# Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Models

arXiv: https://arxiv.org/abs/2507.22817 · HTML: https://mlsanity.com/paper/2507.22817/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 67 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling](https://mlsanity.com/paper/2207.14663/) (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)
- [Physics-informed graph neural networks for flow field estimation in carotid arteries](https://mlsanity.com/paper/2408.07110/) (2024)
- [Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior](https://mlsanity.com/paper/2410.11920/) (2024)
- [Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Models](https://mlsanity.com/paper/2501.09046/) (2025)
- [Active Learning for Deep Learning-Based Hemodynamic Parameter Estimation](https://mlsanity.com/paper/2503.03453/) (2025)
- [Global Control for Local SO(3)-Equivariant Scale-Invariant Vessel Segmentation](https://mlsanity.com/paper/2403.15314/) (2024)

## Built on by (most cited first, 1 of 1)

- [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)

Abdominal aortic aneurysms (AAAs) are pathologic dilatations of the abdominal aorta posing a high fatality risk upon rupture. Studying AAA progression and rupture risk often involves in-silico blood flow modelling with computational fluid dynamics (CFD) and extraction of hemodynamic factors like time-averaged wall shear stress (TAWSS) or oscillatory shear index (OSI). However, CFD simulations are known to be computationally demanding. Hence, in recent years, geometric deep learning methods, operating directly on 3D shapes, have been proposed as compelling surrogates, estimating hemodynamic parameters in just a few seconds. In this work, we propose a geometric deep learning approach to estimating hemodynamics in AAA patients, and study its generalisability to common factors of real-world variation. We propose an E(3)-equivariant deep learning model utilising novel robust geometrical descriptors and projective geometric algebra. Our model is trained to estimate transient WSS using a dataset of CT scans of 100 AAA patients, from which lumen geometries are extracted and reference CFD simulations with varying boundary conditions are obtained. Results show that the model generalizes well within the distribution, as well as to the external test set. Moreover, the model can accurately estimate hemodynamics across geometry remodelling and changes in boundary conditions. Furthermore, we find that a trained model can be applied to different artery tree topologies, where new and unseen branches are added during inference. Finally, we find that the model is to a large extent agnostic to mesh resolution. These results show the accuracy and generalisation of the proposed model, and highlight its potential to contribute to hemodynamic parameter estimation in clinical practice.