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Determination of the Mass-Flow Rate of Blood in a Blood Vessel Using Natural Frequencies of Flexural Vibrations

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Abstract

The natural flexural vibrations of a blood vessel with moving blood are investigated. The vessel is subjected to the action of tensile force and pressure in it. The forces of inertia of the blood vessel, as well as the Coriolis and centrifugal forces induced by the motion of blood, are taken into account. The wave numbers are determined, and the frequency equation is found using the boundary conditions. Two frequencies of flexural vibrations can determine the speed parameter, the relative mass of blood per unit length of the blood vessel, and, as a consequence, the mass-flow rate of blood through the blood vessel. The results obtained can be used for the acoustic method of determining the blood speed, the relative blood mass per unit length of the blood vessel, and the mass-flow rate of blood through it.

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Funding

This work was supported by a State Assignment for 2019–2022, project no. 0246-2019-0088.

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Authors and Affiliations

  1. Bashkir State Medical University, 450008, Ufa, Bashkortostan, Russia

    V. M. Timerbulatov & Sh. V. Timerbulatov

  2. Institute of Mechanics, Russian Academy of Sciences, 450054, Ufa, Bashkortostan, Russia

    A. G. Khakimov

Authors
  1. V. M. Timerbulatov
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  2. Sh. V. Timerbulatov
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  3. A. G. Khakimov
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Corresponding authors

Correspondence to V. M. Timerbulatov, Sh. V. Timerbulatov or A. G. Khakimov.

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Translated by V. Bukhanov

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Timerbulatov, V.M., Timerbulatov, S.V. & Khakimov, A.G. Determination of the Mass-Flow Rate of Blood in a Blood Vessel Using Natural Frequencies of Flexural Vibrations. Dokl. Phys. 65, 190–193 (2020). https://doi.org/10.1134/S1028335820050110

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  • DOI: https://doi.org/10.1134/S1028335820050110

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