Full-wave nonlinear ultrasound simulation in an axisymmetric coordinate system using the discrete sine and cosine transforms

The simulation of ultrasound propagation through biological tissue has a wide range of applications in medicine. However, ultrasound simulation presents a computationally difficult problem, as simulation domains are very large compared with the acoustic wavelengths of interest. This becomes a greater problem when simulating high intensity focussed ultrasound since nonlinear effects increase the required resolution of computational grids. Two common methods for dealing with this difficulty include using spectral methods for solving the acoustic model equations and using an axisymmetric assumption for the system. In this paper, a full-wave nonlinear model similar to the Westervelt equation is solved using pseudospectral methods based on the discrete sine and cosine transforms. These methods can be used to apply homogeneous Neumann and Dirichlet boundary conditions (both of which are present in axisymmetric systems) while retaining the many established benefits of the Fourier spectral method. The accuracy of the model is established through comparison with analytical solutions to several nonlinear wave equations.