{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T04:36:17Z","timestamp":1768970177713,"version":"3.49.0"},"reference-count":59,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T00:00:00Z","timestamp":1626393600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>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 \u221d mBfk (body mass allometry, BMA). Wang et al. used BMA, summed-up energy from all organs and validated Kleiber\u2019s law of the whole body: SMRM \u221d mBb\u2019, b\u2019 = \u22120.25. The issues raised in biology are: (i) why fk and b\u2019 &lt; 0, (ii) how do the organs adjust fk to yield b\u2019? The current paper presents a \u201csystem\u201d 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 \u201cgroup\u201d 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 \u201chypoxic\u201d 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.<\/jats:p>","DOI":"10.3390\/systems9030054","type":"journal-article","created":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T21:18:52Z","timestamp":1626643132000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Oxygen Deficient (OD) Combustion and Metabolism: Allometric Laws of Organs and Kleiber\u2019s Law from OD Metabolism?"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7912-6666","authenticated-orcid":false,"given":"Kalyan","family":"Annamalai","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0040-6031(03)00123-0","article-title":"Calorimetry and thermodynamics of living systems","volume":"405","author":"Lemprecht","year":"2003","journal-title":"Thermochim. Acta"},{"key":"ref_2","unstructured":"Rhoades, R.A. (2009). Chapter 29: The regulation of body temperature. Medical Physiology: Principles for Clinical Medicine, Lippincott Williams & Wilkins. [3rd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1017\/S0950268898001678","article-title":"x Detection of viruses and body fluids which may contain viruses in the domestic environment","volume":"121","author":"Bellamy","year":"1998","journal-title":"Epidemiol. Inf\u00e8ct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1046\/j.1440-1681.2003.03876.x","article-title":"A Comparative View on being the right size: Heart design, mitochondrial efficiency and lifespan potentialx","volume":"30","author":"Dobson","year":"2003","journal-title":"Clin. Exp. Pharmacol. Physiol. Muscle Mech. Energetics"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Annamalai, K., Puri, I., and Jog, M. (2011). Advanced Thermodynamics Engineering, Taylor and Francis (CRC Press). [2nd ed.]. Chapter 14: Biology and Thermodynamics.","DOI":"10.1201\/9781439805718"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/0040-6031(91)87182-V","article-title":"Microcalorimetric monitoring of ischemic tissue metabolism: Influence of incubation conditions and experimental animal species","volume":"187","author":"Singer","year":"1991","journal-title":"Thermochim. Acta"},{"key":"ref_7","unstructured":"Boron Walter, F., and Boulpaep Emile, L. (2009). Medical Physiology, Saunders Elsevier. [2nd ed.]."},{"key":"ref_8","unstructured":"Horowiz, G.L. (2021, June 01). Oxygen Concentration of Blood: PO2, Co-Oximetry, and More, Beth Israel Medical Center. Available online: https:\/\/www.aacc.org\/~\/media\/files\/meetings-and-events\/resources-from-past-events\/conferences\/2013\/professional-practice\/april-28\/gc_oxygen_concentration_of_blood_apr_28_2013.pdf?la=en."},{"key":"ref_9","unstructured":"Atkins, P., and de Paula, J. (2002). Physical Chemistry, W H Freeman Company. [7th ed.]."},{"key":"ref_10","unstructured":"(2021, June 02). Available online: http:\/\/www.scymed.com\/en\/smnxpr\/prgdb276.htm."},{"key":"ref_11","unstructured":"Elnara, M., Negri Bruna, M.P., Luciana, K.M., Carlos, V.P., Shari, A.E., Marcelo, A.F., Elbio, A.D., and Daniel, D. (2020). Heparin therapy improving hypoxia in COVID-19 patients\u2014A case series. MedRxiv."},{"key":"ref_12","unstructured":"Miller, J. (2014). Oxygen Transport and Application of Oxygen Deficient Group Combustion within Vital Organ, MS, Mech Engg, Texas A&M University."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Annamalai, K. (2013). Respiratory quotient (Rq), exhaust gas analyses, CO2 Emission and applications in automobile engineering. Adv. Automob. Eng., 2.","DOI":"10.4172\/2167-7670.1000e116"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1270708","DOI":"10.1155\/2018\/1270708","article-title":"Ranking renewable and fossil fuels on global warming potential using respiratory quotient (RQ) Concept","volume":"2018","author":"Annamalai","year":"2018","journal-title":"J. Combust."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"e0195","DOI":"10.1016\/j.heliyon.2019.e01950","article-title":"Thermodynamic properties of microorganisms: Determination and analysis of enthalpy, entropy, and Gibbs free energy of biomass, cells and colonies of 32 microorganism species","volume":"5","author":"Popovic","year":"2019","journal-title":"Heliyon"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1097\/PAF.0b013e31823d29ad","article-title":"Normal organ weights in men: Part II\u2014The brain, lungs, liver, spleen, and kidneys","volume":"33","author":"Molina","year":"2012","journal-title":"Am. J. Forensic. Med. Pathol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2967","DOI":"10.1093\/jn\/131.11.2967","article-title":"The reconstruction of Kleiber\u2019s law at the organ-tissue level","volume":"131","author":"Wang","year":"2011","journal-title":"J. Nutr."