A numerical model for large-amplitude spherical bubble dynamics in tissue

Abstract

In a variety of therapeutic and diagnostic ultrasound procedures (e.g., histotripsy, lithotripsy, and contrast-enhanced ultrasound), cavitation occurs in soft tissue, which behaves in a viscoelastic fashion. While stable bubble oscillations may occur in ultrasound, the most dramatic outcomes (tissue ablation, bleeding, etc.) are usually produced by inertial cavitation. Historically, Rayleigh-Plesset equations have been used to investigate the dynamics of spherical bubbles, including in biomedical applications. For large-amplitude bubble oscillations in tissue, it is clear that compressibility, heat transfer and nonlinear viscoelasticity play important roles. However, no existing model includes all of these effects. To address this need, we use a compressible Rayleigh-Plesset equation (Keller-Miksis) adjoined with heat conduction in conjunction with an upper-convected Zener viscoelastic model, which accounts for relaxation, elasticity, and viscosity. The partial differential equations describing the stress tensor components in the surrounding medium are solved using a spectral collocation method. The method proves to be robust even for strong bubble collapse. Numerical comparisons with previous models are made, comparisons to experiments are included, and the dependence of bubble dynamics on viscoelastic parameters is explored. This model is used to revisit the inertial cavitation threshold in biomedical settings.