An Adaptively refined Cartesian grid method for moving boundary problems applied to biomedical systems
Sreedevi Krishnan · 2006
A major drawback in the operation of mechanical heart valve \t\t\t\tprostheses is thrombus formation in the near valve region \t\t\t\tpotentially due to the high shear stresses present in the \t\t\t\tleakage jet flows through small gaps between leaflets and the \t\t\t\tvalve housing. Detailed flow analysis in this region during the \t\t\t\tvalve closure phase is of interest in understanding the \t\t\t\trelationship between shear stress and platelet activation. An efficient Cartesian grid method is developed for the \t\t\t\tsimulation of incompressible flows around stationary and moving \t\t\t\tthree-dimensional immersed solid bodies as well as fluid-fluid \t\t\t\tinterfaces. The embedded boundaries are represented using \t\t\t\tLevelsets and treated in a sharp manner without the use of \t\t\t\tsource terms to represent boundary effects. The resulting \t\t\t\talgorithm is implemented in a straightforward manner in three \t\t\t\tdimensions and retains global second-order accuracy. When \t\t\t\tdealing with problems of disparate length scales encountered in \t\t\t\tmany applications, it is necessary to resolve the physically \t\t\t\timportant length scales adequately to ensure accuracy of the \t\t\t\tsolution. Fixed grid methods often have the disadvantage of \t\t\t\theavy mesh requirement for well resolved calculations. A \t\t\t\tquadtree based adaptive local mesh refinement scheme is \t\t\t\tdeveloped to complement the sharp interface Cartesian grid \t\t\t\tmethod scheme for efficient and optimized calculations. Detailed \t\t\t\ttiming and accuracy data is presented for a variety of benchmark \t\t\t\tproblems involving moving boundaries. The above method is then applied to modeling heart valve closure \t\t\t\tand predicting thrombus formation. Leaflet motion is calculated \t\t\t\tdynamically based on the fluid forces acting on it employing a \t\t\t\tfluid-structure interaction algorithm. Platelets are modeled and \t\t\t\ttracked as point particles by a Lagrangian particle tracking \t\t\t\tmethod which incorporates the hemodynamic forces on the \t\t\t\tparticles. Leaflet closure dynamics including rebound is \t\t\t\tanalyzed and validated against previous studies. Vortex shedding \t\t\t\tand formation of recirculation regions are observed downstream \t\t\t\tof the valve, particularly in the gap between the valve and the \t\t\t\thousing. Particle exposure to high shear and entrapment in \t\t\t\trecirculation regions with high residence time in the vicinity \t\t\t\tof the valve are observed corresponding to regions prone to \t\t\t\tthrombus formation.