The natural frequencies of microbubble oscillation in elastic vessels

Abstract

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.

Model for bubble pulsation in liquid between parallel viscoelastic layers

“…12,13,15,[18][19][20]22,35 Although less open to simple physical interpretation, the flexibility of the fully numerical models permits effects due to nonlinear pulsation, bubble jetting and translation, and viscoelastic properties of the surrounding media to be considered. The displacement, strain, and stress fields within the confining media may also be modeled, thus predicting tissue damage resulting from cavitation activity.…”

Interaction between microbubble and elastic microvessel in low frequency ultrasound field using finite element method

“…However, the oscillation frequency response for bubble in elastic vessel seems different from that in rigid vessel. The natural frequency for bubble in elastic vessels has found to be characterized by multi-frequency mode [10]. Thus the oscillation frequency response for bubble in elastic vessel needs to be further explored in future study.…”

“…The numerical results predicted that the circumferential stress in the microvessel wall exceeded the vascular strength under the ultrasonic field with peak negative pressure of 0.5 MPa and center frequency of 1 MHz. The bubble oscillations in a finite length vessel are characterized by high-frequency and low-frequency modes [10]. However, in these two studies the vessel wall compliance was approximated by a nonlinear boundary condition related to intraluminal pressure and the expansion ratio of the vessel radius.…”

Ultrasound contrast agents : dynamics of coated bubbles

“…Recent numerical work is performed on the interaction of uncoated bubbles with elastic boundaries using the boundary element method (BEM) [114] and finite element method (FEM) [115]. Hay et al [116] account for a bubble between two compliant walls with a model similar to the "method of images", where the complex source strength of the image bubble depends on the acoustic wall properties and the thickness of the wall.…”