A limit on the energy transfer rate from the human fat store in hypophagia

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Abstract

A limit on the maximum energy transfer rate from the human fat store in hypophagia is deduced from experimental data of underfed subjects maintaining moderate activity levels and is found to have a value of (290±25) kJ/kg d. A dietary restriction which exceeds the limited capability of the fat store to compensate for the energy deficiency results in an immediate decrease in the fat free mass (FFM). In cases of a less severe dietary deficiency, the FFM will not be depleted. The transition between these two dietary regions is developed and a criterion to distinguish the regions is defined. An exact mathematical solution for the decrease of the FFM is derived for the case where the fat mass (FM) is in its limited energy transfer mode. The solution shows a steady-state term which is in agreement with conventional ideas, a term indicating a slow decrease of much of the FFM moderated by the limited energy transferred from the fat store, and a final term showing an unprotected rapid decrease of the remaining part of the FFM. The average resting metabolic rate of subjects undergoing hypophagia is shown to decrease linearly as a function of the FFM with a slope of (249±25) kJ/kg d. This value disagrees with the results of other observers who have measured metabolic rates of diverse groups. The disagreement is explained in terms of individual metabolic properties as opposed to those of the larger population.

Introduction

The popular assumption made in cases of hypophagia is that energy deficits are balanced by appropriate decreases in the fat mass (FM)1 resulting in the initial constancy of the fat free mass (FFM). It is sometimes assumed that this situation will persist until the total exhaustion of the FM at which point the FFM will then begin to decrease. As reasonable as this paradigm may appear, it will be demonstrated that it is not valid in the case of semi-starvation where the FFM decreases from the start of the dietary regimen. It is deduced from the experimental data that, in the case of severe dietary restriction, the FM can only provide a limited rate of energy transfer to the FFM forcing the energy deficit to be made up by a decrease in the FFM. The ability of the FM to provide whatever energy is required by the FFM is possibly restricted by the rate limited biochemical reactions of the energy transfer processes. If, however, the dietary restriction is not severe, it is possible that “protein sparing” can occur at least until the FM is depleted to the level where its limited energy transfer capability becomes challenged. Both cases of “protein sparing” and “non-protein sparing” are discussed in this paper and the transition from the former condition to the latter is considered.

In order to demonstrate the immediate decrease of the FFM during severe dietary restriction, we make use of data obtained in a humanitarian experiment done during wartime at the University of Minnesota by Keys et al. (1950). This experiment will be referred to as the Minnesota experiment (ME). In the ME, 32 young male volunteers of military status were semi-starved in order to evaluate optimal rehabilitation methods for use in treatment of the food deprived population of parts of wartime Europe. The data of the ME are used in this paper because of the long period of controlled semi-starvation (24 weeks), the multiple measurements of the FM, and the militarily mandated and enforced dietary compliance. Fortunately for this study, the average dietary restriction employed in the ME, (6.56±0.31) MJ/d, was nearly ideal for demonstrating the limit on the energy transfer rate from the FM.

In the ME, the FM was measured at three different times during the 24-week semi-starvation period by densitometric means and corrections were applied to take account of excess fluids and minerals. The corrected data were presented in tabular form without indication of experimental uncertainties. This author has taken the uncorrected data of the FM and has proportionally applied these stated errors directly to the reduced data which is presented in Fig. 1. The error bars in Fig. 1 are indicative of the standard error of the mean and should be considered to be minimal since they do not include the unknown uncertainties introduced by the correction process. A least squares fit was done on the experimental points resulting in the expressionf=9.51exp[-(t/135)],where f is the FM in kg and t is the elapsed time in d. Eq. (1) is shown in Fig. 1 by the solid curve. The correlation coefficient for the fitting process was 0.9991. Also shown in Fig. 1 is the popular, non-dynamic concept (dashed line) that a constant energy deficit results in a fixed rate of decrease of the FM. The dotted–dashed curve in Fig. 1 indicates a dynamic decrease of the FM based on the assumption that there is no limitation on the ability of the FM to transfer whatever energy is needed to the FFM. The equation for this curve will be derived in a later section of this paper and shows that the FM will be exhausted after 98 d of semi-starvation.

