The parabolic approximation in therapeutic ultrasound

Abstract

An ideal mathematical model is both accurate and tractable. It must predict the physics of interest and produce solutions in an efficient manner. In the field of therapeutic ultrasound, where simulations of finite-amplitude sound beams are an important adjunct to bench testing, the parabolic approximation of the wave equation often strikes a balance between these two requirements. In this presentation the common approaches to computing ultrasound fields are introduced and a family of high-order parabolic models is derived and analyzed. This analysis provides the framework for addressing a challenge often encountered in medical ultrasound modeling: controlling spurious effects associated with steep gradients in the source boundary condition. The accuracy of the resulting high-order propagation models is assessed by comparing against solutions of the full wave equation and the degree to which these models capture the salient characteristics of ultrasound beams is analyzed. This approach brings to therapeutic ultrasound a “wide-angle” parabolic model with improved diffraction modeling capability and no penalty to computational efficiency.An ideal mathematical model is both accurate and tractable. It must predict the physics of interest and produce solutions in an efficient manner. In the field of therapeutic ultrasound, where simulations of finite-amplitude sound beams are an important adjunct to bench testing, the parabolic approximation of the wave equation often strikes a balance between these two requirements. In this presentation the common approaches to computing ultrasound fields are introduced and a family of high-order parabolic models is derived and analyzed. This analysis provides the framework for addressing a challenge often encountered in medical ultrasound modeling: controlling spurious effects associated with steep gradients in the source boundary condition. The accuracy of the resulting high-order propagation models is assessed by comparing against solutions of the full wave equation and the degree to which these models capture the salient characteristics of ultrasound beams is analyzed. This approach brings to therapeuti...