Hemodynamic characterization of heart and venous valves based on multi-phase blood flow and FSI modelling

Abstract

This thesis explores physiological phenomena and pathological conditions through the lens of in-silico modeling, a technique that complements traditional in-vitro and in-vivo studies, which often face limitations in replicating complex biological conditions and measuring certain vital parameters. Advances in high-performance computing have significantly enhanced the capability of in-silico models, allowing for the simulation of a wide range of physiological states from rest to stress, which are challenging to achieve through conventional experimental setups. By integrating Fluid-Structure Interaction (FSI) models, this research leverages both fluid mechanics and structural dynamics to effectively simulate intricate physiological processes within the human body, addressing venous valve function, potential risks such as Deep Vein Thrombosis (DVT), and aortic stenosis, contributing to the understanding of blood flow dynamics and guiding potential advancements in therapeutic strategies. Focusing specifically on the dynamics of biological valves, the research highlights their pivotal role and the complexities involved in their dysfunction, which are often linked to severe cardiovascular conditions. The thesis progresses from simulating simple single-phase models of venous valves to more sophisticated multi-phase models, utilizing methodologies to capture the complexities of the multi-phase nature of blood. Employing advanced techniques such as the Immersed Boundary-Finite Element (IBFE) method and the Arbitrary Lagrangian Eulerian (ALE) formulation, the thesis enhances our understanding of valve dynamics under various pathological states and contributes valuable insights for future cardiovascular disease research and potential therapeutic developments. A key aspect of this thesis is the utilization of various computational indices and descriptors derived from FSI simulations, which allows for a more comprehensive understanding of the biomechanical environment surrounding venous and aortic valves. After this general explanation of the thesis scope and a brief description of the methodologies utilized, a concise summary of the individual chapters is presented below. The chapter on geometry modeling explores the complex structures of venous and aortic valves, which are critical for simulating their dynamics in computational studies. It begins by detailing the modeling of the venous valve, chosen for its relative simplicity compared to the aortic valve, and describes the modifications made to synthetic geometries to meet the requirements of both single-phase and two-phase FSI simulations. For aortic valves, the chapter discusses how synthetic geometries, adapted from Computer-Aided Design (CAD) frameworks, are further modified to incorporate representations of calcification, which significantly affects valve functionality. The severity of calcification is categorized, and the models are adjusted to reflect different grades, facilitating the analysis of its impact on valve hemodynamics. This detailed geometric modeling forms the foundation for advanced simulations, providing a deeper insight into the mechanical behavior of these valves under various pathological conditions. The next chapter elaborates on the development and implementation of single-phase FSI simulations using the IBM to model the complex interactions between fluid mechanics and structural dynamics. The focus is on Immersed Boundary Method's (IBM) application in addressing significant displacements in fluid-structure systems, utilizing a computational framework that integrates Lagrangian descriptions for structures and Eulerian descriptions for fluid dynamics. The IBM's methodology is detailed, showcasing how forces and stresses are calculated and interact within the fluid and structure domains using integral transforms with delta function kernels to couple Eulerian and Lagrangian variables. The simulation also employs constitutive laws for material behavior, including a Neo-Hookean hyperelastic model for the aortic valve, to accurately depict the elastic properties of biological tissues. Additionally, the chapter discusses the numerical schemes and boundary conditions critical for capturing the physics of fluid-structure interactions. Advanced discretization techniques for both the fluid and structure domains are employed to ensure high fidelity in the simulation. The chapter on two-phase FSI model development investigates the transition from single-phase blood flow model to more complex two-phase model, crucial for accurately simulating the dynamics of blood flow involving both Red Blood Cells (RBCs) and plasma. The ANSYS Fluent-Structural coupled module, utilizing the ALE method, is employed due to its capability for handling two distinct miscible phases, providing a more realistic representation of blood dynamics where the volume fractions of phases sum to one, ensuring the conservation of mass and momentum. Significantly, the integration of volume fraction equations, conservation laws, and specific equations for the momentum of RBC and plasma phases allow for detailed modeling of interactions within the blood. This method accounts for forces such as drag, which is essential for understanding the complex interactions in blood flow. The use of the ANSYS software for FSI models demonstrates the application of partitioned coupling techniques, maintaining computational efficiency while ensuring accurate modeling of the physics involved in fluid-structure interactions. This setup is vital for understanding the mechanical and hemodynamic behavior of cardiovascular structures like deep veins under realistic physiological conditions. Chapter six presents the hemodynamic characterization parameters, which are essential in studying the valves' function. These metrics include transvalvular, Wall Shear Stress (WSS)-based indices, and the helicity descriptors, offering valuable insights into the behavior of valves under healthy and pathological conditions. The transvalvular indices encompass Geometric Orifice Area (GOA), maximum jet velocity, kinetic energy, energy dissipation, and vorticity intensity, which are critical for assessing valve performance, particularly in the context of aortic stenosis. These indices provide a detailed understanding of the energy transport and flow patterns that influence valve function. In addition to transvalvular indices, WSS-based indices such as Time-Averaged Wall Shear Stress (TAWSS), Oscillatory Shear Index (OSI), and Relative Residence Time (RRT) are examined. They help quantify the interactions between blood flow and the vascular endothelium, shedding light on how shear environments contribute to endothelial health and cardiovascular disease progression. The chapter also introduces helicity-based descriptors, which provide a perspective on the rotational aspects of blood flow in the aortic domain. Helicity, a scalar measure of helical motion in fluid flow, is crucial for evaluating the efficiency of blood transport and identifying potential pathological developments. Six bulk flow helicity descriptors are discussed, each quantifying various aspects of flow topology and helical structure, particularly in the presence of aortic valve calcifications. These descriptors highlight the importance of helical flow patterns in understanding aortic valve performance and the associated hemodynamic consequences under both healthy and calcified conditions. Last chapter presents the critical findings from the single-phase and two-phase FSI simulations. For venous valves, the results highlight the relationship between increased flow rates and the potential for flow disturbances, particularly under conditions of elevated pressure. This includes the identification of regions prone to recirculation, which may correlate with thrombosis risk. Key transvalvular indices and WSS-based metrics provide further insights into the mechanical stresses exerted on the valve leaflets. In the case of aortic valves, the results demonstrate the impact of calcification on hemodynamic patterns. The simulations reveal how varying degrees of calcification influence energy dissipation and helicity, offering a detailed perspective on the altered flow dynamics within the valve. These findings provide a comprehensive understanding of how pathological conditions affect the biomechanical environment of both venous and aortic valves. The two-phase FSI simulations reveal distinct flow behaviors between plasma and RBCs under varying flow rates. Higher velocities lead to vortex formation, pressure fluctuations, and RBC accumulation near valve cusps, especially in low shear regions. WSS-based indices like TAWSS and OSI highlight areas prone to flow disturbances and thrombosis risk. These findings underscore the value of two-phase modeling in understanding venous function and thrombus formation.