Modulational Instability and localized modes for ultrasound contrast microbubbles surface oscillations

Microbubble surface modes appear when contrast agents are insonified with specific ultrasound pulses. In this case, the radius becomes a space-dependent function which can be expanded on the basis of spherical harmonics describing the spatial vibrational modes of the bubble. The radial symmetry-breaking, which appears through a Modulational Instability (MI), is typical of many extended nonlinear systems subjected to an external driving. Here we present a mechanical analogue of bubble pulsations, consisting in a macroscopic ring of coupled oscillators driven by parametric forcing. Depending on the amplitude and the frequency of the driving, the mechanical ring presents a parametric instability leading to surface modes and localized modes oscillating at subharmonics of the parametric excitation. Bubbles are used as contrast agent in medical ultrasound imaging and to carry some drug to special locations. The perspective of this analysis is to define practical optimized ultrasound pulses exciting the bubble and leading to drug delivery applications.