Long-time temperature rise due to absorption of focused gaussian beams in tissue

An analytical technique previously developed to study tissue displacement due to acoustic radiation force is extended to analyze temperature rise in tissue for exposure times that are comparable to, or longer than, the tissue perfusion time. A focused transducer with Gaussian amplitude shading is assumed to radiate into a perfused tissue medium with constant thermal and acoustic properties. A simple closed-form expression is derived for the steady-state temperature rise, and a transient correction term is constructed that allows for computation of the equilibrium time of the medium. Comparisons with temperature calculations for non-Gaussian transducers show that the model may be applied to more general intensity profiles.