A FLUID-STRUCTURE INTERACTION MODEL CAPTURING LONGITUDINAL DISPLACEMENT IN ARTERIES: MODELING, COMPUTATIONAL METHOD, AND COMPARISON WITH EXPERIMENTAL DATA

The focus of this thesis is on numerical modeling of fluid-structure interaction (FSI) problems with application to hemodynamics. Recent in vivo studies, utilizing ultrasound contour and speckle tracking methods, have identified significant longitudinal wall displacements and viscoelastic arterial wall properties over a cardiac cycle. Existing computational models that use thin structure approximations of arterial walls have so far been limited to elastic models that capture only radial wall displacements. In this thesis, we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. In this work arterial walls are modeled by a linearly viscoelastic, cylindrical Koiter shell model capturing both radial and longitudinal displacement. Fluid flow is modeled by the Navier-Stokes equations for an incompressible, viscous fluid. The two are fully coupled via kinematic and dynamic coupling conditions. The proposed numerical scheme is based on a new modified Lie operator splitting that decouples the fluid and structure sub-problems in a way that leads to a loosely coupled scheme that is unconditionally stable. This was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub-problems, leading to an implicit coupling between the fluid and structure velocities. The proposed scheme is a modification of the recently introduced “kinematically coupled scheme” for which the newly proposed modified Lie splitting significantly increases the accuracy. In this work it is shown that the new scheme, called the kinematically coupled β-scheme, is unconditionally stable for all β ∈ [0, 1]. The performance and accuracy of the scheme are studied on a series of instructive examples including a comparison with a monolithic scheme proposed by Quaini and Quarteroni in [77]. It is shown that the accuracy of our scheme is comparable to that of the monolithic scheme, while our scheme retains all the main advantages of partitioned schemes. The results of the computational model are compared with in vivo measurements of the common carotid artery wall motion, and with data capturing stenosed coronary arteries, showing excellent agreement.