A numerical investigation into the effects of increasing pressure amplitude on microbubble resonance frequency

The analysis of the dynamical response of gas filled cavities surrounded by elastic capsules, acting as contrast agent microbubbles, is of importance in elucidating their full diagnostic use for ultrasound imaging. When the frequency of the external acoustic field is at or near the natural frequency of the bubble, resulting in resonance, larger amplitudes of oscillation than would otherwise occur are observed, enhancing the backscattered signal. It is therefore important to medical ultrasound imaging to be able to accurately determine the complex resonant behaviour of the bubble motion. In our work we consider the general Keller-Herring (K-H) model of Prosperetti and Lezzi. Appropriate variations in the cavity diameter, frequency and amplitude of the insonating field show computer-based simulations of microbubble response can be employed to determine resonance frequencies that are directly influenced by the driving pressure amplitude. The implication is therefore that the linear approximation to microbubble resonance is not applicable when considering insonating fields whose amplitudes exceed specific values which can be determined. A natural extension of the single bubble model is the investigation of interacting bubbles. It is shown that both pressure amplitude and the distance between bubble centres influence resonance frequency. A numerical investigation of the bifurcation properties of the K-H model is carried out: the driving frequency threshold for the onset of chaos decreases in the presence of an interacting microbubble or as the bubbles approach each other.