Reliability of body fat estimations from a four-compartment model by using density, body water, and...

764 Am J (un Nuir l992;55:764-70. Printed in USA. © 1992 American Society for Clinical Nutrition

Original Research Communications-general

Reliability of body-fat estimations from a four-compartmentmodel by using density, body water, andbone mineral measurements14

Karl E Fried!, Jane P DeLuca, Louis J Marchiteii, and James A Vogel

ABSTRACF Reliability of body-fat estimation by a four-

compartment model was tested in 10 subjects. Body densities

were measured by underwater weighing (UWW), total body wa-

ter (TBW) by deuterium dilution, and total body bone mass(TBBM) by dual-energy x-ray absorptiometry in three sessionsin 1 wk. Percent body fat was determined by [2.559/density

- 0.734 (TBW/weight) + 0.983 (TBBM/weight) - 1.841] X 100.

Reliability coefficients were 0.991 and 0.994, and within-subjects

standard deviations were ± 1.0 and ± 1 . 1 for percent body-fat

estimations from Sin’s two-compartment and the four-corn-

partment models, respectively; fat mass was ±0.8 kg with both

models. These data suggest that additive errors in the multicorn-

partrnent model do not offset the improved accuracy of fat es-

tirnations over those obtained from UWW alone. The greatest

source of error came from the UWW procedure itself (±0.002

g/crn3, or 1.0% of body weight), followed by error in TBW

(±0.5 L). More reproducible passive methods that are not de-

pendent on hydration or TBBM may be especially useful after

validation against the four-compartment model. Am J Clin

Nuir l992;55:764-70.

KEY WORDS Body composition, body fat, densitometry,

body-water analysis, x-ray absorptiometry, bone mass, reliability,

multicompartrnent models, electrical impedance

Introduction

Over 30 y ago, Allen et al (1) at the Army Medical Research

and Nutrition Laboratory proposed the use of a four-cornpart-

ment model to estimate body fat as an improvement over esti-

mations made by two-compartment models, which assume a

single density for the combined nonfat components (2, 3). At

that time, tracer methods used to measure total body water(TBW) were still relatively unavailable to most laboratories andtotal body bone mineral (TBBM) could only be roughly esti-

mated from anthropometry. Simplification of methods of anal-

ysis for TBW measurement using deuterium (4), and the de-

velopment of dual-energy x-ray absorptiometry (DEXA) for

TBBM (5, 6), have made it possible to practically and safely

measure these two components. This improved technology now

makes it practical to use four-compartment models as a criterion

method against which other indirect methods can be compared

and developed. The accuracy of this approach was demonstratedby Heymsfield et al (7), who compared it with the more-involved

criterion method of neutron-activation analysis, but the repro-

ducibility of these methods has not been examined.

This study was conducted to determine whether the additive

errors from the individual measurements for the four-compart-ment model might introduce more error in precision than gainsin accuracy obtained by assessing the additional major body

components of TBW and TBBM.

Methods

Ten soldiers volunteered to participate in this study and gavetheir written, informed consent; and the study was conductedin accordance with US Army Regulation 70-25, concerning the

use of volunteers in research. There were no selection criteria,other than age (< 40 y) and good health. Descriptive data col-lected at the start of the experiment are shown in Table 1. All

subjects were comfortable with water submersion but all werenaive to the procedure of underwater weighing (UWW) at theoutset of the study. The percentage of forced vital capacity cx-pired in the first second was > 75% for each subject.

General testing procedure

Each subject was studied in three separate sessions within 1wk. Subjects fasted for I 2 h before each experiment and were

encouraged to drink water during this period. Each experiment

began at 0800, with no additional water consumption until the

end ofthe study at 1 100. Subjects emptied their bladders at thebeginning ofthe study and the specific gravity ofurine was mea-

sured in this sample. Subjects were then weighed on an electronic

I From the Occupational Physiology Division, US Army Research

Institute of Environmental Medicine, Natick, MA.2 Presented in part at the Fifth Conference for Federally Supported

Human Nutrition Research Units and Centers, sponsored by the Inter-agency Committee on Human Nutrition Research, NIH, Bethesda, MD,February2O-2l, 1991.

