# Mesh convolutional neural networks for wall shear stress estimation in 3D artery models

arXiv: https://arxiv.org/abs/2109.04797 · HTML: https://mlsanity.com/paper/2109.04797/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 10 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [Graph Convolutional Networks for Coronary Artery Segmentation in Cardiac CT Angiography](https://mlsanity.com/paper/1908.05343/) (2019)
- [Graph convolutional regression of cardiac depolarization from sparse endocardial maps](https://mlsanity.com/paper/2009.14068/) (2020)

## Built on by (most cited first, 9 of 9)

- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [Graph Neural Network with Local Frame for Molecular Potential Energy Surface](https://mlsanity.com/paper/2208.00716/) (2022)
- [LaB-GATr: geometric algebra transformers for large biomedical surface and volume meshes](https://mlsanity.com/paper/2403.07536/) (2024)
- [SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets](https://mlsanity.com/paper/2302.08780/) (2023)
- [An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations](https://mlsanity.com/paper/2206.14709/) (2022)
- [Importance of equivariant and invariant symmetries for fluid flow modeling](https://mlsanity.com/paper/2307.05486/) (2023)
- [End-to-end Wind Turbine Wake Modelling with Deep Graph Representation Learning](https://mlsanity.com/paper/2211.13649/) (2022)
- [A deep learning approach to wall-shear stress quantification: From numerical training to zero-shot experimental application](https://mlsanity.com/paper/2409.03933/) (2024)
- [Real-Time Pulsatile Flow Prediction for Realistic, Diverse Intracranial Aneurysm Morphologies using a Graph Transformer and Steady-Flow Data Augmentation](https://mlsanity.com/paper/2601.19876/) (2026)

## Abstract (arXiv)

Computational fluid dynamics (CFD) is a valuable tool for personalised, non-invasive evaluation of hemodynamics in arteries, but its complexity and time-consuming nature prohibit large-scale use in practice. Recently, the use of deep learning for rapid estimation of CFD parameters like wall shear stress (WSS) on surface meshes has been investigated. However, existing approaches typically depend on a hand-crafted re-parametrisation of the surface mesh to match convolutional neural network architectures. In this work, we propose to instead use mesh convolutional neural networks that directly operate on the same finite-element surface mesh as used in CFD. We train and evaluate our method on two datasets of synthetic coronary artery models with and without bifurcation, using a ground truth obtained from CFD simulation. We show that our flexible deep learning model can accurately predict 3D WSS vectors on this surface mesh. Our method processes new meshes in less than 5 [s], consistently achieves a normalised mean absolute error of ≤ 1.6 [%], and peaks at 90.5 [%] median approximation accuracy over the held-out test set, comparing favourably to previously published work. This demonstrates the feasibility of CFD surrogate modelling using mesh convolutional neural networks for hemodynamic parameter estimation in artery models.