Parabolic models and computational approaches in high-power therapeutic ultrasound

Ultrasound sources employed in high-power therapeutic medical systems are typically strongly focused, with f# = 1 or even lower. The initial design of such sources, acoustic characterization of existing ones, and corresponding treatment planning is a challenging problem, especially for therapies that rely on the formation of pressure shocks at the focus. One-way propagation models based on evolutionary differential equations have been shown to provide an effective way to simplify the analysis and obtain accurate solutions. Among them, the most popular is the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation. The parabolic approximation inherently assumes a quasi-plane nature of the wave, so its direct applicability is limited to weakly focused beams, in practice, with f#>2. However, an accurate analysis of nonlinear phenomena even in strongly focused beams based on the KZ equation in combination with an equivalent source model is possible by taking into account that in the focal region, where the wave is most affected by nonlinearity, the beam structure is close to a quasi-plane wave. Other approaches include transformation of the coordinate system following the geometry of beam focusing and extension to wide-angle parabolic models. This talk will overview the numerical tools that have been recently developed based on the proposed extensions.