3D time-domain modeling of nonlinear medical ultrasound with a contrast source method: behavior of the contrast sources

In order to predict the pulsed, nonlinear ultrasound field from medical phased array transducers, a numerical model has been developed that computes this field in a large-scale, three-dimensional configuration. The model is free of an assumed (quasi-plane) directionality in both the diffraction and nonlinear distortion, and it is solved with a Green's function method, which through proper filtering is efficiently and accurately evaluated with a discrization of two points per wavelength. In the method, the nonlinear terms in the wave equation are treated as constrast source terms, which are iteratively estimated by solving the associated linear wave problem. In this contribution we numerically study the behavior of these contrast sources. Firstly, we show from the computed nonlinear wavefield excited by a point source that the nonlinear distortion is indeed free of directionality. Secondly, we study the distribution of the contrast sources across the spatiotemporal domain, and we show that only the contrast sources between the primary source and the domain of observation have to be accounted for. Thirdly, we study the iterative estimation of the contrast sources for strong nonlinear distortion, and we show that for sufficient accuracy a spatiotemporal filtering of the contrast sources is necessary and may be performed straightforwardly.