Magnitude and variation of ratio of total body potassium to fat-free mass: a cellular level modeling study

Zimian Wang, F. Xavier Pi-Sunyer, Donald P. Kotler, Jack Wang, Richard N. Pierson Jr., and Steven B. Heymsfield

Obesity Research Center, St. Luke's-Roosevelt Hospital, Columbia University College of Physicians and Surgeons, New York, New York 10025


    ABSTRACT
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Potassium is an essential element of living organisms that is found almost exclusively in the intracellular fluid compartment. The assumed constant ratio of total body potassium (TBK) to fat-free mass (FFM) is a cornerstone of the TBK method of estimating total body fat. Although the TBK-to-FFM (TBK/FFM) ratio has been assumed constant, a large range of individual and group values is recognized. The purpose of the present study was to undertake a comprehensive analysis of biological factors that cause variation in the TBK/FFM ratio. A theoretical TBK/FFM model was developed on the cellular body composition level. This physiological model includes six factors that combine to produce the observed TBK/FFM ratio. The ratio magnitude and range, as well as the differences in the TBK/FFM ratio between men and women and variation with growth, were examined with the proposed model. The ratio of extracellular water to intracellular water (E/I) is the major factor leading to between-individual variation in the TBK/FFM ratio. The present study provides a conceptual framework for examining the separate TBK/FFM determinants and suggests important limitations of the TBK/FFM method used in estimating total body fat in humans and other mammals.

water distribution; body fat measurement; body composition


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TBK/FFM MODEL
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ONE OF THE PRIMARY AIMS of body composition research is to study quantitative relationships between components. Several relatively stable body composition ratios are well recognized, such as total body water-to-fat-free mass (TBW/FFM = ~0.73) (27, 34), total body hydrogen-to-body mass (~0.10), and total body oxygen-to-carbon-free body mass (~0.80) (32). The in-depth study of body composition ratios not only provides insight into basic biological processes but also enhances our understanding and application of body composition methods.

Another body composition ratio, total body potassium to fat-free mass (TBK/FFM), has been a widely applied body composition ratio. From whole body chemical analysis data of four cadavers with TBK/FFM ratios of 66.5 (M), 66.6 (M), 72.8 (M), and 66.8 (F) mmol/kg, Forbes and Lewis (13) derived a mean (±SD) TBK/FFM ratio of 68.1 ± 3.1 mmol/kg and then introduced the in vivo method for estimating total body fat mass
body fat<IT>=</IT>body mass<IT>−</IT>FFM (1)

=body mass<IT>−</IT><FR><NU>TBK</NU><DE>TBK<IT>/</IT>FFM</DE></FR>
where body mass and FFM are in kilograms, TBK is in millimoles, and TBK/FFM was initially assumed to be constant at 68.1 mmol/kg. Equation 1 was applied in clinical and body composition studies as a reference standard for estimating total body fat mass (10). The TBK/FFM ratio was also applied to estimate skeletal muscle mass on the basis of the assumption that skeletal muscle makes up 49% of FFM (11).

Although the literature on TBK/FFM has expanded extensively since 1956, this body composition ratio has never been thoroughly examined, and some fundamental questions still remain unanswered. Some studies show that the TBK method (Eq. 1) overestimates total body fat [e.g., by 3.2 kg (P < 0.001)] (30, 31), indicating that the assumed TBK/FFM ratio (68.1 mmol/kg) may be too high. Although the TBK/FFM ratio is assumed constant, large individual and group deviations are recognized. Several investigators report a significant sex difference in TBK/FFM (5, 7, 19). Moreover, low-magnitude TBK/FFM ratios were observed in newborn (9) and elderly (6, 19) humans.

The purpose of the present study was to derive a theoretical TBK/FFM model on the cellular body composition level. Our aim was to probe the observed variability between individuals, across sex groups, and during growth in the TBK/FFM ratio reported in earlier studies. The emphasis was on providing improved and new insights into the fundamental TBK model and the method of estimating total body fat.


    IN VITRO AND IN VIVO STUDIES
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When examining publications on TBK/FFM, we found that previous studies can be divided into two categories, in vitro and in vivo.

In vitro studies. The in vitro studies, based on chemical assays, were often carried out on isolated tissues and organs. The animal cadaver is first anatomically separated into various components, including muscle, adipose tissue, skeleton, skin, organs, and so on. Each isolated tissue/organ is weighed and thoroughly homogenized. The potassium and fat contents are determined by chemical analysis and fat-soluble solvent (e.g., petroleum or ethyl ether) extraction, respectively. FFM is then calculated as the difference between individual tissue/organ mass and fat mass.

