{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:13:46Z","timestamp":1772133226567,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2012,12,12]],"date-time":"2012-12-12T00:00:00Z","timestamp":1355270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Abstract: Past theories on total lifetime energy expenditures and entropy generation in biological systems (BS) dealt with whole systems, but the recent literature suggests that the total metabolic rate of a BS,q\u0307body (W) is a sum of product of specific metabolic rate q\u0307k,m (W\/kg of organ k) of each vital life organ, k {k = brain, heart, kidney and liver, or abbreviated as BHKL, and rest of the organ mass (R)} and mass of each organ k (mk). Using this hypothesis, Kleiber\u2019s law on metabolic rate of BS (q\u0307body) for animals of different sizes was validated. In this work, a similar procedure is adopted in estimating total entropy generation rate of whole human body (\u03c3\u0307body, W\/K) as a sum of product of specific entropy generation rate for each organ, \u03c3\u0307k,m (W\/{K kg of organ k\u00b7}) and the organ mass at any given age (t). Further integrating over life span for each organ (tlife), the lifetime specific entropy generated by organ k, \u03c3k,m,life (J of organ k\/ {K kg organ k}) is calculated. Then lifetime entropy generation of unit body mass, \u03c3body,M,life (J\/{K kg body mass\u00b7}) is calculated as a sum of the corresponding values contributed by all vital organs to unit body mass and verified with previously published literature. The higher the \u03c3k,m,life , the higher the entropy stress level (which is a measure of energy released by unit organ mass of k as heat) and the irreversibility within the organ, resulting in faster degradation of organ and the consequent health problems for the whole BS. In order to estimate \u03c3\u0307k (W\/K of organ k), data on energy release rate (q\u0307) is needed over lifetime for each organ. While the Adequate Macronutrients Distribution Range (AMDR)\/Adequate Intake (AI) publication can be used in estimating the energy intake of whole body vs. age for the human body, the energy expenditure data is not available at organ level. Hence the \u03c3k,m,life was computed using existing allometric laws developed for the metabolism of the organs, the relation between the mk of organ and body mass mB, and the body mass growth data mB(t) over the lifetime. Based on the values of \u03c3k, m, life, the organs were ranked from highest to lowest entropy generation and the heart is found to be the most entropy-stressed organ. The entropy stress levels of the other organs are then normalized to the entropy stress level (NESH) of the heart. The NESH values for organs are as follows: Heart: 1.0, Kidney: 0.92, Brain: 0.46, Liver: 0.41, Rest of BS: 0.027. If normalized to rest of body (R), NESR, heart: 37, Kidney: 34, Brain: 17, Liver: 15, Rest of BS: 1.0; so heart will fail first followed by kidney and other organs in order. Supporting data is provided.<\/jats:p>","DOI":"10.3390\/e14122550","type":"journal-article","created":{"date-parts":[[2012,12,12]],"date-time":"2012-12-12T11:02:13Z","timestamp":1355310133000},"page":"2550-2577","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Entropy Stress and Scaling of Vital Organs over Life Span Based on Allometric Laws"],"prefix":"10.3390","volume":"14","author":[{"given":"Kalyan","family":"Annamalai","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA"}]},{"given":"Carlos","family":"Silva","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA"}]}],"member":"1968","published-online":{"date-parts":[[2012,12,12]]},"reference":[{"key":"ref_1","unstructured":"Olshansky, S.J., and Carnes, B.A. (2001). Quest for Immortality: Science at Frontiers of Aging, W.W. Nortons."},{"key":"ref_2","unstructured":"National Center for Health Statistics, 2001 Data Warehouse on Trends in Health and Aging. extensive data from http:\/\/www.cdc.gov\/nchs\/nvss\/mortality_public_use_data.htm."},{"key":"ref_3","unstructured":"Ebersole, P., Hess, P., and Schmidt, L.A. (2003). Towards Healthy Aging-Human Needs and Nursing, Mosby Inc.. [6th ed.]."},{"key":"ref_4","unstructured":"Schrodinger, E. (1944). What Is Life?, Cambridge University Press."