Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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Mayskov D. I., Sagaidachnyi A. A., Matasov M. D., Fomin A. V., Skripal A. V. Influence of the modulation of the blood flow velocity in peripheral vessels on the temperature of the outer wall of the vessel: Finite element modeling of the adjoint problem. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 3, pp. 332-345. DOI: 10.18500/1816-9791-2022-22-3-332-345, EDN: YEFZXJ

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Influence of the modulation of the blood flow velocity in peripheral vessels on the temperature of the outer wall of the vessel: Finite element modeling of the adjoint problem

Mayskov Dmitry Igorevich, Saratov State University
Sagaidachnyi Andrey A., Saratov State University
Matasov Maksim D., Keldysh Research Center
Fomin Andrey V., Saratov State University
Skripal Anatoly Vladimirovich, Saratov State University
A finite element modelling of the process of the heat transfer from blood to the wall of an arterial vessel was carried out in order to solve a more general problem of determining the relationship between the amplitude-frequency characteristics of fluctuations in the volumetric blood flow velocity in peripheral vessels with temperature oscillations on the skin surface. A model was built in the ANSYS software with Fluid Flow CFX module which includes domains related to blood, the wall of a cylindrical vessel, and skin (bio-tissue). The model takes into account the convective heat transfer from blood to the vessel wall and thermal conductivity in the skin. The corresponding boundary value problem is posed which includes the Navier – Stokes equation and the Fourier heat equation. Dependences of the temperature oscillations of the vessel wall on the amplitude of fluctuations in the volumetric blood flow velocity in a wide frequency range of 0.01–1 Hz were obtained. The selected frequency range covers all currently known rhythms of hemodynamic fluctuations: endothelial, neurogenic, myogenic, respiratory and cardiac. A function is proposed that approximates the dependence of the amplitude of vessel wall temperature oscillations on the amplitude of the oscillations of the volumetric blood flow at various values of the blood flow velocity modulation frequency. The use of the introduced approximating function together with the solution of the heat equation for a thermal wave opens up the possibility of solving the inverse problem of determining the dynamics of volumetric blood flow in an arterial vessel based on the data on the temperature dynamics on the skin surface.
The study was supported by the Russian Science Foundation (project No. 21-75-00035).
  1. Stefanovska A. Physics of the human cardiovascular system. Contemporary Physics, 1999, vol. 40, iss. 1, pp. 31–55. https://doi.org/10.1080/001075199181693
  2. Sagaidachnyi A. A., Volkov I. Yu., Fomin A. V., Skripal A. V. Investigation of thermal wave propagation within the model of biological tissue and the possibility of thermal imaging of vasomotor activity of peripheral vessels. Russian Journal of Biomechanics, 2019, vol. 23, iss. 2, pp. 209–217. https://doi.org/10.15593/RJBiomech/2019.2.07, EDN: XTKRTK
  3. Liu J., Xu L. X. Estimation of blood perfusion using phase shift in temperature response to sinusoidal heating at the skin surface. IEEE Transactions on Biomedical Engineering, 1999, vol. 46, iss. 9, pp. 1037–1043. https://doi.org/10.1109/10.784134
  4. Zhang X., Zheng L., Liu L., Zhang X. Modeling and simulation on heat transfer in blood vessels subject to a transient laser irradiation. Journal of Heat Transfer, 2020, vol. 142, iss. 3, Art. 031201. https://doi.org/10.1115/1.4045669
  5. Deng Z. S., Liu J. Blood perfusion-based model for characterizing the temperature fluctuation in living tissues. Physica A: Statistical Mechanics and its Applications, 2001, vol. 300, iss. 3–4, pp. 521–530. https://doi.org/10.1016/S0378-4371(01)00373-9
  6. Tang Y., Mizeva I., He Y. A modeling study on the influence of blood flow regulation on skin temperature pulsations. Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III. Saratov, 2017, vol. 1033716 (14 April 2017). https://doi.org/10.1117/12.2267952
  7. Luchakov Y. I., Nozdrachev A. D. Mechanism of heat transfer in different regions of human body. Biology Bulletin, 2009, vol. 36, iss. 1, pp 53–57. https://doi.org/10.1134/S1062359009010087
  8. Ivanov D., Dol A., Polienko A. Patient-specific hemodynamics and stress-strain state of cerebral aneurysms. Acta of Bioengineering and Biomechanics, 2016, vol. 18, iss. 2, pp. 9–17. https://doi.org/10.5277/ABB-00373-2015-03
  9. Ivanov D. V., Dol A. V., Kuzyk Yu. I. Biomechanical bases of forecasting occurrence of carotid atherosclerosis. Russian Journal of Biomechanics, 2017, vol. 21, iss. 1, pp. 29–40 (in Russian). https://doi.org/10.15593/RZhBiomeh/2017.1.03
  10. Hristov J. Bio-heat models revisited: concepts, derivations, nondimensalization and fractionalization approaches. Frontiers in Physics, 2019, vol. 9, Art. 189. https://doi.org/10.3389/fphy.2019.00189
  11. Porret C. A., Stergiopulos N., Hayoz D., Brunner H. R., Meister J. J. Simultaneous ipsilateral and contralateral measurements of vasomotion in conduit arteries of human upper limbs. American Journal of Physiology-Heart and Circulatory Physiology, 1995, vol. 269, iss. 6, pp. H1852–H1858. https://doi.org/10.1152/ajpheart.1995.269.6.H1852
  12. Sagaidachnyi A. A, Fomin A. V., Volkov I. Yu. Limit capabilities of modern thermal imaging cameras as a tool for investigation of peripheral blood flow oscillations within different frequency ranges. Meditsinskaya fizika [Medical Physics], 2016, no. 4 (72), pp. 84–93 (in Russian). EDN: XCFWYD