Accelerating Focused Ultrasound Modeling in Heterogeneous Spinal Cord Anatomy with Vision Transformer Operator Networks
TL;DR
The feasibility of operator learning as a powerful framework for accelerating acoustic modeling and optimizing patient-specific therapeutic ultrasound is demonstrated, enabling real-time ultrasound pressure prediction with reduced computational burden.
Abstract
Objective: The purpose of this work is to develop a data-driven framework for real-time prediction of focused ultrasound (FUS) pressure fields in the spinal cord, addressing the limitations of computationally intensive acoustic simulations. FUS therapy offers submillimeter precision for targeted treatment of spinal cord injuries (SCI), 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 (CNN-DeepONet) and a geometry-aware Fourier Neural Operator (Geo-FNO). 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 8,000 simulated pressure maps from porcine spinal cords (N=25), ViT-DeepONet achieves real-time predictions with 3.1% test loss and generalizes to human ultrasound images with 4.4% loss, reducing computation time by over 91,000-fold relative to CPU-based high-fidelity solvers. ViT-DeepONet outperforms CNN-DeepONet (5.1% loss) while using fivefold fewer parameters. Geo-FNO 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 reduced computational burden. These results demonstrate the feasibility of operator learning as a powerful framework for accelerating acoustic modeling and optimizing patient-specific therapeutic ultrasound.