Full-wave nonlinear ultrasound simulation on distributed clusters with applications in high-intensity focused ultrasound

Abstract

Model-based treatment planning and exposimetry for high-intensity focused ultrasound (HIFU) requires the numerical simulation of nonlinear ultrasound propagation through heterogeneous and absorbing media. This is a computationally demanding problem due to the large distances travelled by the ultrasound waves relative to the wavelength of the highest frequency harmonic. Here, the k-space pseudospectral method is used to solve a set of coupled partial differential equations equivalent to a generalised Westervelt equation. The model is implemented in C++ and parallelised using the message passing interface (MPI) for solving large-scale problems on distributed clusters. The domain is partitioned using a 1D slab decomposition, and global communication is performed using a sparse communication pattern. Operations in the spatial frequency domain are performed in transposed space to reduce the communication burden imposed by the 3D fast Fourier transform. The performance of the model is evaluated using grid sizes up to 4096 x 2048 x 2048 grid points distributed over a cluster using up to 1024 compute cores. Given the global nature of the gradient calculation, the model shows good strong scaling behaviour, with a speed-up of 1.7x whenever the number of cores is doubled. This means large-scale simulations can be distributed across high numbers of cores on a cluster to minimise execution times with a relatively small computational overhead. The efficacy of the model is demonstrated by simulating the ultrasound beam pattern for a HIFU sonication of the kidney.