Effect of spatial variations in shear on diffusion at the wall of an arterial branch.

Abstract

The effect of spatially varying shear on transport to the wall of a two-dimensional branch was examined, using oxygen as the test solute and the results of earlier fluid mechanical calculations to provide the shear profiles in a region characterizing the aortic bifurcation. The numerical technique employed allowed both blood-phase and mural resistances to solute uptake to be treated simultaneously and self-consistently. The calculated profiles of wall concentration and mural flux were significantly different from those which would have obtained if the shear had been uniform. The calculations suggest that, even when solute is rapidly taken up from the blood, the occasional high-shear and flow-development sites encountered along the arterial tree prevent the diffusion boundary layer adjacent to the wall from thickening to the point at which nutrition is compromised. The indirect effect of arterial geometry on transport, consequent to its direct effect on the magnitude and the distribution of the relevant hemodynamic variables, was illustrated using the branch area ratio as the geometric parameter. The shapes of the flux and interfacial concentration profiles along the branch wall were markedly dependent on the extent to which wall shear affected intimal permeability.• Certain regions in the arterial tree, such as the inside walls of bends and the neighborhoods of branches and ostia, appear to be particularly prone to develop atheromatous lesions. This predisposition may reflect a variability in arterial properties (i.e., elasticity, permeability, metabolism) along the tree, or it may be related to arterial geometry per se. At present, there is no strong reason to reject either of these nonexclusive alternatives.The latter alternative is the basis of a number of so-called "hemodynamic" theories of atherogenesis, in which the distribution of lesions is related to geometric effects on the pulsatile blood flow through the arterial system. Gessner (1) has presented a critical review of these theories. In general, the hemodynamic theories suggest two closely related mechanisms by which geometric effects on blood flow can affect the wall: by mechanical actions such as shear or turbulence or by alterations in mass transport rates in the neighborhood of the mural interface. In an earlier work (2), we have reported on fluid mechanical calculations directed toward an understanding of wall shear profiles in a branch and their role in atherogenesis; in the present paper, with similar motivation, we will examine the fashion in which these profiles may affect transport phenomena. 446It is well known (3) that mass transfer at the mural boundary of a flowing medium is inextricably related to the fluid mechanical shear at that boundary, even if the properties of the interface are unaffected by shear. In the arterial system, there is ample evidence that shear affects the vascular interface as well as blood-phase transport. The enhancement of arterial uptake of albumin found by Fry (4, 5) and by Carew and Patel (6) to follow...

Pulsatile flow in a coronary artery using multiphase kinetic theory

“…Many researchers have attempted to develop consistent correlations for atherosclerotic lesion locations to WSS (low or high), WSSG t , and WSSG s with little success (Caro et al, 1971;Fry, 1968;Zeng et al, 2003;Friedman and Ehrlich, 1975;Qiu and Tarbell, 2000;Ku et al, 1985;DePaola, et al, 1992). Results computed from the multiphase kinetic theory model are used to identify such potential locations.…”

Computational Modelling of Mass Transport in Large Arteries

“…Early studies as well as recent developments on computational modelling of arterial mass transport are reviewed here. Early studies (Back, 1975a;Friedman and Ehrlich, 1975;Ehrlich and Friedman, 1977) on computational modelling of arterial mass transport focused on trans-lumenal transport in two-dimensional geometries. Following these pioneering studies, a number of researchers extended the trans-lumenal transport model in various aspects.…”

Role of Slip Velocity on the Oscillatory Flow of Blood Through a Porous Vessel in the Presence of Heat Source and Chemical Reaction

“…There might be so many reasons on tackling blood flow in problems in the presence of mass transfer. One major problem is highlighted by Friedman and Ehrlich [17].…”