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Originally, the iterative nonlinear contrast source (INCS) method has been developed to compute the nonlinear, wide‐angle, pulsed ultrasound field in a homogeneous and lossless medium. The method considers the nonlinear term of the lossless Westervelt equation as a distributed contrast source in a linear background medium. The full nonlinear wave field follows from the Neumann iterative solution of the resulting integral equation. Each iteration step involves the spatiotemporal convolution of the background Green’s function with an estimate of the contrast source. Appropriate filtering provides accurate field predictions for a discretization approaching two points per smallest wavelength or period. The current paper first discusses the theoretical generalization of the original contrast source approach, e.g., to include tissue attenuation or inhomogeneity. Next, computational results are presented that show the directional independence (even for the nonlinear distortion) and the wide‐angle performance of the original INCS method. Finally, results are presented for extensions that can deal with power law losses or inhomogeneity in the wave speed. The wide‐angle capability and the versatility of the contrast source approach demonstrate that the INCS method is well‐suited for modeling the various aspects of realistic biomedical tissue behavior. [Work supported by STW and NCF.]

The pulsed ultrasound field in nonlinear biomedical tissue may be computed by the recurrent evaluation of the field of a distributed contrast source in a linear homogeneous background medium. For human organs, the computational domain may easily measure hundreds of wavelengths or periods in each spatiotemporal dimension. Even with today’s supercomputers, the evaluation of the transient field from the contrast sources in these very large inhomogeneous domains is a big challenge, and is only feasible if the applied numerical method is extremely efficient in terms of memory usage and computational speed. Using a Green’s function method, the critical operation is a spatiotemporal convolution over the entire computational domain. It is shown how a systematic filtering and windowing of the involved functions yield accurate numerical convolutions with a discretization approaching the Nyquist limit of two points per wavelength or period of the highest frequency. This minimizes the storage requirement. Application...

A theoretical investigation of the absorption of finite‐amplitude ultrasound in biomedical tissue is reported. The tissue is modeled as a medium having multiple relaxation processes. A generalized Burgers equation, which includes the effects of nonlinearity and relaxation, is derived. Analytical and numerical solutions of this equation for a step shock, a periodic wave, and a temporal Gaussian pulse are presented. The results are used to calculate the finite‐amplitude absorption coefficient and temperature rise in the tissue. It is found that nonlinear distortion causes the absorption and the temperature rise to be significantly higher than that for small‐signal ultrasound. [Work supported by NIH, ONR, and ARL:UT IR&D.]