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 |
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
 |
INTRODUCTION |
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
|
(1)
|
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 |
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).
|
(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).
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).
 |
TBK/FFM MODEL |
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)
|
(3)
|
Fat-free mass can be expressed as the sum of three cellular level
components
|
(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
|
(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
|
(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
|
(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).
 |
MODEL FEATURES |
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
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
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
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
|
(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.
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
|
(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
|
(10)
|
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
|
(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.
 |
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