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

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.

Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior

Cardiovascular hemodynamic fields provide valuable medical decision markers for coronary artery disease. Computational fluid dynamics (CFD) is the gold standard for accurate, non-invasive evaluation of these quantities in vivo. In this work, we propose a time-efficient surrogate model, powered by machine learning, for the estimation of pulsatile hemodynamics based on steady-state priors. We introduce deep vectorised operators, a modelling framework for discretisation independent learning on infinite-dimensional function spaces. The underlying neural architecture is a neural field conditioned on hemodynamic boundary conditions. Importantly, we show how relaxing the requirement of point-wise action to permutation-equivariance leads to a family of models that can be parametrised by message passing and self-attention layers. We evaluate our approach on a dataset of 74 stenotic coronary arteries extracted from coronary computed tomography angiography (CCTA) with patient-specific pulsatile CFD simulations as ground truth. We show that our model produces accurate estimates of the pulsatile velocity and pressure while being agnostic to re-sampling of the source domain (discretisation independence). This shows that deep vectorised operators are a powerful modelling tool for cardiovascular hemodynamics estimation in coronary arteries and beyond.