3 The opinions or assertions contained herein are the private views of

the authors and are not to be construed as official or,as reflecting the

views of the Department ofthe Army or the Department of Defense.4 Address reprint requests to KE Fried!, Occupational Physiology Di-

vision, US Army Research Institute of Environmental Medicine, Natick,

MA 01760-5007.

Received July 19, 1991.Accepted for publication September 25, 1991.

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RELIABILITY OF BODY-FAT ESTIMATIONS 765

TABLE 1Subject characteristics; subjects are ordered by increasing density of

fat-free mass (FFM)*

Smoking

Subject Sex Age status Ethnicity Height BMI

y cm

1 M 19 NS NHW 174 23.42 M 19 FS NHW 174 21.73 M 20 SMK NHW 182 23.84 M 24 FS A/PI 164 27.4

5 M 22 NS NHW 171 23.4

6 F 23 FS NHW 174 23.4

7 M 21 SMK NHW 190 26.88 M 19 NS HISP 168 23.9

9 M 24 NS NHW 182 22.810 M 19 SMK NHW 187 24.4

i±SD 21±2 - - 176.6 ±8.4 24.1 ± 1.7

S NS, nonsmoker; ES, former smoker; SMK, current smoker, NHW,

non-Hispanic white; A/PI, Asian/Pacific Islander; H1SP, Hispanic; BMI,

body mass index (in kg/m2).

balance (model 708, Seca AG, Hamburg, Germany) while wear-

ing light-weight shorts or a swimsuit and their heights were mea-sured with a stadiometer. Volumes micturated during the cx-periment (all occurred after the first 90 mm but before UWW)were measured and deducted from body-water and body-weight

measurements. A baseline venous blood sample was obtained

and subjects were given a fixed dose of 30 g D20 (99.9% purity,

Cambridge Isotope Laboratory, Woburn, MA), which was con-sumed through a straw and was followed by two 30-mL rinsesof tap water. Each subject was then measured by DEXA, bio-electrical impedance, and UWW, in that sequence. Three hours

after the initial dose, at the end of all other testing, a second(deuterium-equilibrated) blood sample was obtained. Serum wasstored in airtight containers at - 135 #{176}Cfor � 3 mo, until deu-terium analysis.

Dual-energy x-ray absorptiometry

TBBM measurements were made by scanning subjects with

DEXA (DPX, Lunar Co, Madison, WI) in the 20-mm (medium

speed) scan mode (6). Bone-mineral-content measurements bythis device were calibrated daily against secondary standardsthat were compared with ashed-bone sections. TBBM was cal-

culated from the measured values obtained by DEXA by usingthe value I .000 g of bone mineral (2.982 g/cm3) yields 0.9582g ash (3). The software in this device also yields an estimate ofpercent body fat based on an extrapolation of fatness from theratio of soft tissue attenuation of two x-ray energies in pixelsnot containing bone. The basis of this body-fat algorithm was

previously described (6, 8).

Bioelectrical impedance

Total body resistance was measured by electrical impedance

plethysmography. Two electrodes were placed on the dorsal sur-

face ofthe right hand and two on the right foot, with 800 jzA at

50 kHz passed between the outer two electrodes (model BIA-

10 1 , RJL Systems, Detroit). Resistance measurements were ob-

tamed within 2 mm of placing subjects in a supine position.

TBW was estimated by using the equation of Kushner and

Schoeller (9).

