Transducer modeling for accurate acoustic simulations of transcranial focused ultrasound stimulation

Abstract

Objective: Low-intensity transcranial ultrasound stimulation (TUS) is emerging as noninvasive brain stimulation technique with superior spatial resolution and the ability to reach deep brain areas. Medical image-based computational modeling could be an important tool for individualized TUS dose control and targeting optimization, but requires further validation. This study aims to assess the impact of the transducer model on the accuracy of the simulations.Approach: Using hydrophone measurements, the acoustic beam of a single-element focused transducer (SEFT) with a flat piezoelectric disc and an acoustic lens was characterized. The acoustic beam was assessed in a homogeneous water bath and after transmission through obstacles (3D-printed shapes and skull samples). The acoustic simulations employed the finite-difference time-domain method and were informed by computed tomography (CT) images of the obstacles. Transducer models of varying complexity were tested, representing the SEFT either as a surface boundary condition with variable curvature, or also accounting for its internal geometry. In addition, a back-propagated pressure distribution from the first measurement plane was used as source model. The simulations and measurements were quantitatively compared using key metrics for peak location, focus size, intensity and spatial distribution.Main results: While a surface boundary with an adapted, 'effective' curvature radius based on the specifications given by the manufacturer could reproduce the measured focus location and size in a homogeneous water bath, it regularly failed to accurately predict the beam after obstacle transmission. In contrast, models that were based on a one-time 1 calibration to the homogeneous water bath measurements performed substantially better in all cases with obstacles. For one of the 3D-printed obstacles, the simulated intensities deviated substantially from the measured ones, irrespective of the transducer model. We attribute this finding to a standing wave effect, and further studies should clarify its relevance for accurate simulations of skull transmission.Significance: Validated transducer models are important to ensure accurate simulations of the acoustic beam of SEFTs, in particular in the presence of obstacles such as the skull.

Transcranial focused ultrasound stimulation with high spatial resolution

“…S11, Table S4), and the wave mechanics within and without the cranial cavity require more extensive numerical modeling, simulations, and preliminary human trials. A complete acoustic model for human skull simulations does not yet exist as far as we know, and research on clinical ultrasound stimulation generally rely on partial ex-vivo skull samples and numerical simulations for accurate targeting through the cranial barrier [43,54,55]. Thus, while the concept of our system can theoretically be modified for clinical applications, significant preliminary experiments and simulations with excised skull samples would be required.…”

“…As a preliminary study, the clinical applicability of our dualcrossed transducer concept was tested with high fidelity acoustic simulations on five human head models using the Sim4Life (ZMT Zurich MedTech AG, Zurich, Switzerland) software, as described in Refs. [43,44]. We modeled the transducer as a single curved element focused transducer with a radius of curvature of 85 mm and an aperture width of 50 mm, working at a center frequency of 500 kHz, which resulted in an elliptical beam of 42 mm by 5 mm in a water background.…”

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

“…Results can be recorded as phasors (at the base frequency and, if relevant, higher harmonics) or transient 3 + 1D fields, and the solver has been verified and validated, 73 also for transcranial focused ultrasound modeling. 74,75 The original hard sources (imposed pressure; sinusoidal with rise-time, or user-defined transient profiles) were extended for the purpose of this work by soft sources (cosine function to avoid slowly decaying low frequency components).…”

ESHO benchmarks for computational modeling and optimization in hyperthermia therapy

“…Depending on the employed physical model, either given pressures or displacements or velocities are applied, which are not equivalent and complicate comparison. Furthermore, it can be important to model the internal structure of transducers [86], which often contain impedance matching and lens elements and can be affected by mechanical factors, such as fixation and friction.…”