Fifth dimension of life and the 4/5 allometric scaling law for human brain.
Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.
He
Ji-Huan
JH
College of Science, Donghua University, 1882 Yan'an Xilu Road, P.O. Box 471, Shanghai 200051, People's Republic of China. jhhe@dhu.edu.cn
Zhang
Juan
J
D001481:Basal Metabolism; D001699:Biometry; D001921:Brain / Q000378:metabolism*; D015444:Exercise; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D015233:Models, Statistical