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.

Unsteady separation in vortex-induced boundary layers.

This paper provides a brief review of the analytical and numerical developments related to unsteady boundary-layer separation, in particular as it relates to vortex-induced flows, leading up to our present understanding of this important feature in high-Reynolds-number, surface-bounded flows in the presence of an adverse pressure gradient. In large part, vortex-induced separation has been the catalyst for pulling together the theory, numerics and applications of unsteady separation. Particular attention is given to the role that Prof. Frank T. Smith, FRS, has played in these developments over the course of the past 35 years. The following points will be emphasized: (i) unsteady separation plays a pivotal role in a wide variety of high-Reynolds-number flows, (ii) asymptotic methods have been instrumental in elucidating the physics of both steady and unsteady separation, (iii) Frank T. Smith has served as a catalyst in the application of asymptotic methods to high-Reynolds-number flows, and (iv) there is still much work to do in articulating a complete theoretical understanding of unsteady boundary-layer separation.

Hemodynamics in the cephalic arch of a brachiocephalic fistula.

The care and outcome of patients with end stage renal disease (ESRD) on chronic hemodialysis is directly dependent on their hemodialysis access. A brachiocephalic fistula (BCF) is commonly placed in the elderly and in patients with a failed lower-arm, or radiocephalic, fistula. However, there are numerous complications such that the BCF has an average patency of only 3.6 years. A leading cause of BCF dysfunction and failure is stenosis in the arch of the cephalic vein near its junction with the axillary vein, which is called cephalic arch stenosis (CAS). Using a combined clinical and computational investigation, we seek to improve our understanding of the cause of CAS, and to develop a means of predicting CAS risk in patients with a planned BCF access. This paper details the methodology used to determine the hemodynamic consequences of the post-fistula environment and illustrates detailed results for a representative sample of patient-specific anatomies, including a single, bifurcated, and trifurcated arch. It is found that the high flows present due to fistula creation lead to secondary flows in the arch owing to its curvature with corresponding low wall shear stresses. The abnormally low wall shear stress locations correlate with the development of stenosis in the singular case that is tracked in time for a period of one year.

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.