Restoration of wall shear stress in the cephalic vein during extreme hemodynamics.

The surgical creation of an artery-vein connection via a Brachicephalic fistula (BCF) in patients with end stage renal disease (ESRD) provides a unique opportunity to study blood vessel response mechanisms to extreme hemodynamic conditions in relatively short timeframes. After BCF creation, the flow rate in the vein increases by an order of magnitude leading to separated flows and corresponding abnormally low, or negative, wall shear stress (WSS) in the curved arch segment of the cephalic vein. Locations of abnormally low WSS are shown to correlate with development of neointimal hyperplasia (NH) and subsequent stenosis. It is found that the stenosis, prior to a surgical intervention, restores the normal physiological WSS in the vein. As a result, this investigation provides evidence that the adaptation principle, known to apply in the arterial system, is also valid in the venous system. A novel graphical method is developed that combines clinical and computational data to assist in interpreting these physiological mechanisms including adaptation that lead to changes in vein geometry over time.

On the Origins of Vortex Shedding in Two-dimensional Incompressible Flows.

An exegesis of a novel mechanism leading to vortex splitting and subsequent shedding that is valid for two-dimensional incompressible, inviscid or viscous, and external or internal or wall-bounded flows, is detailed in this research. The mechanism, termed the Vortex-Shedding Mechanism (VSM), is simple and intuitive, requiring only two coincident conditions in the flow: (1) the existence of a location with zero momentum and (2) the presence of a net force having a positive divergence. Numerical solutions of several model problems illustrate causality of the VSM. Moreover, the VSM criteria is proved to be a necessary and sufficient condition for a vortex splitting event in any two-dimensional, incompressible flow. The VSM is shown to exist in several canonical problems including the external flow past a circular cylinder. Suppression of the von Kármán vortex street is demonstrated for Reynolds numbers of 100 and 400 by mitigating the VSM.

A pressure-gradient mechanism for vortex shedding in constricted channels.

Numerical simulations of the unsteady, two-dimensional, incompressible Navier-Stokes equations are performed for a Newtonian fluid in a channel having a symmetric constriction modeled by a two-parameter Gaussian distribution on both channel walls. The Reynolds number based on inlet half-channel height and mean inlet velocity ranges from 1 to 3000. Constriction ratios based on the half-channel height of 0.25, 0.5, and 0.75 are considered. The results show that both the Reynolds number and constriction geometry have a significant effect on the behavior of the post-constriction flow field. The Navier-Stokes solutions are observed to experience a number of bifurcations: steady attached flow, steady separated flow (symmetric and asymmetric), and unsteady vortex shedding downstream of the constriction depending on the Reynolds number and constriction ratio. A sequence of events is described showing how a sustained spatially growing flow instability, reminiscent of a convective instability, leads to the vortex shedding phenomenon via a proposed streamwise pressure-gradient mechanism.