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arXiv · 2302.08780

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

Julian Suk·Christoph Brune·Jelmer M. Wolterink
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Abstract

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.

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Julian Suk, Christoph Brune, Jelmer M. Wolterink. 2023-08-04. SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets. https://doi.org/10.1007/978-3-031-35302-4_46

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