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

TL;DR

This paper introduces an SE(3)-equivariant graph neural network that efficiently estimates arterial velocity fields from small datasets, significantly reducing computation time compared to traditional CFD methods.

Contribution

The paper presents a novel SE(3)-equivariant GNN architecture that is orientation-independent and requires less training data for accurate arterial velocity estimation.

Findings

36-fold speed-up over CFD simulations

Reduced training data needed due to SE(3)-equivariance

Effective velocity estimation on unseen artery models

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.