Time-dependent acoustic waves generated by multiple resonant bubbles: application to acoustic cavitation

We analyse the ultrasound waves reflected by multiple bubbles in the linearized time-dependent acoustic model. The generated time-dependent wave field is estimated close to the bubbles. The motivation of this study comes from the therapy modality using acoustic cavitation generated by injected bubbles into the region of interest. The goal is to create enough, but not too much, pressure in the region of interest to eradicate anomalies in that region. In a previous work, we already showed that, in case of single bubble, the dominant part of the acoustic pressure near it splits into two main echoes. The primary one is the incident field shifted and amplified at certain order. The secondary one is of periodic form which is related to the resonant frequency (i.e. the Minnaert one) created by the single bubble. This secondary wave can be amplified at will, at certain specific times, by tuning properly the material characteristics of the used bubble. Here, we derive the dominant part of the generated acoustic field by a cluster of bubbles taking into account the (high) contrasts of their mass density and bulk as well as their general distribution in the given region. As consequences of these approximations, we highlight the following features: 1.

If we use dimers (two close bubbles), or generally polymers, then both the primary and the secondary waves can be amplified resulting in a remarkable enhancement of the whole echo in the whole time. The main reason for that is the closeness of the bubbles which translates the fact that the polymers resonate (even if each bubble do not). This feature is shown also when we use a set of separated polymers. Therefore, one can generate desired amount of pressure by injecting such a set of polymers.