Point-by-point subtraction of the FM given by Eq. (1) from the experimental values of the total body mass (TBM) yields the results shown in Fig. 2 for the FFM during the semi-starvation period and for a few weeks prior to the beginning of the food energy restriction. There are three observations to be made from the data presented in Fig. 2. Firstly, there is an immediate decrease of the FFM. Secondly, the FFM reaches a constant value during the last 6 weeks of semi-starvation. This constancy results from energy equilibrium between the slightly increased food energy input rate and both the decreased resting metabolic rate (RMR) and the lessened energy expended on activity. And lastly, it should be noted that the scatter of experimental points from a hypothetical smooth curve is well within the experimental error.

The two-reservoir energy model employed by Alpert (1979) will be used to develop a theory which explains the main features of the experimental data shown in Fig. 1, Fig. 2. The model considers the body to be made up of only the FM and the FFM and that energy is stored in both of these reservoirs. In fact, the body has three separate energy stores: the sugar, glycogen, which is found in muscles and in the liver and is associated with muscular activity; protein which is found in many organ systems and is viewed as being living tissue; and the FM. We include glycogen and protein into the FFM along with many other inactive components such as bone mineral and extra cellular water (ECW). The word, inactive, in the preceding sentence is meant to refer to any body constituent which is not directly involved in oxygen consumption. The fact that glycogen and protein are both included in the FFM means that we will not be able to separate the energy properties of these two energy stores. The main reason for including glycogen and protein into a single entity, the FFM, results from the ability of densitometric experiments only to distinguish and measure the FM and the FFM.

The FM consists of glyceryl esters and fatty acids and should not be confused with adipose tissue of which it is a major component. In the sense used in the model, the FM is considered to be an external load only physiologically active in the transfer of energy to the FFM. It is the FFM which interacts with oxygen.

Since the FFM consists of protein, glycogen, and many other components, we discontinue use of the term “protein sparing” and replace it with a more appropriate term, FFM sparing.

Section snippets

Theoretical considerations

The conservation of energy principle is set forth here asrateofenergystorage=rateofenergyinput-rateofenergyoutput.In terms of the two-reservoir model, this is written asαdf/dt+βd/dt=εQfd-RMR()-δ(f+),where f is the FM and is the FFM. The symbol α is the energy density of change of the FM, is well known and is constant; β is the energy density of change of the FFM and is not well known and may not be of a constant nature. The quantity, β, represents catabolism of protein, the change in

Experimental considerations

Before we can test the validity of the theory presented in the previous section, we must first determine the experimental values of the many parameters which we have introduced.

The value of the maximum energy transfer factor is derived from the solution of Eq. (6) which is given byf=f0exp(-σt/α).Since we know the response time of this equation to be 135 d and we know the energy density of fat, we can calculate the value of σ to be 290 kJ/kg d. An uncertainty can be assigned by consideration of

The transition between FFM sparing and non-FFM sparing

The ME provides data which indicates that there is a limited ability of the FM to transfer energy to the FFM in the case of semi-starvation. A related question is, are there other less severe dieting regimens where the FM is capable of transferring energy at an adequate rate so as to spare the FFM? An experiment by Webb and Abrams (1983) provides an affirmative answer to this question. The experimental subjects of this work were 9 men and women grouped in the 20s and 40s all of whom, with one

Conclusions and speculations

The main thesis of this paper is that the FM is able to transfer energy to the FFM up to a maximum rate of (290±25) kJ/kg d. In realistic energy deficit situations, the actual transfer rate is decreased by activity considerations. The value of the maximum transfer rate is derived from data for young, active male subjects studied by Keys et al. (1950). The applicability of these results have not been directly verified in other populations and conditions.

Experimental studies to determine the value

Acknowledgments

This work is dedicated to the memory of Peter Franken (1928–1999), late Professor of Optical Sciences and Physics at the University of Arizona. Professor Franken was highly gifted with a wide range of curiosities and interests. The author appreciates his kind and critical comments of past years.

I wish to thank Professor Eric Ravussin of the Pennington Biomedical Research Center (PRBC) for inviting me to address the CALERIE Steering Committee meeting, June 10–12, 2003, in Baton Rouge, LA. The

References (25)

  • C. Doré et al.

    Prediction of energy requirements of obese patients after massive weight loss

    Hum. Nutr.Clin Nutr.

    (1982)
  • J.V.G.A. Durnin et al.

    Energy, Work and Leisure

    (1967)
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