Speaker
Description
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 mod-
elling HIFU presents a problem due to nonlinear effects leading to the formation of harmonics
of the source frequency. Each significant harmonic requires a finer grid to resolve, rapidly
increasing computational complexity. We look to use the weakly non-linear ray theory frame-
work to reduce the nonlinear PDE in Rd to a set of one dimensional PDEs. We construct rays
emanating from the transducer on which we calculate the phase of the waves via the Eikonal
equation. In ray coordinates the amplitude can be found by solving the nonlinear transport
equation along the ray. This equation can be transformed into the Burger’s equation which
we then solve and transform back to obtain the amplitude along each ray.
| Preferred Contribution Type | Presentation |
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