Fast marching method to correct for refraction in ultrasound computed tomography

A significant obstacle in the advancement of Ultrasound Computed Tomography has been the lack of efficient and precise methods for the tracing of the bent rays that result from the interaction of sound with refractive media. In this paper, we propose the use of the Fast Marching Method (FMM) to solve the eikonal equation which governs the propagation of sound waves. The FMM enables us to determine with great accuracy and ease the distorted paths that the sound rays take from an emitter to the receivers. We show that knowledge of the accurate path proves crucial for an object reconstruction at high fidelity and accurate geometry. We employ a two-phase approach with an iterative method, SART, to faithfully reconstruct two tissue properties relevant in clinical diagnosis, such as mammography: speed of sound and sound attenuation. We demonstrate our results by ways of a newly designed analytical ultrasound breast phantom.