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.

Frequency domain discriminant analysis of the electroencephalogram.

A frequency domain generalization of the classical quadratic discriminant function was applied to the problem of classifying alpha-band multichannel electroencephalogram recordings in three task conditions. The data consisted of 41-channel recordings obtained in eyes closed, verbal, and spatial task conditions. Classifier performance was measured by deriving a decision rule from a training sample of 42 recordings and then applying the obtained rule to a test sample of 46 recordings. The proportion of correct classification was .93 in the training sample and .85 in the test sample. The classifier performed better when based on the complete cross-spectral matrix than when restricted to power spectrum variables. Classification based on a subset of 16 leads reduced the overall proportion of correct classification to .79 in the training sample and to .70 in the test sample.

Spatio-temporal decomposition of the EEG: a general approach to the isolation and localization of sources.

The principal-component method of source localization for the background EEG is generalized to arbitrary spatio-temporal decompositions. It is shown that as long as the spatial patterns of the decomposition span the same signal space as the principal spatial components, the computational process of attempting to localize the sources is the same. Decompositions other than the principal components are shown to be superior for the EEG in that they appear to enable individual sources to be better isolated. An example is given using the common spatial pattern decomposition and using a raw varimax rotation of a subset of the common spatial patterns. The results show that the principal component decomposition is almost ineffective for isolating spike and sharp wave activity in an EEG from a patient with epilepsy, that the common spatial pattern decomposition is significantly better and that the varimax rotation is better yet. That the varimax rotation is best is demonstrated by attempting to locate dipole sources inside the brain which account for the spike and sharp wave activity on the scalp. The question which remains is whether there exists some oblique rotation of the basis vectors of the EEG signal space which is optimal for isolating individual sources.

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 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.

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.