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We developed an equation which relates blood flow and oxygen metabolic rates in the brain to the oxygen tension in mitochondria (Gjedde et al. (2005) Cerebral metabolic response to low blood flow: Possible role of cytochrome oxidase inhibition. J Cereb Blood Flow Metab 25: in press). The equation is based on the assumption that net delivery of oxygen to brain tissue (J) is regulated by the tissue's conductivity of oxygen (L). Then, the difference between the respective average tensions of oxygen in brain capillaries and mitochondria (PO2cap for capillaries, PO2mit for mitochondria): J = L (PO2cap - PO2mit). This equation can be modified by the Hill equation of oxygen's saturations of hemoglobin in arteries and veins (SaO2 and SvO2), which are functions of oxygen's tension in the capillaries, the Hill coefficient (h), and oxygen's half-saturation tension (P50): J = L (P50 (SaO2+SvO2)/(2-SaO2-SvO2)∧(1/h) - PO2mit). This formula was used to evaluate the relationship between increments of brain work and average mitochondrial oxygen tensions. Increments of brain work were obtained by finger-tapping motions at the rate of 3 steps per second during PET-scanning for blood flow and oxygen consumption. Visual cortex stimulation sustains prolonged increases of oxygen consumption, but motor activity sustains a biphasic change of oxygen consumption in which the later decline correlates with exertion and fatigue (Figure 1 panel A). Oxygen's saturation of arteries and cerebral veins were computed from blood samples and the net extraction fraction of oxygen, and mitochondrial oxygen tensions were computed from the equation. The extraction fraction varied little (panel B), despite substantial focal changes of oxygen consumption, revealing matching relative increments of blood flow and oxygen consumption, and consequently declining mitochondrial oxygen tensions, at the highest rates of oxygen consumption measured in SMA and right putamen (panel C). The conclusion that declining oxygen tension in key centers of the brain limits activity is supported by evidence of declining oxygen tension in brain prior to central fatigue caused by exertion in athletes in whom energy reserves still exist in muscle (Nybo & Secher (2004) Prog Neurobiol. 72: 223-61, Nybo et al. (2003) Acta Physiol Scand. 179: 67-74). The progressive decline of oxygen tensions in brain mitochondria during activity, and the sensitivity of exertion to this decline, may explain fatigue in general and the need to sleep in particular.
Gjedde et al. (Mon,) studied this question.