Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not widely available, such as 4D flow magnetic resonance imaging (MRI). In this work, we create a surrogate model for hemodynamic flow field estimation, powered by machine learning. We train graph neural networks that include priors about the underlying symmetries and physics, limiting the amount of data required for training. This allows us to train the model using moderately-sized, in-vivo 4D flow MRI datasets, instead of large in-silico datasets obtained by computational fluid dynamics (CFD), as is the current standard. We create an efficient, equivariant neural network by combining the popular PointNet++ architecture with group-steerable layers. To incorporate the physics-informed priors, we derive an efficient discretisation scheme for the involved differential operators. We perform extensive experiments in carotid arteries and show that our model can accurately estimate low-noise hemodynamic flow fields in the carotid artery. Moreover, we show how the learned relation between geometry and hemodynamic quantities transfers to 3D vascular models obtained using a different imaging modality than the training data. This shows that physics-informed graph neural networks can be trained using 4D flow MRI data to estimate blood flow in unseen carotid artery geometries.

翻译：血流动力学参数是评估心血管疾病（如动脉粥样硬化）的重要生物医学风险因子。这些参数的无创活体测量仅能通过少数尚未广泛普及的成像技术实现，例如四维血流磁共振成像（4D flow MRI）。本研究构建了一种基于机器学习的血流动力学流场估计替代模型。我们训练了包含底层对称性与物理先验知识的图神经网络，从而减少训练所需的数据量。这使得我们能够使用中等规模的活体4D flow MRI数据集进行训练，而非当前标准所依赖的计算流体力学（CFD）生成的大规模仿真数据集。通过结合经典的PointNet++架构与群可操纵层，我们构建了一个高效的等变神经网络。为融入物理信息先验，我们推导了相关微分算子的高效离散化方案。我们在颈动脉中进行了大量实验，结果表明该模型能够准确估计颈动脉中的低噪声血流动力学流场。此外，我们展示了模型学习到的几何形态与血流动力学参数之间的关联关系，能够迁移至通过不同成像模态获取的三维血管模型。这证明基于物理信息的图神经网络可通过4D flow MRI数据训练，实现对未见颈动脉几何形态中血流状态的准确估计。