Whole body TBK/FFM is equal to the sum of individual tissue/organ potassium contents (KT) divided by the sum of individual tissue/organ fat-free mass (FFMT).
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU><IT>&Sgr;</IT>K<SUB>T</SUB></NU><DE><IT>&Sgr;</IT>FFM<SUB>T</SUB></DE></FR> (2)
As an example of this approach, we calculated K/FFM values of 14 tissues/organs that account for 92.2% of whole body potassium and 90.6% of FFM in Reference Man (Table 1) (29). The K/FFM value for all 14 tissues/organs is 63.1 mmol/kg, which is close to the average TBK/FFM value observed in healthy men. Note from Table 1 that the observed whole body TBK/FFM value is the integrated result of low K/FFM components, including skin, adipose tissue, and blood, and high K/FFM components, such as skeletal muscle, liver, and brain. One component, skeletal muscle, represents 60% of TBK in Reference Man, indicating that the TBK/FFM ratio increases as a function of FFM fraction as skeletal muscle (29).

                              
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Table 1.   Reference Man's K/FFM ratio calculated from 14 tissues/organs

The in vitro study of TBK/FFM can be traced to the pioneering work of Forbes and Lewis in 1956 (13). Chemical analysis of four adult cadavers resulted in a mean (±SD) TBK/FFM ratio of 68.1 ± 3.1 mmol/kg, with a range between 66.5 and 72.8 mmol/kg. In addition, the TBK/FFM ratio was also determined in several species of mammals. The TBK/FFM magnitude, for example, is 73 ± 3 mmol/kg for rat (3) and 68.6 ± 3.6 mmol/kg for pig (14). These studies generally show a reasonably consistent TBK/FFM ratio for each mammalian species, although there is some interspecies variation (10).

In vivo studies. Compared with in vitro studies, in vivo analysis avoids chemical analysis and can be carried out on a large scale in well characterized and clinically stable living humans. The principle of in vivo study of the TBK/FFM ratio is simple: TBK and FFM are measured in vivo separately. The accuracy of observed TBK/FFM thus depends closely on the quality of TBK and FFM measurements.

There are three main methods of quantifying body potassium, by whole body 40K counting (11), by dilution of 42K (22), and as an exchangeable component (Ke) estimated from total body water, exchangeable sodium, and serum water and/or electrolytes (28). Because 40K counting lacks radiation exposure and can be applied for evaluation of most mammals, this method of estimating TBK has proliferated. By the 1970s, more than 180 whole body counters had been built worldwide, with about two-thirds of these performing potassium measurements in human beings, and there are an estimated 75 whole body counters in the United States (7).

Currently available methods for measuring FFM include two-, three-, and four-compartment models (18). FFM can also be measured by the recently developed dual-energy X-ray absorptiometry (DEXA) method (25) and the neutron inelastic scattering method (20).

In vivo studies are widely applied, especially when biological factors are examined that may influence TBK/FFM, including age, sex, fatness, and disease. Although an assumed constant TBK/FFM of 68.1 mmol/kg was initially applied for estimating total body fat, later studies showed that this value was too high (7). Current in vivo studies suggest TBK/FFM values of 59-62 mmol/kg for adult men and 54-59 mmol/kg for adult women (5, 7).

We randomly evaluated a database of 52 male and 89 female healthy adults in the present study. Each subject completed a medical history, physical examination, and routine blood studies to exclude the presence of underlying diseases. The group characteristics are shown in Table 2. TBK was measured by whole body 40K counting with a precision of 3.2% (24), and FFM was measured by DEXA with a technical error of 1.2% (15). TBK was 3,595 ± 509 (SD) mmol for the men and 2,661 ± 508 mmol for the women, respectively. FFM was 58.6 ± 5.2 kg for the men and 44.9 ± 7.9 kg for the women, respectively. The measured TBK/FFM was 61.3 ± 3.3 mmol/kg (mean -1.96 SD to mean +1.96 SD, 54.8-67.8 mmol/kg) for the men and 59.5 ± 5.7 mmol/kg (48.3-70.7 mmol/kg) for the women. The mean TBK/FFM ratio was thus 60.4 mmol/kg for healthy adults, although there was a significant TBK/FFM difference between the men and women (P = 0.016).

