Nonlinear ultrasound simulation in an axisymmetric coordinate system using a k-space pseudospectral method

k-Wave, ultrasound, axisymmetric coordinates, pseudospectral method, discrete trigonometric transforms

A full-wave model for nonlinear ultrasound propagation through a heterogeneous and absorbing medium in an axisymmetric coordinate system is developed. The model equations are solved using a non-standard or k-space pseudospectral time domain (PSTD) method. Spatial gradients in the axial direction are calculated using the Fourier collocation spectral method and in the radial direction using discrete trigonometric transforms. Time integration is performed using a k-space corrected finite difference scheme. This scheme is exact for plane waves propagating linearly in the axial direction in a homogeneous and lossless medium, and significantly reduces numerical dispersion in the more general case. The implementation of the model is described, and performance benchmarks are given for a range of grid sizes. The model is validated by comparison with several analytical solutions. This includes 1D absorption and nonlinearity, the pressure field generated by plane-piston and bowl transducers, and the scattering of a plane wave by a sphere. The general utility of the model is then demonstrated by simulating nonlinear transcranial ultrasound using a simplified head model.