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, body (W) is a sum of product of specific metabolic rate k,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 (m k ). Using this hypothesis, Kleiber's law on metabolic rate of BS ( body ) 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 ( body , W/K) as a sum of product of specific entropy generation rate for each organ, k , m (W/{K kg of organ k·}) and the organ mass at any given age (t). Further integrating over life span for each organ (t life ), the lifetime specific entropy generated by organ k, k,m,life (J of organ k/ {K kg organ k}) is calculated. Then lifetime entropy generation of unit body mass, body,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 k,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 k (W/K of organ k), data on energy release rate ( ) 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 k,m,life was computed using existing allometric laws developed for the metabolism of the organs, the relation between OPEN ACCESSEntropy 2012, 14 2551 the m k of organ and body mass m B , and the body mass growth data m B (t) over the lifetime. Based on the values of k, 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 (NES H ) of the heart. The NES H 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), NES R , 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.

Ranking Renewable and Fossil Fuels on Global Warming Potential Using Respiratory Quotient Concept

“…It has been observed that the heat values of various nutrients expressed on kJ per kg of O 2 consumed (HHV O 2 ) is approximately constant at about 14,000 kJ/kg of O 2 [11,12]. Hence, by knowing the O 2 consumption, the amount of energy released in kJ can be readily estimated.…”

“…Biology literature defines respiratory quotient (RQ) as the ratio of moles of CO 2 produced (or CO 2 eliminated) to stoichiometric oxygen (O 2 ) moles consumed typically during oxidation reaction, for example, oxidation of nutrients in the body. The RQ factor for fat, protein, and carbohydrates-the three basic nutrients (Table 1) of the body-are 0.7, 0.8, and 1, respectively [6][7][8][9][10][11][12]. Thus, with measured CO 2 and O 2 in nasal exhaust one can determine RQ and determine which nutrient or a mixture of CH : F : P is being oxidized.…”

Biological Aging and Life Span Based on Entropy Stress via Organ and Mitochondrial Metabolic Loading

“…For life span metabolic energy per unit volume of mitochondria gk = z (fk − qk) in Equation (18). Previous literature provided details on conversion of allometric laws from body mass mB to organ mass k for various parameters of interest [23]. If cell density is equal to organ density, the allometric law for metabolic rate per unit mitochondrial volume in terms of vfMito,k is given as: Previous literature provided details on conversion of allometric laws from body mass m B to organ mass k for various parameters of interest [23].…”

“…Further the previous work [8,23] converted the "body mass"-based allometric relation for each organ into "organ mass"-based allometric relation:…”

“…Previous literature provided details on conversion of allometric laws from body mass mB to organ mass k for various parameters of interest [23]. If cell density is equal to organ density, the allometric law for metabolic rate per unit mitochondrial volume in terms of vfMito,k is given as: Previous literature provided details on conversion of allometric laws from body mass m B to organ mass k for various parameters of interest [23]. If cell density is equal to organ density, the allometric law for metabolic rate per unit mitochondrial volume in terms of vf Mito,k is given as: …”