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

Abstract

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 paper, we experimentally performed transcranial ultrasound focusing at 900kHz on N=5 human skulls. To reduce the computation time, we propose here to perform the numerical simulation at 450kHz and use the corresponding phase shifts experimentally at 900kHz. We demonstrate that a 450kHz simulation restores 94.2% of the pressure as compared to a simulation performed at 900kHz 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 900kHz simulation to a 450kHz simulation, the grid size is divided by eight and the computation time is divided by ten.

Comparison Between Ray-Tracing and Full-Wave Simulation for Transcranial Ultrasound Focusing on a Clinical System Using the Transfer Matrix Formalism

“…Most of these numerical approaches were tested either numerically only [19], [23], [28], [30], [31], [35], [43], [44] or with a single-element to assess locally the accuracy of the computed phase shifts [26], [36], [45]- [48]. The improvement of the refocusing with multielement arrays compared to no-correction was assessed experimentally in head phantoms [49]- [51], animal models [52]- [54] or on patients during clinical trials [1]- [5], [38] by measuring the thermal rise at focus with MR thermometry [55], [56] or directly via hydrophone measurements [13], [14], [17], [22], [24], [25], [27], [41], [57]. Quantitative assessment of the performance of the simulation should be performed in terms of percentage of the restored pressure at the target compared to hydrophone-based correction.…”

Transcranial focused ultrasound phase correction using the hybrid angular spectrum method

“…Although FDTD and PSTD methods have been used in prior studies to investigate transcranial phase corrections with phased array transducers, this study is the first to use the HAS method with a hemispherical phased array transducer, and the first to compare it against the standard of care InSightec ray tracing method and the gold standard hydrophone method. To contextualize the HAS method’s performance against full-wave FDTD and PSTD methods, we can consider the results from Marsac et al 18 and Maimbourg et al 33 . However, as a caveat, comparison of results across studies are often complicated by differences in experimental setup, including but not limited to skull samples, transducer frequency, and transducer f-number.…”

“…Fourth, the HAS method’s current simulation time is not yet practical for a clinical setting. To seamlessly integrate the method into the current clinical workflow, simulation times that are less than one minute are desired 33 . One way to reduce simulation time is to parallelize computations using more computational resources.…”

“…However, no study to date has benchmarked against both the standard of care InSightec ray tracing method and the gold standard hydrophone method; a direct comparison to both methods is needed to determine a proposed simulation method’s clinical relevance. Most commonly, simulation studies use finite difference time domain (FDTD) 16 , 18 – 28 or pseudo-spectral time domain (PSTD) 29 – 33 methods to simulate the propagation of ultrasound through heterogeneous media. These image-based simulation methods often require many hours of computation time to converge, though recent work has greatly reduced the computation time needed to estimate phase corrections by reducing the computation volume 33 .…”

“…Most commonly, simulation studies use finite difference time domain (FDTD) 16 , 18 – 28 or pseudo-spectral time domain (PSTD) 29 – 33 methods to simulate the propagation of ultrasound through heterogeneous media. These image-based simulation methods often require many hours of computation time to converge, though recent work has greatly reduced the computation time needed to estimate phase corrections by reducing the computation volume 33 . In contrast to these methods, the hybrid angular spectrum (HAS) method 17 , 34 – 38 requires substantially less computation time when simulating a computation volume of the same size, often running 100×–1000× faster than the FDTD and PSTD methods 36 .…”