Low-frequency axisymmetric waves in blood vessels of constant cross-section: an asymptotic approach |
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Authors: | M V Vilde Yu P Gulyaev |
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Affiliation: | 1.Chernyshevskii Saratov State University,Saratov,Russia |
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Abstract: | The asymptotic methods of shell theory are used to study the propagation of axisymmetric waves in blood vessels of constant
cross-section. The initial equations are simplified using the assumption that the shell radius is small compared with the
wave length. We show that the terms corresponding to the shell inertia cannot be omitted if it is required to describe not
only the pressure wave but also the longitudinal wave. We study the influence of external fixation on the pressure wave. In
this case, we compare the following two models: in the first model, the ambient medium is modelled by elastic and damping
elements uniformly distributed over the shell exterior surface and by additional masses; in the second model, the ambient
medium is represented by an infinite elastic space with a cylindrical cavity where the vessel is placed. On the interface
between the elastic space and the vessel, we pose the full contact conditions. We show that, from the qualitative standpoint,
both models lead to the same result: the pressure wave in the first approximation is a wave in the shell whose walls cannot
move in the longitudinal direction. We asymptotically integrate the original equations and hence obtain a one-dimensional
equation for the bulk blood flow. |
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