},{"key":"ref_5","first-page":"453","article-title":"Universal Biological Scaling and Mortality","volume":"91","author":"Azbel","year":"1994","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1038\/270301a0","article-title":"Evolution of Ageing","volume":"270","author":"Kirkwood","year":"1977","journal-title":"Nature"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1086\/413544","article-title":"Energy, Metabolism, Brain Size and Longevity in Mammals","volume":"58","author":"Hofman","year":"1983","journal-title":"Quart. Rev. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0022-5193(83)80011-3","article-title":"Evolution of brain size in neonatal and adult placental mammals: a theoretical approach","volume":"105","author":"Hofman","year":"1983","journal-title":"J. Theor. Biol."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Pearl, R. (1922). The Biology of Death: Being a Series of Lectures Delivered at the Lowell Institute in Boston in December 1920, J. B. Lippincott & Co.","DOI":"10.5962\/bhl.title.55327"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.1242\/jeb.01556","article-title":"Body size, energy metabolism and lifespan-A Review","volume":"208","author":"Speakman","year":"2005","journal-title":"J. Exp. Biol."},{"key":"ref_11","unstructured":"Julie, A.M., George, S.R., Beasley, T.M., Tilmont, E.M., Handy, A.M., Herbert, R.L., Longo, D.L., Allison, D.B., Young, J.E., and Bryant, M. (2012). Impact of caloric restriction on health and survival in rhesus monkeys from the NIA study. Nature."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Annamalai, K., and Puri, I. (2007). Combustion Science and Engineering, CRC Press.","DOI":"10.1201\/9781420003789"},{"key":"ref_13","unstructured":"DNA Repair at Encyclopedia of Aging. Available online: http:\/\/www.encyclopedia.com\/doc\/1G2-3402200112.html\/."},{"key":"ref_14","first-page":"547","article-title":"Free Radical Theory of Aging Matures","volume":"78","author":"Beckman","year":"1998","journal-title":"Phys. Rev."},{"key":"ref_15","unstructured":"Hershey, D., and Wang, H. (1980). A New Age-Scale for Humans, Lexington Books."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Silva, C.A., and Annamalai, K. (2009). Entropy generation and human aging: lifespan entropy and effect of diet composition and caloric restriction diets. J. Thermodyn., 186723.","DOI":"10.1155\/2009\/186723"},{"key":"ref_17","unstructured":"Batato, M., Deriaz, O., Jequier, E., and Borel, L. (, January May). Second Law Analysis of the Human Body. Proceedings of Florence World Energy Research Symposium, Firenze, Italy."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0022-5193(89)80004-9","article-title":"Entropy Flow and Entropy Production in the Human Body in Basal Conditions","volume":"141","author":"Aoki","year":"1989","journal-title":"J. Theor. Biol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/S0022-5193(05)80120-1","article-title":"Effects of Exercise and Chills on Entropy Production in Human Body","volume":"145","author":"Aoki","year":"1990","journal-title":"J. Theor. Biol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF02435047","article-title":"Entropy production in human lifespan: a thermodynamical measure for aging","volume":"1","author":"Aoki","year":"1994","journal-title":"Age"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"75","DOI":"10.2298\/TSCI0701075R","article-title":"A novel Method for Estimating the Entropy Generation in a Human Body","volume":"11","author":"Rahman","year":"2007","journal-title":"Therm. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/S0531-5565(00)00231-X","article-title":"Oxidative Biochemical Markers Cluse To Understanding Aging In Long Lived Species","volume":"36","author":"Flyod","year":"2001","journal-title":"Exp. Gerontol."},{"key":"ref_23","unstructured":"Walford, R.L. (LE Magazine, 1998). Calorie Restriction, Eat Less, Eat Better, Live Longer, LE Magazine."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"E539","DOI":"10.1152\/ajpendo.2000.279.3.E539","article-title":"Resting energy expenditure-fat-free mass relationship: new insights provided by body composition modeling","volume":"279","author":"Wang","year":"2000","journal-title":"Am. J. Physiol. Endocrinol. Metab."},{"key":"ref_25","first-page":"2967","article-title":"The Reconstruction of Kleiber\u2019s Law at the Organ-Tissue Level","volume":"131","author":"Wang","year":"2001","journal-title":"J. Am. Soc. Nutr. Sci."},{"key":"ref_26","unstructured":"Calder, W.A. (1996). Size, Function, and Life History, Dover."