## 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 10^{5}. 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

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 10^{5}. 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)
Equation 1(*1*)

FFM can thus be expressed as the sum of three cellular level components
Equation 2Similarly, TBW can be expressed as the sum of intracellular water (ICW) and extracellular water (ECW)
Equation 3Based on*Eqs*.*
2
* and *
3
*, FFM hydration can be expressed as
Equation 4This 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). *Equation4
* can thus be converted into
Equation 5Intracellular 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.*Equation5
* can be converted and simplified to a secondary cellular level FFM hydration model as
*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.

## 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^{+}, Mg^{2+}, 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/kgH_{2}O. 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.

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/kgH_{2}O (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 {[Ca_{3}(PO_{4})_{2}]_{3}Ca(OH)_{2}} as the major constituent, represent ∼66% of dry bone matrix (Table1). 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
) 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/m^{2}. TBW measured by tritium dilution was 38.1 ± 9.0 kg, total body potassium measured by whole body^{40}K 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*. *
*) can thus be simplified, assuming constant ratios *a*,*b*, and*c*, for discussion purposes to a model that applies in young adults
Equation 7
*Equation7
* 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).

*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
Equation 8
*Equation8
* 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
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
where*M _{i}
* is individual organ-tissue mass,

*W*and FFM

_{i}_{i}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 Equation 11where

*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 × BM

^{0.99}(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 Equation 12The (

*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 (Table3), we derived the following model for characterizing FFM hydration from body mass Equation 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 10

^{5}. 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 Table4. 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
).

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/cm^{3}), 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.

## Acknowledgments

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.

## 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
Equation A1
Equation A2Because TBK and TBW are measurable, ECW and ICW can be solved as
Equation A3
Equation A4The ratio of ECW to ICW can thus be calculated as
Equation A5Previous studies reported similar intracellular potassium concentrations (*m*) in mammals: 150–160 mmol/kgH_{2}O (21), 150 ± 7.2 (SD) mmol/l (22), 152 mmol/kgH_{2}O (21), and 159 mmol/kgH_{2}O (28). In the present investigation *m* was assumed as 155 mmol/kgH_{2}O. The potassium concentration in extracellular fluid (*n*) is much lower than*m* and close to the 5 mmol/kgH_{2}O reported in previous studies. *EquationEA5
* can thus be expressed as
Equation A6where TBW is in kilograms and TBK is expressed in millimoles. Water volume, estimated by^{3}H_{2}O dilution in the present study, was estimated to overestimate TBW by 4% (30, 36).

## Footnotes

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).

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- Copyright © 1999 the American Physiological Society