Hydration of fat-free body mass: new physiological modeling
approach
Zimian
Wang1,
Paul
Deurenberg2,
Wei
Wang1,
Angelo
Pietrobelli1,
Richard N.
Baumgartner3, and
Steven B.
Heymsfield1
1 Obesity Research Center, St.
Luke's-Roosevelt Hospital, Columbia University College of Physicians
and Surgeons, New York, New York 10025;
2 Department of Human Nutrition
and Epidemiology, Wageningen Agricultural University, 6700 EV
Wageningen, The Netherlands; and
3 Clinical Nutrition Research
Center, University of New Mexico School of Medicine, Albuquerque, New
Mexico 87131
 |
ABSTRACT |
Water is an
essential component of living organisms, and in adult mammals the
fraction of fat-free body mass (FFM) as water is remarkably stable at
~0.73. The stability of FFM hydration is a cornerstone of the widely
used water isotope dilution method of estimating total body fat. At
present, the only suggested means of studying FFM hydration is by
experimental total body water (TBW) and FFM measurements. Although
deviations from the classical hydration constant are recognized, it is
unknown if these are explainable physiological aberrations and/or
methodological errors. Moreover, many questions related to hydration
stability prevail, including body mass and age effects. These
unresolved questions and the importance of the TBW-fat estimation
method led us to develop a cellular level FFM hydration model. This
physiological model reveals that four water-related ratios combine to
produce the observed TBW-to-FFM ratio. The mean and range of FFM
hydration observed in adult humans can be understood with the proposed
physiological model as can variation in the TBW-to-FFM ratio over the
human life span. An extension of the model to the tissue-organ body composition level confirms on a theoretical basis a small but systematic decrease in hydration observed in mammals ranging in body
mass by a factor of 105. The
present study, the first to advance a physiological hydration model,
provides a conceptual framework for the TBW-fat estimation method and
identifies important areas that remain to be studied.
total body water; body composition
 |
INTRODUCTION |
THE SHREW AND THE WHALE, both mammals, share in common
a similar hydration of fat-free body mass (FFM). Defined as the ratio of total body water (TBW) to FFM (TBW/FFM) and measured by
in vitro chemical analysis, the mean ± SD hydration is 0.739 ± 0.015 for nine mammals, including mouse, rat, hamster, Rhesus monkey, baboon, goat, sheep, gray seal, and human (25, 27, 29, 31, 36). The
importance of TBW/FFM is that estimation of TBW by dilution methods
allows derivation of total body fat from the following equations: body
mass
TBW/0.73 or body mass
1.37 × TBW (30).
Studies of body composition (16), energy balance (12), and
thermoregulation (29) in mammals often rely on fat estimates by the TBW
method. No other body composition method applied in vivo is capable of
providing fat estimates in such a wide range of mammals, which differ
in body mass by a factor of 105.
Moreover, the assumed stable TBW/FFM serves as the basis of dual-energy
X-ray absorptiometry and hydrodensitometry body composition models (26)
and TBW-derived FFM prediction models used to calculate other body
composition components, such as skeletal muscle (0.50 × FFM), body cell mass (0.57 × FFM), total body protein (0.18 × FFM), and resting energy expenditure.
Although FFM hydration is generally assumed constant in mammals,
including humans, some deviations from a TBW/FFM of ~0.73 are
recognized. Newborn humans and other mammals share in common a high FFM
hydration (~0.81) (15). Similarly, FFM hydration may be increased in
elderly humans (13, 33) and in obese humans (34) and monkeys (20).
Moreover, Pitts and Bullard (27) reported a small but statistically
significant decline in TBW/FFM observed across mammals of increasing
body mass when TBW and FFM were directly quantified in autopsied
animals caught in the wild. Animals with outer exoskeletons, such as
the armadillo, had particularly low FFM hydration levels
(0.70-0.71, Ref. 27).
The question thus arises: is FFM hydration of ~0.73 a biological
constant in adult mammals, reflecting underlying physiological regulation? Alternatively, is the value of 0.739 ± 0.015 observed across mammals a coalescence of several independent factors that generally result in a TBW/FFM of ~0.73 with only minimal variability? The importance of the TBW-fat estimation method in the field of body
composition research led us to explore these questions.
