Am J Physiol Endocrinol Metab 284: E267–E273, 2003;
10.1152/ajpendo.00151.2002.
Magnitude and variation of fat-free mass density: a
cellular-level body composition modeling study
ZIMIAN WANG,1 STANLEY HESHKA,1 JACK WANG,1
LUCIAN WIELOPOLSKI,2 AND STEVEN B. HEYMSFIELD1
1
Obesity Research Center, St. Luke’s-Roosevelt Hospital, College of Physicians
and Surgeons, Columbia University, New York 10025; and 2Department of
Applied Science, Brookhaven National Laboratory, Upton, New York 11973
Submitted 10 April 2002; accepted in final form 12 August 2002
body composition; body fat measurement; bone mineral; total
body water
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
BM ⫽ fat ⫹ FFM
(1)
BM/Db ⫽ fat/Dfat ⫹ FFM/DFFM
(2)
Address for reprint requests and other correspondence: ZM. Wang,
Weight Control Unit, 1090 Amsterdam Ave., 14th Fl., New York, NY
10025 (E-mail: [email protected]).
http://www.ajpendo.org
where Db is body density, Dfat is the density of fat, and
DFFM is the FFM density. Solving the two equations
fat/BM ⫽
Dfat ⫻ (DFFM ⫺ Db)
Db ⫻ (DFFM ⫺ Dfat)
(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. Brožek 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), Brožek 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
fat/BM ⫽ 4.95/Db ⫺ 4.50
or
fat ⫽ 4.95 ⫻ BM/Db ⫺ 4.50 ⫻ BM
(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 anThe 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.
0193-1849/03 $5.00 Copyright © 2003 the American Physiological Society
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Wang, ZiMian, Stanley Heshka, Jack Wang, Lucian
Wielopolski, and Steven B. Heymsfield. Magnitude and
variation of fat-free mass density: a cellular-level body composition modeling study. Am J Physiol Endocrinol Metab
284: E267–E273, 2003; 10.1152/ajpendo.00151.2002.—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 twocompartment 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.
E268
FAT-FREE MASS DENSITY
Table 1. In vitro measurement of FFM density in 8 adult cadavers
Fraction of FFM as
Gender
Age,
yr
BM,
kg
FFM,
kg
Water
Protein
Mineral
DFFM,
g/cm3
Reference
No.
F
M
M
F
M
M
M
M
Mean ⫾ SD
67
35
48
59
63
25
60
46
50 ⫾ 15
43.4
70.6
62.0
25.9
58.6
71.8
73.5
53.8
57.5 ⫾ 16.3
39.7
61.6
59.7
18.2
48.0
61.1
53.5
42.7
48.1 ⫾ 14.7
0.806
0.778
0.735
0.731
0.729
0.727
0.695
0.696
0.737 ⫾ 0.038
0.139
0.166
0.204
0.203
0.200
0.195
0.236
0.234
0.197 ⫾ 0.032
0.055
0.057
0.060
0.066
0.071
0.079
0.069
0.070
0.066 ⫾ 0.008
1.072
1.081
1.097
1.101
1.104
1.108
1.114
1.114
1.099 ⫾ 0.015
13
12
8
11
11
30
8
3
BM, body mass; F, female; FFM, fat-free mass; DFFM, density of FFM; M, male.
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)
FFM ⫽ BCM ⫹ ECF ⫹ ECS
An FFM density model is derived based on Eqs. 5
and 6
DFFM ⫽
BCM ⫹ ECF ⫹ ECS
BCM/DBCM ⫹ ECF/DECF ⫹ ECS/DECS
(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
DFFM ⫽
ICW/a ⫹ ECW/b ⫹ c ⫻ (ICW ⫹ ECW)
ICW/(a ⫻ DBCM) ⫹ ECW/(b ⫻ DECF)
⫹ c ⫻ (ICW ⫹ ECW)/DECS
(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
(5)
Similarly, the volume of FFM can be expressed as the
sum of the volumes of the three components
FFM volume
⫽ BCM/DBCM ⫹ ECF/DECF ⫹ ECS/DECS
(6)
where DBCM, DECF, and DECS are the densities of BCM,
ECF, and ECS, respectively.
