It has been well-known for many years that cerebral oxygen consumption remains constant during moderate changes of blood flow, as measured during hypo- or hypercapnia or indomethacin administration. Current models of flow-metabolism coupling link blood-brain transfer of oxygen to oxygen metabolism in mitochondria. The resulting quantitative relations between flow and metabolism reveal that a close link between diffusion and metabolism prevents the enzyme from maintaining a constant oxygen consumption when blood flow changes, unless the enzyme's affinity towards oxygen is adjusted commensurately.