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 silico. 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 (approximation disparity 0.368 $\pm$ 0.079) while being agnostic ($p < 0.05$ in a one-way ANOVA test) to re-sampling of the source domain, i.e. discretisation-independent. This shows that deep vectorised operators are a powerful modelling tool for cardiovascular hemodynamics estimation in coronary arteries and beyond.