Comparison of ray-tracing and diffraction methods for correcting aberrations in transcranial focusing of ultrasound field

The study theoretically evaluated the possibilities of using ray-tracing and diffraction-based methods to aberration correction, 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. A mosaic 1 MHz phased array shaped as a spherical bowl with radius of curvature and diameter of 200 mm, and absolutely dense filling of the surface with 256 elements, was considered as the transducer. In the ray-tracing method, aberration correction was carried out by calculating the phase shift along the rays emanating from the target point to the centers of the elements. In the diffraction-based method, a combination of the Rayleigh integral and a pseudospectral numerical method for solving the wave equation in an inhomogeneous medium, implemented in the k-Wave software package, was used for aberration correction and ultrasound focusing simulations. It is shown that the strongest field distortions are observed for skulls with more pronounced variations of bone thickness. The diffraction-based method allows for increasing the focusing efficiency, as well as performing correction at shallower depths in the brain compared to the ray-based method.