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

TL;DR

This paper introduces a machine learning-based surrogate model using deep vectorised operators for efficient, discretisation-independent estimation of pulsatile hemodynamics in coronary arteries, validated against CFD simulations.

Contribution

It presents a novel neural architecture leveraging deep vectorised operators and permutation-equivariance for discretisation-independent hemodynamics estimation.

Findings

Accurate pulsatile velocity and pressure estimates with low approximation disparity.

Model is discretisation-independent and statistically similar across different sampling schemes.

Deep vectorised operators effectively model cardiovascular hemodynamics in coronary arteries.

Abstract

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.