Development of a multiscale 1D-0D cardiovascular model to investigate orthostatic stress responses

The study of orthostatic stress effects on the cardiovascular system has gained significant attention since the 1960s, initially driven by the space race, and more recently by advances in medicine and technology. The full extent of the physiological responses to orthostatic stress still remains not fully understood, owing to the complex interplay between multiple body systems and external factors that influence cardiovascular function. To address this complexity, increasingly sophisticated computational models of the cardiovascular system have been developed. The accuracy of these models in reproducing physiological responses to orthostatic stress depends on the physical description of the problem, on the numerical methods used to approximate the solution, and on the representation of the physiological mechanisms involved. A clear and realistic formulation of the physical processes is essential for capturing the fundamental features of the modeled interactions. At the same time, numerical aspects can significantly influence the accuracy and reliability of simulations. Finally, the extent to which the model captures the complexity of regulatory responses directly impacts the model’s ability to reflect real-world behavior under orthostatic stress. This Ph.D. thesis tackles all these challenges, presenting an extension of the anatomically detailed arterial-venous network (ADAVN) model, a multiscale model originally developed to reproduce hemodynamics of the entire circulation with high anatomical fidelity. The ADAVN model comprises a unique 3D spatial characterization of both arterial and venous networks that captures the anatomical geometry of the human vasculature. Blood flow in these networks is described using partial differential equations (PDEs) in one-dimension (1D). In particular, it adopts a 1D blood flow model, where a viscoelastic tube law is used to represent the mechanics of the vessels’ wall. To incorporate the effects of gravity, an additional term has been introduced in the governing equations of the 1D blood flow model, leading to a novel and unique cardiovascular model that accounts for gravitational influences in both arterial and venous networks based on vessels’ geometrical properties. The first part of this thesis focuses on examining how different parameterizations of selected tube laws alter the mathematical properties (namely hyperbolicity and genuine non-linearity of characteristic fields) of the considered 1D blood flow model. We investigate how constraining admissible parameter ranges influences the tube law’s ability to fit human and ovine experimental data. Notably, we demonstrate that the viscoelastic tube law, employed in the ADAVN model, preserves the mathematical properties of the 1D blood flow model despite the imposed parametrization, making it a robust tool for further developments of the ADAVN model. The second part of this thesis addresses the challenge of accurately computing the numerical solution of our model. To this end, we propose a well-balanced high-order path-conservative numerical method capable of solving non-conservative hyperbolic PDEs. This method is able to describe steady-state solutions in presence of geometric- and algebraic-type source terms, as well as to correctly estimate transient solutions. Particularly, we show its crucial ability to accurately reproduce hydrostatic pressure distributions when applied to solve the 1D blood flow model with gravity in complex vascular networks. The third part of this thesis is dedicated to the physiological aspects of the cardiovascular response to orthostatic stress. Due to the reduced availability of data on the venous system and the limited understanding of the regulatory mechanisms involved, we collaborated with a team of physiologists from the University of Auckland (New Zealand) to answer specific questions regarding the lack of venous data and the functioning of the regulatory mechanisms, aiming to clarify how these elements coordinate to regulate blood flow and pressure under different orthostatic conditions. We present the outcomes of this collaboration, detailing the design of an experiment to collect relevant physiological data in compliance with ethical and privacy standards. We describe the recruitment of volunteers, the data acquisition, and the processing of raw measurements into meaningful metrics for model validation. Notably, we underline that the collected data confirm existing findings in literature and provide new insights into the venous system and the regulatory mechanisms. Finally, the last part of this thesis concentrates on simulating orthostatic stress using the extended ADAVN model. This application integrates all previously developed theoretical knowledge, numerical tools and incorporates the acquired experimental data. We detail the simulation setup and validate the obtained results. Furthermore, we identify the current limitations of the ADAVN model and highlight the aspects that require further refinement to capture the key physiological mechanisms involved in the cardiovascular response to orthostatic stress. This thesis brings together multidisciplinary studies that represent an important first step towards the development of a cardiovascular model capable of reproducing essential physiological processes during postural transitions. The resulting framework offers a valuable tool for advancing our understanding of the cardiovascular system’s response to orthostatic stress.