Secrets of Kleiber’s and Maximum Metabolic Rate Allometries Revealed with a Link to Oxygen-Deficient Combustion Engineering

The biology literature addresses two puzzles: (i) the increase in specific metabolic rate of organs (SOrMR, W/kg of organ) with a decrease in body mass (M_B) of biological species (BS), and (ii) how the organs recognize they are in a smaller or larger body and adjust metabolic rates of the body (${\dot{q}}_B$) accordingly. These puzzles were answered in the author’s earlier work by linking the field of oxygen-deficient combustion (ODC) of fuel particle clouds (FC) in engineering to the field of oxygen-deficient metabolism (ODM) of cell clouds (CC) in biology. The current work extends the ODM hypothesis to predict the whole-body metabolic rates of 114 BS and demonstrates Kleiber’s power law {${\dot{q}}_B=a{M}_B{}^b$}. The methodology is based on the postulate of Lindstedt and Schaeffer that “150 ton blue whale. and the 2 g Etruscan shrew.. share the same.. biochemical pathways” and involve the following steps: (i) extension of the effectiveness factor relation, expressed in terms of the dimensionless group number G (=Thiele Modulus²), from engineering to the organs of BS, (ii) modification of G as G_OD for the biology literature as a measure of oxygen deficiency (OD), (iii) collection of data on organ and body masses of 116 species and prediction of SOrMR_k of organ k of 114 BS (from 0.0076 kg Shrew to 6650 kg elephant) using only the SOrMR_k and organ masses of two reference species (Shrew, 0.0076 kg: RS-1; Rat Wistar, 0.390 kg: RS-2), (iv) estimation of ${\dot{q}}_B$ for 114 species versus M_B and demonstration of Kleiber’s law with a = 2.962, b = 0.747, and (v) extension of ODM to predict the allometric law for maximal metabolic rate (under exercise, {${\dot{q}}_{B,MMR}=a_{MMR}{M}_B{}^{b_{MMR}}$}) and validate the approach for MMR by comparing b_MMR with the literature data. A method of detecting hypoxic condition of an organ as a precursor to cancer is suggested for use by medical personnel.