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

• URL: http://arxiv.org/abs/2212.05023v2
• Date: Fri, 14 Jun 2024 18:34:21 GMT
• Title: Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall
• Authors: Julian Suk, Pim de Haan, Phillip Lippe, Christoph Brune, Jelmer M. Wolterink,
• Abstract summary: 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. 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.
• Score: 13.113110989699571
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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