Numerical methods capable of modeling nonlinear pressure wave fields propagating through inhomogeneous biomedical tissue are essential for the design and optimization of ultrasound transducers or devices. The Iterative Nonlinear Contrast Source (INCS) method is an accurate method for modeling three-dimensional nonlinear acoustic wave fields. Originally it was capable of modeling nonlinear wave fields in homogeneous lossy tissue. Recently, it has been extended to deal with spatially varying coefficient of nonlinearity and attenuation. The method recasts a generalized form of the Westervelt equation into an integral equation which was originally solved using a Neumann scheme. This scheme allows to model moderate losses and non-linearity. Problems with the convergence may occur for realistic speed of sound contrast. Here, we present a different solution method which makes it possible to treat, besides spatially varying coefficient of nonlinearity and attenuation, also realistic speed of sound contrasts. The nonlinear integral equation is solved using a steepest descent scheme. The method has been used to compute the three-dimensional nonlinear pressure wave field generated by a 40 element linear array and propagating through a medium with spatially varying coefficient of nonlinearity, attenuation and speed of sound. Simulations have been performed up to the 5th harmonic component.

Research on nonlinear medical ultrasound has been increased over the lastdecade and has resulted in a wide range of numerical methods for the modeling ofthe nonlinear distortion of a propagating pressure wave. However, when appliedto realistic configurations, the majority of these methods are eithercomputationally expensive or limited by the applied approximations. TheIterative Nonlinear Contrast Source (INCS) method is able to accurately computethe pulsed nonlinear pressure wave field that is generated in a largethree-dimensional domain by an arbitrary transducer transmitting under a largesteering angle. The method is based on the Neumann iterative solution of anonlinear integral equation that is equivalent to the Westervelt equation. Toimprove the performance of the method, it would be beneficial to employiterative schemes (e.g. Conjugate Gradient based schemes) that are efficient forsolving linear integral equations. This motivates the development of alinearized version of the INCS method, as presented in this paper. To test thepresented approach, a Bi-CGSTAB scheme is used to solve the linearizedWestervelt equation. For the one-dimensional case, results are obtained andcompared with the solution obtained with the original INCS method, and theFubini solution. All the results have been obtained up to the third harmoniccomponent and are in agreement with each other.

Biomedical tissues usually show inhomogeneity in their acoustic mediumparameters. These inhomogeneities cause refraction and scattering of diagnosticand therapeutic ultrasound waves. A method that is able to model the effects ofinhomogeneity in the attenuation and in the nonlinearity is essential for thedesign of transducers for new ultrasound modalities and the development of novelultrasound applications. The Iterative Nonlinear Contrast Source (INCS) methodhas originally been designed for the accurate modeling of nonlinear acousticwave fields in homogeneous media. It considers the nonlinear term from theWestervelt equation as a distributed contrast source, and the correspondingintegral equation is solved using an iterative Neumann scheme. This paperpresents an extension of the INCS method that can handle inhomogeneity in theattenuation and in the coefficient of nonlinearity. Results are presented forthe one-dimensional case. These show that in this case the presented methodcorrectly predicts the effects related to nonlinear propagation and scatteringby inhomogeneities in the attenuation and the coefficient of non-linearity.