Key result
The deep vectorised operator model produced accurate estimates of pulsatile velocity and pressure with an approximation disparity of 0.368 ± 0.079 compared to computational fluid dynamics.
Why the study?
Cardiovascular hemodynamic fields provide valuable decision markers for coronary artery disease, but computational fluid dynamics requires a time-efficient surrogate model for estimating pulsatile hemodynamics from steady-state priors.
Does a deep vectorised operator machine learning model accurately estimate pulsatile hemodynamics in coronary arteries compared to computational fluid dynamics?
Does a deep vectorised operator machine learning model accurately estimate pulsatile hemodynamics in coronary arteries compared to computational fluid dynamics?
Deep vectorised operators provide a time-efficient and accurate machine learning surrogate for estimating pulsatile hemodynamics in coronary arteries, potentially overcoming the high computational costs of standard CFD.
BACKGROUND AND OBJECTIVE: 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. METHODS: 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. RESULTS: We show that our model produces accurate estimates of the pulsatile velocity and pressure (approximation disparity 0.368 ± 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. CONCLUSION: This shows that deep vectorised operators are a powerful modelling tool for cardiovascular hemodynamics estimation in coronary arteries and beyond.
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Suk et al. (2025) studied Coronary artery disease (n=74). Deep vectorised operators (machine learning model) vs. Computational fluid dynamics (CFD) simulations was evaluated on Approximation disparity of pulsatile velocity and pressure estimation. The deep vectorised operator model produced accurate estimates of pulsatile velocity and pressure with an approximation disparity of 0.368 ± 0.079 compared to computational fluid dynamics.
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