Abstract

High Intensity Focused Ultrasound (HIFU) is a therapy that uses ultrasound waves to non-invasively destroy malignant cells inside the human body. The technique works by sending a high-energy beam of ultrasound into the tissue using a focused transducer. Numerically modelling HIFU presents a problem due to nonlinear effects leading to the formation of harmonics of the source frequency. Each harmonic requires a finer grid to resolve, rapidly increasing computational complexity.  I will present the derivation and benefits of two ray tracing methods using weakly nonlinear ray theory formed by different asymptotic expansions of the governing acoustic equations. The first has the same ray equations as the linear case while the transport equation is a nonlinear transformation of the Burgers’ equation. The final method has its Eikonal equation coupled with the transport equation producing ray trajectories which depend on the amplitude. This is work done in collaboration with Marta Betcke (UCL), Ben Cox (UCL), Bradley Treeby (UCL)