Numerical Simulation of Unsteady Flows of Physiological Relevance

University dissertation from Philip Evegren

Abstract: Pulsatile flows in geometries of physiological relevance have been investigated. Atherosclerotic plaques are (initiated) near junctions and bifurcations in larger arteries. The flow in these regions is characterized by flow separation and unsteadiness, which indicates that local flow conditions contribute to atherogenesis. Flows in curved and bifurcating pipes have been investigated over many years. However, details of dynamical patterns of pulsating flow, near wall effects, and differential diffusion effects are not well documented. The effect of wall elasticity on the flow has been assumed to be small but no quatification data exist. There are same basic difficulties in studying physiological flow: The geometries have large inter-individual variations. The mechanical properties of the vessels are unknown. Equally, the boundary conditions (temporal and spatial distribution of the blood velocity) are not know. Additional difficulties arise due to measuring difficulties both in-vivo and in-vitro. The flow itself may be rather complex (time-dependent 3-D, transitional with locally strong effects of viscosity and unsteadiness, leading to variable phase lag between pressure gradient and the local flow). The aim of this study is to enhance understanding of the time-dependent, physiologically relevant, flow field in bifurcations, and relate that to hypotheses of atherosclerotic disease. Additionally, an FSI-model has been developed with the purpose to model flow through elastic pipes, and to assess the effect of wall elasticity on the flow. The investigations have shown clear patterns of wall shear stress (WSS) variations. Local regions of temporal and spatial variations of the WSS was found at sites usually referred to as risk-sites of atherosclerosis, but also at locations often referred to as ``safe''. Some of the characteristics of the WSS are further related to changes in the secondary flow field. The secondary flow shows similar characteristics for an increased Reynolds number, although unsteady asymmetric patterns appear at peak flow, while a large Womersley number shows more simple secondary flow structures. It is also shown that the effects of upstream geometrical variations on the flow field itself, are important mainly over one stage of arterial bifurcation. On the other hand, blood components (modeled as passive scalars with different values of Schmidt numbers) do exhibit upstream effects over a longer range.An important finding is that Schmidt number effects may lead to redistribution of the different scalars. The variations in the concentrations of the scalars are of the same order as the local concentration themselves. The FSI-model developed combines an Immersed Boundary-Finite Difference code with a shell model for the arterial wall. The shell model is solved on a (surface 2D) using a Finite Element Method (FEM) code. The structural solver is verified against an analytical expression for bending of a thin-walled pipe. The studies with respect to the importance of arterial wall elasticity on the flow, are not yet completed.

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