AJP-Endocrinol Metab • VOL
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.
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thropometric 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 densitometrybased 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 cellularlevel 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.
E269
FAT-FREE MASS DENSITY
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.
ICW/a ⫹ ICW ⫻ (E/I)/b
⫹ c ⫻ [ICW ⫹ ICW ⫻ (E/I)]
DFFM ⫽
ICW/(a ⫻ DBCM) ⫹ ICW ⫻ (E/I)/(b ⫻ DECF)
⫹ c ⫻ [ICW ⫹ ICW ⫻ (E/I)]/DECS
⫽
1/a ⫹ (E/I)/b ⫹ c ⫹ c ⫻ (E/I)
1/(a ⫻ DBCM) ⫹ (E/I)/(b ⫻ DECF)
⫹ c/DECS ⫹ (E/I) ⫻ c/DECS
(9)
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
DFFM ⫽
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
Brožek 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.
1/0.70 ⫹ 0.95/0.98 ⫹ 0.135 ⫹ 0.135 ⫻ 0.95
1/(0.70 ⫻ 1.078) ⫹ 0.95/(0.98 ⫻ 1.010)
⫹ 0.135/1.96 ⫹ 0.95 ⫻ 0.135/1.96
⫽ 1.10 g/cm3
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
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
AJP-Endocrinol Metab • VOL
Table 2. Body composition and in vivo measurement
of DFFM in group 1 subjects
n
Age, yr
Body mass,
kg
Height, m
BMI, kg/m2
TBW, kg
TBN, kg
Protein, kg
Mo, kg
TBK, mmol
TBNa, g
TBCl, g
TBCa, g
Ms, kg
FFM, kg
DFFM,
g/cm3
Mean ⫾ SD
Range
233
50.4⫾13.3
66.7⫾9.9
26M, 207F
20–81
48.0–96.5
1.65⫾0.07
24.6⫾3.6
32.9⫾4.6
1.47⫾0.19
9.11⫾1.20
2.66⫾0.46
2618⫾465
66.3⫾7.7
71.0⫾11.3
703⫾118
0.426⫾0.057
45.1⫾6.1
1.48–1.89
16.4–39.0
24.5–53.1
0.96–2.46
5.96–15.28
1.48–3.85
1,821–4,743
49.8–94.7
46.6–111.7
437–1126
0.310–0.661
32.5–70.5
1.102⫾0.007
1.084–1.115
Method
3
H2O or 2H2O dilution
In vivo neutron activation
Equation A2 calculation
DEXA
Whole body 40K counting
In vivo neutron activation
In vivo neutron activation
In vivo neutron activation
Equation A3 calculation
TBW ⫹ protein ⫹ Mo ⫹
Ms
Equation A1 calculation
BMI, body mass index; DEXA, dual-energy X-ray absorptiometry;
Mo, bone minerals; TBW, total-body water; Ms, soft tissue minerals;
TBCa, total body calcium; TBCl, total body chlorine; TBK, total body
potassium; TBN, total body nitrogen; TBNa, total body sodium.
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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.
