ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Borovkova E. I., Ishbulatov Y. М., Hramkov A. Н., Karavaev A. S. Using a mathematical model of cardiovascular system for preparing surrogate data for testing methods of phase synchronization analysis. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 3, pp. 356-364. DOI: 10.18500/0869-6632-2021-29-3-356-364

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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English
Article type: 
Article
UDC: 
530.182, 004.942

Using a mathematical model of cardiovascular system for preparing surrogate data for testing methods of phase synchronization analysis

Autors: 
Borovkova Ekaterina Igorevna, Saratov State University
Ishbulatov Yuri Максимович, Saratov State University
Hramkov Alexey Николаевич, Saratov State University
Karavaev Anatolij Sergeevich, Saratov State University
Abstract: 

The aim of present research is refinement of the parameters and statistical properties of methods for diagnosing
phase synchronization areas based on the dependence of the instantaneous phase difference of oscillations on time.
Methods. Two methods are compared that allow one to identify of synchronization modes based on the dependence of
the instantaneous phase difference of oscillations on time: a method based on an estimate of the phase coherence coefficient
and a method based on a linear approximation of the instantaneous phase difference in a sliding window and an estimate of the
slope of the approximating straight line. The phase synchronization of the low-frequency (0.04–0.15 Hz) components of the
time series of interbeat intervals and blood pressure is analyzed. A mathematical model of the cardiovascular system is used to
generate an ensemble of test data when analyzing the statistical properties of methods of phase synchronization analysis and
refining their parameters. Test data is generated by modulating the coupling parameters between the autonomic control loops
of blood circulation in the model, providing the known presence and absence of synchronization modes. Results. During the
analysis of the model data, the values of the method parameters were refined. The sensitivity and specificity of the methods
were evaluated. A higher sensitivity of the previously proposed method for detecting phase synchronization intervals in the
analysis of non-stationary time series of the cardiovascular system is shown. Conclusion. In the analysis of non-stationary time
series of the cardiovascular system shown the higher sensitivity of the method for detecting phase synchronization intervals,
what based on a piecewise linear approximation of the instantaneous phase difference in a sliding window and an estimate of
the slope of the approximating straight line.

Acknowledgments: 
This work was supported by Russian Foundation for Basic Research, grant No. 20-02-00702 and grant No. 19-32-90206
Reference: 
  1. Karavaev AS, Prokhorov MD, Ponomarenko VI, Kiselev AR, Gridnev VI, Ruban EI, Bezruchko BP. Synchronization of low-frequency oscillations in the human cardiovascular system. Chaos 2009;19(3):033112. DOI: 10.1063/1.3187794.
Received: 
01.11.2020
Accepted: 
23.12.2020
Published: 
31.05.2021