Deep-Learning and POD-based modelling framework for real-time simulations of coronary pressure profiles

Coronary Artery Disease (CAD) is a leading cause of death worldwide, with 315 million cases reported in 2022. CAD onset is characterized by coronary arteries obstruction that reduce blood flow to the heart, increasing the risk of major cardiovascular events. In recent years, the physiological evaluation of CAD has gained momentum both in research and clinical practice, complementing diagnostic imaging techniques. Specifically, pressure gradient-based methods are currently considered a reference standard for assessing obstruction severity, but require invasive procedures with associated risks. A non-invasive alternative is offered by Computational Fluid Dynamics (CFD), but its adoption in the clinical practice is hampered by high computational costs. To overcome this inherent limitation, both Reduced Order Models (ROMs) and Deep Learning (DL) have been explored to accelerate CFD simulations. While ROMs effectively reduce costs, their use in patient-specific cases is hindered by the complexity of parametrizing anatomical variability. In contrast, DL can learn directly from varied geometries, thriving in patient specific applications. The aim of this thesis is to propose a DL-ROMs framework to predict pressure profiles along patient-specific 3D coronary artery geometries obtained from quantitative coronary angiography. A dataset of 184 patients was considered. CFD simulations were carried out on the reconstructed 3D coronary geometries. The resulting pressure fields were processed via Proper Orthogonal Decomposition (POD) to extract key pressure profile features. Subsequently, a 1D-CNN network architecture was adopted to map coronary vessels geometric and functional parametrizations to POD weights, enabling pressure field reconstruction for new coronary geometries. The developed workflow was validated using Monte Carlo simulations (MCs) and a Nested Cross-Validation (NCV) procedure. In both approaches, the original dataset of 184 coronary geometries was systematically partitioned to ensure a robust performance evaluation. Specifically, the MC method involved training 20 1D-CNN models with randomly resampled training and validation sets, tested on a hold-out test set. In parallel, NCV was implemented with an 8-fold outer loop and a 7-fold inner loop, allowing for unbiased performance assessment. The median normalized root mean square error (NRMSE) was 0.129 ± 0.119 for the MCs and 0.165 ± 0.043 for the NCV, demonstrating good predictive capabilities. However, the analysis of the entire coronary dataset in the NCV simulation revealed that certain 3D coronary geometries exhibited higher prediction errors. This was reflected in the 95° percentile of the NRMSE, which was 0.207 ± 0.165 for the MCs and 0.437 ± 0.372 for the NCV. The analysis of the Absolute Percentage Error (APE) and Normalized Dynamic Error (NDE) distributions confirmed the overall accuracy of the proposed approach. In the MCs, 95% of pointwise predictions showed an APE below 4.64% and an NDE below 0.35. As for the NCV, the APE 95° percentile resulted in 4.85%, while the NDE 95° percentile was 0.43, showing that most errors fell within a narrow range. In conclusion, this study highlights the potential of a simple, modular and customizable AI and POD-based framework for coronary hemodynamic predictions. While generalizable results are yet to be achieved, future improvements in dataset size and representativeness of geometric complexity could enhance the accuracy and the robustness of the proposed approach.