Journal
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
Volume 126, Issue 6, Pages 2963-2972Publisher
ACOUSTICAL SOC AMER AMER INST PHYSICS
DOI: 10.1121/1.3243292
Keywords
bioacoustics; biomechanics; biomedical ultrasonics; blood vessels; bubbles; elasticity; fluid oscillations; Navier-Stokes equations; surface acoustic waves
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Funding
- EPSRC [EP/E029310/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E029310/1] Funding Source: researchfish
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A theoretical model for the dynamics of a bubble in an elastic blood vessel is applied to study numerically the effect of confinement on the free oscillations of a bubble. The vessel wall deformations are described using a lumped-parameter membrane-type model, which is coupled to the Navier-Stokes equations for the fluid motion inside the vessel. It is shown that the bubble oscillations in a finite-length vessel are characterized by a spectrum of frequencies, with distinguishable high-frequency and low-frequency modes. The frequency of the high-frequency mode increases with the vessel elastic modulus and, for a thin-wall vessel, can be higher than the natural frequency of bubble oscillations in an unconfined liquid. In the limiting case of an infinitely stiff vessel wall, the frequency of the low-frequency mode approaches the well-known solution for a bubble confined in a rigid vessel. In order to interpret the results, a simple two-degree-of-freedom model is applied. The results suggest that in order to maximize deposition of acoustic energy, a bubble confined in a long elastic vessel has to be excited at frequencies higher than the natural frequency of the equivalent unconfined bubble.
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