Model of blood flow along the arterial bed, taking into account the bioactivity of the vessel wall

O. M. Solovjova; N. M. Kizilova

doi:10.17721/1812-5409.2019/2.11

Authors

O. M. Solovjova Kharkiv National Polytechnical University («KhPI»), 61002, Kharkov, Kirpichova st., 2
N. M. Kizilova V.N. Karazin Kharkov National University, 61022, Kharkov, Svobody sq., 4 https://orcid.org/0000-0001-9981-7616

DOI:

https://doi.org/10.17721/1812-5409.2019/2.11

Abstract

The modification of a two-dimensional model of incompressible viscous fluid motion along a deformed thick-walled tube from viscoelastic bioactive material is proposed in connection to the modeling of blood flow along the arterial bed is proposed. The motion of a viscous incompressible fluid is described by a system of equations including the Navier-Stokes equations and the continuity equation. The behavior of the tube wall material is described by a 5-element rheological model with one active element. The solution of the problem is solved setting boundary conditions on the interface of the two media, the outer surface of the tube is considered as non-moving. At the end of the tube, a zero-dimensional Frank model with regulation is considered, as a model of the microcirculatory bed. The dispersion equation for the propagation of wave velocity is obtained for the case of active properties of tube, the amplitudes of fluid velocities, wall displacements, and fluid and tube pressures. Numerical computations have been carried out for the model parameters corresponded to the normal and pathological arterial wall.

Key words: the model of arterial bed, pulse waves, wave dispersion, active material.

Pages of the article in the issue: 88 - 92

Language of the article: Ukrainian

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