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"315","DOI":"10.3733\/hilg.v06n11p315","article-title":"Body size and metabolism","volume":"6","author":"Kleiber","year":"1932","journal-title":"Hilgardia"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.3945\/ajcn.2010.29885","article-title":"Specific metabolic rates of major organs and tissues across adulthood: Evaluation by mechanistic model of resting energy expenditure","volume":"92","author":"Wang","year":"2010","journal-title":"Am. J. Clin. Nutr."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Annamalai, K., and Nanda, A. (2017). Biological aging and life span based on entropy stress via organ and mitochondrial metabolic loading. Entropy, 19.","DOI":"10.3390\/e19100566"},{"key":"ref_21","unstructured":"Elia, M. (1992). Organ and tissue contribution to metabolic rate. Energy Metabolism: Tissue Determinants and Cellular Corollaries, Raven Press, Ltd."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0006-3002(50)90032-1","article-title":"Body size and tissue respiration","volume":"4","author":"Krebs","year":"1950","journal-title":"Biochem. Biophys. Acta"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1007\/PL00000902","article-title":"Allometry of mammalian cellular oxygen consumption","volume":"58","author":"Porter","year":"2001","journal-title":"Cell. Mol. Life Sci."},{"key":"ref_24","unstructured":"Gutierrez, W.R. (2019, February 26). xSite Model of Allometric Scaling and Fractal Distribution Networks of Organs 2019. Available online: https:\/\/arxiv.org\/pdf\/q-bio\/0404039."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.tca.2006.05.006","article-title":"Size relationship of metabolic rate: Oxygen availability as the missing link between structure and function? Review","volume":"446","author":"Singer","year":"2006","journal-title":"Thermochim. Acta"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/0360-1285(94)90002-7","article-title":"Interactive processes in gasification and combustion-III: Coal particle arrays, streams and clouds","volume":"20","author":"Annamalai","year":"1994","journal-title":"J. Prog. Energy Combust. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/00102207708946823","article-title":"Group combustion of liquid droplets","volume":"17","author":"Chiu","year":"1977","journal-title":"Combust. Sci. Technol."},{"key":"ref_28","unstructured":"Sirignano, W.A. (2014). Fluid Dynamics and Transport of Droplets and Sprays, Cambridge University Press. [2nd ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Annamalai, K., and Puri, I.K. (2007). Combustion Science and Engineering, CRC Press\/Taylor & Francis.","DOI":"10.1201\/9781420003789"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0010-2180(93)90054-7","article-title":"Determination of kinetic data for soot oxidation. modeling of competition between oxygen diffusion and reaction during thermogravimetric analysis","volume":"95","author":"Gilot","year":"1993","journal-title":"Combust. Flame"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1146\/annurev.nu.13.070193.002123","article-title":"Is Oxygen Essentail Nutrient?","volume":"13","author":"Forster","year":"1993","journal-title":"Annu. Rev. Nutr."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Trayhun, P. (2019). Oxygen\u2014A Critical, but Overlooked, Nutrient. Front. Nutr. Hypothesis Theory Artic., 6.","DOI":"10.3389\/fnut.2019.00010"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1152\/physiol.00016.2017","article-title":"Lactic Acid: No Longer an Inert and End Product of Glycolysis","volume":"32","author":"Sun","year":"2017","journal-title":"Physiology"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"164","DOI":"10.2174\/1871520616666161031143301","article-title":"The Warburg Effect and the Hallmarks of Cancer","volume":"17","author":"Schwartz","year":"2017","journal-title":"Anticancer. Agents Med. Chem."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1743-7075-7-7","article-title":"Cancer as a metabolic disease","volume":"7","author":"Seyfried","year":"2010","journal-title":"Nutr. Metab."},{"key":"ref_36","first-page":"24S","article-title":"Causes and Consequences of Increased Glucose Metabolism of Cancers","volume":"49","author":"Robert","year":"2008","journal-title":"J. Uclear Med."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"305","DOI":"10.2174\/187152008783961932","article-title":"The warburg effect: Why and how do cancer cells activate glycolysis in the presence of oxygen?","volume":"8","year":"2008","journal-title":"Anticancer. Agents Med. Chem."