Painter Page R
Office of Environmental Health Hazard Assessment, California Environmental Protection Agency, Sacramento, California 95812, USA.
Theor Biol Med Model. 2005 Aug 11;2:30. doi: 10.1186/1742-4682-2-30.
A prominent theoretical explanation for 3/4-power allometric scaling of metabolism proposes that the nutrient exchange surface of capillaries has properties of a space-filling fractal. The theory assumes that nutrient exchange surface area has a fractal dimension equal to or greater than 2 and less than or equal to 3 and that the volume filled by the exchange surface area has a fractal dimension equal to or greater than 3 and less than or equal to 4.
It is shown that contradicting predictions can be derived from the assumptions of the model. When errors in the model are corrected, it is shown to predict that metabolic rate is proportional to body mass (proportional scaling).
The presence of space-filling fractal nutrient exchange surfaces does not provide a satisfactory explanation for 3/4-power metabolic rate scaling.
对代谢的3/4幂异速生长缩放的一个重要理论解释提出，毛细血管的营养交换表面具有空间填充分形的特性。该理论假设营养交换表面积的分形维数等于或大于2且小于或等于3，并且由交换表面积填充的体积的分形维数等于或大于3且小于或等于4。
研究表明，该模型的假设可得出相互矛盾的预测。当模型中的误差得到纠正时，结果表明它预测代谢率与体重成正比（比例缩放）。
空间填充分形营养交换表面的存在并不能为3/4幂代谢率缩放提供令人满意的解释。
