Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach

A fast non-linear pulsed ultrasound field simulation is presented. It is implemented based on an angular spectrum approach (ASA), which analytically solves the non-linear wave equation. The ASA solution to the Westervelt equation is derived in detail. The calculation speed is significantly increased compared to a numerical solution using an operator splitting method (OSM). The ASA has been modified and extended to pulsed non-linear ultrasound fields in combination with Field II, where any array transducer with arbitrary geometry, excitation, focusing and apodization can be simulated. The accuracy of the non-linear ASA is compared to the non-linear simulation program - Abersim, which is a numerical solution to the Burgers equation based on the OSM. Simulations are performed for a linear array transducer with 64 active elements, focus at 40mm, and excitation by a 2-cycle sine wave with a center frequency of 5MHz. The speed is increased approximately by a factor of 140 and the calculation time is 12min with a standard PC, when simulating the second harmonic pulse at the focal point. For the second harmonic point spread function the full width error is 1.5% at -6dB and 6.4% at -12dB compared to Abersim.