An adaptively refined Cartesian grid method for moving boundary problems applied to biomedical systems

by Krishnan, Sreedevi.

A major drawback in the operation of mechanical heart valve prostheses is thrombus formation in the near valve region potentially due to the high shear stresses present in the leakage jet flows through small gaps between leaflets and the valve housing. Detailed flow analysis in this region during the valve closure phase is of interest in understanding the relationship between shear stress and platelet activation. An efficient Cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three-dimensional immersed solid bodies as well as fluid-fluid interfaces. The embedded boundaries are represented using Levelsets and treated in a sharp manner without the use of source terms to represent boundary effects. The resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second-order accuracy. When dealing with problems of disparate length scales encountered in many applications, it is necessary to resolve the physically important length scales adequately to ensure accuracy of the solution. Fixed grid methods often have the disadvantage of heavy mesh requirement for well resolved calculations. A quadtree based adaptive local mesh refinement scheme is developed to complement the sharp interface Cartesian grid method scheme for efficient and optimized calculations. Detailed timing and accuracy data is presented for a variety of benchmark problems involving moving boundaries. The above method is then applied to modeling heart valve closure and predicting thrombus formation. Leaflet motion is calculated dynamically based on the fluid forces acting on it employing a fluid-structure interaction algorithm. Platelets are modeled and tracked as point particles by a Lagrangian particle tracking method which incorporates 2 the hemodynamic forces on the particles. Leaflet closure dynamics including rebound is analyzed and validated against previous studies. Vortex shedding and formation of recirculation regions are observed downstream of the valve, particularly in the gap between the valve and the housing. Particle exposure to high shear and entrapment in recirculation regions with high residence time in the vicinity of the valve are observed corresponding to regions prone to thrombus formation. Abstract Approved: ____________________________________ Thesis Supervisor ____________________________________ Title and Department ____________________________________ Date