Doctoral Thesis colloquium - Inverse Problems and Mathematical Imaging
Date: Monday, June 26, 2023
Time: 10:30 am, S2 416-1
Title: Time-Dependent Acoustic Waves Generated by Multiple Resonant Bubbles: Application to Acoustic
Cavitation
Abstract: 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. We showed that,in case of single bubble, the
dominant part of the acoustic pressure near it splits into two main echos. 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.
We also 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), 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 two bubbles which translates the fact the Dimers resonate (even if each bubble
don’t). This feature is shown also when we use a set of separated Dimers. Therefore, one can generate
desired amount of pressure by injecting such a set of Dimers.
2. If we distribute the bubbles every where in the region of interests, in a periodic way for instance, then
we can derive the effective acoustic model which turns out to be a dispersive one (due to the resonant
behavior of the bubbles). Therefore, the original question of generating desired acoustic pressure can
be related to the effective model. We show that, for a given desired pressure, we can tune the effective
model to generate it. This is possible at the expanse of a numerical differentiation.