脑代谢和血流量的缩放与毛细血管和神经缩放的关系
Scaling of brain metabolism and blood flow in relation to capillary and neural scaling
摘要：
脑是哺乳动物中最需要能量的器官之一，其总代谢率与脑体积的5/6次方成正比。该值明显高于动物和植物中更常见的指数3/4，该指数将全身静息代谢与体重和其他几个生理变量联系起来。本文从微血管水平探讨了脑异速生长差异的原因。基于收集的经验数据，发现跨灰质的局部脑血流CBF与皮质体积$V$成比例为$CBF \sim V^{-1/6}$，脑毛细血管直径增加为$V^{1/12}$，毛细血管长度密度减少为$V^{-1/6}$。据预测，毛细血管血液的速度几乎是不变的（$\sim V^ε$），毛细血管通过时间尺度为$V^{1/6}$，毛细血管长度增加为$V^{1/6+ε}$，毛细血管数量增加为$V^{2/3-ε}$，其中由于血液粘度依赖于毛细血管半径，$ε$通常是中型和大型脑的小校正。结果表明，在哺乳动物中，每个皮层神经元的毛细血管长度和血流量基本上是保守的。这些结果表明，几何和动力学的全球神经血管耦合有一个相称的字符。此外，脑代谢，血流动力学和微血管变量的比例与异速生长指数是1/6的简单倍数，而不是1/4，这表明大脑代谢更类似于有氧代谢比休息身体。这些研究结果的关系，脑功能成像研究涉及脑代谢和血流之间的联系进行了讨论。
英文摘要：
Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body resting metabolism with body mass and several other physiological variables in animals and plants. This article investigates the reasons for brain allometric distinction on a level of its microvessels. Based on collected empirical data it is found that regional cerebral blood flow CBF across gray matter scales with cortical volume $V$ as $CBF \sim V^{-1/6}$, brain capillary diameter increases as $V^{1/12}$, and density of capillary length decreases as $V^{-1/6}$. It is predicted that velocity of capillary blood is almost invariant ($\sim V^ε$), capillary transit time scales as $V^{1/6}$, capillary length increases as $V^{1/6+ε}$, and capillary number as $V^{2/3-ε}$, where $ε$ is typically a small correction for medium and large brains, due to blood viscosity dependence on capillary radius. It is shown that the amount of capillary length and blood flow per cortical neuron are essentially conserved across mammals. These results indicate that geometry and dynamics of global neuro-vascular coupling have a proportionate character. Moreover, cerebral metabolic, hemodynamic, and microvascular variables scale with allometric exponents that are simple multiples of 1/6, rather than 1/4, which suggests that brain metabolism is more similar to the metabolism of aerobic than resting body. Relation of these findings to brain functional imaging studies involving the link between cerebral metabolism and blood flow is also discussed.
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