Hemodynamics of Native and Bioprosthetic Aortic Valves: Insights from a Reduced Degree-of-Freedom Model

Heart disease is the leading cause of deaths in the US with aortic valve (AV) diseases being major contributors. Valve replacement is the primary therapeutic indication for AV diseases and transcatheter aortic valve replacement (TAVR) provides a safe and minimally invasive option. However, post-TAVR patient outcomes show considerable variability with deployment parameters. TAVR valves are also susceptible to failure mechanisms like leaflet thrombosis which increase the risk for serious thromboembolic events. Early detection and intervention can avert such outcomes, but symptoms often manifest at advanced stages of valve failure. Continuous monitoring can facilitate early detection, but regulatory and technological challenges may hinder developing such technology through experimental or clinical means. Computer simulations enable unprecedented predictive capabilities which can help gain insights into the pathophysiology of valvular diseases, conduct in silico trials to design novel monitoring technologies and even guide surgeries for optimal valve deployment. However, accurate, yet efficient numerical models are required. This study describes the implementation of a versatile, efficient AV dynamics model in a previously developed fluid-structure interaction solver, and its application to each of these tasks. The model accelerates simulations by simplifying the constitutive parameter space and equations governing leaflet motion without compromising accuracy. It can simulate native and prosthetic valve dynamics exhibiting physiological and pathological function in idealized and personalized aorta anatomies. This computational framework is used to generate canonical and patient-specific simulation datasets describing hemodynamic differences secondary to healthy and pathological AVs. These differences help identify biomarkers which reliably predict the risk of valvular and vascular diseases. Changes in these biomarkers are used to assess whether TAVR can deter aortic disease progression. Next, statistical differences in such biomarkers recorded by virtual wearable or embedded sensor systems, between normal and abnormal AV function, are analyzed using data-driven methods to infer valve health. This lays the groundwork for inexpensive, at-home diagnostic technologies, based on digital auscultation and in situ embedded-sensor platforms. Finally, a simulation describing the deployment of a commercially available TAVR valve in a patient-specific aorta anatomy and the associated hemodynamics is presented. Such simulations empower clinicians to optimize TAVR deployment and, consequently, patient outcomes

Implicit-Explicit Time stepping for a Two-Dimensional Inviscid Fluid-Structure Interaction Solver

This thesis describes the development of a two-dimensional, high-order, fluid-structure interaction (FSI) solver. The well-established spectral difference (SD) method is used for spatial discretization of the Euler equations over deforming, unstructured quadrilateral grids. The Geometric Conservation Law (GCL) is incorporated into the conservative Euler equations, before discretization. After simplification, the equations reduce to a form, in the computational domain, identical to the equations in the physical domain. In this form, the equations can be integrated implicitly in time, without the requirement of any additional source term, to guarantee free-stream preservation. The fluid and structure sub-systems are individually integrated in time using the explicit first stage, single diagonal, diagonally implicit Runge-Kutta (ESDIRK) method. As the first step to solving the coupled, non-linear Euler equations, implicit in time, we linearize the governing equations. The resulting linearized simultaneous equations are then solved sequentially using lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation sweeps. The fluid and structure sub-systems are loosely coupled and the coupling term is integrated in time using an explicit RK method, resulting in an implicit-explicit (IMEX) RK coupling. The spatial accuracy and the free-stream preserving ability of the solver are demonstrated by testing a supersonic, isentropic vortex in a curved channel. Next, the temporal accuracy of the solver is established using an Euler vortex propagation test case. It is also demonstrated that the four-stage ESDIRK is capable of handling time-steps 50 times larger than the four-stage explicit RK. In each of these cases, third- and fourth-order SD for spatial discretization and second-order backward difference (BDF2) and third-order, four stage ESDIRK for time integration were tested. Since the loose (explicit) FSI coupling restricts permissible structural deformation, we limit ourselves to small harmonic oscillations resulting from linearized perturbed Euler equations. The interaction between a linear piston and an inviscid, compressible fluid is simulated to demonstrate that the IMEX coupling does not contaminate the spatial or temporal accuracy of the implemented high-order methods. Through rigorous testing, this development is expected to lay a foundation for a powerful computational framework for various fluid-structure interaction problems