Magnitude and variation of fat-free mass density: a
cellular-level body composition modeling study
Zimian
Wang1,
Stanley
Heshka1,
Jack
Wang1,
Lucian
Wielopolski2, and
Steven B.
Heymsfield1
1 Obesity Research Center, St. Luke's-Roosevelt
Hospital, College of Physicians and Surgeons, Columbia University,
New York 10025; and 2 Department of Applied Science,
Brookhaven National Laboratory, Upton, New York 11973
 |
ABSTRACT |
The
mean density of fat-free mass (FFM) is remarkably stable at 1.10 g/cm3 in healthy adult humans, and this stability is a
cornerstone of the widely applied densitometry-based two-compartment
model for estimating total body fat. At present, the usual means of exploring FFM density is by in vitro or in vivo experimental studies. The purpose of the present investigation was to develop a
cellular-level body composition model that includes seven factors that
determine FFM density. The model, when applied with available empirical coefficients, predicted an FFM density similar to that observed in
vivo. An analysis of the seven model components indicates that the
ratio of extracellular solids to total body water is a major determinant of individual variation in FFM density. The difference in
FFM density across sex, race, and age groups was examined with the
developed model. The present study thus provides a conceptual framework
for the systematic study of FFM density in humans.
body composition; body fat measurement; bone mineral; total body
water
 |
INTRODUCTION |
AN IMPORTANT
AIM of body composition research is to identify stable component
relationships such as the fraction of fat-free mass (FFM) as water
(i.e., total body water/FFM = 0.73; see Ref. 27). The
origin of these observed stable component relationships is of
scientific interest, and some of these presumed stable associations are
the basis of body composition methods (e.g., fat = body mass
total body water/0.73; see Refs. 17, 20,
26).
A classic body fat estimation method relies on the densitometry-based
two-compartment model in which body mass (BM) is expressed as the sum
of fat and FFM. Two simultaneous equations can be written
|
(1)
|
|
(2)
|
where Db is body density, Dfat is the
density of fat, and DFFM is the FFM density. Solving the
two equations
|
(3)
|
Inserting the values of Dfat at 0.900 g/cm3 (5) and the assumed constant
DFFM, one can estimate the fraction of BM as fat based on
the measurement of body density.
Up to the present time, the usual means of exploring FFM density
in humans is by cadaver analysis or by in vivo experimental studies. On
the basis of the analysis of several cadavers, Siri (21)
proposed an FFM density value of 1.100 g/cm3. Bro
ek
et al. (1) compiled data based on the body composition of
Reference Man. The authors assumed that the FFM fractions as water,
protein, bone mineral (Mo), and soft tissue minerals (Ms) are 0.737, 0.194, 0.056, and 0.012, respectively. With the combination of the
known densities of water (0.9937 g/cm3 at 36°C; see Ref.
3), protein (1.34 g/cm3), Mo (2.982 g/cm3), and Ms (3.317 g/cm3), Bro
ek et
al. calculated the density of FFM as 1.100 g/cm3 for
Reference Man. On the basis of the results obtained from nine in vitro
cadaver studies from 1945 to 1986, we calculate an FFM density
(mean ± SD) of 1.099 ± 0.015 g/cm3, with a
range from 1.072 to 1.114 g/cm3 (Table
1).
With FFM density taken to be 1.100 g/cm3 and fat density at
0.900 g/cm3, Eq. 3 can be simplified to
or
|
(4)
|
Body fat mass can thus be predicted from BM and body density
measured by underwater weighing or air displacement plethysmography (9). The two-compartment method based on Eq. 4
is often applied as the criterion for body fat measurement. Other
clinically applied and less-accurate body fat prediction methods, such
as anthropometric estimations and bioelectrical impedance analysis,
have been calibrated and cross-validated against fat estimates derived
using Eq. 4.
Although the literature on FFM density has expanded greatly over
the past five decades and a value of 1.100 g/cm3 is the
cornerstone of the densitometry-based two-compartment model, there
remain fundamental questions related to the density of FFM.
Specifically, we still lack a body composition model that can provide
insights into the magnitude and constancy of FFM density in humans.
