Oxygen Deficient (OD) Combustion and Metabolism: Allometric Laws of Organs and Kleiber’s Law from OD Metabolism?

Kalyan Annamalai

doi:10.3390/systems9030054

Abstract

The biology literature presents allometric relations for the specific metabolic rate (SMRk) of an organ k of mass mk within the body of mass mB: SMRk ∝ mBfk (body mass allometry, BMA). Wang et al. used BMA, summed-up energy from all organs and validated Kleiber’s law of the whole body: SMRM ∝ mBb’, b’ = −0.25. The issues raised in biology are: (i) why fk and b’ < 0, (ii) how do the organs adjust fk to yield b’? The current paper presents a “system” approach involving the field of oxygen deficient combustion (ODC) of a cloud of carbon particles and oxygen deficient metabolism (ODM), and provides partial answers by treating each vital organ as a cell cloud. The methodology yields the following: (i) a dimensionless “group” number GOD to indicate extent of ODM, (ii) SMRk of an organ in terms of the effectiveness factor; (iii) curve fitting of the effectiveness factor to yield the allometric exponents for the organ mass-based allometric laws (OMA); (iv) validation of the results with data from 111 biological species (BS) with mB ranging from 0.0075 to 6500 kg. The “hypoxic” condition at organ level, particularly for COVID-19 patients, and the onset of cancer and virus multiplication are interpreted in terms of ODM and glycolysis.

Highlights

IntroductionAir breathing thermal power systems, such as automobile engines, convert chemical energy into thermal energy via combustion of fuels (a high temperature oxidation) of fuels with O2 supplied from the air
The mass fractions of oxygen in capillaries of an organ k depends on the equilibrium mass fractions of oxygen (YO2,cap ≈ YO2,a ) in the arterial blood
In COVID-19 patients, Hb denaturation occurs, reducing available (Hb)in for oxidation to Hb (O2 ) in [45] and the transfer of oxygen across alveoli membrane to the capillary is disrupted, sometimes as low as 50% saturation of arterial blood. It affects the transfer of CO2 from blood to alveoli

Summary

Introduction

Air breathing thermal power systems, such as automobile engines, convert chemical energy into thermal energy via combustion of fuels (a high temperature oxidation) of fuels with O2 supplied from the air. Air-breathing biological species (BS), including humans, are in many ways like those thermal systems and calorimetry and thermodynamics are strongly coupled to metabolic processes within BS [1]. Unlike rapid oxidation (combustion) of fuel in thermal systems, n o the BS uses a slow oxidation process to convert 2/3 of chemical energy {q} into heat Q , and the n

Objectives

Methods

Results

Conclusion