A full wave method for modeling nonlinear acoustic wave fields in media with inhomogeneous wave speed, attenuation, and parameter of nonlinearity

Abstract

The iterative nonlinear contrast source (INCS) method is a numerical method that has originally been developed for modeling transient nonlinear acoustic wave fields in homogeneous (i.e., spatially independent) lossless or lossy media. Starting from the Westervelt equation, the INCS method considers the nonlinear term of the latter as a nonlinear contrast source in an otherwise linear wave equation and iteratively solves the corresponding nonlinear integral equation using a Neumann scheme. By adding an attenuative contrast source, the method has recently been extended to deal with spatially dependent attenuation, and a spatially dependent parameter of nonlinearity has also been introduced. This presentation is about the introduction of an additional contrast source that account for a spatially dependent wave speed. In this case, convergence problems arise with the Neumann scheme. This problem is solved by replacing the Neumann scheme with a conjugate gradient scheme in which the error functional is based on the complete nonlinear integral equation. Results show that this approach yields very accurate results for the nonlinear wave field (tested up to the fifth harmonic) in media with a spatially dependent wave speed, attenuation, and parameter of nonlinearity, as encountered in realistic medical ultrasound applications.