Coherent-Phase Analysis of the Electroencephalograms Based on Their Mathematical Modeling
In our previous studies, the integral equations have been developed to describe the features of the brain membrane potentials averaged for their ensembles that are thought to model summarized electrical activity of various brain areas - their electroencephalograms. Qualitative nonlinear analysis revealed that in the area of stability of electroencephalographic rhythms, the characteristic equation should include a set of oscillations with negative decrements, whose convolution with discrete (evenly discontinuous) white Gaussian noise adequately modeled the electroencephalograms. The methods of electroencephalogram decrements calculation through correlation functions were suggested earlier and tested on models and with the use of electroencephalography in rats and mice. In this study with the aim of understanding the results arising from the coherent-phase analysis of electroencephalograms, which were registered in experiments with transgenic (the 5xFAD model of Alzheimer's disease) and control mice, the model signals/electroencephalograms with adjusted decrements and frequencies were used. It is shown that for the development of an adequate model of coherent-phase relationships in real electroencephalograms, it is necessary to use partially dependent Gaussian noise.