Dawson Thomas H
United States Naval Academy, 590 Holloway Road, Annapolis, MD 21402, USA.
Proc Biol Sci. 2003 Apr 7;270(1516):755-63. doi: 10.1098/rspb.2002.2304.
A general derivation is presented for the scaling laws governing the size and number of capillary blood vessels in mammals. The derivation is based on the assumption of three idealized similarity principles known to apply, at least approximately, to resting mammals: (i) size-invariant blood pressure; (ii) size-invariant fraction of blood in the capillaries; and (iii) size-invariant oxygen consumption and uptake, per unit of body mass, during each heart cycle. Results indicate that the radius and length of capillaries, and the number that are open and active in the resting state, should scale with mammal mass to the powers 1/12, 5/24 and 5/8, respectively, consistent with earlier work by the author. Measurements are presented supporting the results. Physiological changes accompanying strenuous exercise are accounted for by a change in the scaling law for capillary number, from scaling exponent 5/8 to 3/4.
本文给出了适用于哺乳动物毛细血管大小和数量的标度律的一般推导。该推导基于三个理想化的相似性原理，已知这些原理至少近似适用于静息状态的哺乳动物：（i）血压与体型大小无关；（ii）毛细血管中血液的比例与体型大小无关；（iii）每个心动周期中，单位体重的耗氧量和摄氧量与体型大小无关。结果表明，毛细血管的半径和长度，以及静息状态下开放且活跃的毛细血管数量，应分别与哺乳动物体重的1/12次幂、5/24次幂和5/8次幂成比例，这与作者早期的研究结果一致。文中给出了支持这些结果的测量数据。剧烈运动时伴随的生理变化可通过毛细血管数量标度律的变化来解释，即标度指数从5/8变为3/4。
