Structure Differences of Topographical EEG Mappings

Abstract

In recent years great efforts have been undertaken to compute two-dimensional mappings from EEG recordings. The algorithms have been taken from applied theory of stochastic processes or from electrodynamics. Regarding the first method, namely the computation of the second-order moments, the correlation function, or its integral transform the power spectra, are extended to vector-valued processes, including some additional features like cross-correlation, cross-spectra or coherency. It must be noted, however, that due to the registration procedure the signals are taken as potential differences between a local electrode and a reference point, including their statistical inferences. In such cases the correlation functions or their equivalent transforms are meaningless and therefore produce erroneous and misleading results. Methods based on electrodynamics, on the other hand, compute mappings by relaxation methods. The raw material is obtained by digital fourier transform (DFT) and means, physically, power. The mathematical background to this computation is Laplace’s equation, which is not valid in the case of charges existing in the region of interest. A comprehensive study including various techniques based on the above principles was reported by Duffy (1986).