Concentration of blood-borne agonists at the endothelium

The delivery of endothelial ligands and macromolecules, such as lipoproteins. from the circulation to the arterial wall is of central importance in modulating endothelial cell function and physiology and, consequently, in the onset of vascular disease. Given the strong spatial correlation between areas of disturbed blood flow and occurrence of atherosclerotic plaque, a detailed understanding of the effects of different fluid flow characteristics on the delivery of factors in the bloodstream to the endothelium is an essential step towards understanding the observed localization of vascular disease to certain focal sites within the vasculature. In this paper, a model of biochemical mass transport in a two-dimensional flow chamber with spatially varying wall shear stress is presented. The advantage of the relatively simple arterial geometry is that all the essential features of blood flow in vivo are captured, but the underlying effects on mass transport, and, hence, on endothelial cell function, are not masked by complex three-dimensional flow. Indeed, it is demonstrated that a previously derived similarity solution, in terms of the shear stress on the endothelial wall, is an asymptotically close approximation to the exact solution to the advection-diffusion equation. The mathematical analysis is then used to identify fundamental links between the wall shear stress and the distribution of chemical species along the endothelium. The physiological implications of these links are discussed, in particular the location of maximum chemical concentration on the endothelium, which is of great significance to the regulation of intracellular signalling and, consequently, endothelial cell function.