# Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Models

arXiv: https://arxiv.org/abs/2501.09046 · HTML: https://mlsanity.com/paper/2501.09046/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 15 Jan 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [Geometric Algebra Transformer](https://mlsanity.com/paper/2305.18415/) (2023)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks](https://mlsanity.com/paper/2303.07310/) (2023)
- [Automated generation of 0D and 1D reduced-order models of patient-specific blood flow](https://mlsanity.com/paper/2111.04878/) (2021)
- [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)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [Attention-based Multi-fidelity Machine Learning Model for Computational Fractional Flow Reserve Assessment](https://mlsanity.com/paper/2311.11397/) (2023)

## Built on by (most cited first, 2 of 2)

- [Active Learning for Deep Learning-Based Hemodynamic Parameter Estimation](https://mlsanity.com/paper/2503.03453/) (2025)
- [Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Models](https://mlsanity.com/paper/2507.22817/) (2025)

## Abstract (arXiv)

Coronary artery disease, caused by the narrowing of coronary vessels due to atherosclerosis, is the leading cause of death worldwide. The diagnostic gold standard, fractional flow reserve (FFR), measures the trans-stenotic pressure ratio during maximal vasodilation but is invasive and costly. This has driven the development of virtual FFR (vFFR) using computational fluid dynamics (CFD) to simulate coronary flow. Geometric deep learning algorithms have shown promise for learning features on meshes, including cardiovascular research applications. This study empirically analyzes various backends for predicting vFFR fields in coronary arteries as CFD surrogates, comparing six backends for learning hemodynamics on meshes using CFD solutions as ground truth. The study has two parts: i) Using 1,500 synthetic left coronary artery bifurcations, models were trained to predict pressure-related fields for vFFR reconstruction, comparing different learning variables. ii) Using 427 patient-specific CFD simulations, experiments were repeated focusing on the best-performing learning variable from the synthetic dataset. Most backends performed well on the synthetic dataset, especially when predicting pressure drop over the manifold. Transformer-based backends outperformed others when predicting pressure and vFFR fields and were the only models achieving strong performance on patient-specific data, excelling in both average per-point error and vFFR accuracy in stenotic lesions. These results suggest geometric deep learning backends can effectively replace CFD for simple geometries, while transformer-based networks are superior for complex, heterogeneous datasets. Pressure drop was identified as the optimal network output for learning pressure-related fields.