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.

Predictions of nonlinear ultrasound beams of a medical phased array transducer, steered at 0, 22.5 and 45 degrees, and generated by a forward-wave and a full-wave numerical model are presented. The results from both models show a good agreement in the unsteered situation and in all fundamental field profiles, but they deviate significantly in the harmonic field profiles for the steered situations.

A full wave 3d time domain algorithm is presented that calculates the nonlinear acoustic wavefield of medical phased array transducers emitting an arbitratily steered, focused apodized beam. The algorithm can be used for computer simulation studies of the occuring second and higher harmonic wavefields in these configurations and for the optimization of the transducer design. It is based on the iterative employment of a Green's Function (or impulse response) method with the nonlinearity included as a contrast source. Several comparisons with validated algorithms are made, showing a perfect agreement.

Nowadays, the design of phased array transducers for medical diagnostic ultrasound asks for an understanding of the nonlinear propagation of acoustic wavefields. In the last decade an imaging modality called Tissue Harmonic Imaging (THI) has become the standard for many echography investigations. THI specifically benefits from the nonlinear distortion of ultrasound propagation in tissue. Since most existing numerical models are based on a linear approximation of the underlying nonlinear physical reality, they cannot account for this kind of disortion. Several numerical models have been developed in recent years that incorporate weak nonlinear propagation. However, as yet no model has enabled the computation of large scale, full-wave nonlinear wavefields in the time domain. In this study, we present an approach that handles weak nonlinear propagation by means of an iterative Neumann scheme. This approach enables the successive use of the solution of a linear wave problem, where the nonlinearity is treated as a contrast source. Thus, we can employ well-known linear methods for large scale wave problems to obtain the desired nonlinear wavefield. The general formalism is outlined and applied to a one-dimensional nonlinear wave problem to obtain the desired nonlinear wavefield. The general formalism is outlined and applied to a one-dimensional nonlinear wave problem. The wavefield is evaluated, including harmonic frequencies up to the fifth harmonic. For each successive linear step a Green's function approach is employed. The results that already after a small number of iterations the results are in very good agreement with this exact result. The proposed method can easily be extended can easily be extended to more complex problems. The Green's function approach enables us to discretize the spatiotemporal domain very efficiently, which opens the road to solving time domain nonlinear wave problems in three dimensions. Furthermore, media with attenuation and inhomogeneity can be inlcuded straightforwardly in the algorithm.