tFUSFormer: Physics-Guided Super-Resolution Transformer for Simulation of Transcranial Focused Ultrasound Propagation in Brain Stimulation

Transcranial focused ultrasound (tFUS) has emerged as a new mode of non-invasive brain stimulation (NIBS), with its exquisite spatial precision and capacity to reach the deep regions of the brain. The placement of the acoustic focus onto the desired part of the brain is critical for successful tFUS procedures; however, acoustic wave propagation is severely affected by the skull, distorting the focal location/shape and the pressure level. High-resolution (HR) numerical simulation allows for monitoring of acoustic pressure within the skull but with a considerable computational burden. To address this challenge, we employed a 4× super-resolution (SR) Swin Transformer method to improve the precision of estimating tFUS acoustic pressure field, targeting operator-defined brain areas. The training datasets were obtained through numerical simulations at both ultra-low (2.0
$\text{mm}$
) and high (0.5
$\text{mm}$
) resolutions, conducted on
in vivo
CT images of 12 human skulls. Our multivariable datasets, which incorporate physical properties of the acoustic pressure field, wave velocity, and skull CT images, were utilized to train three-dimensional SR models. We found that our method yielded 87.99
$\pm$
4.28% accuracy in terms of focal volume conformity under foreseen skull data, and accuracy of 82.32
$\pm$
5.83% for unforeseen skulls, respectively. Moreover, a significant improvement of 99.4% in computational efficiency compared to the traditional 0.5
$\text{mm}$
HR numerical simulation was shown. The presented technique, when adopted in guiding the placement of the FUS transducer to engage specific brain targets, holds great potential in enhancing the safety and effectiveness of tFUS therapy.