The draining vein problem is recognized as one of the most severe constraints on the spatial resolution of BOLD contrast fMRI, used widely in imaging neuroscience. Changes in blood oxygenation arising from local brain activity-related changes in blood flow propagate downstream in veins and can give rise to spurious activation at sites remote from neuronal activity. The geometry of the venous vasculature is quite regular in structure and is well depicted in photomicrographs. Quantitative analysis of this geometry, together with hydrodynamic considerations, permit upper bounds dependent on the area of cortical neuronal activity to be derived for the spatial extent of draining vein contamination. It is estimated that an activated cortical area of 100 mm(2) will generate an oxygenation change in venous blood that extends without dilution along the vein no more than 4.2 mm beyond the edge of the activated area. At greater distances along the draining vein this oxygenation change will be diluted. The model leads to a quantitative prediction of the functional form of this dilution.