MODEL FEATURES
E270
FAT-FREE MASS DENSITY
DFFM ⫽
1/0.69 ⫹ 1.36/0.97 ⫹ 0.12 ⫹ 0.12 ⫻ 1.36
1/(0.69 ⫻ 1.067) ⫹ 1.36/(0.97 ⫻ 1.008)
⫹ 0.12/1.94 ⫹ 1.36 ⫻ 0.12/1.94
⫽ 1.083 g/cm3
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
1/0.71 ⫹ 0.58/0.99 ⫹ 0.16 ⫹ 0.16 ⫻ 0.58
DFFM ⫽
1/(0.71 ⫻ 1.089) ⫹ 0.58/(0.99 ⫻ 1.012)
⫹ 0.16/1.98 ⫹ 0.58 ⫻ 0.16/1.98
⫽ 1.124 g/cm3
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 modAJP-Endocrinol Metab • VOL
eling purposes. The FFM density model (i.e., Eq. 9) can
thus be simplified to
DFFM ⫽
1.429 ⫹ 1.020 ⫻ (E/I) ⫹ c ⫹ c ⫻ (E/I)
1.325 ⫹ 1.010 ⫻ (E/I) ⫹ 0.510
⫻ c ⫹ 0.510 ⫻ c ⫻ (E/I)
(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 ⬎
Table 3. Body composition and in vivo measurement
of DFFM in group 2 subjects
Mean ⫾ SD
Range
n
267
127M, 140F
Age, yr
41.8⫾15.4
18–86
Body mass, kg 75.3⫾15.5
40.8–114
Height, m
1.70⫾0.10
1.44–1.92
BMI, kg/m2
26.1⫾4.8
16.9–41.3
Fat, kg
21.8⫾11.0
2.6–56.2
FFM, kg
53.5⫾11.8
31.5–82.9
TBW, kg
39.4⫾8.9
22.0–70.0
Mo, kg
2.85⫾0.60
1.59–4.55
TBK, mmol
3203⫾874
1,610–5270
E/I
1.00⫾0.20
0.54–1.50
Mo/TBW
0.073⫾0.008 0.048–0.103
DFFM, g/cm3
1.102⫾0.015 1.062–1.150
Method
DEXA
Body mass-fat
3
H2O dilution
DEXA
Whole body 40K counting
Equation A5 calculation
Equation A4 calculation
E/I, ratio of extracellular water to intracellular water; Mo/TBW,
ratio of bone minerals to TBW.
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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
E271
FAT-FREE MASS DENSITY
DFFM ⫽
2.398 ⫹ 3.374 ⫻ (Mo/TBW)
2.285 ⫹ 1.720 ⫻ (Mo/TBW)
(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.
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
Table 4. Effects of sex, race, and age on FFM
density in group 2 subjects
Women, yr
Race
Black
n
Mo/TBW, kg/kg
DFFM (predicted),
g/cm3
DFFM (measured),
g/cm3
White
n
Mo/TBW, kg/kg
DFFM (predicted),
g/cm3
DFFM (measured),
g/cm3
20–59
ⱖ60
Men
(20–59 yr)
36
0.0757
8
0.0717
33
0.0732
1.099
1.096
1.097
1.100 ⫾ 0.016
1.096 ⫾ 0.017
1.102 ⫾ 0.009
51
0.0766
13
0.0686
41
0.0696
1.099
1.094
1.095
1.105 ⫾ 0.014
1.085 ⫾ 0.014
1.097 ⫾ 0.010
Means ⫾ SD shown for measured DFFM.
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 (ⱖ60 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
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.
AJP-Endocrinol Metab • VOL
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
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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-toTBW 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
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FAT-FREE MASS DENSITY
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
DFFM ⫽ FFM mass/FFM volume ⫽ (TBW ⫹ protein
⫹ Mo⫹ Ms)/(TBW/0.9937 ⫹ protein/1.34
(A1)
⫹ Mo/2.982 ⫹ Ms/3.317)
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)
protein ⫽ 6.25 ⫻ TBN
(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)
Ms ⫽ 2.76 ⫻ TBK ⫹ TBNa ⫹ 1.43
⫻ TBCl ⫺ 0.038 ⫻ TBCa
(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
DFFM ⫽
0.900 ⫻ Db ⫻ (BM ⫺ fat)
0.900 ⫻ BM ⫺ fat ⫻ Db
(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)
E/I ⫽ (155 ⫻ TBW ⫺ TBK)/(TBK ⫺ 5 ⫻ TBW)
(A5)
where TBK is expressed in millimoles and TBW is in kilograms. TBK was measured by whole body 40K counting.
AJP-Endocrinol Metab • VOL
This work was supported by National Institute of Diabetes and
Digestive and Kidney Diseases Grant DK-42618.
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Two subject groups were evaluated in the present study.
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