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.

本研究解决了目前非侵入性测量颈动脉血流动力学参数难度大的问题。通过引入物理信息图神经网络，我们的模型能在仅需适量4D流动MRI数据的情况下，精确估计颈动脉血流场。研究显示，该方法能有效转移于不同几何结构的3D血管模型，具有广泛应用潜力。

物理信息图神经网络在颈动脉流场估计中的应用