Variational method for estimating the effects of continuously varying lenses in HIFU, sonography, and sonography-based cross-correlation methods.

The effects of high intensity focused ultrasound (HIFU)-induced continuously varying thermal gradients on sound ray propagation were modeled theoretically. This modeling was based on Fermat's variational principle of least time for rays propagating in a continuously varying thermal gradient described by a radially symmetric heat equation. Such thermal lenses dynamically affect HIFU beam focusing, and simultaneously create ultrasonic geometric and intensity distortions and artifacts in monitoring devices. Techniques which are based upon ultrasonic cross-correlation methods, such as elastography and two-dimensional temperature estimation, also suffer distortion effects and generate artifacts.