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Hemodynamic velocity fields in coronary arteries could be the basis ofvaluable biomarkers for diagnosis, prognosis and treatment planning incardiovascular disease. Velocity fields are typically obtained frompatient-specific 3D artery models via computational fluid dynamics (CFD).However, CFD simulation requires meticulous setup by experts and istime-intensive, which hinders large-scale acceptance in clinical practice. Toaddress this, we propose graph neural networks (GNN) as an efficient black-boxsurrogate method to estimate 3D velocity fields mapped to the vertices oftetrahedral meshes of the artery lumen. We train these GNNs on synthetic arterymodels 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-foldspeed-up compared to CFD. We demonstrate how to construct an SE(3)-equivariantGNN that is independent of the spatial orientation of the input mesh and showhow this reduces the necessary amount of training data compared to a baselineneural network.

SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets