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The natural frequencies of microbubble oscillation in elastic vessels
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10.1121/1.3243292
/content/asa/journal/jasa/126/6/10.1121/1.3243292
http://aip.metastore.ingenta.com/content/asa/journal/jasa/126/6/10.1121/1.3243292
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Geometry and dimensions of a bubble located in the middle of a cylindrical blood vessel. are the global coordinates, and are the local coordinates on the bubble surface.

Image of FIG. 2.
FIG. 2.

A spring-mass system for analysis of the bubble oscillations in an elastic vessel. The axis is arranged in such a way that its direction coincides with the direction of the axis and is opposite to the direction of the axis in Fig. 1.

Image of FIG. 3.
FIG. 3.

(a) The effect of vessel length and wall stiffness on the volumetric oscillations of a bubble. [(b) and (c)] The radial displacements of the vessel wall and the radial and axial deformations of the bubble (, , and ).

Image of FIG. 4.
FIG. 4.

The effect of the vessel wall stiffness on the spectrum for the radial oscillations of a bubble of equilibrium radius in a vessel with , , and . Solid curve, ; dotted curve, .

Image of FIG. 5.
FIG. 5.

The effect of the vessel wall elastic modulus, thickness of the embedding tissue, and vessel length on the natural frequency of the modes of bubble oscillation (, , and ).

Image of FIG. 6.
FIG. 6.

The effect of the vessel radius and elastic modulus on the natural high-frequency mode of bubble oscillations in a long vessel (, , and ). Comparison of the results of computations using the FEM and 1D models, and the results from Fig. 5 in the paper by Qin and Ferrara (2007).

Image of FIG. 7.
FIG. 7.

The effect of the vessel wall elastic modulus on the natural frequency of the modes of bubble oscillation (, , , and ).

Image of FIG. 8.
FIG. 8.

Radius vs. time curves for free oscillations of a spherical microbubble of equilibrium radius based on the solution using the FEM model (points) and the Rayleigh–Plesset equation (A1) (solid line).

Image of FIG. 9.
FIG. 9.

The effect of vessel length on the natural frequency of a bubble confined in a rigid vessel. Comparison of the frequency obtained from the finite element solution (points) and the theory by Oguz and Prosperetti (1998) (solid line).

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/content/asa/journal/jasa/126/6/10.1121/1.3243292
2009-12-14
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The natural frequencies of microbubble oscillation in elastic vessels
http://aip.metastore.ingenta.com/content/asa/journal/jasa/126/6/10.1121/1.3243292
10.1121/1.3243292
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