                              
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Table 2.   Body composition of the healthy adult subjects in the present study


    TBK/FFM MODEL
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Previous studies have made major contributions to the investigation of the ratio of TBK to FFM. However, both in vitro and in vivo experimental approaches in general have two primary limitations. First, a large sample is necessary to explore the full range of TBK/FFM ratios for each population studied. Second, even small errors in measuring the TBK/FFM ratio may have a significant effect on the calculation of body fat mass.

A new strategy for investigating TBK/FFM, which differs from the earlier experimental approach, was applied in the present study. Our approach was to develop a TBK/FFM model at the cellular body composition level with the aim of exploring biological factors that influence the magnitude and variability of the TBK/FFM ratio.

The ~40 major components in the human body can be organized into atomic, molecular, cellular, tissue-organ, and whole body levels (35). Although each level and its multiple components are distinct, connections exist between the different levels. The cellular level is the first level at which biological characteristics of living organisms appear. For example, potassium distributes almost exclusively within cells, and the potassium concentrations in various cells are relatively constant. Therefore, we chose the cellular level as the base for developing our TBK/FFM model.

Body mass is composed of three compartments on the cellular level: cells, extracellular fluid (ECF), and extracellular solids (ECS). According to Moore et al. (22), body cell mass (BCM) is the "component of body composition containing the oxygen-exchanging, potassium-rich, glucose-oxidizing, work-performing tissue." Hence, BCM includes the protoplasm in fat cells but does not include the stored fat. Cells can thus be divided into BCM and fat (22)
body mass<IT>=</IT>cells<IT>+</IT>ECF<IT>+</IT>ECS (3)

=fat<IT>+</IT>BCM<IT>+</IT>ECF<IT>+</IT>ECS
Fat-free mass can be expressed as the sum of three cellular level components
FFM<IT>=</IT>BCM<IT>+</IT>ECF<IT>+</IT>ECS (4)
Because almost all potassium exists within intracellular fluid (ICF) and ECF, TBK can be expressed as the sum of potassium within intracellular fluid (KICF) and potassium within extracellular fluid (KECF) (i.e., TBK = KICF + KECF). A primary TBK/FFM model is derived
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU>K<SUB>ICF</SUB><IT>+</IT>K<SUB>ECF</SUB></NU><DE>BCM<IT>+</IT>ECF<IT>+</IT>ECS</DE></FR> (5)
In the next stage of model development, our aim was to resolve Eq. 5 into relevant compartment ratios.

Intracellular water (ICW) and extracellular water (ECW) are the largest compartments of BCM and ECF, respectively. The BCM can be expressed as ICW/a and the ECF as ECW/b, where a and b are the water fractions of BCM and ECF, respectively. Similarly, extracellular solids can be expressed as a function of total body water (TBW), ECS = c × TBW = c × (ICW + ECW), where c is the ratio of ECS to TBW. In addition, the KICF can be expressed as a product of the potassium concentration in intracellular water ([K]ICW) and ICW (i.e., KICF = [K]ICW × ICW). Similarly, the KECF is a product of the potassium concentration in ECW ([K]ECW) and ECW (i.e., KECF = [K]ECW × ECW). Equation 5 can thus be converted into
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU>[K]<SUB>ICW</SUB><IT>×</IT>ICW<IT>+</IT>[K]<SUB>ECW</SUB><IT>×</IT>ECW</NU><DE>ICW<IT>/a+</IT>ECW<IT>/b+c×</IT>(ICW<IT>+</IT>ECW)</DE></FR> (6)
Both ICW and ECW are water compartments, and ECW can be expressed as a function of ICW [i.e., ECW = (E/I) × ICW], where E/I is the ratio of ECW to ICW. Equation 6 can be converted and simplified to a secondary cellular-level TBK/FFM model as
TBK<IT>/</IT>FFM

=<FR><NU>[K]<SUB>ICW</SUB><IT>×</IT>ICW<IT>+</IT>[K]<SUB>ECW</SUB><IT>×</IT>ICW<IT>×</IT>(<IT>E/I</IT>)</NU><DE>ICW<IT>/a+</IT>ICW<IT>×</IT>(<IT>E/I</IT>)<IT>/b+c×</IT>[(ICW<IT>+</IT>ICW<IT>×</IT>(<IT>E/I</IT>)]</DE></FR>

=<FR><NU>[K]<SUB>ICW</SUB><IT>+</IT>[K]<SUB>ECW</SUB><IT>×</IT>(<IT>E/I</IT>)</NU><DE><IT>1/a+1/b×</IT>(<IT>E/I</IT>)<IT>+c+c×</IT>(<IT>E/I</IT>)</DE></FR> (7)
Equation 7 reveals that the TBK/FFM ratio is determined by six factors, potassium concentration in ICW ([K]ICW), potassium concentration in ECW ([K]ECW), cellular hydration (a), extracellular fluid hydration (b), ratio of ECS to TBW (c), and water distribution (E/I). We now explore the six individual TBK/FFM determinants.

