Scaling model for laser-produced bubbles in soft tissue

The generation of vapor-driven bubbles is common in many emerging laser-medical therapies involving soft tissues. To successfully apply such bubbles to processes such as tissue break-up and removal, it is critical to understand their physical characteristics. To complement previous experimental and computational studies, an analytic mathematical model for bubble creation and evolution is presented. In this model, the bubble is assumed to be spherically symmetric, and the laser pulse length is taken to be either very short or very long compared to the bubble expansion timescale. The model is based on the Rayleigh cavitation bubble model. In this description, the exterior medium is assumed to be an infinite incompressible fluid, while the bubble interior consists of a mixed liquid-gas medium which is initially heated by the laser. The heated interior provides the driving pressure which expands the bubble. The interior region is assumed to be adiabatic and is described by the standard water equation-of- state, available in either tabular, or analytic forms. Specifically, we use adiabats from the equation-of-state to describe the evolution of the interior pressure with bubble volume. Analytic scaling laws are presented for the maximum size and duration of bubbles as functions of the laser energy and initially heated volume.