  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.
