Resting energy expenditure-fat-free mass relationship: new
insights provided by body composition modeling
Zimian
Wang,
Stanley
Heshka,
Dympna
Gallagher,
Carol
N.
Boozer,
Donald P.
Kotler, and
Steven B.
Heymsfield
Obesity Research Center, St. Luke's-Roosevelt Hospital, College of
Physicians and Surgeons, Columbia University, New York, New York 10025
 |
ABSTRACT |
The relationship between
resting energy expenditure (REE) and metabolically active fat-free mass
(FFM) is a cornerstone in the study of physiological aspects of body
weight regulation and human energy requirements. Important questions,
however, remain unanswered regarding the observed linear REE-FFM
association in adult humans. This led us to develop a series of
REE-body composition models that provide insights into the widely used
simple linear REE-FFM prediction model derived experimentally in adult
humans. The new models suggest that the REE-FFM relationship in mammals as a whole is curvilinear, that a segment of this function within a FFM
range characteristic of adult humans can be fit with a linear equation
almost identical to that observed from a composite review of earlier
human studies, and that mammals as a whole exhibit a decrease in the
proportion of FFM as high metabolic rate organs with greater FFM. The
present study thus provides a new approach for examining REE-FFM
relationships, advances in a quantitative manner previously observed
albeit incompletely formulated REE-body composition associations, and
identifies areas in need of additional research.
energy metabolism; body composition
 |
INTRODUCTION |
ALL LIVING ORGANISMS
expend energy for the maintenance of cellular homeostasis. Energy
produced by metabolic processes in humans consists of three main
portions, resting energy expenditure (REE), the thermic effect of food,
and physical activity-induced energy expenditure (6,
19). REE, measured at rest after an overnight fast, is
usually the largest portion (~60-75%) of total energy expenditure.
A major investigative focus of energy metabolism research over the past
four decades is the development of REE prediction formulas based on
fat-free mass (FFM). Most investigators have reported that, for healthy
adult humans, the relationship between REE and FFM is fit by a linear
function
|
(1)
|
where a and b are the regression line
intercept and the slope, respectively. Fifteen descriptive REE-FFM
linear regression equations are presented in Table
1 (4-6,
13, 14, 17, 18, 24-31). FFM has been measured by the use of diverse
body composition methods such as anthropometry, underwater weighing,
total body potassium, 3H2O and
2H2O dilution techniques, and, more recently,
dual-energy X-ray absorptiometry. Despite the dissimilar methodologies
used to estimate FFM, all of these descriptive regression equations
report a positive intercept varying from 186 to 662 kcal/day and
similar slopes varying from 19.7 to 24.5 kcal · kg
FFM
1 · day
1 (Table 1).
Although investigators have expressed an increasing interest in REE-FFM
relationships, several fundamental questions remain unanswered. For
example, when REE in adult humans is plotted against FFM, a linear
relationship with a non-zero intercept is observed within the FFM range
of ~40-80 kg. This provides the implausible inference that a
component of REE (~400 kcal/day) remains when there exists no (i.e.,
zero) FFM by extrapolation. The non-zero positive intercept of this
relation also implies that subjects with a small FFM have a relatively
high resting metabolic rate compared with those with a large FFM. If
FFM is a homogeneous heat-producing metabolically active compartment,
how can these observations be reconciled?
The aim of this paper is to present a new modeling approach aimed at
elucidating the biological and related mathematical relationships between REE and FFM. The chosen strategy involved creating REE-FFM models at the whole body level and the tissue/organ body composition level, respectively. Several fundamental unanswered questions regarding
REE-FFM relationships were then examined in the context of the
developed models. The present study extends the work of Brody
(2), Grande (12), Holliday and colleagues
(15, 16), Elia (6), Calder III
(3), and Weinsier et al. (37) on REE-body
composition relationships.
 |
RESTING ENERGY EXPENDITURE AND BODY COMPOSITION |
The presently available REE-body composition models are based on
two fundamental concepts: 1) that only metabolically active components contribute to REE; and 2) that there are
quantitative and measurable associations between REE and metabolically
active components. All metabolically active components can be organized according to the five-level model, which indicates that the ~40 body
components are distributed into five distinct but connected levels:
atomic, molecular, cellular, tissue/organ, and whole body (36). The available literature allows us to derive the
quantitative associations between REE and metabolically active
components at four levels: molecular, cellular, tissue/organ, and whole
body (Wang ZM, Gallagher D, Heshka S, Zhang K, Boozer C, Testolin C, and Heymsfield SH, unpublished observations).
