Izvestiya of Saratov University.

Physics

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

For citation:

Sagaidachnyi A. A., Volkov I. Y., Zaletov I. S., Mayskov D. I., Fomin A. V., Antonov A. V., Tsoy M. O., Skripal A. V. Restoration of microhemodynamics on the human body surface using the fractional derivative of temperature oscillations. Izvestiya of Saratov University. Physics , 2025, vol. 25, iss. 3, pp. 316-332. DOI: 10.18500/1817-3020-2025-25-3-316-332, EDN: MDMFNR

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
29.08.2025
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Language: 
Russian
Heading: 
Biophysics and medical physics
Article type: 
Article
UDC: 
57.087.3:612.1
DOI: 
10.18500/1817-3020-2025-25-3-316-332
EDN: 
MDMFNR

Restoration of microhemodynamics on the human body surface using the fractional derivative of temperature oscillations

Autors: 
Sagaidachnyi Andrey Aleksandrovich, Saratov State University
Volkov Ivan Yu., Saratov State University
Zaletov Ivan Sergeevich, Saratov State University
Mayskov Dmitriy Igorevich, Saratov State University
Fomin Andrey Vladimirovich, Saratov State University
Antonov Andrey V., Saratov State University
Tsoy Mariya Olegovna, Saratov State University
Skripal Anatoliy Vladimirovich, Saratov State University
Abstract: 

Background and Objectives: The possibility of restoring microhemodynamics on the human body surface was investigated through the analysis of skin temperature oscillation signals using integer and fractional order derivatives. Materials and Methods: Microhemodynamic data were simultaneously recorded via photoplethysmographic imaging and infrared thermography in four regions of the hand. To reconstruct microhemodynamics from temperature data, a previously described thermal wave model, along with integer and fractional order derivatives, were applied. A comparative analysis of the amplitude-frequency and phase-frequency characteristics of these transformations was conducted. The fractional-order derivative of temperature oscillations was calculated as the Riemann – Liouville differintegral. For a group of subjects, correlations were computed between the reconstructed microhemodynamic results during a 15-minute resting state using the thermal wave model and the integer/fractional-order derivatives of temperature. Results: It has been established that employing a fractional-order derivative of order 0.4 has yielded the best correlation between the frequency characteristics and those of the thermal wave model. The enhanced temporal-domain signal correlation achieved with the fractional-order derivative, compared to the integer-order derivative, is attributed to more accurate amplitude-frequency and phase-frequency transformations of temperature oscillations. These transformations align with the attenuation and dispersion processes of thermal waves in the skin. Conclusions: For precise restoration of microhemodynamics using skin temperature time derivatives, a the fractional-order derivative of 0.4 is preferable over integer-order derivatives. The described method can serve as a thermalbased technique for investigating blood flow oscillations in microvessels across multiple anatomical regions simultaneously.

Key words: 
photoplethysmographic imaging
photoplethysmography
thermography
heat wave model
microhemodynamics
hemodynamics
derivative
fractional derivative
differintegral
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Received: 
13.03.2025
Accepted: 
15.05.2025
Published: 
29.08.2025
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