At present, the only suggested means of studying FFM hydration is by
experimental TBW and FFM measurements. Both in vitro and in vivo
experimental approaches in general have two primary limitations (36).
First, a large population sample is necessary to explore the full range
of FFM hydration for each mammalian species. Second, even small errors
in measuring TBW and FFM may have a significant effect on the magnitude
of calculated TBW/FFM, which only varies by several percent under
normal physiological conditions.
The long-term aim of our research is to establish the molecular and
physiological determinants of FFM hydration magnitude and variability.
A new strategy of investigating FFM hydration, which differs from the
earlier experimental approach, was applied in the present report. Our
approach was to develop a FFM hydration model at the cellular body
composition level. The nature of living organisms first becomes
manifest at this level, and we reasoned that FFM hydration could be
effectively modeled at this level. The model was then used to examine
individually the cellular level determinants of FFM hydration in an
attempt to establish if any regulatory processes underlie the widely
observed TBW/FFM of ~0.73. Organs and tissues have cellular and
molecular level components as their basis, and a useful approach when
making interspecies hydration comparisons is to analyze TBW/FFM with a
tissue-organ level model. We introduce this concept in a final section
of the paper when we explore the stability of hydration across a wide range of mammals.
 |
HYDRATION MODEL |
The developed hydration model is based on the five-level body
composition model that indicates that the ~40 major components in
humans and mammals can be organized into atomic, molecular, cellular,
tissue-organ, and whole body levels (37). At the cellular body
composition level, body mass consists of cells, extracellular fluid
(ECF), and extracellular solids (ECS). The cellular component can be
further divided into fat and body cell mass (BCM), defined as a
"component of body composition containing the oxygen-exchanging, potassium-rich, glucose-oxidizing, work-performing tissue"
(22)
|
(1)
|
(1)
FFM can thus be expressed as the sum of three cellular level
components
|
(2)
|
Similarly,
TBW can be expressed as the sum of intracellular water (ICW) and
extracellular water (ECW)
|
(3)
|
Based on
Eqs.
2 and 3, FFM hydration can be expressed as
|
(4)
|
This
is the primary FFM hydration model on the cellular body composition
level. In the next stage of model development, our aim was to resolve
Eq. 4
into relevant compartment ratios.
Body cell mass and extracellular fluid consist of aqueous and solid
compartments (Fig. 1), and both components
can be expressed as hydration ratios, BCM = ICW/a and ECF = ECW/b, where
a and b are the fractions of body cell mass
and extracellular fluid as water, respectively. In addition,
extracellular solids can be expressed as a function of TBW as follows:
ECS = c × TBW = c × (ICW + ECW), where
c is the ratio of ECS to TBW
(ECS/TBW). Equation 4 can thus be converted into
|
(5)
|
Intracellular
water and extracellular water are interrelated compartments of body
water, and extracellular water can be expressed as a function of
intracellular water as follows: ECW = (E/I) × ICW, where
E/I
is the ratio of extracellular water to intracellular water.
Equation 5 can be converted and simplified to a
secondary cellular level FFM hydration model as
|
(6)
|
Equation 6 reveals that FFM hydration is
determined by four factors: hydration of body cell mass
(a), hydration of extracellular fluid (b), ratio of extracellular
solids to TBW (c), and ratio of
extracellular water to intracellular water
(E/I).
Equation 6 indicates that hydration of FFM can
be analyzed from aqueous and solid compartments, and this approach
allows us to explore the four individual hydration determinants,
a, b,
c, and
E/I, in healthy humans.

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Fig. 1.
Cellular body composition level model of fat-free body mass (FFM),
which contains three components: body cell mass (BCM), extracellular
fluid (ECF), and extracellular solids (ECS). ICW, intracellular water
compartment of BCM; ECW, extracellular water compartment of ECF.
|
|
 |
MODEL COEFFICIENTS |
Physiological aspects and the magnitude and variation range for each of
the four hydration determinants are presented in this section. Sources
of body composition information based on "Reference Man" data
(32) are presented in Table 1.