The purpose of this study was to develop a cellular-level body
composition model that permits a systematic examination of the factors
that lead to the magnitude of and variation in FFM density. In our
previous studies, we developed two cellular-level body composition
models, one for FFM hydration and the other for the ratio of total body
potassium to FFM (25, 28). The current study is the third
investigation in our modeling series.
 |
FFM DENSITY MODEL |
The strategy of the present study, which differs from earlier
empirical approaches, was to separate FFM into several components on
the cellular body composition level and then to construct FFM density
from interconnected ratios. BM is composed of the following three
components on the cellular level: cells, extracellular fluid (ECF), and
extracellular solids (ECS; see Ref. 27). The cellular component can be further divided into fat and body cell mass (BCM). According to Moore et al. (14), BCM includes intracellular
water (ICW), protein, and Ms but does not include stored fat. On the basis of this definition, FFM can be expressed as (Fig.
1)
|
(5)
|
Similarly, the volume of FFM can be expressed as the sum of the
volumes of the three components
|
(6)
|
where DBCM, DECF, and DECS are
the densities of BCM, ECF, and ECS, respectively.

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Fig. 1.
Cellular-level body composition model of fat-free mass
(FFM), which contains the following three components: body cell mass
(BCM), extracellular fluid (ECF), and extracellular solids (ECS). The
intracellular water (ICW) compartment of BCM, extracellular water (ECW)
compartment of ECF, and the bone mineral (Mo) and protein compartments
of ECS are shown.
|
|
An FFM density model is derived based on Eqs. 5 and 6
|
(7)
|
In the next stage, our aim was to resolve the model into relevant
component ratios.
Both BCM and ECF contain aqueous compartments as ICW and
extracellular water (ECW). Components BCM and ECF can thus be
expressed, respectively, as BCM = ICW/a and ECF = ECW/b, where a is the ratio of ICW to BCM and
b is the ratio of ECW to ECF. In addition, ECS is expressed
as a function of total body water (TBW, the sum of ICW and ECW),
ECS = c × TBW = c × (ICW + ECW), where c is the ratio of ECS to TBW
(25). Equation 7 can be converted to
|
(8)
|
ECW can be expressed as a function of ICW, ECW = (E/I) × ICW, where E/I is the ratio of ECW to ICW. Equation 8 can
thus be simplified to a secondary cellular-level FFM density model as
|
(9)
|
Equation 9 reveals that the density of FFM at the
cellular body composition level is determined by the following seven
factors: cellular hydration (a), ECF hydration
(b), the ratio of ECS to TBW (c), the ratio of
ECW to ICW (E/I), the density of BCM (DBCM), the density of
ECF (DECF), and the density of ECS (DECS). The mean magnitude and assumed variation range of determinants
a, b, c, and E/I were discussed in our
previous study (25). Specifically, in healthy adults,
a is 0.70 with a range from 0.69 to 0.71, b is
0.98 with a range from 0.97 to 0.99, c is 0.135 with a range from 0.12 to 0.16, and E/I is 0.95 with a range from 0.58 to 1.36 (25). We now briefly discuss the three remaining
determinants of FFM density.
Density of BCM
Although there is great variation in cell size, shape, and
distribution, all cells share a similar composition, including water,
protein, and intracellular minerals. Cell composition in health is
maintained highly stable by homeostatic regulatory mechanisms. According to Bro
ek et al. (1), the average density
of human cells is 1.078 g/cm3. If the variation in cell
density is ±1%, then the range would be 1.067-1.089
g/cm3.
Density of ECF
ECF is a nonmetabolizing component surrounding cells. The
composition of ECF includes water, protein, and extracellular Ms. In
Reference Man, the fractions of ECF as plasma and nonplasma (e.g.,
cerebrospinal fluid) are 0.172 and 0.828, respectively (22). The mean densities of plasma and cerebrospinal fluid
are 1.027 g/cm3 with a range from 1.025 to 1.029 g/cm3 and 1.007 g/cm3 with a range from 1.005 to 1.009 g/cm3, respectively (3). The mean ECF
density is thus 1.010 g/cm3 (i.e., 1/DECF = 0.172/1.027 + 0.828/1.007) with a range from 1.008 to 1.012 g/cm3.
Density of ECS
The ECS distributes in several tissues, including cortical and
trabecular bone, cartilage, periarticular tissue, tendons, and fascia.
