Coherent-Phase Analysis of Electroencephalograms Based on their Mathematical Modeling

Abstract

Abstract—The authors previously derived integral equations to describe ensemble-averaged membrane potentials of the brain, which are believed to simulate the total electrical activity of different areas of the brain, that is, of their electroencephalogram. Qualitative nonlinear analysis showed that in the region of stability of rhythms of electroencephalograms the characteristic equation contains a set of harmonic oscillations with negative decrements; its convolution with discrete (uniformly discontinuous) white Gaussian noise adequately models electroencephalograms. We previously proposed methods for computing the decrements of electroencephalograms using correlation functions and tested them on the models and real electroencephalograms of rats and mice. In this study, in order to understand the results of coherent phase analysis of electroencephalograms recorded in experiments on transgenic (the 5xFAD model of Alzheimer’s disease) and control mice, model signals with specified decrements and frequencies were used. It has been shown that it is necessary to use partially dependent Gaussian noise for the development of an adequate model of coherent phase relations in real electroencephalograms.