Wall shear stress modulation of ATP/ADP concentration at the endothelium

A mathematical model of ATP/ADP reaction at the surface of the endothelium for any two-dimensional or axisymmetric nonsingular functional form of the wall shear stress has been presented. Excellent agreement is obtained with the numerical solution for the parallel plate case. For spatially varying wall shear stress, such as the stagnation point flow and a backward facing step the ATP concentrations are shown to have a maximum at the stagnation point streamline and the reattachment point respectively. Increasing the Reynolds number increases both the ATP and ADP concentrations. For the backward facing step significant spatial variations occur in the concentration. Hence, a strong controlling factor for physiological kinetic values is the geometry of the arterial vessel since this determines the wall shear stress and thence the transport to the reactive surface. The area of high concentration also occurs where the wall shear stress is low (limiting case is zero shear stress). Atherosclerotic plaques are known to occur in areas of low wall shear stress and at vessel bifurcations where the wall shear stress is spatially varying. The ATP/ADP concentrations at these particular points may very well contribute to the formation of plaques.