Entropy Stress and Scaling of Vital Organs over Life Span Based on Allometric Laws

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,q̇body (W) is a sum of product of specific metabolic rate q̇k,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’s law on metabolic rate of BS (q̇body) 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 (σ̇body, W/K) as a sum of product of specific entropy generation rate for each organ, σ̇k,m (W/{K kg of organ k·}) 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, σk,m,life (J of organ k/ {K kg organ k}) is calculated. Then lifetime entropy generation of unit body mass, σbody,M,life (J/{K kg body mass·}) 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 σk,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 σ̇k (W/K of organ k), data on energy release rate (q̇) 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 σk,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 σk, 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.