1. Introduction and Rationale

Living Biological systems (BS) are open systems exchanging mass, energy and entropy with the surroundings. The required energy for sustaining the life is released through the oxidation of glucose (carbohydrates, CH), fat (F) and proteins (P) (called macro-nutrients) carried by the blood stream to all the organs (a group of tissues which are self-contained and are specialized in performing a particular function) and a part of the chemical energy of nutrients is converted into another form of chemical energy, which is stored within Adenosine Tri-Phosphate (ATP) molecules, called the energy currency of the body and which can be readily used to deliver work (W, organized energy; e.g., lifting weights and placing them on shelve resulting in energy transfer in the form of work, which causes potential energy gain of weight) and/or supply cellular energy for endothermic biological reactions, active transport of species against adverse gradient (e.g., transport of glucose in intestines) and for repair/reproduce of cells for sustaining life functions while the remainder of the chemical energy is released as heat (Q, random energy) to overcome heat loss from the body and to maintain the normal body temperature.

One may define aging as an indication of decrease in physiological life sustaining functions, which leads to an increase in age related mortalities along with a decrease in reproductive functions [ 1 ]. Weinert et al. [ 2 ] presented a comprehensive review on aging and listed multiple trajectories for aging: evolutionary [ 3 ], molecular, cellular and whole body (system) levels including the environmental factors. Medvedev [ 4 ] listed more than 300 hypotheses on aging. The evolutionary concept outlined in [ 3 ] deals with genetic variants which cause Alzheimerʹs disease are found to be less in people with longer lifespans (i.e., slower rate of aging), indicating that Darwin’s natural selection at work allowing better ones (without genetic mutants) to survive. Lee et al. [ 5 ] studied the regulatory effects of nutrients on aging and suggested that the nutrient composition may be altered rather than using CR for improving life span. Kirkwood’s theory on aging falls under evolutionary and cellular [ 6 ] trajectories and mostly relies on copying errors. The ROS theory falls under cellular mechanism. Under ROS theory, the aging is attributed to accumulated damage to the cells of various organs via the production of radical oxygen species (ROS) during oxidation process/electron transport chain, resulting in impaired functions of cells within organs in repairing and replacing dead cells and eventually result in its inability to overcome the adverse environmental factors. It is cautioned that there are many other factors and interventions that modulate speed of aging but not necessarily related to ROS production [ 7 ]. Thus, aging is a “multi-factor” process.

M,life (≈ 835 MJ/kg body mass, a first law hypothesis, “live fast, die young” [ M,life . Living systems are characteristics of systems being far from equilibrium and hence must generate entropy since birth/conception. Thus Silva and Annamalai [ M ), proposed the second law hypothesis on biological aging with a fixed amount of life span entropy generation/irreversibility, σ M,life (10,000 kJ/(K kg body mass)) for the whole body. Such a hypothesis is also consistent with Andresan’s concept on constant total lifetime entropy production per unit body mass for all BS [ M,life . The σ M,life depends on the heat part, “Q M ” (= MJ of energy released as heat/kg body mass) of specific energy release rate, (SERR) or called as specific metabolic rate (SMR) in biology. Rubner’s rate of living theory (ROL) assumes a fixed amount of specific metabolic energy release. q(≈ 835 MJ/kg body mass, a first law hypothesis, “live fast, die young” [ 2 ]) over life span irrespective of metabolic efficiency (i.e., proportional to ATP production per unit mole of oxygen consumption) for every living organism and falls under systemic trajectory. The biological aging rate (BAR) is based on how fast or slow one reaches q. Living systems are characteristics of systems being far from equilibrium and hence must generate entropy since birth/conception. Thus Silva and Annamalai [ 8 9 ] adopted the availability concepts from thermodynamics, showing that availability/exergetic efficiency in thermodynamics is almost same as metabolic efficiency (η), proposed the second law hypothesis on biological aging with a fixed amount of life span entropy generation/irreversibility, σ(10,000 kJ/(K kg body mass)) for the whole body. Such a hypothesis is also consistent with Andresan’s concept on constant total lifetime entropy production per unit body mass for all BS [ 10 ] except that Silva’s hypothesis includes the effect of metabolic efficiency. Unlike Rubner’s hypothesis, the energy release along with metabolic efficiency (i.e., ATP production efficiency) affects the entropy generation rate. Thus, BAR is based on how fast or slow one reaches σ. The σdepends on the heat part, “Q” (= MJ of energy released as heat/kg body mass) of specific energy release rate, (SERR) or called as specific metabolic rate (SMR) in biology.