Underwater weighing

UWW was performed after all other measurements. Subjects

were weighed in 1.0 m water in a 0.9 X 1.2 X 1.2 m aluminum

tank after residual volume determinations were made. Residualvolumes were measured by oxygen dilution by using the method

of Wilmore et al (10), with subjects in a bent-forward sitting

position; measurements were duplicated to within 50 mL. Sub-

jects were then submerged while in the same position while sittingon an aluminum chair suspended from an electronic load cell(model 6000, Ametek, Largo, FL), sensitive to 10 g; tare weightof the chair was established with the subject in the tank. The

load cell voltage was analyzed by a weight-calibrated analog-to-

digital converter and the weights were sampled at a rate of 4

samplings/s by computer (HP-85, Hewlett-Packard, Corvallis,OR), which computed an underwater weight of the subject av-

eraged over 4-7 s after complete exhalation. Each subject was

strongly encouraged to produce a complete exhalation during

each residual-volume measurement and during each of 10 UWWtrials. The density of a subject was calculated by using the twohighest underwater weights within 100 g of each other, of ten

trials; water temperature was corrected for (usually 37 #{176}C).Gas-trointestinal gas volume was assumed to be negligible becausethe subjects were fasted and no fixed estimate was deducted inthe density calculation.

Total body water

TBW volume was calculated from serum concentrations of

deuterium. Deuterium was equilibrated between equal volumes(1.5 mL) of serum and deionized water at 37 #{176}Cfor 48 h in

8.3-cm diameter, Conway diffusion dishes (Bel-Air Products,

Pequannock, NJ) tightly sealed with Parafilm (American Can

Company, Greenwich, CT) ( I 1). These volumes were found tobe within the optimum range of recoveries in a test of all com-

binations ofO.5-mL increments between 1.0 and 2.5 mL. Each

baseline and 3-h postdosing serum sample was purified in trip-

licate samples. Recoveries by this method averaged 98% of initial

concentrations (ranging from 95% to 102%) and the methodyielded the same results obtained after vacuum sublimation pu-

rification in this laboratory (JP DeLuca, unpublished observa-

tions, 1991).

Absorption was measured by using a single-beam, infra-red spectrophotometer with a 4.0-tim fixed filter (Miran 1FF,Foxboro, Foxboro, MA) and a digital display device (Applied

Measurement, Acton, MA) in a cold ( 1 5 #{176}C)room. Samples

were measured in a calcium fluoride cell with a path length of

0.2 mm and deuterium oxide concentrations were calculated

from a linear standard curve. Measured concentrations rangedfrom 0.5 to 0.8 g/L after a single deuterium dose, with a 1.0%intraassay CV (for three replicates), equivalent to �0.5 L of

TBW. Measurements were calculated as liters ofTBW and this

was converted to mass by using 0.9937 g/mL. An additional

correction of 2% was used to account for the overestimate of

TBW due to proton exchange (12, 13), which is known to occur

between the tracer and proteins and carbohydrates in the bodywithin the first few hours of equilibration (14).

Percent-body-fat calculations

Percent-body-fat calculations were made as follows. Two-

compartment models, from density (2):

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%BFuww [4.95/density - 4.5] 100

766 FRIEDL El AL

TABLE 2Principal measurements and characteristics of FFM calculated from the four-compartment model

