Physics-informed graph neural networks for flow field estimation in carotid arteries

TL;DR

This paper introduces a physics-informed graph neural network model that accurately estimates blood flow in carotid arteries using limited 4D MRI data, leveraging symmetry priors and transferability across modalities.

Contribution

The work develops an equivariant graph neural network with physics-informed priors that can be trained on moderate MRI datasets to estimate flow in unseen vascular geometries.

Findings

Accurately estimates low-noise flow fields in carotid arteries.

Transfers learned relations to different imaging modalities.

Requires less data than traditional CFD-based models.

Abstract

Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not widely available, such as 4D flow magnetic resonance imaging (MRI). In this work, we create a surrogate model for hemodynamic flow field estimation, powered by machine learning. We train graph neural networks that include priors about the underlying symmetries and physics, limiting the amount of data required for training. This allows us to train the model using moderately-sized, in-vivo 4D flow MRI datasets, instead of large in-silico datasets obtained by computational fluid dynamics (CFD), as is the current standard. We create an efficient, equivariant neural network by combining the popular PointNet++ architecture with group-steerable layers. To incorporate the physics-informed priors, we derive an efficient discretisation scheme for the involved differential operators. We perform extensive experiments in carotid arteries and show that our model can accurately estimate low-noise hemodynamic flow fields in the carotid artery. Moreover, we show how the learned relation between geometry and hemodynamic quantities transfers to 3D vascular models obtained using a different imaging modality than the training data. This shows that physics-informed graph neural networks can be trained using 4D flow MRI data to estimate blood flow in unseen carotid artery geometries.