Apart from thermodynamics governing internal biological processes, there is a perpetual outflow of energy in the form of heat loss, Q and hence disposal of entropy generated within the whole body in the form of heat to the environment. In layman’s language, the entropy generation within a system is a measure of how things can go wrong irreversibly [ 11 ].

There is striking similarity between the field of combustion science, which deals with oxidation at high temperature (order of 1200–1500 °C, without use of catalysts) [ 12 ], and the field of metabolism in BS where oxidation at low temperature (37 °C) is aided by enzymes. Thus, currently efforts are under way to translate, modify and link the extensive results from fields of thermodynamics and combustion science to the field of biology particularly in the following areas:

First and second Law and availability analyses of oxidation of nutrients: CH, F and P and their mixtures and the relation to life span of BS.

Adiabatic temperature rise in combustion of fuels [ 12 ] vs. maximum temperature rise of blood leaving the organs either from basic principles of nutrient oxidation or from allometric laws.

Oxidation of a single carbon particle and carbon particle temperature vs. oxidation of nutrients in cells and single cell temperature.

k (W/(kg of organ k)) or specific metabolic rate of organ k (SMR k ) (k = Brain, heart, kidney, etc.), and bridging of gap between data on body mass independent SMR k data of Elia [ k data of Wang [ k will be a function of size of organ or mass of organ k when one of the following conditions are satisfied: (1) diffusion of oxygen dominates for large organ (i.e., there are a large number of cells within organ or abundant active enzymes are present in mitochondria); (2) the energy release rate is kinetically limited with first order (Michaelis Menten (MM)) kinetics (enzymes are limited or not active) SMR k is independent of organ mass under zero order kinetics or when organ size is small which leads to Elia constant in biology [ Adoption of literature on SERR from oxygen deficient carbon cloud in engineering [ 7 ] to specific energy release rate SERR(W/(kg of organ k)) or specific metabolic rate of organ k (SMR) (k = Brain, heart, kidney, etc.), and bridging of gap between data on body mass independent SMRdata of Elia [ 8 ] (but still depends on type of organ or its enzyme) with those of body mass-dependent SMRdata of Wang [ 13 ] and Singer’s data [ 10 ] in biology. The SMRwill be a function of size of organ or mass of organ k when one of the following conditions are satisfied: (1) diffusion of oxygen dominates for large organ (i.e., there are a large number of cells within organ or abundant active enzymes are present in mitochondria); (2) the energy release rate is kinetically limited with first order (Michaelis Menten (MM)) kinetics (enzymes are limited or not active) SMRis independent of organ mass under zero order kinetics or when organ size is small which leads to Elia constant in biology [ 13 ].

14,15, Deduction of allometric laws/constant for organs and the whole-body Kleiber’s law using Combustion Science and Thermodynamics [ 9 16 ].

The present work concerns the extension of availability analyses to mitochondrial level (Item 1), estimation of maximum possible temperature rise of blood from each organ (Item 2; i.e., non-ATP process) and presents methods of determining BAR. A brief literature review is presented summarizing previous work, followed by objectives and methodology adopted, a summary of results, and basic and derived allometric constants in tabular forms, quantitative results for ranking entropy stresses of organs and finally methods of estimating BAR.