Principal measurements Four-compart ment-model measurements

SubjectBody

weight Body density TBBM TBW�� TBW�

Residual

volume FFM density

TBBM/FFM

TBW�/FFM

kg g/cm3 kg L L L g/cm3 % %

I #{149}

2

3

45

67

89

10

70.2 ± 0.9

65.5 ± 0.2

79.4 ± 0.4

73.7 ± 0.268.3 ± 0.2

70.6 ± 0.496.3 ± 0.3

68.1 ±0.675.2 ± 0.4

84.9±0.4

1.077 ± 0.006

1.077 ± 0.0011.058 ± 0.002

1.039 ± 0.0011.063 ± 0.002

1.037 ± 0.0031.051 ± 0.002

1.062±0.0021.063 ± 0.0011.069±0.001

2.87 ± 0.01

3.04 ± 0.013.18 ± 0.01

2.71 ± 0.05

2.98 ± 0.02

3.09 ± 0.024.45 ± 0.09

3.07±0.013.23 ± 0.033.96±0.02

48.7 ± 0.5

44.2 ± 0.648.4 ± 0.9

39.4 ± 1.2

41.7 ± 0.3

36.6 ± 0.353.7 ± 1.539.9± 1.443.9 ± 1.850.7±0.1

47.0 ± 0.9

43.4 ± 0.650.6 ± 0.2

41.1 ± 0.3

42.7 ± 0.3

36.8 ± 0.153.7 ± 1.5

42.8±0.448.3 ± 1.052.5±0.5

1.44 ± 0.16

0.81 ± 0.020.95 ± 0.050.96 ± 0.06

1.31 ± 0.040.95 ± 0.041.65 ± 0.040.91 ±0.031.68 ± 0.061.06±0.05

1.096 ± 0.0031.098 ± 0.002

1.098 ± 0.0011.101 ± 0.0031.102 ± 0.002

1.106 ± 0.0021.107 ± 0.004

1.108±0.0051.108 ± 0.005

1.110±0.001

5.62 ± 0.026.55 ± 0.086.20 ± 0.126.45 ± 0.086.67 ± 0.017.92 ± 0.057.71 ± 0.25

7.09±0.086.76 ± 0.21

7.14±0.03

74.2 ± 0.973.8 ± 0.473.3 ± 0.172.8 ± 1.072.7 ± 0.572.9 ± 0.772.4 ± 1.171.6± 1.471.1 ± 1.3

71.1±0.1

i±SDWithin-

subject

SD

75.2±9.4

0.4

1.060±0.014

0.002

3.26±0.53

0.04

44.7±5.6

1.0

45.9±5.4

0.7

1.17±0.32

0.06

1.103±0.006

0.003

6.81 ±0.67

0.12

72.6± 1.3

0.9

and from TBW (15):

%BFTBw [(body weight - TBW/0.732)/body weight]lOO

Three-compartment model, from density and TBW (2):

%BFUWWTBW [2. 1 1 8/density

- 0.780(IBW/weight) - 1.354] 100Four-compartment model, from density, TBW mass, and

IBBM:

%BFUWWTBwTBBM = [2.559/density - 0.734(IBW/weight)

+ 0.983(IBBM/weight) - l.841J100

This four-compartment model was derived by using essen-tially the same density assumptions used by Selinger (16) andHeymsfield et al (7), with component densities of 0.9007 (fat),0.9937 (water), and 2.982 (bone mineral) from the original es-

timations of Brozek et al (3) but with the remainder (largelyprotein, nonosseous mineral, and glycogen) based on the actualdensity measurements for the residual mass made by Allen etal (17): 1 .39 g/cm3. The results obtained by our equation and

the calculations suggested by Heymsfieid et al (7) were very

similar.

Statistics

Data were analyzed by using reliability procedures, t test, and

analysis of variance (ANOVA) with SPSS-X statistical software

(SPSS, Inc, Chicago). Repeatability of the measurements and

fat estimations was expressed by within-subjects standard de-viations and by the standardized Cronbach’s alpha reliability

statistic.

Results

Means and group standard deviations for each ofthe principal

measurements in this experiment are shown in Table 2. Thereliability coefficients for these measurements were 0.999 forweight and TBBM, 0.992 for density and residual volume, and0.989 for TBW�. Within-subjects standard deviations were0.4 kg for body weight, 0.002 g/cm3 for body density, 0.06 L forresidual volumes, 0.04 kg for TBBM, 1.0 L for TBW�, and0.7 L for TBWBIA.

