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

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.