Ultrasonically induced dynamics of a contrast agent microbubble between two parallel elastic walls

This work presents the derivation of a Rayleigh-Plesset-like equation that describes the radial oscillation of a contrast agent microbubble between two elastic walls, assuming that the bubble is attached to one of them. The obtained equation is then used in numerical simulations in order to establish how the presence of the second wall affects the resonance properties and the scattered echo of the contrast microbubble. The effect of encapsulation on the dynamics of the microbubble is simulated by the Marmottant shell model which is commonly used for the modeling of the dynamics of lipid-shelled contrast agents. Two cases are examined. In the first, the mechanical properties of the walls are set to correspond to OptiCell chambers which are widely used in experiments on microbubble contrast agents. In the second, the properties of the walls correspond to walls of blood vessels. It is shown that the presence of the second wall increases the resonance frequency of the contrast microbubble and decreases the amplitudes of the radial oscillation and the scattered echo of the microbubble as compared to the case that the second wall is absent. It is also shown that the presence of the second wall can change noticeably the intensity of the second harmonic in the spectrum of the scattered pressure. It is demonstrated that, depending on the value of the driving frequency, the presence of the second wall can either increase or decrease the intensity of the second harmonic as compared to its intensity in the case that the second wall is absent.