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

TL;DR

This paper introduces an SE(3)-equivariant neural network using group convolution on triangular meshes to efficiently estimate blood flow dynamics on artery walls, significantly reducing computation time compared to CFD.

Contribution

The work presents a novel end-to-end neural network that operates directly on surface meshes for accurate, fast hemodynamic estimation, leveraging group equivariance for improved performance.

Findings

Estimates wall shear stress with 7.6% error and 0.4% NMAE.

Achieves up to 100x faster predictions than CFD.

Accurately predicts transient WSS over cardiac cycles.

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.