Cellular hydration: ratio a. Prebiotic
conditions in the primordial ocean are hypothesized to have allowed
development of eobionts, protoplasmic masses with the capacity to
divide but that lacked cell walls (1). These primordial cells
purportedly had an aqueous protoplasm identical in electrolyte and
mineral composition to that of the early oceans (1, 21). The present operational concept is that formation of prokaryotic cells along with
appropriate membrane pumps led to stable intracellular hydration, electrolyte content, and osmolality even as the surrounding ocean changed composition with an influx of sodium leached from igneous rocks
and an efflux of potassium through silicate formation (6, 21).
Accession of land by animals required preservation of the "milieu interieur" with the "private ocean"
extracellular fluid maintained by renal mechanisms.
Although an agreed-on physical model for cellular water is still
lacking (1, 6, 19), empirical observations reveal striking similarities
in the hydration and electrolyte content of prokaryotic and eukaryotic
cells that relate to their common evolutionary heritage. By weight,
cells from Escherichia coli to mammals
consist of ~70% water even though there is a 100-fold difference in
the volumes of bacterial and mammalian cells.
The "typical" mammalian cell contains 70% water, 18% protein,
5% phospholipids, 1% inorganic ions (e.g.,
K+,
Na+,
Mg2+,
Cl
), 1.35% RNA and DNA,
2% polysaccharides, and 3% miscellaneous small metabolites (1). In
the present investigation, cellular hydration was thus assumed to be a
mean of 0.70, representing a typical mammalian cell.
Body cell mass includes water, protein, and minerals in all cell types,
and water is the largest chemical compartment of body cell mass (22,
36). Because different cell types have specific functions, it is not
surprising that they may differ with respect to their precise chemical
composition, including water fraction. For example, the intracellular
water fraction of red blood cells is relatively low and varies between
0.65 and 0.68. In contrast, skeletal muscle cells, accounting for about
two-thirds of body cell mass, have water fractions of 0.718-0.728
in healthy dogs (10, 18). Whole body cellular hydration must be larger
than that in red blood cells and smaller than that in skeletal muscle cells. The present study thus assumed a ±1% variation range about the assumed mean whole body cellular hydration of 0.70 (i.e., 0.693-0.707).
Extracellular fluid hydration: ratio
b. Extracellular fluid is a nonmetabolizing component
that surrounds cells and provides a medium for gas exchange, transfer
of nutrients, and excretion of metabolic end products. Extracellular
fluid is distributed into two main compartments, with about one-sixth
as plasma in the intravascular space and the remaining five-sixths as
interstitial fluid in the extravascular space (Table 1). Extracellular
fluid consists of water, protein, and minerals, with water accounting for ~94% of plasma and ~99% of interstitial fluid (14, 21). In
the present investigation, extracellular fluid hydration was assumed to
be equal to ~0.98 (i.e., a proportional mix of plasma and
interstitial fluid), with a range of ~0.97-0.99 that reflects extreme plasma and interstitial fluid proportions.
The highly hydrated extracellular fluid component, which accounts for
~32% of FFM (Table 1), has a major effect on observed hydration
levels. It is also evident that any change in the proportional relationship between extracellular fluid with water fraction ~0.98 and body cell mass with water fraction ~0.70 will result in changes in FFM hydration.
Ratios a and
b represent body cell mass hydration
and extracellular fluid hydration, respectively. The water contents of
body cell mass and extracellular fluid appear to be maintained
remarkably stable within individuals, between subjects, and even
between mammals. What are the regulatory mechanisms that control and
maintain extracellular fluid and intracellular hydration and thus
preserve the stable milieu interieur?
Most mammals maintain an extracellular fluid osmolality of ~300
mosmol/kgH2O. The main determinant
of extracellular fluid osmolality is sodium and associated anions.
There are two parallel regulatory systems, antidiuretic hormone and
renin-angiotensin-aldosterone, which maintain extracellular fluid
osmolality, sodium concentration, and extracellular water content
extremely stable in health (Fig. 2). An
inference from these well-established relationships is that
extracellular fluid hydration [i.e., extracellular
water-to-extracellular fluid ratio (ECW/ECF)] is stable within
individuals, species, and perhaps across all mammals.

