Hemodynamic velocity fields in coronary arteries could be the basis of valuable biomarkers for diagnosis, prognosis and treatment planning in cardiovascular disease. Velocity fields are typically obtained from patient-specific 3D artery models via computational fluid dynamics (CFD). However, CFD simulation requires meticulous setup by experts and is time-intensive, which hinders large-scale acceptance in clinical practice. To address this, we propose graph neural networks (GNN) as an efficient black-box surrogate method to estimate 3D velocity fields mapped to the vertices of tetrahedral meshes of the artery lumen. We train these GNNs on synthetic artery models and CFD-based ground truth velocity fields. Once the GNN is trained, velocity estimates in a new and unseen artery can be obtained with 36-fold speed-up compared to CFD. We demonstrate how to construct an SE(3)-equivariant GNN that is independent of the spatial orientation of the input mesh and show how this reduces the necessary amount of training data compared to a baseline neural network.

翻译：冠状动脉中的血流动力学速度场可作为心血管疾病诊断、预后及治疗规划中具有价值的生物标志物基础。速度场通常通过计算流体动力学（CFD）从患者特异性三维动脉模型获得。然而，CFD模拟需要专家进行精细的配置且耗时较长，这阻碍了其在临床实践中的大规模应用。为解决这一问题，我们提出将图神经网络（GNN）作为一种高效的黑箱替代方法，用于估计映射到动脉腔体四面体网格顶点上的三维速度场。我们在合成动脉模型及基于CFD的真实速度场上训练这些GNN。一旦GNN训练完成，对于新且未见过的动脉，其速度估计相较于CFD可实现36倍的加速。我们展示了如何构建与输入网格空间方向无关的SE(3)等变GNN，并证明了相较于基准神经网络，这能减少所需的训练数据量。