Comparison of Ray-Tracing and Diffraction Methods for Correcting Aberrations in Transcranial Focusing of Ultrasound Field

Abstract The study theoretically evaluates the capabilities of ray-tracing and diffraction-based aberration-correction methods, which are used in noninvasive neurosurgery for focusing high-intensity ultrasound through the skull bones at various depths in the human brain. The analysis is based on using head computed tomography (CT) data of skulls with various geometric characteristics from an anonymized set of eight patients. The transducer is a mosaic 1 MHz phased array shaped like a spherical bowl with a radius of curvature and a diameter of 200 mm, and fully-populated, 256-element layout. In the ray-tracing method, aberrations were corrected by calculating the phase shift along the rays emanating from the target point to the centers of the elements. In the diffraction-based method, calculation of the Rayleigh integral was combined with a pseudospectral numerical method for solving the wave equation in an inhomogeneous medium, implemented in the k -Wave software package and used for aberration correction and ultrasound focusing simulations. It is shown that the strongest field distortions are observed for skulls with more pronounced variations in bone thickness. Compared with the ray-based method, the diffraction-based method provided higher focusing efficiency and enabled aberration correction at shallower depths in the brain.