A parametric study of error in the parabolic approximation of focused axisymmetric ultrasound beams

Abstract

The parabolic approximation results in a tractible model for studying ultrasound beams, but the limits of validity of the approximation are often presented only qualitatively. In this work the most common model for axisymmetric ultrasound beam propagation, the Kuznetsov-Zabolotskaya-Khokhlov equation, is directly compared with the more general Westervelt equation with regard to diffractive and absorptive effects in continuous wave beams. The parametric study compares the solutions of the two models as a function of source frequency and focusing geometry using peak focal pressure, the axial location at which that peak occurs, and the loss due to absorption as metrics.