$\mathrm{SE}(3)$-equivariant hemodynamics estimation on arterial surface meshes using graph convolutional networks

Julian Suk, Pim De Haan, Phillip Lippe, Christoph Brune, Jelmer M. Wolterink

Keywords: Geometric Deep Learning, Computational Fluid Dynamics, Wall Shear Stress

TL;DR: Learning wall shear stress on the artery surface using group-equivariant graph neural networks.

Abstract: Hemodynamic field estimation on the artery surface is valuable for patient-specific prognosis, diagnosis, and treatment of cardiovascular disease. Medical biomarkers like wall shear stress (WSS) can be obtained from computational fluid dynamics (CFD) simulation of the blood flow. Machine-learning methods could accelerate or replace the time-intensive CFD simulation. We propose a graph convolutional network (GCN) that predicts hemodynamic fields mapped to the vertices of a finite-element surface mesh. Our neural network is end-to-end $\mathrm{SE}(3)$-equivariant and uses anisotropic convolution filters, as well as pooling layers, informed by the mesh structure. We generate a large dataset of CFD simulations in synthetic arteries which we use to train and evaluate our neural network. We show that our method can accurately predict WSS, up to two orders of magnitude faster than CFD.