High-intensity focused ultrasound is a noninvasive therapy in which an ultrasound probe positioned outside the body is used to deliver acoustic energy to a target volume inside the body. In the thermal regime, the treatment planning challenge is to deliver enough energy to coagulate the tissue within this volume, while leaving the surrounding areas unharmed. This equates to solving an optimization problem using coupled acoustic and thermal equations. The acoustic part is complicated by the fact the tissue is heterogeneous, the wave propagation is nonlinear, and the domain size can be on the order of hundreds or thousands of wavelengths. This talk will focus on efficient large scale nonlinear ultrasound models based on the Fourier collocation pseudospectral method, which are utilized in the open-source k-Wave toolbox. In particular, I will discuss recent work on spectral moving mesh methods, domain decomposition using a local Fourier basis, viscoelastic wave models, and pseudospectral solutions for Pennes’ bioheat equation.

This is joint work with J. Jaros, B. Cox, E. Wise, F. Vaverka, and K. Kadlubiak. This work was supported by the EPSRC, grant numbers EP/L020262/1, EP/M011119/1, EP/P008860/1.