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

Abstract

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 nonstandard or k-space pseudospectral time domain method. Spatial gradients in the axial direction are calculated using the Fourier collocation spectral method, and spatial gradients in the radial direction are calculated 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 one-dimensional 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.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

“…Benchmarks 1–6 were computed using the axisymmetric version of k-Wave to provide a high-resolution reference simulation. 58 Benchmarks 1, 2, 3, and 5 used 60 PPW and 2400 PPP, while benchmarks 4 and 6 used 60 PPW and 6000 PPP. In both cases, the total grid size was 2700 × 864 grid points, including the PML, and the simulation time was 120 μ s, giving 144 000 and 360 000 time steps, respectively.…”

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

“…52 Benchmarks 1 to 6 were computed using the axisymmetric version of k-Wave to provide a high-resolution reference simulation. 53 Benchmarks 1, 2, 3, and 5 used 60 PPW and 2400 PPP, while benchmarks 4 and 6 used 60 PPW and 6000 PPP. In both cases, the total grid size was 2700 × 864 grid points including the PML and the simulation time was 120 µs, giving 144,000 and 360,000 time steps, respectively.…”

Characterisation of hydrophone sensitivity with temperature using a broadband laser-generated ultrasound source

“…In order to determine the distance between the LGUS source and the hydrophone required to resolve the direct ultrasound wave from any edge waves, an axisymmetric time-domain simulation of wave propagation (using kspaceFirstOrderAS function [34] in k-Wave [35]) was performed. The simulation was run for each hydrophone separately as the required source-hydrophone separation depends on the hydrophone's active element size.…”