the sources of the EEG inside the brain are reviewed along with the current and emerging approaches to the problem. The concepts mentioned include monopolar and dipolar source models and head models ranging from the spherical to the more realistic based on boundary and finite elements. The forward and inverse problems in electroencephalography are discussed, including the non-uniqueness of the inverse problem. The approaches to the solution of the inverse problem described include single and multiple time-slice localization, equivalent dipole localization and the weighted minimum norm. The multiple time-slice localization approach is highlighted as probably the best available at this time and is discussed in terms of the spatiotemporal model of the EEG. The effect of noise corruption, artifacts and the number of recording electrodes on the accuracy of source localization is also mentioned. It is suggested that the main appeal of the minimum norm is that it does not assume a model for the sources and provides an estimate of the current density everywhere in the three dimensional volume of the head.

Spatial patterns underlying population differences in the background EEG

SummaryA method is described which can be used to extract common spatial patterns underlying the EEGs from two human populations. These spatial patterns account, in the least-squares sense, maximally for the variance in the EEGs from one population and minimally for the variance in the other population and therefore would seem to be optimal for quantitatively discriminating between the individual EEGs in the two populations. By using this method, it is suggested that the problems associated with the more common approach to discriminating EEGs, significance probability mapping, can be avoided. The method is tested using EEGs from a population of normal subjects and using the EEGs from a population of patients with neurologic disorders. The results in most cases are excellent and the misclassification which occurs in some cases is attributed to the nonhomogeneity of the patient population particularly. The advantages of the method for feature selection, for automatically classifying the clinical EEG, and with respect to the reference-free nature of the selected features are discussed.

EEG source localization: implementing the spatio-temporal decomposition approach

OBJECTIVES The spatio-temporal decomposition (STD) approach was used to localize the sources of simulated electroencephalograms (EEGs) to gain experience with the approach for analyzing real data. METHODS The STD approach used is similar to the multiple signal classification method (MUSIC) in that it requires the signal subspace containing the sources of interest to be isolated in the EEG measurement space. It is different from MUSIC in that it allows more general methods of spatio-temporal decomposition to be used that may be better suited to the background EEG. RESULTS If the EEG data matrix is not corrupted by noise, the STD approach can be used to locate multiple dipole sources of the EEG one at a time without a priori knowledge of the number of active sources in the signal space. In addition, the common-spatial-patterns method of spatio-temporal decomposition is superior to the eigenvector decomposition for localizing activity that is ictal in nature. CONCLUSIONS The STD approach appears to be able to provide a means of localizing the equivalent dipole sources of realistic brain sources and that, even under difficult noise conditions and only 2 or 3 s of available EEG, the precision of the localization can be as low as a few mm.

A source-imaging (low-resolution electromagnetic tomography) study of the EEGs from unmedicated males with depression

Imaging studies and quantitative EEG have often, but not consistently, implicated the right hemisphere and the left prefrontal cortex in depression. To help clarify this picture, a spatial filter shown to be effective for enhancing differences between EEG populations was combined with an electrical tomographic approach called low-resolution electromagnetic tomography and used to compare the source-current densities from a group of 25 male subjects with depression and a group of 65 matched controls. To elicit differences, comparisons were made during resting conditions and during verbal and spatial cognitive challenges to the subjects. Estimates of the source-current density were derived from 43-electrode recordings of the EEG reduced to the delta, alpha and beta frequency bands. The depressed subjects were unmedicated and selected according to DSM IV criteria. Regions of significantly increased current density in depression compared to controls were generally right hemispheric, while regions of significantly decreased current density were generally frontal and left hemispheric. A within-group comparison of the depressed subjects during the two cognitive challenges suggested a left anterior functional hypoactivation in depression. Retrospective classification of the two groups indicated that the spatial challenge best separated the groups irrespective of frequency band.

Principal-component localization of the sources of the background EEG

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 EEGs. 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.<<ETX>>

A computationally efficient method for accurately solving the EEG forward problem in a finely discretized head model

OBJECTIVE Solution of the forward problem using realistic head models is necessary for accurate EEG source analysis. Realistic models are usually derived from volumetric magnetic resonance images that provide a voxel resolution of about 1 mm3. Electrical models could, therefore contain, for a normal adult head, over 4 million elements. Solution of the forward problem using models of this magnitude has so far been impractical due to issues of computation time and memory. METHODS A preconditioner is proposed for the conjugate-gradient method that enables the forward problem to be solved using head models of this magnitude. It is applied to the system matrix constructed from the head anatomy using finite differences. The preconditioner is not computed explicitly and so is very efficient in terms of memory utilization. RESULTS Using a spherical head model discretized into over 4 million volumes, we have been able to obtain accurate forward solutions in about 60 min on a 1 GHz Pentium III. L2 accuracy of the solutions was better than 2%. CONCLUSIONS Accurate solution of the forward problem in EEG in a finely discretized head model is practical in terms of computation time and memory. SIGNIFICANCE The results represent an important step in head modeling for EEG source analysis.