[K]ICW and [K]ECW. The mean potassium concentration of the cell compartment as a whole is one of the most stable physiological measures in mammals. Previous studies have reported similar intracellular potassium concentrations in mammals: 150-160 mmol/kgH2O (21), 150 ± 7.2 (SD) mmol/l (22), 152 mmol/kgH2O (21), and 159 mmol/kgH2O (26). In the present investigation, [K]ICW was thus assumed to be 155 mmol/kgH2O, with a range of 150-160 mmol/kgH2O.

The potassium concentration in ECF is very low and relatively stable (21). In the present study, the potassium concentration in ECF was assumed to be 5 mmol/kgH2O, with a range of 4-6 mmol/kgH2O.

Determinants a, b, and c. In a previous study we discussed physiological aspects of the three determinants (33). The same magnitude and variation range for each determinant was applied in the present study: a is 0.70, with a variation range of 0.69-0.71; b is 0.98, with a variation range of 0.97-0.99; and c is 0.14, with a range between 0.12 and 0.16.

Determinant E/I. In a previous study (33) we calculated the E/I ratio from TBK and TBW (0.82 ± 0.16 for men and 1.07 ± 0.22 for women) (33). These E/I values are TBK dependent and thus cannot be reasonably applied to study the TBK/FFM ratio. In the present study, a subject database was applied that included measured TBW and ECW by the 3H2O dilution and bromide dilution methods, respectively. ICW was calculated as the difference between TBW and ECW. The subjects' physical characteristics and body composition measurements are shown in Table 2. The measured E/I ratio was 0.79 ± 0.13 (mean -1.96 SD to mean +1.96 SD, 0.54-1.04) for the men and 1.03 ± 0.19 (0.66-1.40) for the women. The mean E/I ratio was 0.91, with a range from 0.54 to 1.40 for adult humans, although there was a significant between-gender E/I ratio difference (P < 0.001).


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Investigators have expressed interest in the potassium concentration of FFM for 50 years. In this section, we demonstrate how the proposed model can provide new insights into the TBK/FFM ratio.

Can TBK/FFM modeling reconstruct the mean and range observed in adults? The proposed cellular level model indicates that the TBK/FFM ratio is determined by six cellular level factors. The approximate mean value of each determinant in adult humans is known, as described in the previous section: [K]ICW = 155 mmol/kg, [K]ECW = 5 mmol/kg, a = 0.70, b = 0.98, c = 0.14, and E/I = 0.91. The mean TBK/FFM ratio for healthy adult humans can therefore be calculated according to Eq. 7
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU>155+5×0.91</NU><DE>1/0.70+0.91/0.98+0.14+0.14×0.91</DE></FR>

=60.8 mmol<IT>/</IT>kg
The model-predicted TBK/FFM ratio is similar to the mean TBK/FFM value (60.4 mmol/kg) observed in the present study.

Previous studies demonstrate that the TBK/FFM ratio varies in adults. As indicated above, each of the six determinants may vary within an assumed range for healthy adults: [K]ICW from 150 to 160 mmol/kg, [K]ECW from 4 to 6 mmol/kg, 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 0.54 to 1.40. Determinants [K]ICW, [K]ECW, a, and b are in direct proportion, and c and E/I are in inverse proportion, to TBK/FFM magnitude. One can estimate the range of TBK/FFM if the six determinants take their extreme values. When [K]ICW = 150 mmol/kg, [K]ECW = 4 mmol/kg, a = 0.69, b = 0.97, c = 0.16, and E/I = 1.40, TBK/FFM may reach its low value according to Eq. 7
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU>150+4×1.40</NU><DE>1/0.69+1.40/0.97+0.16+0.16×1.40</DE></FR>

=47.5 mmol<IT>/</IT>kg
When [K]ICW = 160 mmol/kg, [K]ECW = 6 mmol/kg, a = 0.71, b = 0.99, c = 0.12, and E/I = 0.54, TBK/FFM may reach its high value
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU>160+6×0.54</NU><DE>1/0.71+0.54/0.99+0.12+0.12×0.54</DE></FR>

=76.3 mmol<IT>/</IT>kg
The model-predicted variation range of the TBK/FFM ratio for healthy adults is thus approximately from 48 to 76 mmol/kg. This range is similar to the variation range observed in the present in vivo study, 48.3-70.7 mmol/kg.

