Learning hemodynamic scalar fields on coronary artery meshes: A benchmark of geometric deep learning models

Coronary artery disease involves the narrowing of coronary vessels due to atherosclerosis and is currently the leading cause of death worldwide. The gold standard for its diagnosis is the fractional flow reserve (FFR) examination, which measures the trans-stenotic pressure ratio during maximal vasodilation. However, the invasiveness and cost of this procedure have prompted the development of computer-based virtual FFR (vFFR) computation, which simulates coronary flow using computational fluid dynamics (CFD) techniques. Geometric deep learning algorithms have recently shown the capability to learn features on meshes, including applications in cardiovascular research. In this work, we aim to conduct a comprehensive empirical analysis of different backends for predicting vFFR fields in coronary arteries, serving as surrogates for CFD simulations. We evaluate six different backends and compare their performance in learning hemodynamics on meshes using CFD solutions as ground truth. This study is divided into two main parts: i) First, we use a dataset of 1,500 synthetic bifurcations of the left coronary artery. Each model is trained to predict various pressure-related fields, from which the vFFR field is reconstructed. We compare the models' performance when different learning variables are used during training. ii) Second, we use a dataset of 427 patient-specific CFD simulations from a previous study by our group. Here, we repeat the experiments conducted on the synthetic dataset, focusing on the learning variable that yielded the best performance in the synthetic dataset. Most backends achieved very good performance on the synthetic dataset, particularly when learning the pressure drop over the manifold. For other network output variables (e.g., pressure and the vFFR field), transformer-based backends outperformed all other architectures. When trained on patient-specific data, transformer-based architectures were the only ones to achieve strong performance, both in terms of average per-point error and in accurately predicting vFFR in stenotic lesions. Our findings indicate that various geometric deep learning backends can serve as effective CFD surrogates for problems involving simple geometries. However, for tasks involving datasets with complex and heterogeneous topologies, transformer-based networks are the optimal choice. Additionally, pressure drop emerged as the optimal network output for learning pressure-related fields.