Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall

Abstract

Computational fluid dynamics (CFD) is a valuable asset for patient-specific cardiovascular-disease diagnosis and prognosis, but its high computational demands hamper its adoption in practice. Machine-learning methods that estimate blood flow in individual patients could accelerate or replace CFD simulation to overcome these limitations. In this work, we consider the estimation of vector-valued quantities on the wall of three-dimensional geometric artery models. We employ group equivariant graph convolution in an end-to-end SE(3)-equivariant neural network that operates directly on triangular surface meshes and makes efficient use of training data. We run experiments on a large dataset of synthetic coronary arteries and find that our method estimates directional wall shear stress (WSS) with an approximation error of 7.6% and normalised mean absolute error (NMAE) of 0.4% while up to two orders of magnitude faster than CFD. Furthermore, we show that our method is powerful enough to accurately predict transient, vector-valued WSS over the cardiac cycle while conditioned on a range of different inflow boundary conditions. These results demonstrate the potential of our proposed method as a plugin replacement for CFD in the personalised prediction of hemodynamic vector and scalar fields.

Published in "Computers in Biology and Medicine"

References in corpus (1)

• CNNs on Surfaces using Rotation-Equivariant Features

Cited by in corpus (3)

• Physics-informed graph neural networks for flow field estimation in carotid arteries
• Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior
• Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs