Ranjith S. Wijesinghe

A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging

Two different methods to improve the spatial resolution of EEG are discussed: the surface Laplacian (e.g., current source density) and cortical imaging (e.g., spatial deconvolution). The former methods tend to be independent of head volume conductor model, whereas the latter methods are more model-dependent. Computer simulation of scalp potentials due to either a few isolated sources or 4200 distributed cortical sources and studies of actual EEG data both indicate that the two methods provide similar estimates of cortical potential distribution. Typical correlation coefficients between either spline-Laplacian or cortical image and simulated (calculated) cortical potential are in the 0.8-0.95 range, depending partly on CSF thickness. By contrast, correlation coefficients between simulated scalp and cortical potential are in the 0.4-0.5 range, suggesting that high resolution methods provide much better estimates of cortical potential than is obtained with conventional EEG. The two methods are also applied to steady-state visually evoked potentials and spontaneous EEG. Correlation coefficients obtained from real EEG data are in the same general ranges as correlations obtained from simulations. The new high resolution methods can provide a dramatic increase in the information content of EEG and appear to have widespread application in both clinical and cognitive studies.

EEG coherency II: experimental comparisons of multiple measures.

OBJECTIVE A concentric spheres model was used in an earlier paper to estimate the effects of volume conduction, reference electrode and spatial filtering on different EEG coherence measures. EEG data are used here to verify theoretical predictions. METHODS Three EEG data sets were: (1) 64 channel, recorded during 7 alternating periods of resting and mental calculation. (2) 128 channel, for comparison of eyes open versus eyes closed coherence. (3) 128 channel, recorded during deep sleep (stages 3 and 4) and REM. RESULTS The directions of large scale (lobeal) coherency changes between brain states are relatively independent of coherence measure. However, coherence between specific electrode pairs is sensitive to method and frequency. Average reference and digitally linked mastoids provide reasonable semi-quantitative estimates of large-scale neocortical source coherence. Close bipolar, Laplacian, and dura image methods remove most reference electrode and volume conduction distortion, but may underestimate coherence by spatial filtering. CONCLUSION Each EEG coherence method has its own potential sources of error and provides coherence estimates for different neural population sizes located in different locations. Thus, studies of coherence and brain state should include several different kinds of estimates to take full advantage of information in recorded signals.

High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces

Spline generated surface Laplacians are introduced as an effective method for estimating neocortical source activity at moderate scales. The method appears to be robust to the unavoidable perturbations of measured potentials and errors of head geometry and resistivity that are certain to occur in clinical or research settings. In particular, the surface Laplacian is derived for general ellipsoidal surfaces in terms of the spline function. The spline-Laplacian accurately estimates isolated dipoles or distributed sources, is insensitive to subcortical sources and to sources which originate outside the boundaries of the electrode array, and acts as a bandpass spatial filter whose characteristics appear to provide a good match to the volume conduction of intracranial sources through human heads. As a result, spatial resolution is improved over that obtained with conventional EEG by at least a factor of three. This improvement is likely to have a significant impact on both medical and cognitive studies involving EEG.<<ETX>>

The activating function for magnetic stimulation derived from a three-dimensional volume conductor model

A three-dimensional volume conductor model of magnetic stimulation is proposed that relates transmembrane potential of an axon to the induced electric field in a uniform volume conductor. This model validates assumptions used previously to derive a one-dimensional cable model of magnetic stimulation (B.J. Roth and P.J. Basser, ibid., vol.37, p.588-97, 1990) of unmyelinated axons. The three-dimensional volume conductor model reduces to this one-dimensional cable equation forced by the activating function, - delta E/sub A//sup z// delta /sub z/.<<ETX>>

Comparison of high resolution EEG methods having different theoretical bases

SummaryMathematically simulated data is used to obtain direct comparisons of the accuracies of spline/Laplacian and cortical imaging algorithms in predicting cortical potential. Even though the two approaches have quite different theoretical bases, the two methods provide nearly identical estimates of cortical activity at scales greater than about 2 or 3 cm when 64 electrodes are used.

Magnetic stimulation of axons in a nerve bundle: effects of current redistribution in the bundle.

Recently, we developed a model of magnetic stimulation of a concentric axon in an anisotropic nerve bundle. In that earlier paper, we considered a single axon surrounded by a nerve bundle represented as a homogeneous anisotropic monodomain medium. In this paper we extend our previous calculations to examine excitation of axons within a nerve bundle without neglecting the presence of other axons in the nerve bundle. A three-dimensional axial symmetry volume conductor model is used to determine the transmembrane potential response along an axon due to induced electric fields produced by a toroidal coil. Our principal objective is to examine the effect of current redistribution to other axons in the bundle on excitation characteristics. We derive the transmembrane potential along an axon for two currently available models of current redistribution: the biodomain model and the spatial-frequency monodomain model. Results indicate that a reduction in the transmembrane potential along an axon due to the presence of other nerve fibers in the bundle is observed. Axons located at the periphery of a nerve bundle have lower thresholds and different excitation sites compared with axons located near the center of a nerve bundle.

A method to localize source activity in neocortex using measured scalp potential

Spline based surface Laplacians are used as an accurate method for estimating the source activities in the brain. The spline-Laplacian accurately estimates distributed sources and it is insensitive to subcortical sources including the sources which are located outside the boundaries of the electrode array which the author uses to record EEG. It also acts as a bandpass spatial filter improving the spatial resolution obtained by this method over that obtained with conventional EEG by at least a factor of three. The author outlines the surface Laplacian method for general ellipsoidal surfaces in terms of the spline function.<<ETX>>