Does growth influence the TBK/FFM ratio? We now apply this model (Eq. 7) to explore several biological questions of interest. Clearly, the average potassium concentration of the human body is not stable during the entire life cycle (2). At birth, the reported mean TBK/FFM is low (49 mmol/kg) (9). A reasonable question thus arises: can the proposed model be applied in exploring the relationship between TBK/FFM and growth?

Of the six determinants of Eq. 7, [K]ICW = 155 mmol/kg, [K]ECW = 5 mmol/kg, a = 0.70, and b = 0.98 can be assumed for modeling purposes to be stable throughout life (33). The cellular level TBK/FFM model (Eq. 7) can be simplified to
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU>155+5×(<IT>E/I</IT>)</NU><DE>1.429+c+(1.020+c)×(<IT>E/I</IT>)</DE></FR> (8)
In Eq. 8, both c and E/I are in inverse proportion to TBK/FFM magnitude. Based on Reference Children data (9), c is very low (i.e., 0.07) at birth and then increases rapidly to 0.14 at adolescence. In contrast, E/I is maximal (i.e., 1.7) at birth and then decreases rapidly to 0.91 in adults.

We are thus able to predict the change in the TBK/FFM ratio during growth. At birth, because c = 0.07 and E/I = 1.7, predicted TBK/FFM is 48.8 mmol/kg, according to Eq. 8. The TBK/FFM then increases to 60.8 mmol/kg for adults when c = 0.14 and E/I = 0.91. As indicated by Eq. 8, the increase of TBK/FFM ratio during growth is caused by a rapid decrease in the ratio of ECW to ICW. However, the increase of determinant c (i.e., ECS/TBW) partially counteracts the effect of E/I change on TBK/FFM.

Does sex influence the TBK/FFM ratio? Some authors studied the influence of sex on the TBK/FFM ratio by in vivo assays (Table 3). Cohn et al. (4) chose values of 64.5 mmol/kg for adult men and 57.9 mmol/kg for adult women, whereas Heymsfield et al. (17) suggested 60.0 mmol/kg for men and 52.0 mmol/kg for women. Recently, Ellis (7) suggested a TBK/FFM range of 59-62 mmol/kg for adult men and 54-59 mmol/kg for adult women.

                              
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Table 3.   The TBK/FFM ratio (in mmol/kg) predicted by modeling approach and measured by in vivo studies

The previous experimental studies did not provide insight into why sex influences the TBK/FFM ratio. Of the six determinants of Eq. 7, [K]ICW = 155 mmol/kg, [K]ECW = 5 mmol/kg, a = 0.70, b = 0.98, and c = 0.14 can be assumed to be stable, as there are no obvious differences in these variables between adult men and women. The E/I ratio is the only determinant that changes substantially between adult men and women. Equation 7 can therefore be converted for discussion purposes to a simplified model
TBK<IT>/</IT>FFM<IT>=</IT><FR><NU>155+5×(<IT>E/I</IT>)</NU><DE>1.569+1.16×(<IT>E/I</IT>)</DE></FR> (9)
Equation 9 produces a nonlinear curve, showing that the E/I ratio strongly influences the TBK/FFM ratio. When E/I increases, TBK/FFM is a decreasing concave curve. The E/I was 0.79 ± 0.13 for men and 1.03 ± 0.19 for women in the present study (Table 2). According to Eq. 9, the mean TBK/FFM ratios are 64.0 mmol/kg for men and 57.9 mmol/kg for women. The model-predicted TBK/FFM ratio is very close to the values measured in the subjects of the present study (i.e., 64.0 vs. 61.3 ± 3.3 mmol/kg for men and 57.9 vs. 59.5 ± 5.7 mmol/kg for women).