At the molecular level, the human body can be divided into fat
and FFM, with FFM considered the only metabolically active component.
Although experimental studies reveal a linear relationship between REE
and FFM in healthy adult humans (Table 1), the previously mentioned
questions regarding these models remain unanswered. In the present
investigation, therefore, we examine the REE-FFM relationship in adult
humans at the whole body and tissue/organ levels.
The cellular level is the first body composition level at which
discrete sites of energy production can be identified. The cellular
level is thus central when examining REE-body composition relationships. At the cellular level, the human body is composed of
various categories of cells, extracellular fluid, and extracellular solids. Cells are the only metabolically active compartment at this
level, and various cell types differ in their resting metabolic rates.
Although the cellular level is important in the study of energy
metabolism, very little REE-body composition research has been directed
at this level, perhaps because of the difficulty in quantifying
specific cell categories. Improved in vivo methods of quantifying cell
mass (e.g., nuclear magnetic resonance) and energy exchange (e.g.,
positron emission tomography) of individual cell categories are needed
in future REE studies. At present, therefore, we are not able to
explore REE-FFM relationships at the important cellular level.
At the tissue/organ level, all tissues and organs are metabolically
active components, and various tissues and organs differ in their
resting metabolic rates. Whole body REE is thus determined by two
factors, the individual mass of tissues/organs and their corresponding
resting metabolic rates. The quantitative relationships between
tissues/organs and FFM allow us to examine and model the REE-FFM relationship.
At the whole body level, the only metabolically active component is
body mass (BM), and REE is a function of body mass (2, 3). The quantitative relationship between BM and FFM
allows us to explore and model the REE-FFM function.
 |
WHOLE BODY LEVEL REE MODEL |
BM, which can be measured easily and with high accuracy, was
the first physical characteristic applied in the development of
descriptive REE equations. Kleiber (20) was one of the
first investigators to report the relationship between REE and BM in mammals. He surveyed REE estimates for mature mammals, ranging from
rats to steers, with an ~2,800-fold difference in body size. By
expressing REE as a function of BM, Kleiber found a nonlinear relationship between REE (in kcal/day) and BM (in kg). The best fit for
his data was
|
(2)
|
Several years later, Brody (2) included some
additional species, ranging from mice to elephants, and published the
well known mouse-to-elephant curve. The power of Brody's equation, 0.734, was nearly identical with that of Eq. 2
|
(3)
|
In 1961, Kleiber (21) suggested a new descriptive
REE-BM equation
|
(4)
|
Equations 2-4 are very similar, and Kleiber
pointed out that the numerical difference in the exponent between 0.75 and 0.734 and in the coefficient between 70 and 73.3 is not
statistically significant. These REE-BM models were aimed at providing
broad insights and did not consider gender, age, and other secondary factors in their development. In the following years, there was considerable discussion devoted to explaining why mammalian REE scales
to ~BM0.75 (3, 23,
32, 38).
These whole body level observations can be applied to examination of
the experimentally observed linear REE-FFM relationship in adult humans
(Eq. 1 and Table 1). Previous studies indicate that adipose
tissue (AT, in kg) is an exponential function of BM across mature
mammals, AT = 0.075 × BM1.19 (3).
Assuming that 80% of AT is fat (34), FFM can be
calculated as
|
(5)
|
BM can thus be used to calculate for REE and FFM using Eqs.
4 and 5, respectively. The derived function, presented
graphically in Fig. 1, shows that the
REE-FFM relationship is nonlinear across the FFM range in mammals. For
the FFM range observed in normal adult humans (40 to 80 kg), however,
the relationship between REE (in kcal/day) and FFM (in kg) can be fit
by a linear function (r = 0.99, P < 0.001)

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Fig. 1.
Whole body modeling approach. Whole body resting energy
expenditure (REE, in kcal/day) on the ordinate is indicated vs.
fat-free mass (FFM, in kg) on the abscissa. REE and FFM were calculated
from Eqs 4 and 5, respectively. The REE-FFM
relationship ( ) is curvilinear. When FFM varies within the
interval from 40 to 80 kg, the REE-FFM relation ( ) can be fit by a
linear equation, REE = 21.7 × FFM + 374, as developed
by linear regression analysis.
|
|
|
(6)
|
Equation 6 and the experimentally derived composite
REE-FFM equation have very similar slopes (21.7 vs. 21.5 ± 1.4 kcal · kg FFM
1 · day
1) and
intercepts (374 vs. 407 ± 128 kcal/day) (Table
2). The curvilinear interspecies REE-FFM
model for mammals as a whole is thus consistent with the linear REE-FFM
model for adult humans.
 |
TISSUE/ORGAN LEVEL REE MODEL |
Although the whole body level REE model may guide us in examining
the relationships between REE and FFM, the model per se does not
provide insight into the underlying sources of energy expenditure.
