Cookies on this website

We use cookies to ensure that we give you the best experience on our website. If you click 'Accept all cookies' we'll assume that you are happy to receive all cookies and you won't see this message again. If you click 'Reject all non-essential cookies' only necessary cookies providing core functionality such as security, network management, and accessibility will be enabled. Click 'Find out more' for information on how to change your cookie settings.

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.

Original publication




Journal article


J acoust soc am

Publication Date





2963 - 2972


Acoustics, Algorithms, Blood Vessels, Computer Simulation, Elasticity, Humans, Microbubbles, Models, Cardiovascular, Motion, Periodicity, Time Factors