As described above, the E/I ratio is the major determinant of the TBK/FFM ratio. A relevant question is, why do growth, sex, and potentially disease affect the E/I ratio? Many physiological factors are known to change the ECW/ICW ratio, and there exists no direct physiological regulation of relative water distribution. Children have a larger fraction of small young cells and a larger ECF-to-cell mass ratio compared with adults (10). The large E/I ratio in children permits rapid movement of end products from cells to ECF and nutrients from extracellular fluid to cells. Diseases or conditions associated with dehydration may decrease the E/I ratio. Conversely, obesity, acquired immunodeficiency syndrome, chronic renal failure, edema with malnutrition, and sepsis may cause an increase in the E/I ratio. Therefore, the E/I ratio and, concomitantly, the TBK/FFM ratio vary widely in health and disease.

Reliability of TBK-body fat method. The TBK/FFM ratio is applied in body composition studies for estimating total body fat mass (Eq. 1). Another well known body composition ratio, the TBW/FFM, is also widely applied in estimating body fat mass
body fat<IT>=</IT>body mass<IT>−</IT>FFM (10)

=body mass<IT>−</IT><FR><NU>TBW</NU><DE>TBW<IT>/</IT>FFM</DE></FR>
where body mass, FFM, and TBW are in kilograms, and TBW/FFM is the assumed constant (i.e., 0.73). To accurately estimate body fat mass, the basic requirement of the two methods is that the TBK/FFM and TBW/FFM ratios must be relatively stable. For exploring the reliability of the TBK-body fat method, we compared the constancy of TBK/FFM and TBW/FFM ratios. In our previous investigation (33), a simplified cellular level model was derived in evaluating the TBW/FFM ratio
TBW<IT>/</IT>FFM<IT>=</IT><FR><NU><IT>1+E/I</IT></NU><DE>1.569+1.16×(<IT>E/I</IT>)</DE></FR> (11)
Equations 9 and 11 indicate that the impact of E/I variability on the constancy of TBK/FFM and TBW/FFM is different. For example, when E/I increases from 1.0 to 1.1, according to Eqs. 9 and 11, TBK/FFM changes 3.8% (decreases from 58.6 to 56.4 mmol/kg), whereas TBW/FFM only changes 0.7% (increases from 0.733 to 0.738).

Another example is the influence of sex on the constancy of TBK/FFM and TBW/FFM ratios. The mean E/I ratio is significantly different between adult men and women (0.79 ± 0.13 vs. 1.03 ± 0.19, P < 0.001). According to Eq. 9, the mean TBK/FFM ratio in men is 9.5% higher than that in women (64.0 vs. 57.9 mmol/kg). In contrast, according to Eq. 11, the mean TBW/FFM ratio in men is only 2.1% lower than in women (0.722 vs. 0.737).

Hence, the TBK/FFM ratio is much more susceptible to E/I variation than is the TBW/FFM ratio. This model analysis confirms that, although the TBK method based on Eq. 1 was applied in many early body composition studies, it is not a reliable method for estimating total body fat unless correction is made for both sex and age (8, 19).

Summary and conclusion. Previous studies, along with actual subject measurements, demonstrate that the TBK/FFM ratio varies widely and is strongly influenced by growth and sex. The cellular level model provides a new approach for exploring the TBK/FFM ratio. According to our model, the mean TBK/FFM ratio is 60.4 mmol/kg, with a wide variation range from 48.3 to 70.7 mmol/kg. Water distribution (i.e., the ratio of extracellular to intracellular water) is the major factor influencing the TBK/FFM ratio.

Our findings clearly show that the method for estimating total body fat on the basis of an assumed constant TBK/FFM ratio is flawed, as the range of anticipated ratio values is extremely variable in relation to biological factors such as sex, age, hydration, and, presumably, disease status. Another widely used two-compartment model, based on the TBW/FFM ratio, appears far less prone to model errors secondary to biological factors, such as sex and age.

The proposed new model thus congregates and provides a coherent pattern for the many observed earlier findings of variability in the TBK/FFM ratio and suggests biological mechanisms leading to this variation. Our findings also emphasize the need for new modeling strategies if the TBK method of estimating total body fat is to remain a viable option in humans and other mammals.


    ACKNOWLEDGEMENTS

This study was supported by National Institute of Diabetes and Digestive and Kidney Diseases Grant 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. Section 1734 solely to indicate this fact.

Received 30 October 2000; accepted in final form 22 February 2001.


    REFERENCES
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ABSTRACT
INTRODUCTION
IN VITRO AND IN...
TBK/FFM MODEL
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REFERENCES

1.   Allen, TH, Anderson EC, and Langham WH. Total body potassium and gross body composition. J Gerontol 15: 348-357, 1960[ISI].

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