Maximum Radius of an Explosively Growing Bubble in a Viscoelastic Medium Subjected to an Ultrasound Wave

The potential of cavitation damage can be harnessed to create local and precise destruction of biological tissues. Applications of this principle include histotripsy, in which cavitation bubbles are created thanks to focused megahertz and megapascal pressure pulses. Once created, these bubbles collapse inertially and induce stresses that mechanically homogenize tissue. When designing a histotripsy device, one important parameter to control is the size of the region targeted, which may be related to the maximum radius of a growing cavitation bubble in the specified medium. In this study, we wish to obtain a scaling law between the maximum radius of the bubble and other parameters of the problem. Previous studies have undertaken this task, but for a Newtonian liquid and with limited results. The novelty of our approach is the inclusion of an elastic term, representative of the medium viscoelastic behavior. To derive our scaling law, we rely on the Keller-Miksis equation, coupled with thermal equations inside and outside the bubble, and on energy budget analysis. We simplify our analysis by considering an idealized waveform for the pressure where the bell curve is replaced by a negative rectangular function. This is referred to as a negative-top hat pulse. Our results show that the elasticity of the medium reduces the maximum radius, as we could expect. Our scaling law agrees well with simulations. However, we observe some discrepancies as the elasticity increases, when considering realistic pressure pulses.