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

2025-07-30

AI Summary

Accurate and efficient estimation of wall shear stress (WSS) in abdominal aortic aneurysms (AAA) remains challenging due to the high computational cost of patient-specific computational fluid dynamics (CFD) simulations. Method: We propose an E(3)-equivariant geometric deep learning surrogate model that replaces CFD. It integrates robust geometric descriptors with projective geometric algebra to explicitly encode vascular topological variations, boundary condition perturbations, and mesh resolution differences. The model is trained on 100 clinically derived patient cases, jointly generated from CT image segmentation and high-fidelity CFD. Results: Our model achieves accurate prediction of transient WSS and demonstrates strong generalization and robustness across external test sets, geometric reconstructions, boundary condition shifts, and diverse topological configurations. This work presents the first synergistic integration of E(3)-equivariance and projective geometric algebra in AAA hemodynamic modeling, significantly enhancing clinical deployability.

Technology Category

• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• Estimating wall shear stress in abdominal aortic aneurysms efficiently
• Developing generalizable neural models for hemodynamic parameter prediction
• Reducing computational cost of CFD simulations using deep learning

Innovation

• E(3)-equivariant deep learning model
• Robust geometrical descriptors
• Projective geometric algebra