Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Borovkova E. I., Vasilieva D. V., Karavaev A. S., Ishbulatov Y. M., Ponomarenko V. I., Bezruchko B. P., Prokhorov M. D. Estimation of the stationarity time of infra-slow oscillations of brain potentials using electroencephalogram signals. Izvestiya of Saratov University. Physics , 2025, vol. 25, iss. 4, pp. 474-484. DOI: 10.18500/1817-3020-2025-25-4-474-484, EDN: WXKHKE

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.11.2025
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Language: 
Russian
Heading: 
Biophysics and medical physics
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/1817-3020-2025-25-4-474-484
EDN: 
WXKHKE

Estimation of the stationarity time of infra-slow oscillations of brain potentials using electroencephalogram signals

Autors: 
Borovkova Ekaterina Igorevna, Saratov State University
Vasilieva Dariya V., Saratov State University
Karavaev Anatoly Sergeevich, Saratov State University
Ishbulatov Yuri Mikhailovich, Saratov State University
Ponomarenko Vladimir Ivanovich, Saratov State University
Bezruchko Boris Petrovich, Saratov State University
Prokhorov Mikhail Dmitrievich, Saratov State University
Abstract: 

Background and Objectives: Infra-slow oscillations of brain potentials with a frequency of less than 0.5 Hz, reflect the activity of the autonomic regulation centers and are markers of the psychophysiological state of a person. Such oscillations are characterized by non-stationary dynamics, which complicates their experimental study. Materials and Methods: We have proposed a method for estimating the characteristic time of stationarity of infra-slow oscillations of brain potentials based on the analysis of experimental time series of electroencephalograms. The method includes the stages of dividing the time series into segments, constructing approximating polynomials for each segment, calculating the matrix of Euclidean distances between the coefficients of the polynomials, clustering the segments to determine areas of quasi-stationary dynamics, and analyzing the durations of the combined segments to obtain statistical characteristics. The proposed method can be used to estimate the stationarity time of other electroencephalograms rhythms, as well as the frequency components of the sequence of RR-interval. The method was used to analyze electroencephalograms signals and RR-intervals of 50 healthy volunteers at rest. Results: It has been shown that oscillations in different frequency ranges of the studied signals have different durations of quasi-stationary behavior. In the frequency ranges of 0.05–0.15 Hz and 0.15–0.50 Hz, reflecting the activity of the sympathetic and parasympathetic branches of regulation, respectively, the stationarity time of infra-slow oscillations in electroencephalograms signals was 30 s and 36 s, respectively. Conclusion: The durations of quasi-stationary sections of infra-slow oscillations in electroencephalograms correspond well to the durations of sections of quasi-stationary dynamics of the sequence of RR-interval in the frequency ranges associated with the processes of sympathetic and parasympathetic regulation of the heart rhythm. 

Key words: 
time series
non-stationarity
electroencephalograms
RR-intervals
autonomic regulation
infra-slow oscillations of brain potentials
Acknowledgments: 
The work was carried out within the framework of the State assignment of the Saratov Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences (project No. FFWZ-2025-0016).
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Received: 
01.07.2025
Accepted: 
10.09.2025
Published: 
28.11.2025
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