Nonlinear modeling of therapeutic ultrasound

The authors describe experimental finite element modeling of tissue ablation by focused ultrasound. Emphasis is on nonlinear coupling of high intensity sound temperature, and tissue properties. The numerical basis for modeling nonlinearity is an incrementally linear, time-domain, finite element algorithm solving the electromechanical and bioheat equations in 2D/3D inhomogeneous elastic and acoustic media. Nonstandard modeling issues examined include harmonic generation/absorption and focal “bubble” evolution with consistent sound and thermal redistribution. The nonlinear pressure-density relation generates harmonics that increase absorption and heating, particularly in the focal zone. In the tissues modeled, harmonic heating is negligible for peak focal intensities of a few kW/cm ². As the focal hot spot ablates tissue it may also generate “bubbles”. Prefocal growth of a bubbly region is modeled using a simple boiling threshold and strong coupling between the scattered ultrasound and temperature redistribution as the region spreads. Generally, these experiments are intended to develop a more comprehensive modeling basis for quantifying tissue ablation phenomenology