ECS are a nonmetabolizing component that consists of inorganic and
organic compounds. The inorganic ECS, with calcium hydroxyapatite
[Ca3(PO4)2]3Ca(OH)2
as the major constituent, represents 57.7% of dry bone matrix
(22). The organic ECS, representing the remaining 42.3%
of dry bone matrix, includes the following three types of fiber
protein: collagen, reticular, and elastic (22). In the
present investigation, the fractions of ECS were assumed to be 0.577 as
Mo with a density of 2.982 g/cm3 and 0.423 as protein with
a density of 1.34 g/cm3. The mean ECS density is thus 1.96 g/cm3 (i.e., 1/DECS = 0.577/2.982 + 0.423/1.34). If the variation in ECS density is ±1%, the range would
be from 1.94 to 1.98 g/cm3.
 |
MODEL FEATURES |
Many authors have studied the magnitude and variation in FFM
density and its relation to sex, race, and age (2, 16,
24). In the present study, we evaluated two groups of healthy
subjects (APPENDIX) to demonstrate how the proposed
cellular-level model can provide new insights into factors responsible
for the density of FFM.
Can the Model Reproduce the Mean and Range of FFM Density Observed
in Adults?
Mean values of the seven model determinants are described above,
i.e., a = 0.70, b = 0.98, c = 0.135, E/I = 0.95, DBCM = 1.078 g/cm3, DECF = 1.010 g/cm3, and DECS = 1.96 g/cm3.
The mean density of FFM can thus be calculated for healthy adults
Model-predicted FFM density is identical or similar to the mean
FFM densities of Reference Man (1.100 g/cm3; see Ref.
1), in vitro cadaver studies (1.099 g/cm3;
Table 1), and our in vivo study (1.102 g/cm3 for
group 1; Table 2). FFM density
in group 1 (n = 233) was calculated using a
multicomponent model with measurements provided by dilution of labeled
water, in vivo neutron activation analysis, dual-energy X-ray
absorptiometry (DEXA), and whole body counting (Eq. A1).
In previous studies, the reported FFM densities vary within a
narrow range in adults (Table 1 and Ref. 1). As indicated above, each of the seven determinants may vary within a range: a from 0.69 to 0.71, b from 0.97 to 0.99, c from 0.12 to 0.16, E/I from 0.58 to 1.36, DBCM
from 1.067 to 1.089 g/cm3, DECF from 1.008 to
1.012 g/cm3, and DECS from 1.94 to 1.98 g/cm3. Of the seven determinants, only E/I is in inverse
proportion to FFM density, whereas the other six determinants are in
direct proportion to FFM density. We can thus predict the variation
range of FFM density if the seven determinants take their extreme
values. When a = 0.69, b = 0.97, c = 0.12, E/I = 1.36, DBCM = 1.067 g/cm3, DECF = 1.008 g/cm3, and DECS = 1.94 g/cm3,
FFM density reaches its low value
When a = 0.71, b = 0.99, c = 0.16, E/I = 0.58, DBCM = 1.089 g/cm3, DECF = 1.012 g/cm3, and DECS = 1.98 g/cm3,
FFM density reaches its high value
The model-predicted range of FFM densities for healthy adults is
thus approximately from 1.083 to 1.124 g/cm3. This
variation range is similar to the results of cadaver studies (1.072-1.114 g/cm3; Table 1) and our in vivo study
(1.084-1.115 g/cm3 for group 1; Table 2).
The proposed model thus indicates that the observed FFM density range
can be accounted for by variation in the seven determinants.
Does FFM Density Vary with Growth?
Previous studies indicate that FFM density varies with growth
(18). Moulton (15), in his classic
investigation, summarized the chemical analysis results of nine
mammals, including mice, rats, guinea pigs, rabbits, cats, dogs, pigs,
cattle, and humans. At birth, all mammals show a high FFM hydration
(e.g., 0.82 for humans) and low FFM fractions as protein and minerals
(e.g., respectively, 0.14 and 0.03 for humans). During growth in
mammals, FFM hydration rapidly declines, and protein and mineral
concentrations increase. The density of FFM is thus low at birth (1.064 g/cm3) and high in adults (1.100 g/cm3).
Can the Proposed Model be Applied in Exploring the Relationship
Between FFM Density and Growth?
