Key result
The radius, length, and number of open capillaries in resting mammals scale with body mass to the powers 1/12, 5/24, and 5/8, respectively, changing to 3/4 for capillary number during exercise.
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Provides a theoretical derivation and measurement support for how capillary dimensions and numbers scale with body mass in mammals during rest and exercise.
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.
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Thomas H. Dawson (2003) studied Mammalian capillary physiology. The radius, length, and number of open capillaries in resting mammals scale with body mass to the powers 1/12, 5/24, and 5/8, respectively, changing to 3/4 for capillary number during exercise.
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