Wall shear stress and near-wall convective transport: Comparisons with vascular remodelling in a peripheral graft anastomosis
Fluid dynamic properties of blood flow are implicated in cardiovascular diseases. The interaction between the blood flow and the wall occurs through the direct transmission of forces, and through the dominating influence of the flow on convective transport processes. Controlled, in vitro testing in simple geometric configurations has provided much data on the cellular-level responses of the vascular walls to flow, but a complete, mechanistic explanation of the pathogenic process is lacking. In the interim, mapping the association between local haemodynamics and the vascular response is important to improve understanding of the disease process and may be of use for prognosis. Moreover, establishing the haemodynamic environment in the regions of disease provides data on flow conditions to guide investigations of cellular-level responses. This work describes techniques to facilitate comparison between the temporal alteration in the geometry of the vascular conduit, as determined by in vivo imaging, with local flow parameters. Procedures to reconstruct virtual models from images by means of a partition-of-unity implicit function formulation, and to align virtual models of follow-up scans to a common coordinate system, are outlined. A simple Taylor series expansion of the Lagrangian dynamics of the near-wall flow is shown to provide both a physical meaning to the directional components of the flow, as well as demonstrating the relation between near-wall convection in the wall normal direction and spatial gradients of the wall shear stress. A series of post-operative follow-up MRI scans of two patient cases with bypass grafts in the peripheral vasculature are presented. These are used to assess how local haemodynamic parameters relate to vascular remodelling at the location of the distal end-to-side anastomosis, i.e. where the graft rejoins the host artery. Results indicate that regions of both low wall shear stress and convective transport towards the wall tend to be more associated with regions of inward remodelling. A strong point-wise correlation was not found to exist however between local changes in wall location and either quantity.
wall shear stress gradient taylor series of lagrangian dynamics near-wall exchange flow field approximation from no-slip parameters steady state medical image reconstruction rigid body registration