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Fig. 2.
Model depicting regulation of mammalian total body water content,
sodium concentration, and fluid osmolality. ADH, antidiuretic hormone;
ICF, intracellular fluid.
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|
The intracellular fluid compartment is separated from extracellular
fluid by a selectively permeable membrane (Fig. 2). Sodium content of
intracellular fluid is maintained low by limiting membrane effects and
the sodium-potassium-ATPase pump (28). Water flows freely across cell
membranes, and hence intracellular fluid also maintains a stable
osmolality of ~300 mosmol/kgH2O
(11). Cellular hydration and cell volume are thus maintained stable
through the same regulatory mechanisms as for extracellular fluid.
Maintenance of stable cell volume is the highest organismic priority,
and even small volume changes constitute a potent signal for modifying cell metabolism and gene expression (17, 19, 35).
The implication of these well-established homeostatic regulatory
mechanisms is that extracellular fluid hydration and cellular hydration
are maintained extremely stable in healthy mammals, including humans
(11, 24). Accordingly, it is likely that factors
a and
b vary minimally in healthy adult subjects.
ECS/TBW: ratio c. Extracellular solids
are also a nonmetabolizing component that consists of organic and
inorganic compounds. The organic extracellular solids include three
types of fiber: collagen, reticular, and elastic. Inorganic
extracellular solids, with calcium hydroxyapatite
{[Ca3(PO4)2]3Ca(OH)2}
as the major constituent, represent ~66% of dry bone matrix (Table
1). Because there is no water in the extracellular solids component,
larger proportional contributions to FFM correspondingly lower observed levels of FFM hydration.
ECS/TBW can be estimated from previous studies. Cohn et al. (7)
measured total body calcium by in vivo neutron activation analysis.
Assuming constant bone mineral-to-total body calcium and extracellular
solids-to-bone mineral ratios, the authors calculated extracellular
solids from total body calcium (8). ECS/TBW was similar between young
and old adult men (0.15 vs. 0.15) and women (0.16 vs. 0.14; Ref. 9).
ECS and TBW in Reference Man are 5.68 and 42 kg, respectively, with
ECS/TBW = 0.135 (Table 1). Ratio c,
ECS/TBW, was assumed in the present study to range between 0.12 and
0.16 with a mean of ~0.14 for a healthy adult.
Although extracellular hydration and body cell mass hydration are
physiologically regulated, as noted earlier, there is no direct
regulatory linkage between water and extracellular solids. Moreover,
extracellular solids and closely related bone are minimally developed
in the newborn at a time when the fraction of FFM as water is high.
This suggests that ratio c, considered
over the whole life span, may be age dependent in humans, and this
possibility needs to be explored. Some mammals, such as the armadillo,
have chitenous shells that are included in the extracellular solids component, and ratio c would
correspondingly be larger in magnitude relative to other mammals.
E/I.
Unlike the three other model components, many physiological factors are
known to change relative extracellular and intracellular water
distribution over the life span, such as growth, gender, exercise,
fluid intake, and sweating (16). Children have a larger fraction of
small young cells and a larger extracellular fluid-to-cell mass ratio
than do adults. The large ratio of extracellular fluid to cell mass in
children permits rapid movement of nutrients from extracellular fluid
to cells and of end products from cells to extracellular fluid (16).
Obesity, acquired immunodeficiency syndrome, chronic renal failure,
edema with malnutrition, and sepsis may also cause overhydration and an
increase in
E/I.
Conversely, diseases or conditions associated with dehydration may
decrease E/I.
Hence, there exists no direct physiological regulation of relative
water distribution, and
E/I
varies widely in health and disease.
There is no method for directly measuring total body intracellular
water, and it is often calculated as the difference between TBW and
extracellular water. A number of dilution techniques (e.g., bromide,
sulfate, and inulin; Refs. 16, 30) and total body chlorine measured by
in vivo neutron activation analysis are applied for extracellular water
estimation (38). However, the available methods, based on different
assumptions, may vary in their estimates of extracellular water. The
observed
E/I
thus varies according to the applied method.
