Modeling nonlinear acoustic wave fields in media with inhomogeneity in the attenuation and in the nonlinearity

Biomedical tissues usually show inhomogeneity in their acoustic medium parameters. These inhomogeneities cause refraction and scattering of diagnostic and therapeutic ultrasound waves. A method that is able to model the effects of inhomogeneity in the attenuation and in the nonlinearity is essential for the design of transducers for new ultrasound modalities and the development of novel ultrasound applications. The Iterative Nonlinear Contrast Source (INCS) method has originally been designed for the accurate modeling of nonlinear acoustic wave fields in homogeneous media. It considers the nonlinear term from the Westervelt equation as a distributed contrast source, and the corresponding integral equation is solved using an iterative Neumann scheme. This paper presents an extension of the INCS method that can handle inhomogeneity in the attenuation and in the coefficient of nonlinearity. Results are presented for the one-dimensional case. These show that in this case the presented method correctly predicts the effects related to nonlinear propagation and scattering by inhomogeneities in the attenuation and the coefficient of non-linearity.