An iterative method for the computation of nonlinear, wide-angle, pulsed acoustic fields of medical diagnostic transducers

Abstract

The development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field. A prospective method should provide the wide-angle, pulsed field emitted by an arbitrary planar source distribution and propagating in a three-dimensional, large scale domain holding a nonlinear acoustic medium. In this paper, a method is presented that is free of any assumed wavefield directionality. The nonlinear acoustic wave equation is solved by treating the nonlinear term as a contrast source. This formulation leads to an iterative scheme that involves the repetitive solution of a linear wave problem through Green's function method. It is shown that accurate field predictions may be obtained within a few iterations. Moreover, by employing a dedicated numerical convolution technique, the method allows for a discretization down to two points per wavelength or period of the highest frequency of interest. The performance of the method is evaluated through a number of nonlinear field predictions for pulsed transducers with various geometries. The results demonstrate the directional independence of the method. Moreover, comparison with results from several existing methods shows that the method accurately predicts the nonlinear field for weak to moderate nonlinearity.