The influence of metrics on the revealed structure of time delayes of signals in the evaluating brain electrogenesis

Abstract

The article proposes a new approach to studying the interaction of biomedical signals, in particular, electroencephalogram (EEG) data, by analyzing the structure of time delays of signal pairs relative to each other. An analysis of the literature has shown that most methods for evaluating signal interaction in EEG analysis are based on calculating the coherence function, which does not take into account signal time delays relative to each other. In view of this, it is proposed to consider a method for analyzing the structure of time delays of signal pairs using EEG data, consisting of the following stages: filtering signals in several overlapping frequency ranges; finding the sequence of time delays of a pair of signals; calculating the matrix of differences between the time delays sequences using the Euclidean distance, Manhattan distance and Chebyshev distance; estimating the distribution density for the distances between time delays sequences. The article presents a study of the properties of the proposed method on model signals based on functions with well-known properties, as well as the application of the method on real EEG data, which made it possible to identify and analyze delays in people’s reactions to photostimulation depending on different EEG leads. The results show that the difference in signal time delays between different EEG leads is absent in most cases, but for some people it is about 0.3 seconds. (when calculated using the Euclidean metric), which is a significant delay in photostimulation between different parts of the brain. At the same time, metrics other than Euclidean give a different estimate of the distances between time delays sequences, allowing you to get a more detailed, or, conversely, a more general picture. This method can be useful in brain mapping based on EEG data.