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

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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.

About the authors

Anna Mikhailovna Vakhlaeva

Saratov State University

ul. Astrakhanskaya, 83, Saratov, 410012, Russia

Yuri Michailovich Ishbulatov

Saratov State University

ORCID iD: 0000-0003-2871-5465
Scopus Author ID: 57160264200
ResearcherId: I-1506-2016
ul. Astrakhanskaya, 83, Saratov, 410012, Russia

Anatolij Sergeevich Karavaev

Saratov State University; Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences; Saratov State Medical University named after V. I. Razumovsky

ORCID iD: 0000-0003-4678-3648
SPIN-code: 10808548
Scopus Author ID: 7003666161
ResearcherId: D-8137-2013
ul. Astrakhanskaya, 83, Saratov, 410012, Russia

Vladimir Ivanovich Ponomarenko

Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

ORCID iD: 0000-0002-1579-6465
Scopus Author ID: 35613865300
ResearcherId: H-2602-2012
ul. Zelyonaya, 38, Saratov, 410019, Russia

Mihail Dmitrievich Prokhorov

Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

ORCID iD: 0000-0003-4069-9410
ul. Zelyonaya, 38, Saratov, 410019, Russia

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