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1113\/jphysiol.1919.sp001839","article-title":"The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue","volume":"52","author":"Krogh","year":"1919","journal-title":"J. Physiol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1080\/10739680801938289","article-title":"Theoretical Models of Microvascular Oxygen Transport to Tissue","volume":"15","author":"Daniel","year":"2008","journal-title":"Microcirculation"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1098\/rspa.1957.0068","article-title":"A Theory of Inflammability Limits and Flame-Quenching","volume":"240","author":"Spalding","year":"1957","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/0034-5687(86)90118-0","article-title":"Cross-sectional PO2 distributions in Krogh cylinder and solid cylinder models","volume":"64","author":"Piiper","year":"1986","journal-title":"Respir Physiol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1089\/ten.tec.2015.0375","article-title":"Analytic Models of Oxygen and Nutrient Diffusion, Metabolism Dynamics, and Architecture Optimization in Three-Dimensional Tissue Constructs with Applications and Insights in Cerebral Organoidsvol","volume":"22","author":"McMurtrey","year":"2016","journal-title":"Tissue Eng. Part C Methods"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1038\/jcbfm.1989.2","article-title":"ATP and Brain Function","volume":"9","author":"Erekinsca","year":"1989","journal-title":"J. Blood Flow Metab."},{"key":"ref_44","unstructured":"(2021, June 02). Available online: https:\/\/www.health.harvard.edu\/blog\/the-hidden-long-term-cognitive-effects-of-covid-2020100821133."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.4081\/cp.2020.1271","article-title":"COVID-19: Hemoglobin, iron, and hypoxia beyond inflammation. A narrative review","volume":"10","author":"Corrao","year":"2020","journal-title":"Clin. Pract."},{"key":"ref_46","first-page":"e575","article-title":"A Prospective Study of Neurologic Disorders in Hospitalized Patients with COVID-19 in New York City","volume":"96","author":"Frontera","year":"2021","journal-title":"J. Neurol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"672","DOI":"10.2174\/092986710790416263","article-title":"Inhibitors of lactate dehydrogenase isoforms and their therapeutic potentials","volume":"17","author":"Granchi","year":"2010","journal-title":"Curr. Med. Chem."},{"key":"ref_48","unstructured":"Melkonian, E.A., and Schury, M.P. (2021, June 02). Biochemistry, Anaerobic Glycolysis. [Updated 21 August 2019], StatPearls, Available online: https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK546695\/."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0040-6031(94)02072-V","article-title":"Size effects on metabolic rate in cell, tissue, and body calorimetry","volume":"251","author":"Singer","year":"1995","journal-title":"Thermochim. Acta"},{"key":"ref_50","unstructured":"Kapteijn, F., Marin, G.B., and Moulijn, J.A. (1999). Catalytic Reaction Engineering. Catalysis: An Integrated Approach, Elsevier."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Wang, Z., Zhang, J., Ying, Z., and Heymsfield, S.B. (2012). Organ-Tissue Level Model of Resting Energy Expenditure Across Mammals: New Insights into Kleiber\u2019s Law. Int. Sch. Res. Netw. ISRN Zool., 9.","DOI":"10.5402\/2012\/673050"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1098\/rspb.2002.2304","article-title":"Scaling laws for capillary vessels of mammals at rest and in exercise","volume":"270","author":"Dawson","year":"2003","journal-title":"Proc. R. Soc. Lond. B"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"186","DOI":"10.3390\/systems2020186","article-title":"A Sceptics View: Kleiber\u2019s Law or the 3\/4 Rule is neither a Law nor a Rule but Rather an Empirical Approximation","volume":"2","author":"Hulbert","year":"2014","journal-title":"Systems"},{"key":"ref_54","unstructured":"Ahulwalia, A. (2021, July 01). Allometric Scaling In-Vitro, Scientific Reports. Available online: www.nature.com\/scientificreports."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.3892\/ol.2012.928","article-title":"Energy metabolism of cancer: Glycolysis versus oxidative phosphorylation (Review)","volume":"4","author":"Zheng","year":"2012","journal-title":"Oncol. Lett."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1101\/gad.189365.112","article-title":"Links between metabolism and cancer","volume":"26","author":"Dang","year":"2012","journal-title":"Genes Dev."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.trecan.2016.06.009","article-title":"Evolutionary Ecology of Organs: A Missing Link in Cancer Development?","volume":"2","author":"Thomas","year":"2016","journal-title":"Trends Cancer"},{"key":"ref_58","unstructured":"Epstein, T., Gatenby, R.A., and Joel SBrown, J.S. (2017). Fluctuations in energy demand. PLoS ONE."},{"key":"ref_59","unstructured":"Cooper, G.M. (2000). The Cell: A Molecular Approach, Sinauer Associates. [2nd ed.]."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/9\/3\/54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:31:01Z","timestamp":1760164261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/9\/3\/54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,16]]},"references-count":59,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["systems9030054"],"URL":"https:\/\/doi.org\/10.3390\/systems9030054","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,16]]}}}