A general mathematical model for the delivery of O2 to the brain is presented, based on the assumptions that all of the brain capillaries are perfused at rest and that all of the oxygen extracted from the capillaries is metabolized. The model predicts that disproportionately large changes in blood flow are required in order to support small changes in the O2 metabolic rate. Interpreted in terms of this model, previous positron emission tomography (PET) studies of the human brain during neural stimulation demonstrating that cerebral blood flow (CBF) increases much more than the oxygen metabolic rate are consistent with tight coupling of flow and oxidative metabolism. The model provides a basis for the quantitative interpretation of functional magnetic resonance imaging (fMRI) studies in terms of changes in local CBF.