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

TL;DR

This work systematically benchmarked six geometric deep learning backends for learning hemodynamic scalar fields on coronary artery meshes to predict vFFR, using steady CFD ground truth from 1,500 synthetic bifurcations and 427 patient-specific cases. Transformers, particularly LaB-GATr, provided the best generalization to real patient anatomies, while training on the pressure drop as the learning target yielded the most accurate vFFR reconstructions across synthetic and real data. The study highlights the importance of including local geometric and boundary features (e.g., normals, geodesics, inflow, inlet pressure) and demonstrates that while CFD surrogates work well for simple geometries, complex patient-specific meshes necessitate global-context architectures. Overall, the results position transformer-based GDL models as effective surrogates for accelerating vFFR estimation in CAD diagnostics, with pressure-drop learning as a robust objective.

Abstract

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.

Figures (6)

• Figure 1: Representation of the workflow adopted for the training of all models. First, models are trained on the synthetic dataset to learn one of three output variables; after evaluation, they are retrained on the patient-specific dataset using the best-performing variable, with per-vertex feature encoding applied consistently across both datasets. Blue boxes and arrows refer to the pipeline applied to synthetic datasets; orange ones refer to patient-specific data.
• Figure 2: Maps of vFFR computed from CFD (ground truth) on the synthetic bifurcation dataset, and inferred by each model, using different learning variables for one case of the test set.
• Figure 3: Boxplots showing the performance of each model on the test set, learning pressure field, in terms of point-wise differences (top row) and approximation disparities (bottom row) between vFFR predictions and CFD-derived values.
• Figure 4: Boxplots showing the performance of each model on the test set, learning pressure drop field, in terms of point-wise differences (top row) and approximation disparities (bottom row) between vFFR predictions and CFD-derived values.
• Figure 5: Boxplots showing the performance of each model on the test set, learning vFFR field, in terms of point-wise differences (top row) and approximation disparities (bottom row) between vFFR predictions and CFD-derived values.