| Blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel. Moreover, wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid. However, computational methods for simulating blood flow in three-dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries when modeling blood flow in deformable arteries. Computing blood flow in deformable domains using standard techniques like the ALE method remains a formidable problem for large, realistic anatomic and physiologic models of the cardiovascular system.; We have developed a new method termed the Coupled-Momentum Method for Fluid-Solid Interaction to simulate blood flow in three-dimensional deformable models of arteries. In this method, the effect of the vessel wall boundary is added in a monolithic way to the fluid equations using a shear-enhanced membrane model for the wall, resulting in a remarkably robust scheme. We present here the mathematical formulation of the method and discuss issues related to the fluid-solid coupling, membrane formulation, time integration method, and boundary and initial conditions.; We have verified the method by comparing it against Womersley's analytical solution for pulsatile flow in a straight cylindrical elastic vessel, and have obtained excellent agreement between the numerical and analytical solutions.; The method was then applied to a number of different geometries, ranging from simple, idealized models to large, patient-specific models with over 1 million element finite element meshes. The simple geometries have provided a clear framework to illustrate concepts like wave propagation phenomena, impact of boundary conditions, etc. The patient-specific models have demonstrated the potential of the method to be applied to surgical-planning and disease-research problems in a clinically-relevant timeframe.; This research shows great promise for the application of computational methods representing fluid-solid interactions to clinical applications. We have suggested future directions to expand the work developed in this thesis to obtain even more realistic models of blood flow in arteries, while still maintaining an emphasis on computational efficiency so essential to clinical applications. |
