Mathematical modeling of bioactive arterial wall

Solovyova, Helen; Kizilova, Natalya

doi:10.26565/2221-5646-2018-88-05

MAMM

2018

DOI: 10.26565/2221-5646-2018-88-05

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Mathematical modeling of bioactive arterial wall

Helen Solovyova¹,

Natalya Kizilova

Abstract: Biological tissues and their artificial substitutes are composed by different fibers and possess complex viscoelastic properties. Here the most popular 3-element and 5-element rheological models of human soft tissues as viscoelastic bodies are considered accounting for the time delay between the load and mechanical respond of the material.The obtained data compared to the experimental curves got on the vessel wall and heart tissues.

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2019

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

Solovjova

Kizilova

2019

BKNUPhM

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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.

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

Solovjova

Kizilova

2019

BKNUPhM

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Mathematical modeling of bioactive arterial wall

Cited by 1 publication

References 7 publications

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

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

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