We evaluated
E/I
in the present study with TBW and total body potassium (see
APPENDIX) in 384 healthy adults (220 men and 164 women). These group characteristics (mean ± SD) were
age, 45 ± 20 yr; body mass, 64.1 ± 11.9 kg; and body mass
index, 22.5 ± 2.7 kg/m2. TBW
measured by tritium dilution was 38.1 ± 9.0 kg, total body potassium measured by whole body
40K counting was 3,132 ± 903 mmol, and the calculated
E/I
was 0.97 ± 0.20. Although the mean
E/I
is close to 1.0 for the whole group, a significantly larger
E/I
was present in women (1.07 ± 0.22) than in men (0.82 ± 0.16, P < 0.001). In the
present study, the E/I
was thus assumed to range between 0.58 (mean
1.96 × SD) and 1.36 (mean + 1.96 × SD) with a mean of 0.97 for healthy adults.
 |
MODEL FEATURES |
Although investigators have expressed interest in FFM hydration for
over 50 years, fundamental questions remain unanswered. Why do healthy
young adult humans demonstrate a relatively stable mean magnitude of
FFM hydration of ~0.73? Why does hydration in adult humans vary
within a narrow range? Does this observed range primarily represent
biological variation? Does body size in mammals influence FFM
hydration? In this section, we demonstrate how the proposed model can
be used to explore these fundamental questions.
Why is FFM hydration in adult humans relatively stable
at ~0.73? The proposed cellular level model indicates
that FFM hydration is a function of four determinants, i.e., TBW/FFM = f (a,
b, c, E/I),
and the approximate mean value of each determinant is known as
described above (i.e., a = ~0.70,
b = ~0.98,
c = ~0.14, and E/I = ~0.97). The mean TBW/FFM can therefore be predicted for healthy young
adult humans according to Eq.
6
The
model-predicted mean FFM hydration is similar to that in in vitro
studies on human cadavers (0.737) and in Reference Man as suggested by
Brozek et al. (0.737) and Snyder et al. (0.741; Refs. 4, 32). In
addition, the calculated TBW/FFM is almost identical to that in other
mammals (0.739 ± 0.015, coefficient of variation = 2.0%)
ranging in average body mass from 0.036 kg for mice to 214 kg for gray
seals, indicating hydration stability between species (31, 36).
Can the relative constancy of FFM hydration be explained with the
proposed cellular level model? Even though small changes (e.g.,
±1%; Table 2) in cellular hydration
(a) and extracellular fluid
hydration (b) would have relatively
large effects on FFM hydration (i.e., ~0.5%), these two determinants
are maintained stable by physiological mechanisms in humans and other
mammals. The ratio of extracellular solids to TBW
(c) is also stable in adult humans,
although a change in ratio c of
±1% would cause a corresponding FFM hydration change of ±0.1%
(Table 2).
Water distribution (i.e.,
E/I)
is highly variable within subjects over time and between subjects. The
cellular level model (Eq.
6) can thus be simplified, assuming
constant ratios a,
b, and
c, for discussion purposes to a model
that applies in young adults
|
(7)
|
Equation 7 indicates that both numerator and
denominator contain
E/I
terms that have the same operational symbol (+) and similar
coefficients (1 and 1.16). This mathematical feature indicates that
relative changes in water distribution have only a small effect on
TBW/FFM. For example, when
E/I
increases by 50% (e.g., from 0.80 to 1.20), TBW/FFM, according to
Eq.
7, increases by only 3% (from 0.721 to 0.743). Hence, although
E/I
is highly variable between subjects or in the same subject over long
time periods, the impact of this variability on the observed FFM
hydration is relatively small.
Why does FFM hydration in adult humans vary within a
narrow range? Both in vitro and in vivo studies
demonstrate that FFM hydration varies within a narrow range for adults
(31, 36). However, it is unknown if these variations are explainable
physiological deviations and/or methodological errors.
