An allometric scaling law between gray matter and white matter of cerebral cortex

An allometric scaling relationship between cortical white and gray volumes is derived from a general model that describes brain's remarkable efficiency and prodigious communications between brain areas. The model assumes that (1) a cell's metabolic rate depends upon cell's surface; (2) the overall basal metabolic rates of brain areas depend upon their fractal structures; (3) differential brain areas have same basal metabolic rate at slow wave sleep. The obtained allometric exponent scaling white matter to gray matter is 1.2, which is very much close to Zhang and Sejnowski's observation data.