Narcisse N'Dri, Ph.D.
Post Doctoral Fellow
Non-Newtonian Blood Flow in Human Coronary Arteries
Understanding blood flow in the circulatory system and how it affects intimal thickening is important with respect to atherogenesis. While the assumption of Newtonian blood flow in large arteries is widely accepted, questions remain unanswered for blood flow in the coronaries. In this study we compare the Newtonian to three non-Newtonian models by studying the blood flow in the right and the left coronaries using computational fluid dynamics. The coronary geometries were reconstructed from MRI images. Although difference in wall shear stress is observed between the non-Newtonian rheological models and the Newtonian, Newtonian model can still be used for predicting plaque location.
Figure: Comparison of the time average wall shear stress for both Newtonian and non-Newtonian models along the LAD. The left figure indicates where TAWSS is computed along the LAD.
Cartesian Method for Multiphase Flow Computations
Many flows of biological and industrial significance take place in multi-connected domains with complex flexible immersed boundaries. The computation of these type of flows involves several issues that often make the task challenging. In the cardiovascular system, the fluid/structure interaction dominates the dynamic of the flow. The boundary-fitted techniques based on the so-called Arbitrary Lagrangian Eulerian (ALE) approaches are better suited for high Reynolds number simulation, but due to the need to re-mesh to conform to the body deformation, they are mostly limited to problem with moderate deformations. In order to overcome this difficulty, a fixed Cartesian grid can be used to solve for the Navier-Stokes equations away from the interface. While proper boundary treatment can be used to find the solution at the grid points near the interface. The advantage of this approach is that the grid remains fixed while the interface can undergo large deformations. The challenge of implementing this approach is establishing boundary conditions between the Lagrangian coordinates of the body and the underlying Cartesian grids (Eulerian approach). Two different approaches can be found in the literature, the sharp interface method or the cut-cell technique and the immersed boundary method. In the cut-cell technique, the grid cells at the body interface are modified according to the way they intersect with the underlying grids. This technique allows a clear distinction between the body and the Cartesian domain. The difficulty encounters in this approach is the multiple ways the intersection between the underlying grid and the body interface occur making the implementation tedious. In the immersed boundary method, an unstructured mesh representing the immersed body is tracked on a stationary mesh used to solve the transport equations. The two meshes are kept separate and information between them is done in the course of the computation. This method was originated by Peskin for fluid-fluid interface and Goldstein et al. for fluid-solid interface. In this study, both approaches are developed.
Figure: Rotating sphere in a quiescent flow (left) and 3D droplet deforming in a flow (right).
Figure: Carotid artery blood flow, Geometry (left) and velocity vectors (right).