As indicated above, each of the four cellular level determinants may
vary within an assumed range for young adults:
a, from 0.69 to 0.71;
b, from 0.97 to 0.99;
c, from 0.12 to 0.16; and E/I
from 0.58 to 1.36. Ratios a,
b, and
E/I
are in direct proportion, and c is in
inverse proportion, to TBW/FFM magnitude. One can thus estimate the
range of FFM hydration if the four determinants take their extreme
values. When a is 0.69, b is 0.97, c is 0.16, and
E/I
is 0.58, TBW/FFM may reach its low value according to Eq. 6
When
a is 0.71, b is 0.99, c is 0.12, and
E/I
is 1.36, TBW/FFM may reach its high value
The
predicted variation range of FFM hydration for healthy young adult
humans is thus approximately from 0.69 to 0.77. This range is similar
to the results of in vitro human cadaver studies (0.68-0.81; Refs.
31, 36). The proposed model thus indicates that the observed variation
in FFM hydration can be attributed primarily to variation in the four
cellular level determinants.
An interesting observation reported by Pitts and Bullard (27) was that
mammals with a hard chitenous shell, such as the armadillo, had
particularly low hydration levels (0.70-0.71). These
exoskeleton-clad animals would be expected to have a disproportionately large extracellular solids component and a high ratio
c. A high ratio
c, according to the proposed cellular
level model, would cause a low hydration of FFM. This prediction is
supported in the Pitts and Bullard study.
Of the four cellular level model ratios,
E/I
is the only factor that changes substantially in adult humans. The
influence of
E/I
on FFM hydration is illustrated in Fig. 3.
Figure 3, middle, shows the
hypothetical normal state for water distribution and hydration:
E/I
and TBW/FFM are ~1.0 and ~0.73, respectively. If E/I
increases for any physiological or pathological reason, as shown in
Fig. 3, top, this may cause a small
increase in FFM hydration (e.g., when
E/I > 1.2, TBW/FFM > 0.74). In contrast, if
E/I
decreases for physiological or pathological reasons, as shown in Fig.
3, bottom, this may cause a low FFM
hydration (e.g., when
E/I < 0.8, TBW/FFM < 0.72).

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Fig. 3.
Effect of ECW-to-ICW ratio
(E/I)
change on FFM hydration [total body water-to-FFM ratio
(TBW/FFM)]. Middle, normal
E/I
of ~1.0 with TBW/FFM of ~0.73.
Increase in
E/I
(e.g., ECW increase and ICW decrease,
E/I > 1.2) may cause a TBW/FFM of >0.74
(top). In contrast, a decrease in
E/I
(e.g., ECW decrease and ICW increase,
E/I < 0.8) may cause a TBW/FFM of <0.72
(bottom).
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|
Does growth influence FFM hydration?
Previous studies indicate that FFM hydration is significantly
influenced by biological factors such as growth (16). Moulton, in his
classical investigation (23), summarized chemical analysis results of
nine mammals, including mouse, rat, guinea pig, rabbit, cat, dog, pig,
cattle, and human. At birth, all mammals show a high FFM hydration
(~0.81) and low concentrations of protein and mineral. FFM hydration
then rapidly declines, and protein and mineral content increase from early life until chemical maturity is reached.
A reasonable question thus arises: can the proposed cellular level
model be applied in modeling the relationship between FFM hydration and
growth? Of the four determinants of FFM hydration, ratios
a, which equals ~0.70, and
b, which equals ~0.98, can be assumed for modeling purposes to be stable throughout life. The cellular level hydration model (Eq.
6) can therefore be simplified to
|
(8)
|
Equation 8 shows that ratio
c changes in inverse proportion to,
and
E/I
changes directly with, FFM hydration. Based on Reference Children data
(15), ratio c is very low at birth
(i.e., ~0.07) and then increases rapidly to adolescence (i.e.,
~0.14). In contrast, E/I
is maximal (i.e., ~1.7) at birth and then decreases rapidly to ~1.0
in adults.
We were thus able to predict the change of FFM hydration during growth.
At birth, when c is ~0.07 and
E/I
is ~1.7, predicted FFM hydration, according to
Eq.
