Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues. However, its efficacy is highly sensitive to the placement of the ultrasound source, as the spinal cord's complex geometry and acoustic heterogeneity distort and attenuate the FUS signal. Current approaches rely on computer simulations to solve the governing wave propagation equations and compute patient-specific pressure maps using ultrasound images of the spinal cord anatomy. While accurate, these high-fidelity simulations are computationally intensive, taking up to hours to complete parameter sweeps, which is impractical for real-time surgical decision-making. To address this bottleneck, we propose a convolutional deep operator network (DeepONet) to rapidly predict FUS pressure fields in patient spinal cords. Unlike conventional neural networks, DeepONets are well equipped to approximate the solution operator of the parametric partial differential equations (PDEs) that govern the behavior of FUS waves with varying initial and boundary conditions (i.e., new transducer locations or spinal cord geometries) without requiring extensive simulations. Trained on simulated pressure maps across diverse patient anatomies, this surrogate model achieves real-time predictions with only a 2% loss on the test set, significantly accelerating the modeling of nonlinear physical systems in heterogeneous domains. By facilitating rapid parameter sweeps in surgical settings, this work provides a crucial step toward precise and individualized solutions in neurosurgical treatments.

翻译：聚焦超声（FUS）疗法是一种前景广阔的工具，可用于脊髓损伤（SCI）的精准靶向治疗，其亚毫米级精度能够增强损伤部位的血流，同时最大限度地减少对周围组织的影响。然而，其疗效对超声源放置位置高度敏感，因为脊髓的复杂几何结构和声学异质性会扭曲并衰减FUS信号。目前的方法依赖于计算机模拟来求解控制波传播方程，并利用脊髓解剖结构的超声图像计算患者特异性压力分布图。虽然精确，但这些高保真模拟计算量大，完成参数扫描需要长达数小时，这对于实时手术决策而言并不实用。为解决这一瓶颈，我们提出了一种卷积深度算子网络（DeepONet），用于快速预测患者脊髓中的FUS压力场。与传统神经网络不同，DeepONet能够很好地逼近参数偏微分方程（PDEs）的解算子，这些方程控制着具有不同初始和边界条件（即新的换能器位置或脊髓几何结构）的FUS波的行为，而无需进行大量模拟。该代理模型基于不同患者解剖结构的模拟压力分布图进行训练，在测试集上仅损失2%即可实现实时预测，显著加速了异质域中非线性物理系统的建模。通过促进手术环境中的快速参数扫描，这项工作为神经外科治疗中实现精准个体化解决方案迈出了关键一步。