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

For citation:

Vakhlaeva A. ., Ishbulatov Y. M., Karavaev A. S., Ponomarenko V. I., Prokhorov M. D. Mathematical model of the photoplethysmogram for testing methods of biological signals analysis. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 5, pp. 586-596. DOI: 10.18500/0869-6632-003059, EDN: WGKVOM

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003059
EDN: 
WGKVOM

Mathematical model of the photoplethysmogram for testing methods of biological signals analysis

Autors: 
Vakhlaeva Anna Mikhailovna, Saratov State University
Ishbulatov Yurii Michailovich, Saratov State University
Karavaev Anatolij Sergeevich, Saratov State University
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

The purpose of this study was to develop a mathematical model of the photoplethysmogram, which can be used to test methods that introduce the instantaneous phases of the modulating signals. The model must reproduce statistical and spectral characteristics of the real photoplethysmogram, and explicitly incorporate the instantaneous phases of the modulating signals, so they can be used as a reference during testing.

Methods. Anacrotic and catacrotic phases of the photoplethysmogram pulse wave were modeled as a sum of two density distributions for the skew normal distribution. The modulating signals were introduced as harmonic functions taken from the experimental instantaneous phases of the VLF (0.015...0.04 Hz), LF (0.04...0.15 Hz) and HF (0.15...0.4 Hz) oscillations in the real photoplethysmogram. The spectral power in the VLF, LF, and HF frequency ranges was calculated to compare the model and experimental data.

Results. The model qualitatively reproduces the shape of the experimental photoplethysmogram pulse wave and shows less than 1% error when simulating the spectral properties of the signal.

Conclusion. The proposed mathematical model can be used to test the methods for introduction of the instantaneous phases of the modulating signals in photoplethysmogram time-series.

Key words: 
mathematical modeling
photoplethysmogram
phase analysis
spectral analysis
synchronization
directional coupling
Acknowledgments: 
The work was carried out within the framework of the state task of the Saratov Branch of the Institute of Radioengineering and Electronics of Russian Academy of Sciences
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Received: 
15.05.2023
Accepted: 
22.06.2023
Available online: 
19.09.2023
Published: 
29.09.2023
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