Therefore, the next step in this expanded analysis involves a REE model
at the tissue/organ body composition level. The fundamental REE model
at the tissue/organ level can be expressed as
|
(7)
|
where Ti is the mass of individual tissue or organ,
ki is the corresponding resting metabolic rate
of the tissue or organ, and n is component number.
Recently, Gallagher et al. (11) used multiscan magnetic
resonance imaging (MRI) to measure the mass of seven tissue/organ level
components, including liver, kidney, brain, heart, skeletal muscle, AT,
and miscellaneous tissues. The authors then predicted REE based on
these individual tissue/organ masses and their corresponding resting
metabolic rates (k values), as provided by Elia (Table 3). They found a strong correlation
between the REE predicted by Eq. 7 and REE measured by
indirect calorimetry (r = 0.94, P = 0.0001), with no significant difference between the predicted REE
(1,666 ± 348 kcal/day) and the measured REE (1,685 ± 347 kcal/day) of 13 healthy young adult subjects. This study strongly
supports the concept that whole body REE can be predicted at the
tissue/organ level with Eq. 7. We now discuss the two REE
determinants, tissue/organ resting metabolic rate (k) and
corresponding mass (T).
Tissue/organ resting metabolic rate.
Expanding upon previous reviews, Elia (6) highlighted the
existence of large between tissue and organ differences in resting metabolic rate in adult humans (Table 3).
Although skeletal muscle and adipose tissue are the largest components,
their resting metabolic rates are low. In contrast, organs, including
liver, kidneys, heart, and brain, which account for only ~5-6%
of body mass, have much higher resting metabolic rates. Other body
components, including skeleton, skin, and lungs, have low resting
metabolic rates, and an average k value (12 kcal · kg
1 · day
1) was applied for these
components. The k values of the individual tissues and
organs were assumed to be relatively stable among healthy adult humans,
although some factors, such as training and disease, might affect the
metabolic function of various tissues and organs.
Tissue/organ mass-BM relationships.
In developing our expanded REE model, we considered 14 major tissues
and organs, including liver, kidneys, brain, heart, skeletal muscle,
AT, lungs, thyroid, adrenals, spleen, gut, skin, blood, and skeleton.
For a 70-kg human, the sum of these 14 tissues and organs is 69.2 kg,
or 98.9% of BM (34). Among mature mammals ranging in BM
from mice to elephants, each tissue and organ mass can be expressed as
an exponential function of BM (2, 3, 6)
|
(8)
|
where T is the individual tissue/organ mass, p is a
constant, and q is a scaling exponent. Previous studies
provide us with the allometric functions that relate these tissues and
organs to BM (Table 3). Allometric scaling is based on the concept that organisms are not isometric; rather, specific proportions change in a
regular manner. Nonisometric scaling in biology is often referred to as
"allometric," from the Greek "allos" meaning
"different" (32).
Tissue/Organ Level Model
Combining Eqs. 7 and 8, we develop a REE-BM
model at the tissue/organ body composition level
|
(9)
|
Using k, p, and q values
of individual tissues and organs (Table 3), whole body REE in Eq. 9 can be expressed as
|
(10)
|
where REE is in kilocalories per day, and BM is in kilograms.
Equation 10 is an expansion of Kleiber's allometric model,
in which total BM in Eq. 4 is replaced by each tissue/organ
level component.
Whole body REE and FFM can be calculated from BM with Eqs. 10 and 5, respectively. One is thus able to model REE as a
function of FFM (Fig. 2), again showing
that the relationship between REE and FFM is curvilinear across the FFM
range of mammals. Accordingly, REE increases with FFM but at a rate
less than BM1.0.

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Fig. 2.