Of the seven determinants, a = 0.70, b = 0.98, DBCM = 1.078 g/cm3, DECF = 1.010 g/cm3, and
DECS = 1.96 g/cm3 are assumed stable
throughout life for modeling purposes. The FFM density model (i.e.,
Eq. 9) can thus be simplified to
|
(10)
|
Determinant c changes directly, and the E/I ratio
changes inversely with FFM density. Based on Reference Child data
(5), factor c is very low at birth (i.e., 0.07)
and increases rapidly to adolescence (i.e., 0.135). In contrast, E/I is
high at birth (i.e., 1.7) and decreases rapidly to 1.0 in adults.
We are thus able to predict the change in FFM density during
growth. At birth, c = 0.07 and E/I = 1.7;
according to Eq. 10, the calculated FFM density is 1.07 g/cm3. The FFM density then increases to 1.10 g/cm3 for adults when c = 0.135 and E/I = 1.0. This trend is the same as measured FFM densities, 1.064 g/cm3 at birth and 1.100 g/cm3 in adults
(15). As indicated by Eq. 10, both an increase
in determinant c and a decrease in E/I cause an increase in
FFM density during growth.
Are There Major Model Determinants of FFM Density?
In the present study, we evaluated a second large group of healthy
adult subjects (group 2, n = 267;
APPENDIX and Table 3) to
examine the major model determinants of FFM density. The FFM density in
this group was calculated from measured body density, body fat, and BM
(Eq. A4).
Among the seven model determinants, a, b,
DBCM, DECF, and DECS can be assumed
for practical purpose to be stable in adults. Factor c and
water distribution (E/I) are the only two determinants that vary
substantially among healthy adults and possibly affect the density of
FFM (i.e., Eq. 10).
Water distribution in group 2 was measured with total body
potassium and TBW as described in the APPENDIX (Eq. A5). There was no significant correlation between the E/I ratio
and FFM density (r = 0.01, P > 0.05)
in the 267 healthy group 2 subjects. Fluid distribution
(i.e., E/I ratio) is thus not a major determinant of FFM density in
healthy adults.
Determinant c is the ratio of ECS to TBW. A direct method of
measuring ECS is unavailable at present, although Mo account for
~60% of ECS and can be measured by DEXA. We thus substitute the
Mo-to-TBW ratio for the closely related ECS-to-TBW ratio. The
correlation between the Mo-to-TBW ratio and FFM density was significant
(r = 0.34, P < 0.001) for the
group 2 subjects. The Mo-to-TBW ratio, a measure of bone
mass relative to soft tissue hydration, is thus a major model
determinant of FFM density.
As described above, the ECS fraction as Mo was assumed to be 0.577 (i.e., Mo/ECS = 0.577 or ECS = 1.73 × Mo; see Ref.
22). Equation 10 can be further simplified for
review purposes to
|
(11)
|
Equation 11 indicates that the relationship between
Mo/TBW and FFM density is nonlinear, although this function is almost linear within the Mo/TBW biological range (Fig.
2). The Mo/TBW ratio is 0.0729 ± 0.0082 with a variation range 0.048-0.103 for the 267 group
2 subjects of the present study (Table 3). When the Mo/TBW ratio
increases from 0.05 to 0.10, according to Eq. 11, FFM
density increases from 1.083 to 1.113 g/cm3, showing that
the Mo/TBW ratio strongly influences the magnitude of FFM density.

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Fig. 2.
Density of FFM by the simplified model (Eq. 11) on the ordinate and the ratio of Mo to total body water
(Mo/TBW) on the abscissa. The simplified model, FFM density = [2.398 + 3.374 × (Mo/TBW)]/[2.285 + 1.720 × (Mo/TBW)], is a nonlinear function. However, this function is almost
linear within the range of Mo/TBW from 0.05 to 0.11.
|
|
Does FFM Density Vary with Sex, Race, and Age?
On the basis of the group 2 database, we explored the
possible affects of sex, race, and age on the FFM density. The
densities of FFM were predicted from the Mo/TBW ratio, as described by
Eq. 11. The predicted FFM densities are close to the
measured FFM densities for different sex, race, and age groups (Table
4).
Sex.
Women have a higher Mo/TBW ratio than men (Table 4). According to
Eq. 11, the predicted FFM densities are 1.099 and 1.097 g/cm3 for black women and men <60 yr and 1.099 and 1.095 g/cm3 for white women and men <60 yr, respectively,
indicating that the sex difference in FFM density (0.002-0.004
g/cm3) might be detected by in vivo measurements
(P < 0.01 for women vs. men; Table 4). Women thus
appear to have a slightly higher Mo/TBW ratio and FFM density than men.
