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