Tissue/organ level modeling approach. Whole body REE (in
kcal/day) predicted from Eq. 10 on the ordinate vs. FFM (in
kg) on the abscissa. The REE-FFM relationship ( ) is
curvilinear. When FFM varies within the interval from 40 to 80 kg, the
REE-FFM relationship ( ) can be fit by a linear equation, REE = 24.6 × FFM + 175, as developed by linear regression
analysis.
|
|
The REE-FFM relationship for humans can be evaluated on the
tissue/organ level. When FFM = 0, as shown in Fig. 2, predicted REE = 0. Although the relationship between REE and FFM is
nonlinear for the entire range of available mammalian data, the REE-FFM function within the FFM interval from 40 to 80 kg for adult humans is
characterized by the linear regression equation (r = 0.99, P < 0.001)
|
(11)
|
Equation 11 and the experimentally derived composite
REE-FFM equation (Table 2) have similar slopes (24.6 vs. 21.5 ± 1.4 kcal · kg FFM
1 · day
1)
and positive intercepts (i.e., 175 vs. 407 ± 128 kcal/day).
 |
CURVILINEAR REE-FFM FUNCTION ACROSS MAMMALS |
An important inference can be derived from the whole body and
tissue/organ level interspecies REE-FFM mammalian models. As shown in
Figs. 1 and 2, small mammals like the rat and guinea pig may have
linear REE-FFM regression line slopes larger than that observed in
humans and other large mammals. Support for interspecies FFM-related
differences in the mammalian REE-FFM relationship (larger FFM
associated with smaller REE vs. FFM slope) comes from our own
laboratory, in which humans and rats had measurements of both REE and
FFM. The slope of REE vs. FFM in adult humans was 22.9 kcal/kg in the
study of Heshka et al. (13). In contrast, the REE vs. FFM
slope in adult Sprague-Dawley rats was 139.5 kcal/kg [REE
(kcal/day) = 139.5 × FFM (kg)
25.3;
r2 = 0.62, P < 0.01;
unpublished data].
Several relevant questions thus arise. Why is the REE-FFM relationship
a curvilinear function across mammalian species? Why would small and
large mammals differ in the relationship between REE and the mass of
metabolically active tissue expressed as the FFM component? We explored
these interrelations with the tissue/organ level REE-FFM model,
extending the qualitative observations of earlier investigators.
Specifically, we examined the influence of body size on k
values and on the proportion of FFM as individual tissues and organs.
Mammalian tissue/organ resting metabolic rate.
Individual tissues and organs can be divided into two groups, one with
high resting metabolic rates (e.g., brain, heart, liver, and kidney)
and the other with low metabolic rates (e.g., skeletal muscle,
skeleton, and adipose tissue; Table 3). Although Elia (6)
provided the resting metabolic rates of individual tissues and organs
for adult humans, it is questionable whether these k values
can also be applied to estimate REE in other mammals. Early studies
favored the hypothesis that the resting metabolic rates of homologous
tissues and organs (e.g., liver) are relatively constant, irrespective
of body size (35). However, subsequent well controlled
studies showed that the resting metabolic rates of homologous tissues
and organs were lower with greater body size (33).
Recently, Couture and Hulbert (4) determined the resting
metabolic rates of liver and kidney cortex from mouse, rat, rabbit, sheep, and cattle, representing a ~12,000-fold difference in BM. There was a highly significant "hypoallometric" (P < 0.01) relationship (scaling factor <0) between the oxygen
consumption rate of slices from both organs and BM. Mouse liver and
kidney slices respired per unit mass 5.9 and 3.4 times faster than the
corresponding slices from cattle. The higher respiration rate of slices
from smaller animals could not be explained by interspecies differences in tissue extracellular space or tissue protein content. The
observations of Couture and Hulbert strongly support the concept that
mammals with a small BM, such as the mouse and rat, have higher
k values than humans. In contrast, high BM mammals like the
cow and elephant have lower k values than humans.
Between-mammal tissue/organ mass-BM relationship.
The proportion of BM as individual tissue/organ is not constant across
mammalian species. With increasing BM, most organs are hypoallometric
(q < 1) as they occupy a decreasing fraction of BM.
Skeletal muscle is almost directly proportional (q = 1) to BM. In contrast, AT and skeleton are "hyperallometric" (q
> 1) across mammalian species because they occupy increasing
fractions of BM (Table 3).
We explored this question by calculating for representative body
weights the mass of five respective tissues and organs (heart, liver,
brain, skeleton, and fat-free portion of AT) with Eq. 8 and
the data in Table 3. The corresponding FFM was then calculated with
Eq. 5. The fraction of FFM as each of the five tissues and organs is plotted in Fig. 3 as a function
of FFM. The figure indicates that, with greater FFM, skeleton
and the fat-free portion of adipose tissue increase, and brain, liver,
and heart decrease or remain unchanged in mammals as a fraction of FFM.

