Evoked responses: Electrogenesis, models, methodology, and wavefront reconstruction and tracking analysis

Abstract

This paper has two objectives. First, to present an overview of the electrophysiologial origins of brain waves, i.e, the evoked response (ER) and the electroencephalogram (EEG); to discuss models that have been used to reconstruct the ER and the EEG at the scalp; to describe the methodology of ER data acquisition; and to provide a few ER applications. This first section presents material which is generally common to the other ER papers in this special issue. The second objective is to illustrate how the spatio-temporal ER monitored by a multielectrode scalp array can be analyzed by the frequency-wavenumber (f - k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> ) spectrum analysis procedure to determine estimates of the velocity (direction and speed) of ER or EEG wavefronts propagating across the array. The problem of estimating the trajectories of multiple planewaves in a noisy environment is analyzed. First, the scalp electrode array is considered planar, a simplifying assumption. Estimates of the number of planewaves and their respective vector velocities are obtained from the f - k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> power spectral density. The tracking of specific wavefronts is performed by the application of f - k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">→</sup> digital filters. The three-dimensional fast Filtering transform (FFT) is used in both the spectral estimation and digital filtering procedures. The analysis techniques are evaluated on simulated data and then applied to actual ER data. Next the scalp electrode array is considered to be nonplanar, i.e., three-dimensional, a realistic description due to the curvature of the skull. ER wavefront velocity vectors are reconstructed from their projections onto the planes of the three-dimensional array. Among the unique specific results to be illustrated and discussed are the planar ER vector velocity trajectory patterns and the reconstruction of nonplanar (three-dimensional) ER velocity vectors for various situations, e.g, the presentation of visual stimuli to normal humans. Thus for the first time the vector velocity of the "traveling wave" across the array is estimated as well as the vector velocity component of the wave emanating from within the brain (or along the z-axis). Problems of spatial aliasing and data interpolation are discussed among others. The work is described within the context of the computational complexity required to obtain the results presented.