Transducer modeling for accurate acoustic simulations of transcranial focused ultrasound stimulation

Low-intensity transcranial ultrasound stimulation (TUS) is emerging as a non-invasive 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.

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.

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 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.

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.