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Fig. 3.
Ratio of tissue and organ mass to FFM (in kg/kg) on the
ordinate vs. FFM (in kg) on the abscissa. Tissue/organ mass and FFM
were calculated with Eqs. 8 and 5, respectively.
FF-AT, fat-free adipose tissue.
|
|
We also explored this question in humans, because there have been
relatively few published evaluations comprehensive in vivo tissue/organ
mass. Data from the Columbia Body Composition Program Project Grant
allow an initial analysis of these associations in healthy young men
and premenopausal women (age <45 yr). There were 174 subjects with
measured FFM, AT mass, skeletal muscle mass, and bone-mineral mass. A
subset of these subjects (n = 13) also had brain,
heart, liver, and kidney mass measured, as previously reported
(11). The tissue/organ mass-to-FFM ratios plotted as a
function of FFM are presented in Fig. 4
as two pooled groups, one with high resting metabolic rates (i.e., sum
of brain, heart, liver, and kidneys) and the other with low resting
metabolic rates (i.e., sum of fat-free AT, skeletal muscle, and bone
mineral). The observed trends are qualitatively similar to those
developed earlier for mammals as a whole, with a relative decrease in
high metabolic rate organs and a corresponding increase in low
metabolic rate tissues with greater FFM.

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Fig. 4.
Ratio of low metabolic rate tissues (LMR) and high
metabolic rate organs (HMR) to FFM on the ordinate vs. FFM on the
abscissa in 174 healthy adult humans. LMR is the sum of FF-AT, skeletal
muscle, and bone mineral; and HMR is the sum of brain, heart, liver,
and kidneys. LMR/FFM = 0.56 + 0.001 × FFM,
r = 0.24, P = 0.004; HMR/FFM = 0.102 0.0006 × FFM, r = 0.81, P <0.001; n = 13/subgroup.
|
|
Hence, although specific details remaining to be elucidated may vary, a
similar and highly consistent pattern emerges in mammals as a whole:
small mammals have larger proportions of FFM as organs with higher
resting metabolic rates compared with large mammals having higher
proportions of tissues with lower resting metabolic rates.
This interanimal anatomic difference, combined with a difference in
specific tissue/organ metabolic rates (k values), is
consistent with the curvilinear REE-FFM relationship observed in
mammals and with the finding that small mammals have larger REE-to-FFM ratios compared with their larger mammalian counterparts.
 |
SUMMARY AND CONCLUSIONS |
This study presents for the first time a series of models at the
whole body and tissue/organ levels designed specifically to explore the
observed relationships between REE and FFM. The segments of the
curvilinear interspecies mammalian functions between 40 and 80 kg FFM
typical of adult humans fit well with linear models and were similar to
the average REE prediction model formulated from 15 published
experimental studies.
Our modeling efforts, based on available information, thus support the
hypothesis that the linear REE-FFM relationship long observed in adult
humans is qualitatively consistent with the curvilinear REE-BM
relationship observed in mammals as a whole. Our analysis, supported by
preliminary human experimental data, also suggests that mammals exhibit
a decrease in the proportion of FFM as high metabolic rate organs with
greater FFM. FFM may thus not be a "metabolically homogeneous"
compartment across mammals generally, and humans specifically, varying
widely in BM.
Our literature review identified a limited number of studies, other
than those for small rodents and humans, in which REE, FFM, and various
organs and tissues were quantified in the same animals. That
information would be useful for extending the modeling efforts
presented in this report.
The derived whole body level and tissue/organ level REE-FFM models are
general and unsuitable for individual REE prediction. Future studies
are needed to extend these observations and to analyze gender- and
age-related, hormonal, ethnic, and other sources of variation in
REE-FFM relationships (8-10, 26,
39). Major advances in our understanding of these
relationships require linking additional body composition information
across the human life span with an analysis of individual tissue/organ
resting metabolic rates, an area in which there presently exists large
gaps in our knowledge.
 |
ACKNOWLEDGEMENTS |
This study was supported by National Institutes of Health Grant PO1
DK-42618.
 |
FOOTNOTES |
Address for reprint requests and other correspondence: Z. Wang,
Weight Control Unit, 1090 Amsterdam Ave., 14th Floor, New York, NY
10025 (E-mail: ZW28{at}Columbia.edu).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Received 13 September 1999; accepted in final form 6 April 2000.
 |
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