Acoustic scattering from a contrast agent microbubble near an elastic wall of finite thickness.

Interest in the problem under consideration in this study is motivated by targeted ultrasound imaging where one has to deal with microbubble contrast agents pulsating near blood vessel walls. A modified Rayleigh–Plesset equation is derived that describes the oscillation of a contrast agent microbubble near an elastic wall of finite thickness. It is assumed that the medium behind the wall is a fluid but it is shown that the equation obtained is easily transformable to the case that the medium behind the wall is an elastic solid. In contrast to the model of a rigid wall, which predicts decreasing natural frequency of a bubble near the wall, the elastic wall model reveals that the bubble natural frequency can both decrease and increase, and in cases of interest for medical applications, the bubble natural frequency usually increases. It is found that the influence of an elastic wall on the acoustic response of a bubble is determined by the ratio between a cumulative parameter, which integrally characterizes the mechanical properties of the wall and has the dimension of density, and the density of the liquid surrounding the bubble. It is shown that the acoustic influence of the arterial wall on the bubble is weak and apparently cannot be used to recognize the moment when the bubble approaches the wall. However, in experiments where the behavior of bubbles near various plastic walls is observed, changes in the bubble response, such as increasing natural frequency and decreasing oscillation amplitude, are detectable.