8, is 0.81. The theoretical FFM hydration then decreases to 0.73 for adults when
c is ~0.14 and E/I
is ~1.0. This trend is similar to measured changes in FFM hydration,
0.810 at birth and 0.746 for 10-yr-old boys (15). As indicated by
Eq. 8, both an increase in ratio
c and a decrease in
E/I
cause a rapid decline in FFM hydration during growth.
Does body size influence FFM hydration in
mammals? A pervasive finding in the biological
literature is that mammals share in common a FFM hydration of ~0.73
(31, 36). Although this observation generally has ample support, there
are notable deviations. Pitts and Bullard's classic study (27)
examined FFM hydration in a wide range of mammals captured in their
native habitat. The investigators noted a small but consistent decrease
in TBW/FFM with increasing FFM from mouse to cattle. The empirical
equation derived by Pitts and Bullard is
|
(9)
|
where
FFM is in kilograms. According to Eq.
9, FFM hydration is higher in mouse
(0.760, FFM 0.03 kg) than in monkey (0.726, FFM 12 kg) and human
(0.718, FFM 55 kg). Can the mammalian FFM hydration of ~0.73 in
general and specifically the small downward trend with increasing body
size be theoretically explained?
One approach to examining this question is to extend our analysis of
FFM hydration from the cellular level to the tissue-organ level. Whole
body FFM hydration can be calculated by summing the water and FFM of
individual organs and tissues
|
(10)
|
where
Mi is individual
organ-tissue mass,
Wi and
FFMi represent water mass and
fat-free mass of individual organ-tissue, and
(W/M)i
and
(FFM/M)i
is the fraction of individual organ-tissue mass as water and FFM,
respectively. Both cadaver and in vivo measurements by computerized
axial tomography or magnetic resonance imaging show that individual
organ-tissue mass can be expressed as a function of body mass among
mammals ranging in body mass from rat to elephant (2, 5, 12). The
general relationship between organ-tissue mass (M)
and body mass (BM) is
|
(11)
|
where
k is constant and
m is a scaling exponent. Most organs,
including liver, kidneys, brain, heart, and lung, occupy a decreasing
fraction of body mass (i.e., m < 1)
as body size increases. Skeletal muscle is almost directly proportional
to body mass (i.e., m = 1): skeletal
muscle is 0.468 × BM0.99 (5). In
contrast, bone and adipose tissue occupy increasing fractions of body
mass (i.e., m > 1) as body size
increases (Table 3). The tissue-organ level
FFM hydration model (Eq.
10) can be converted to
|
(12)
|
The
(W/M)i
and
(FFM/M)i
values for 14 organs and tissues of Reference Man are shown in Table 3
(32). These organs and tissues account for 87.3% of the body mass of Reference Man. It is assumed that the fractions of individual organ-tissue mass as water
(W/M)i
and as fat-free mass (FFM/M)i
are similar among adult mammals. According to the known
(W/M)i,
(FFM/M)i,
k, and
m for individual organs-tissues (Table
3), we derived the following model for characterizing FFM hydration
from body mass
|
(13)
|
where
BM is in kilograms. According to Eq.
13, FFM hydration is 0.784 for mouse
(BM = 0.04 kg), 0.738 for monkey (BM = 15 kg), and 0.727 for humans (BM = 70 kg). Although there is a small systematic difference in FFM
hydration prediction, Pitts and Bullard's (27) empirical formula
(Eq.
9) and our prediction model
(Eq. 13) show the same trend, with FFM
hydration decreasing minimally but systematically with a remarkable
increase in animal size by a factor of
105. The tissue-organ level FFM
hydration model thus provides a basis for the small downward trend in
hydration as a function of body mass observed by Pitts and Bullard in
mammals living within their natural habitats.
 |
POTENTIAL RESEARCH AREAS |
There are many important unanswered questions related to FFM hydration.
We have selected several of these questions to highlight the need for more research in this important area. Some examples of
unresolved or incompletely understood aspects of FFM hydration in
health and disease are summarized in Table
4. Table 4 also suggests directional
changes in each of the four cellular level model determinants and their
collective impact on FFM hydration. Experiments can be designed to test
the validity of the hypotheses presented in Table 4.
