Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element method (FEM) is a proven technique to effectively approximate soft tissue deformation through biomechanical formulations, their degree of success boils down to a trade-off between accuracy and speed. To circumvent this problem, the most recent works in this domain have proposed leveraging data-driven models obtained by training various machine learning algorithms -- e.g., random forests, artificial neural networks (ANNs) -- with the results of finite element analysis (FEA) to speed up tissue deformation approximations by prediction. These methods, however, do not account for the structure of the finite element (FE) mesh during training that provides information on node connectivities as well as the distance between them, which can aid with approximating tissue deformation based on the proximity of force load points with the rest of the mesh nodes. Therefore, this work proposes a novel framework, PhysGNN, a data-driven model that approximates the solution of the FEM by leveraging graph neural networks (GNNs), which are capable of accounting for the mesh structural information and inductive learning over unstructured grids and complex topological structures. Empirically, we demonstrate that the proposed architecture, PhysGNN, promises accurate and fast soft tissue deformation approximations, and is competitive with the state-of-the-art (SOTA) algorithms while promising enhanced computational feasibility, therefore suitable for neurosurgical settings.

翻译：正确捕捉成像制神经外科手术中大脑内部变化的操作性大脑在图像制导神经外科程序中的变化是一个关键的任务,将预操作性数据与内操作性几何方法相匹配,以确保精确的外科导航。虽然有限元素方法(FEM)是经实践证明的通过生物机械配方有效接近软组织畸形的技术,但其成功程度归结为精确度和速度之间的权衡。为回避这一问题,该领域最近的工作提议利用通过培训各种机器学习算法 -- -- 例如随机森林、人工神经网络 -- -- 获得的数据驱动模型,以有限元素分析(FEA)的结果来加速通过预测加速组织畸形。不过,这些方法并不说明通过生物机械化配方配方的软组织结构结构结构(FE),在提供无偏差连接性连接和速度的训练期间,它们之间的距离,这可以帮助在与内表节节节节点的其余部分相比,使组织变形模型(Phys-GNNN) -- 和内结构结构结构的升级模型,用来将精度的精度定位定位定位定位定位定位定位定位系统进行。