tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins
Authors: Minjee Seo, Haris Ghafoor, Minju Seol, Seonaeng Cho, Kyungho Yoon
Organizations: School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, Republic of Korea · Innovative & Intelligent Computational Science Institute (IN2CSI), Seoul, Republic of Korea
Abstract
Transcranial focused ultrasound (tFUS) requires accurate estimation of the intracranial acoustic field, which is distorted by skull-induced aberrations. Numerical solvers are accurate but computationally expensive for digital twins, where the field must be re-estimated repeatedly as treatment conditions change. Existing deep-learning surrogates are fast but typically use voxel-to-voxel regression on a fixed grid, with no mechanism reflecting how acoustic energy propagates through the skull. We instead cast tFUS simulation as an operator learning problem and propose tFUSOperator, a coordinate-aware neural operator that maps the free-field pressure, skull anatomy, and treatment parameters to the intracranial field within a shared physical coordinate frame. To our knowledge, this is the first operator-based formulation of tFUS field prediction. On both seen and unseen skulls, the model localizes the acoustic focus accurately-reaching about 90% and 72% Dice, respectively-and it performs nearly as well from magnetic resonance (MR) as from computed tomography (CT) input while running 5.6×104 times faster than numerical simulation. These results suggest a fast, radiation-free route to safe and practical digital twins for patient-specific tFUS treatment. The code is available at: https://github.com/CMME-Lab/tFUSOperator.git.
Transcranial focused ultrasound (tFUS) is a non-invasive technique that delivers focused acoustic energy through the skull for neuromodulation and therapeutic applications. However, the heterogeneous structure of the skull induces complex, patient-specific phase and amplitude aberrations that distort the acoustic focus and deviate it from the intended target, compromising therapeutic efficacy and safety. Conventional time-reversal (TR) simulations can correct these aberrations but rely on computationally expensive full-wave solvers, making them impractical for real-time use and iterative treatment planning. We propose a few-shot deep surrogate framework that predicts per-element phase and amplitude corrections for a 96-element 3D phased-array transducer from patient CT images. A geometry-aware encoder extracts skull-path features shared across dedicated phase classification and amplitude regression branches, where phase periodicity is handled via circular expectation decoding. The framework is pretrained on diverse skull geometries and fine-tuned with only ten target points, enabling rapid adaptation to unseen patients without full patient-specific simulation. Evaluated via leave-one-out cross-validation across 12 skulls, it achieves a mean phase CMAE of 0.155 rad and amplitude rMAE of 9.089%, a focal centroid error of 0.467 mm, Dice score of 94.422%, and peak pressure ratio of 92.332%, with an approximately 2,535 times speedup over TR simulation. The code is available at https://github.com/Minju-Seol/fewshot-tfus-correction.
Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space. In this work, we introduce UFO (Domain-Unification-Free Operator), a cross-domain neural operator framework that realizes operators through adaptive, jointly conditioned interactions among representations defined on distinct domains. UFO enables discretization decoupling: the input function can be observed at resolutions or locations different from those used during training, while the solution can be queried at arbitrary output resolutions. Across four complementary benchmarks covering discontinuous inputs, irregular sampling with spectral mismatch, nonlinear dynamics, and stochastic high-frequency fields, UFO delivers accurate, robust, and physically coherent predictions under distribution shifts. These results establish cross-domain, phase-modulated realization as a powerful framework for discretization-decoupled neural operator learning.
Hanli Qiao, George Em Karniadakis, Muhammad Muniruzzaman
Computed tomography (CT) is indispensable for clinical diagnosis and image-guided interventions but exposes patients to ionizing radiation, motivating the development of safer imaging alternatives. Ultrasound (US) is non-ionizing and widely accessible; however, it is highly operator dependent and lacks quantitative tissue characterization, often leading to diagnostic uncertainty and unnecessary CT examinations. This work presents a 3D ultrasound-derived pseudo-CT (UD-pCT) framework that generates CT-like anatomical reference volumes inferred from US, without aiming to reproduce physically accurate Hounsfield Units. Paired 3D kidney US and CT volumes from the TRUSTED dataset are first spatially aligned using a landmark-based multimodal registration pipeline, creating high-quality paired inputs for supervised training of an adversarial framework. The proposed Bottleneck Transformer Residual U-Net3D (BT-ResUNet3D) model employs a 3D residual encoder-decoder generator augmented with a transformer bottleneck, enabling effective modeling of fine-grained local anatomical structures as well as long-range volumetric dependencies, while a 3D Conditional PatchGAN discriminator enforces local structural realism in the synthesized pseudo-CT volumes. Quantitative evaluation using PSNR and SSIM demonstrates that the proposed method outperforms established baselines in structural fidelity and perceptual image quality. The UD-pCT volumes provide real-time anatomical reference for operator guidance, potentially reducing acquisition variability and unnecessary CT use. A limitation of this study is the relatively small paired dataset, which may limit the generalizability of the proposed model.