Although our general FFM hydration models (e.g.,
Eqs.
4, 6,
10, and
12) are mathematically valid for
various species, many biological assumptions regarding the four
cellular level model determinants (i.e.,
a, b,
c, and
E/I)
were made in the discussions that followed. There remain opportunities
for verifying these assumptions and expanding on the concepts presented
in this report.
How might the four cellular level model determinants be compared
between individuals or across groups? Body cell mass hydration, ratio
a, requires primarily in vitro
analysis. Extracellular fluid hydration, ratio
b, can best be inferred from analysis
of easily obtained blood samples. The third ratio,
c (= ECS/TBW), can be evaluated from
bone mineral or total body ash. Bone mineral can be measured in vivo
with dual-energy X-ray absorptiometry (26), and bone or total body ash
can be evaluated in vitro in animal or human cadavers. TBW is easily
quantified with labeled isotopes in vivo (30) or by desiccation in
vitro. Finally,
E/I
can be calculated from total body potassium and water masses as in this report (see APPENDIX).
FFM hydration was reexamined with the proposed cellular level model in
the present study. There are also several other classic body
composition constants, such as the ratio of total body potassium to FFM
(~68 mmol/kg FFM) and FFM density (~1.10
g/cm3), that are
presently used in body composition research. These assumed stable
constants, as well as FFM hydration, form the cornerstone of widely
used body composition methods, and the origin of their constancy is of
fundamental scientific interest. Similar cellular level models could be
developed that may be useful in improving understanding of these widely
used body composition constants.
 |
CONCLUSION |
The empirical relationship between TBW and FFM in mammals has been
recognized for over five decades. The relative constancy of FFM
hydration led to the widely used TBW method of estimating fatness in
mammals ranging widely in body size. Deviations from "constant"
hydration in earlier reports were often viewed as aberrations or
methodological errors. The present study, to our knowledge, is the
first effort aimed at providing a physiological basis for FFM
hydration, and, in so doing, our developed model provides new insights
into earlier, poorly understood phenomena, such as why hydration is
high in newborns. The model and our accompanying review identify
important potential research areas and present several testable
hypotheses. Moreover, our review of earlier reports identified little
research on FFM hydration outside of mammals (36). Many opportunities
still exist for advancing understanding and application of the TBW-fat
estimation method, even though it is among the earliest body
composition methods.
 |
APPENDIX |
Water Distribution Measurement
The water distribution was measured based on total potassium and water
(15). It is known that almost all body potassium exists in
intracellular water (ICW) and extracellular water (ECW), and given
m and
n as the potassium concentrations in
intracellular and extracellular fluid, respectively, the following
simultaneous equations may be written
|
(A1)
|
|
(A2)
|
Because
TBK and TBW are measurable, ECW and ICW can be solved as
|
(A3)
|
|
(A4)
|
The
ratio of ECW to ICW can thus be calculated as
|
(A5)
|
Previous
studies reported similar intracellular potassium concentrations
(m) in mammals: 150-160
mmol/kgH2O (21), 150 ± 7.2 (SD) mmol/l (22), 152 mmol/kgH2O (21), and 159 mmol/kgH2O (28). In the present
investigation m was assumed as 155 mmol/kgH2O. The potassium
concentration in extracellular fluid
(n) is much lower than
m and close to the 5 mmol/kgH2O reported in previous studies. Equation A5 can thus be expressed as
|
(A6)
|
where
TBW is in kilograms and TBK is expressed in millimoles. Water volume,
estimated by
3H2O
dilution in the present study, was estimated to overestimate TBW by 4%
(30, 36).
 |
ACKNOWLEDGEMENTS |
This research was supported by National Center for Research
Resources Grant RR-00645 and National Institute of Diabetes and Digestive and Kidney Diseases Grant DK-42618.
 |
FOOTNOTES |
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.
Address for reprint requests and other correspondence: ZM. Wang, Weight
Control Unit, 1090 Amsterdam Ave., 14th Floor, New York, NY 10025 (E-mail: ZW28{at}Columbia.edu).
Received 14 August 1998; accepted in final form 19 February 1999.
 |
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