Quantifying numerical errors in the simulation of transcranial ultrasound using pseudospectral methods

Effective transcranial transmission of focused ultrasound is desirable for various therapeutic applications. Time-reversal (TR) focusing based on numerical simulations of ultrasound propagation can be used to correct for the aberrating skull layer. For weakly heterogeneous media, k-space and pseudospectral time domain (PSTD) methods have been shown to have increased accuracy and efficiency compared to the finite-difference time domain (FDTD) methods typically used in TR. However, their suitability for highly heterogeneous, transcranial simulations is less clear. Here, this is established in terms of spatial and temporal sampling requirements through numerical testing and comparison with FDTD schemes. PSTD schemes are shown to give equal or better accuracy compared to FDTD schemes for modelling propagation through tissue-realistic heterogeneities, which, combined with the reduction in numerical dispersion obtained with k-space correction, recommends them for use in simulated TR.