Pipeline de simulation de perfusion du myocarde reposant sur des méthodes calculatoires d'apprentissage automatique

Coronary artery disease (CAD), affecting millions of people annually, is the leading cause of death worldwide. In recent decades, imaging-based computational models for blood flow simulation have emerged as a non-invasive and cost-effective approach for CAD diagnosis. A notable example is HeartFlow Inc., which provides patient-specific vascular models extracted from X-ray CT images to identify functionally significant disease in large coronary arteries. More recent advancements have extended such models to directly quantify myocardial blood flow by simulating the different scales of the cardiovascular network. These models typically extend segmented large coronary arteries from CT scans to the capillary bed by generating synthetic vascular trees. Blood flow is then modeled using a coupled approach, combining 3D or reduced-order Navier-Stokes (NS) equations for coronary arteries and Darcy's law to simulate myocardial perfusion. While these models have shown promising results, accurately assessing microvascular function and spatial blood flow distribution in the myocardium remains a challenge.This thesis aims to integrate myocardial perfusion simulation with machine learning (ML) to generate realistic myocardial perfusion images. By leveraging the strengths of both physics-based modeling and data-driven learning, this approach incorporates physical knowledge at various stages of the algorithm, potentially reducing the need for extensive patient data. The proposed methodology replaces individual components of the simulation—such as synthetic vessel generation and perfusion modeling—with ML-based models, leading to the development of an end-to-end ML pipeline. Real perfusion images can then be used to fine-tune the training of each component, which is initially pre-trained on simulation results.The first part of the thesis focuses on the generation of synthetic vascular trees. Traditional methods such as Constrained Constructive Optimization (CCO) are analyzed, and a novel approach is proposed, yielding more optimal solutions while improving computational efficiency. The method relies on solving an optimal transport problem using gradient-based optimization, opening the possibility of employing deep learning for synthetic tree generation.The second part explores deep learning techniques for solving Partial Differential Equations (PDEs), specifically the Darcy model for myocardial perfusion simulation. A Finite Volume Informed Graph Neural Network (FVINN) is introduced to approximate Darcy equation solutions on patient-specific myocardial meshes. This method integrates finite volume numerical discretization with Graph Neural Networks, enabling accurate and computationally efficient solutions.The third part presents a gradient-based solver for the coupled reduced-order NS and Darcy models for myocardial perfusion. This framework incorporates the previously introduced FVINN model alongside a differentiable solver for the 1D NS equations governing coronary artery flow. The approach has the potential to efficiently solve inverse problems by matching simulations to patient-specific data for non-invasive microvascular disease assessment. Additionally, this solver serves as a first step toward an ML-based approach for coupled perfusion modeling.Finally, the thesis investigates the prediction of patient-specific coronary total flow derived from perfusion imaging using ML models. This approach integrates CT images and simulation-based features, significantly improving baseline estimates.Overall, this work contributes to the fields of patient-specific myocardial perfusion simulation and physics-informed machine learning: it introduces novel methods for synthetic vascular tree generation, Deep Learning-based PDE solvers, and differentiable computational fluid dynamics solvers. The proposed methodologies pave the way for an end-to-end ML pipeline that integrates physical knowledge.