Abstract
Non-invasive, focal neurostimulation with ultrasound is a potentially powerful neuroscientific tool that requires effective transcranial focusing of ultrasound to develop. Time-reversal (TR) focusing using numerical simulations of transcranial ultrasound propagation can correct for the effect of the skull, but relies on accurate simulations. Here, focusing requirements for ultrasonic neurostimulation are established through a review of previously employed ultrasonic parameters, and consideration of deep brain targets. The specific limitations of finite-difference time domain (FDTD) and k-space corrected pseudospectral time domain (PSTD) schemes are tested numerically to establish the spatial points per wavelength and temporal points per period needed to achieve the desired accuracy while minimizing the computational burden. These criteria are confirmed through convergence testing of a fully simulated TR protocol using a virtual skull. The k-space PSTD scheme performed as well as, or better than, the widely used FDTD scheme across all individual error tests and in the convergence of large scale models, recommending it for use in simulated TR. Staircasing was shown to be the most serious source of error. Convergence testing indicated that higher sampling is required to achieve fine control of the pressure amplitude at the target than is needed for accurate spatial targeting.
Highlights
The use of implanted electrodes for deep brain stimulation (DBS) is a well-established, invasive treatment for multiple neurological conditions and has directly resulted in a greater understanding of functional neuroanatomy and deep brain circuitry.1 its usefulness is limited by the inherent risks of the required neurosurgery combined with difficulties in targeting and repositioning the stimulatory focus.2 Non-invasive alternatives such as transcranial magnetic and direct current stimulation have both met with success in research and clinical settings
The specific limitations of finite-difference time domain (FDTD) and k-space corrected pseudospectral time domain (PSTD) schemes are tested numerically to establish the spatial points per wavelength and temporal points per period needed to achieve the desired accuracy while minimizing the computational burden
Transmission to the edge of the grid remains constant at below À70 dB for both schemes until spatial sampling drops beneath 3 PPW, below which the k-space scheme shows an increase in transmission and the FDTD scheme shows a reduction in transmission
Summary
The use of implanted electrodes for deep brain stimulation (DBS) is a well-established, invasive treatment for multiple neurological conditions and has directly resulted in a greater understanding of functional neuroanatomy and deep brain circuitry. its usefulness is limited by the inherent risks of the required neurosurgery combined with difficulties in targeting and repositioning the stimulatory focus. Non-invasive alternatives such as transcranial magnetic and direct current stimulation have both met with success in research and clinical settings. Non-invasive alternatives such as transcranial magnetic and direct current stimulation have both met with success in research and clinical settings They are limited in terms of their ability to achieve tight spatial focusing, and their penetration deep into tissue.. In model-driven TR, numerical models simulate the propagation of ultrasound from a target area to a virtual transducer using acoustic property maps of the head derived from CT or MRI images.. These numerical schemes are briefly described, and the various factors affecting the rate of numerical convergence are examined This is quantified in terms of the spatial and temporal sampling required to obtain acceptable accuracy in the simulation of ultrasound propagation from the scalp to a deep brain target. While the criteria used are established for the application of transcranial UNMS, these results are applicable to other therapies that require accurate transcranial ultrasound simulation, such as high intensity focused ultrasound (HIFU) ablation and opening the blood brain barrier with ultrasound
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