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 ∼ r2, where r is the radius of the cell; that of a brain cell scales as B ∼ rd, 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.

[1]  Ji-Huan He,et al.  Allometric Scaling and Instability in Electrospinning , 2004 .

[2]  Tian-Hu Hao.  Application of the Lagrange Multiplier Method the Semi-Inverse Method to the Search for Generalized Variational Principle in Quantum Mechanics , 2003 .

[3]  C. R. White,et al.  Mammalian basal metabolic rate is proportional to body mass2/3 , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  S. Orszag,et al.  Extended Boltzmann Kinetic Equation for Turbulent Flows , 2003, Science.

[5]  J. Weitz,et al.  Re-examination of the "3/4-law" of metabolism. , 2000, Journal of theoretical biology.

[6]  G. Burness.  Elephants, Mice, and Red Herrings , 2002, Science.

[7]  Julie H. Campbell,et al.  Cell Biology International , 2019 .

[8]  Qian Guo,et al.  Thermo-electro-hydrodynamic model for electrospinning process , 2004 .

[9]  C A Beuchat.  Allometric scaling laws in biology. , 1997, Science.

[10]  P. Srere.  17th Fritz Lipmann Lecture. Wanderings (wonderings) in metabolism. , 1993, Biological chemistry Hoppe-Seyler.

[11]  D Mackenzie.  New Clues to Why Size Equals Destiny , 1999, Science.

[12]  Allometric scaling in animals and plants , 2001, Journal of mathematical biology.

[13]  Ji-Huan He,et al.  Mysterious Pi and a Possible Link to DNA Sequencing , 2004 .

[14]  J. Damuth,et al.  Scaling of growth: Plants and animals are not so different , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Jyrki T. Kuikka,et al.  Scaling Laws in Physiology: Relationships between Size, Function, Metabolism and Life Expectancy , 2003 .

[16]  M. Kleiber.  Body size and metabolism , 1932 .

[17]  Amos Maritan,et al.  Size and form in efficient transportation networks , 1999, Nature.

[18]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[19]  J. Kuikka,et al.  Fractal Analysis in Medical Imaging , 2002 .

[20]  Roberto Benzi.  Getting a Grip on Turbulence , 2003, Science.

[21]  James H Brown,et al.  Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Geoffrey B. West,et al.  Why does metabolic rate scale with body size?: Physiology (communication arising) , 2003 .

[23]  J J Blum,et al.  On the geometry of four-dimensions and the relationship between metabolism and body mass. , 1977, Journal of theoretical biology.

[24]  Raul K. Suarez,et al.  Allometric cascade as a unifying principle of body mass effects on metabolism , 2002, Nature.

[25]  Gesellschaft für Biochemie und Molekularbiologie,et al.  Biological chemistry Hoppe-Seyler , 1985 .

[26]  Hong-Mei Liu,et al.  Variational Approach to Nonlinear Electrochemical System , 2004 .

[27]  Haymo Kurz,et al.  Allometric Scaling in Biology , 1998 .

[28]  S. Heymsfield,et al.  The reconstruction of Kleiber's law at the organ-tissue level. , 2001, The Journal of nutrition.

[29]  E R Weibel,et al.  Design of the mammalian respiratory system. III Scaling maximum aerobic capacity to body mass: wild and domestic mammals. , 1981, Respiration physiology.

[30]  Ewald R. Weibel,et al.  Symmorphosis: On Form and Function in Shaping Life , 2000 .

[31]  James H. Brown,et al.  The fourth dimension of life: fractal geometry and allometric scaling of organisms. , 1999, Science.

[32]  Andrea Rinaldo,et al.  Physiology: Allometric cascades. , 2003 .

[33]  Samuel Brody,et al.  Bioenergetics and growth. With special reference to the efficiency complex in domestic animals. , 1946 .

[34]  Ji-Huan He,et al.  Effects of Size and pH on Metabolie Rate , 2003 .

[35]  Ewald R. Weibel,et al.  Physiology: The pitfalls of power laws , 2002, Nature.

[36]  Riisgård.  No foundation of a “3/4 power scaling law” for respiration in biology , 1998 .