Accelerating Focused Ultrasound Modeling in Heterogeneous Spinal Cord Anatomy With Vision Transformer Operator Networks.

OBJECTIVE: The purpose of this work is to develop a data-driven framework for real-time prediction of focused ultrasound pressure fields in the spinal cord, addressing the limitations of computationally intensive acoustic simulations. Focused ultrasound therapy offers submillimeter precision for targeted treatment of spinal cord injuries, but its efficacy depends critically on transducer placement due to the spinal cord's complex geometry and acoustic heterogeneity across anatomical layers. METHODS: Conventional computational models rely on wave propagation simulations to generate patient-specific pressure maps, but these can take hours to complete parameter sweeps and are impractical for surgical decision-making. To address this bottleneck, we introduce a vision transformer-based Deep Operator Network (ViT-DeepONet), benchmarked against a convolutional DeepONet (convolutional neural network [CNN]-DeepONet) and a geometry-aware Fourier Neural Operator. By learning the solution operator of the governing partial differential equations, these models generalize across transducer positions and spinal geometries without new simulations. RESULTS: Trained on 8000 simulated pressure maps from porcine spinal cords (n=25), ViT-DeepONet achieves realtime predictions with 3.1% test loss and generalizes to human ultrasound images with 4.4% loss, reducing computation time by more than 91,000-fold relative to central processing unit-based high-fidelity solvers. ViT-DeepONet outperforms CNN-DeepONet (5.1% loss) while using fivefold fewer parameters. A geometry-aware Fourier Neural Operator attains the lowest loss (2.6%), but with eightfold higher complexity. CONCLUSION: ViT-DeepONet accurately captures spatial and geometric dependencies in heterogeneous acoustic domains, enabling real-time ultrasound pressure prediction with a lower computational burden. These results demonstrate the feasibility of operator learning as a powerful framework for accelerating acoustic modeling and optimizing patient-specific therapeutic ultrasound imaging.