Systematic comparisons of interpolation techniques in topographic brain mapping

The performance of one local interpolation technique, the nearest neighbors, and two global spline techniques, one planar and the other spherical, commonly used for topographic mapping of brain potential data has been quantitatively evaluated. The method of evaluation was one of cross-validation where the potential at each site in a 31-electrode full scalp recording montage is predicted by interpolation from the other sites. Errors between the measured potentials and those predicted by interpolation were quantified using 4 measures defined as inaccuracy, precision, bias and tolerance. The evaluation was applied to the background EEGs from 5 normal volunteers and from 4 patients with epilepsy, tumor or stroke. The results indicate that none of the interpolation techniques performed well and that for localized components in the EEG, the errors can increase almost without limit. Further, the global techniques performed significantly better than the local technique with 2 being the best order for the nearest-neighbor technique and 3 for the spline techniques. It is concluded that interpolation should not be used with electrode densities of the order of that provided by the international 10-20 system neither to increase the spatial resolution of the electroencephalogram nor in more sophisticated analysis techniques in quantitative EEG for estimates such as the radial-current density.

A High-Resolution Anisotropic Finite-Volume Head Model for EEG Source Analysis

Solution of the electroencephalogram (EEG) forward problem in a realistic head model is necessary for accurate source analysis. Realistic head models are usually derived from volumetric magnetic resonance images that provide a voxel resolution of about 1 mm3 . The availability of an electrical head model with this resolution would therefore be extremely advantageous. Head models with resolution in the millimeter range that incorporate the anisotropic properties of their elements have been formulated with the finite element method (FEM). However, these FEM models are fraught with complications related to irregular grids and meshes, along with the incumbent segmentation problems. Presented here is a finite volume method (FVM) formulation of the realistic head model in cubic elements that can ameliorate some of these problems, can incorporate tissue anisotropy, and is both physically intuitive and simple to implement

Low-resolution electrical tomography of the brain during psychometrically matched verbal and spatial cognitive tasks

EEGs were recorded from 75 normal, young, female subjects during psychometrically matched verbal (WF) and spatial (DL) cognitive tasks to elicit the differences in the electrical source distribution inside the brain. Recordings were obtained using 43 EEG and 3 guard electrodes then visually edited and spatially filtered to remove extracerebral artifacts. Twenty 1‐sec artifact‐free epochs were obtained and analyzed from 42 and 60 subjects during WF and DL respectively. Of these subjects, 20 were placed in a training set and the remainder into a test set. The baseline for the comparison of the two tasks was established by factoring the average cross‐spectral matrices of the training‐set EEGs, computed in the theta, alpha, and beta frequency bands into spatial patterns common to the two tasks. Only those spatial patterns that contributed to the correct classification of subjects in the test set were included in the source analysis. The source‐current density distributions were obtained using the LORETA‐KEY© algorithm. The results show that the source‐current density distribution is related to the putative functional activity in the brain in all three frequency bands. The electrical effects of the tasks are both most highly localized and lateralized in the theta band. The effects in the alpha and beta bands are much more generalized and are strongly lateralized only during one and the other of the tasks respectively. The conclusion is that WF is mainly a left central and bilateral frontal cerebral process while DL is mainly a right central and bilateral posterior cerebral process. Hum. Brain Mapping 12:144–156, 2001.

Gender Differences in Brain Functional Organization During Verbal and Spatial Cognitive Challenges

This is a quantitative EEG study of gender-related differences in brain function. It is novel in that to elicit gender differences, it was necessary to apply a spatial filter to the EEGs that was effective for suppressing components common to different cognitive states. The study involved estimates of both the source-current power density in the brain and the complex coherence between different regions in the brain, the latter probably unique in EEG source analysis. Gender effects are shown in terms of differences in both lateralized source power and complex coherence in response to verbal and spatial cognitive challenges. The results provide evidence that verbal and spatial challenges are more lateralized in males than in females, that females are more verbal than males, that males are more spatial than females, that females verbalize more interpretively than males and that males verbalize more consequentially than females.