},{"key":"ref_27","unstructured":"Kinney, J.M., and Tucker, H.N. (1992). Energy Metabolism: Tissue Determinants and Cellular Corollaries, Raven."},{"key":"ref_28","first-page":"E249","article-title":"Organ tissue mass measurement allows modeling of resting energy expenditure and metabolically active tissue mass","volume":"275","author":"Gallagher","year":"1998","journal-title":"Am. J. Physiol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Annamalai, K., Puri, I., and Jog, M. (2011). Advanced Thermodynamics Engineering, Taylor and Francis. [2nd ed.]. Chapter 14.","DOI":"10.1201\/9781439805718"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"100","DOI":"10.3390\/entropy-e10020100","article-title":"Entropy generation and human aging: lifespan entropy and effect of physical activity level","volume":"10","author":"Silva","year":"2008","journal-title":"Entropy"},{"key":"ref_31","unstructured":"Cardiovascular System at Wikibooks. Available online: http:\/\/en.wikibooks.org\/wiki\/Anatomy_and_Physiology_of_Animals\/Cardiovascular_System\/Blood_circulation."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1139\/tcsme-1986-0014","article-title":"Second law analyses of energy processes. IV\u2013The exergy of hydrocarbon fuels, Second Law analysis of Energy Processes","volume":"10","author":"Brzustowski","year":"1986","journal-title":"Trans. Canad. Soc. Mech. Eng."},{"key":"ref_33","unstructured":"National Center for Environmental Assessment, Office of Research and Development, U.S. Environmental Protection Agency (2007, January 14\u201315). Summary Report of a Peer Involvement Workshop on the Development of an Exposure Factors Handbook for the Aging, Arlington, VA, USA."},{"key":"ref_34","unstructured":"Health Survey at the National Archives, Available online: http:\/\/www.dh.gov.uk\/en\/Publicationsandstatistics\/PublishedSurvey\/HealthSurveyForEngland\/Healthsurveyresults\/DH_4001334."},{"key":"ref_35","unstructured":"Snyder, W.S., and Cook, M.J. Pergamon Press. International Commission on Radiological Protection, 1975."},{"key":"ref_36","unstructured":"(2002). Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids (Macronutrients), National Academy Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1111\/j.1474-9726.2009.00480.x","article-title":"Lifespan extension by dietary restriction is not linked to protection against somatic DNA damage in Drosophila melanogaster","volume":"8","author":"Edman","year":"2009","journal-title":"Aging Cell"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wong, G., Hayen, A., Chapman, J., Webster, A., Wang, J., Mitchell, P., and Craig, J. (2009). Association of CKD and Cancer Risk in Older People. Clin. J. Am. Soc. Nephrol.","DOI":"10.1681\/ASN.2008090998"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1126\/science.1132191","article-title":"Transgenic Mice with a Reduced Core Body Temperature Have an Increased Life Span","volume":"314","author":"Conti","year":"2006","journal-title":"Science"},{"key":"ref_40","unstructured":"Madya, C., Keutenedjian, E., and de Oliveira, S. (2012, January 26\u201329). Human body exergy metabolism. Proceedings Of Ecos 2012\u2013The 25th International Conference on Efficiency, Cost, Optimization, Simulation And Environmental Impact Of Energy Systems, Perugia, Italy."},{"key":"ref_41","unstructured":"Hayne, D.T. (2008). Cambridge University Press."},{"key":"ref_42","unstructured":"American Society of Heating, Refrigerating and Air-Conditioning Engineers (1993). Handbook of Fundamentals, ASHRAE."},{"key":"ref_43","unstructured":"Annamalai, K. (2012, January 22\u201324). Group Combustion of Char Particles and Metabolism in Large Organs. Spring Technical Meeting of the Central States Section of the Comb. Inst., Dayton, OH, USA. Paper No. 12S-130."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1242\/jeb.01503","article-title":"Review: Multi-level regulation and metabolic scaling","volume":"208","author":"Suarez","year":"2005","journal-title":"J. Exp. Biol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/12\/2550\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:54:11Z","timestamp":1760219651000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/12\/2550"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,12]]},"references-count":44,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2012,12]]}},"alternative-id":["e14122550"],"URL":"https:\/\/doi.org\/10.3390\/e14122550","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,12]]}}}