Computationally Efficient Transcranial Ultrasonic Focusing: Taking Advantage of the High Correlation Length of the Human Skull

The phase correction necessary for transcranial ultrasound therapy requires numerical simulation to noninvasively assess the phase shift induced by the skull bone. Ideally, the numerical simulations need to be fast enough for clinical implementation in a brain therapy protocol and to provide accurate estimation of the phase shift to optimize the refocusing through the skull. In this article, we experimentally performed transcranial ultrasound focusing at 900 kHz on ${N} = {5}$ human skulls. To reduce the computation time, we propose here to perform the numerical simulation at 450 kHz and use the corresponding phase shifts experimentally at 900 kHz. We demonstrate that a 450-kHz simulation restores 94.2% of the pressure when compared with a simulation performed at 900 kHz and 85.0% of the gold standard pressure obtained by an invasive time reversal procedure based on the signal recorded by a hydrophone placed at the target. From a 900- to 450-kHz simulation, the grid size is divided by 8, and the computation time is divided by 10.