Arterial stenoses and luminal-surface irregularities at anastomoses cause blood-flow disturbances with slow recirculation. The authors created a computer simulation to study the rates of the release into blood of atherogenic substances such as low-density lipoproteins and their breakdown products from within the arterial walls at stenoses. Finite-difference methods were used to solve the Navier-Stokes equations (in the form of stream function and vorticity function) and the steady-state mass transfer equation for bell-shaped stenoses with two different degrees of constriction. This simulation indicated that the efflux rates of lipids and their breakdown products from the vessel walls were suppressed in the region of disturbed flow, with slow circulation distal to stenoses. The lowest efflux rate was found at the point of flow separation, and this rate was much lower than rates in regions of undisturbed flow. Therefore, this mathematical model predicts that locally disturbed blood flow at arterial stenoses and arterial anastomoses is responsible for two distinct phenomena: first, it provides favourable conditions for lipid infiltration into vessel walls; and, second, it impairs the release into the blood of atherogenic substances accumulated in the vessel wall. Such mass transfer abnormalities may account for atherogenesis and the late failures of arterial reconstructions at these sites.