Race.
No significant difference in FFM density was detected in an earlier
investigation between black and white adults (24).
However, this experimental study did not provide insights into why
black and white subjects had nonsignificant differences in FFM density. In the present study, black women <60 yr had a slightly lower Mo/TBW
ratio (difference: 0.0009) than white women, whereas black men <60 yr
had a slightly higher Mo/TBW ratio (difference: 0.0036) than white men
(Table 4). According to Eq. 11, the differences in predicted
FFM densities between black and white groups are very small, although
the trend is for slightly higher FFM densities in black subjects. This
small difference in FFM density may not be detected by in vivo studies
(P > 0.05 for black vs. white women and black vs.
white men; Table 4).
Age.
Elderly subjects (
60 yr) in group 2 have a smaller Mo/TBW
ratio than young adults (Table 4). According to Eq. 11, the
predicted FFM densities are 1.099 and 1.096 g/cm3 for black
young and old subjects and 1.099 and 1.094 g/cm3 for white
young and old subjects, respectively. These differences in FFM density
(0.003-0.005 g/cm3) were detected by in vivo
measurements (P < 0.05 for young and old subjects;
Table 4).
 |
DISCUSSION |
The constancy of FFM density in healthy adults has been recognized
for over five decades and led to the classic densitometry-based method
of estimating fatness in humans. Deviations from "constant" FFM
density in earlier reports were often recognized as aberrations or
methodological errors. The present study, to our knowledge, is the
first effort aimed at providing an explanation for the observed
variation in FFM density with a cellular-level body composition model.
The derived model, when combined with available data, accounts for the
magnitude and variation range of FFM density and explores the effects
of sex, race, and age on FFM density. Moreover, although there are
seven determinants in the model, the ratio of ECS to TBW (i.e., ECS/TBW
or related Mo/TBW) is a major factor leading to the variability in FFM
density. This study thus provides new insights into our understanding
and application of FFM density for quantifying total body fat mass.
 |
APPENDIX |
Two subject groups were evaluated in the present study. Each
subject completed a medical history, physical examination, and blood
studies to exclude the presence of underlying diseases. We applied two
different approaches in calculating the density of FFM.
There were 233 healthy adults, 26 males and 207 females, in group
1 (Table 2). At the molecular body composition level, FFM is
composed of the following four components: TBW, protein, Mo, and Ms
(27). The density of FFM can thus be calculated as
|
(A1)
|
where TBW was measured by the 3H2O or
2H2O dilution method (19); protein
is calculated from total body nitrogen (TBN) by prompt-
in vivo
neutron activation analysis (4)
|
(A2)
|
Total body Mo was measured by DEXA; and total body Ms was
calculated from total body potassium (TBK), sodium (TBNa),
chlorine (TBCl), and calcium (TBCa, all in kg; Ref.
10)
|
(A3)
|
TBK was measured by whole body 40K counting, and
TBNa, TBCl, and TBCa were measured by delayed-
in vivo neutron
activation analysis (4).
There were 267 healthy adults, 127 males and 140 females,
evaluated in group 2 (Table 3). At the molecular level,
there are well-known simultaneous two-compartment models, as defined by Eqs. 1 and 2. Solving the two equations and
inserting the value for fat density at 0.900 g/cm3
(5), we calculate FFM density as
|
(A4)
|
where Db is measured by underwater weighing
(9), and fat is body fat mass estimated by DEXA. Fat
estimates by DEXA are not measurably influenced by hydration
fluctuations in healthy adults (23).
Water distribution (i.e., the ratio of ECW to ICW or E/I) was
measured in both groups based on TBK and TBW (6, 25)
|
(A5)
|
where TBK is expressed in millimoles and TBW is in kilograms.
TBK was measured by whole body 40K counting. Water volume,
estimated by 3H2O or
2H2O dilution, was assumed to overestimate TBW
by 4% (19).
 |
ACKNOWLEDGEMENTS |
This work was supported by National Institute of Diabetes and
Digestive and Kidney Diseases Grant DK-42618.
 |
FOOTNOTES |
Address for reprint requests and other correspondence:
ZM. Wang, Weight Control Unit, 1090 Amsterdam Ave.,
14th Fl., 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.
10.1152/ajpendo.00151.2002
Received 10 April 2002; accepted in final form 12 August 2002.
 |
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