Modelling cardiopulmonary interactions. Towards anatomically detailed and physiologically accurate cardiorespiratory models

In the last decades, there has been a growing interest in understanding the complex physiological mechanisms that regulate the cardiovascular and respiratory systems and their interactions, due to the increasing healthcare burden related to cardiorespiratory diseases. To this end, physiologically accurate mathematical and computational models can provide an effective tool for the analysis of several physiopathological states and therapeutic strategies through in-silico experiments. Most existing cardiorespiratory models rely on lumped parameter (0D) descriptions not only for the respiratory system and the heart, but also for systemic and pulmonary circulatory districts. This work introduces a novel geometrically multiscale 1D-0D model that couples the fine description of blood flow in 1D domains obtained through the closed-loop Anatomically-Detailed Arterial-Venous Network (ADAVN) model with a PDE model for passive scalar transport and ODE models describing lung and peripheral gas exchange, lung mechanics and local autoregulation. After a brief literature review, the first part of this thesis presents the methodological framework, detailing the different components of our model and the numerical methods necessary for an accurate solution of the coupled 1D blood flow-transport system. We describe the vascular networks employed for simulations, including a reduced arterial-venous network (ADAVN86) model developed to accelerate the model building and parameter tuning process, and 0D models of the heart (accounting both for a linear and nonlinear end diastolic pressure volume relationship), pulmonary circulation, lungs, peripheral terminals and gas exchange. We propose a first and a second order numerical method for the solution of the 1D coupled blood flow-transport problem, examining the numerical challenges posed by the need to guarantee mass conservation at a discrete level. Finally, we introduce a well-balanced high-order numerical method for the solution of non-conservative hyperbolic PDEs with source terms, able to accurately describe steady-state solutions in the presence of algebraic and/or geometric source terms. The second part of this thesis focuses on the verification, validation and application of increasingly comprehensive physiological models, transitioning from a purely cardiovascular setting (the original ADAVN model), to anatomically and physiologically accurate descriptions of cardiopulmonary interactions. We first assess the impact of cardiopulmonary mechanical interactions on system haemodynamics, validating our results against patient data published in the literature, and assessing their robustness by means of a local sensitivity analysis. These tests, performed with a cardiac model with a linear end-diastolic PV relationship, required substantial reparametrization of chamber elastances to guarantee physiological results in the presence of respiration. This motivated the adoption of a nonlinear end‑diastolic model for subsequent studies, introducing a more realistic constraint on chamber volume changes. We then extend our model to include a description of tracer/gas transport and gas exchange. The transport module is validated through a bolus test against patient data and simulation results obtained through physiology-based pharmacokinetic models. The gas exchange model, parametrized to exploit the anatomical detail provided by our vascular networks, is validated under baseline physiological conditions against literature data and 0D model predictions. Finally, we examine three cerebral local autoregulation models: a purely myogenic one, its combination with a carbon dioxide reactivity model, and a purely metabolic autoregulation model which responds to oxygen and carbon dioxide perturbations. All reproduce the expected physiological responses across multiple test scenarios. The myogenic model, with modified parameters, is further applied to study foot perfusion in the presence of stenoses and occlusions during a cuff‑induced ischaemia test. By combining methodological advances with the development of a comprehensive and extensible framework for the multiscale modelling of cardiorespiratory physiology, which was extensively verified and validated against clinical data, this work establishes a robust foundation for future in‑silico investigations of complex cardiopulmonary interactions. The resulting framework is designed to support both fundamental physiological research and the development of patient‑specific simulations, ultimately contributing to the improvement of our understanding, diagnosis, and treatment of cardiorespiratory diseases.