A learning effect for the underwater exhalation procedure was

evident for halfofthe subjects and this also produced an overalltrend to a reduction in estimated %BF��, between the threeexperiments, with average estimates increased by 0.002 g/cm3

or reduced by � 1 %BF from the first to the third experiment;there was no comparable change in the residual-volume mea-surements or body weights. The within-subjects standard devia-tion for UWW encompassed this between-experiments learningdecrement: ±0.002 g/cm3, or 1.0 %BF.

Body-water measurements by deuterium dilution varied

within subjects between trials by ± 1.0 L (range ofactual within-

subjects differences: 0.2-3.4 L) (Table 2). As a fraction of thefat-free mass (FFM) (determined from the four-compartment

model), TBW averaged 72.6% but individual means varied sig-nificantly (ANOVA, P < 0.003), ranging from 7 1 . 1 ± 0.01% for

a subject with consistently poor hydration (average urine speci-fic gravity = 1.031 ± 0.002), to 74.1 ± 0.9% (urine specificgravity = 1.021 ± 0.006). This is a significant difference betweennormal individuals because the difference between these cx-tremes was larger than the within-individual variations (±0.9%TBW/FFM) and the precision of the deuterium purificationand analysis (±0.5 L).

Body-water estimations from the Kushner and Schoeller

equation (10), in which height, weight, and resistance are used,were very close approximations ofthe deuterium-measured vol-

umes (r = 0.92; TBW�o TBWsIA average = - 1.2 ± 2.1 L)

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RELIABILITY OF BODY-FAT ESTIMATIONS 767

* Within-subjects standard deviation.

TABLE 3Percent body fat estimated by various methods in this study

Three-compartment Four-compartmentSubject DEXA TBW UWW method method

%

1 8.7 ± 0.3 5.8 ± 0.2 9.6 ± 2.4 7.4 ± 1.1 7.1 ± 1.3

2 9.3 ± 0.7 8.4 ± 1.1 9.8 ± 0.1 9.0 ± 0.7 9.2 ± 0.6

3 17.6 ± 0.4 17.2 ± 1.1 17.9 ± 0.9 17.6 ± 1.0 17.4 ± 1.1

4 25.7 ± 0.6 27.4 ± 2.2 26.6 ± 0.4 27.1 ± 1.4 27.1 ± 1.3

5 16.0 ± 0.2 17.0 ± 0.5 15.6 ± 0.8 16.4 ± 0.3 16.5 ± 0.36 31.5 ± 0.5 29.6 ± 0.1 27.3 ± 1.2 28.6 ± 0.5 29.3 ± 0.67 24.4 ± 0.9 24.3 ± 2.1 21.0 ± 0.8 22.9 ± 1.2 23.4 ± 1.2

8 18.3 ± 0.2 20.5 ± 2.9 16.1 ± 0.8 18.7 ± 1.6 18.8 ± 1.59 15.4 ± 0.4 20.8 ± 2.9 15.8 ± 0.4 18.7 ± 1.5 18.6 ± 1.4

10 13.1 ± 0.4 18.9 ± 0.6 13.0 ± 0.6 16.4 ± 0.6 16.5 ± 0.6

i±SD* 18.0±0.5 19.0± 1.7 17.3± 1.0 18.3± 1.1 18.4± 1.1Cronbach’s ‘� 0.999 0.986 0.99 1 0.994 0.994

S Within-subjects standard deviation.

and yielded a greater precision (±0.7 L) than the TBW values parison with the measurement by the four-compartment modelfrom direct measurement by deuterium (± 1.0 L). is shown in Figure 2. Four-compartment corrected values showed

The measurement ofTBBM varied within subjects by ±40 g, consistent differences (ie, adjustments in the same direction inwith the largest individual difference shown as ±90 g. As a per- three experiments) for subjects where the mean difference wascentage ofthe FFM determined by the four-compartment model, > � 1 kg fat.

TBBM ranged from 5.6% to 7.9% of FFM (Table 2) and this The DEXA soft tissue analysis, which did not involve UWW,did not vary appreciably between trials within subjects. reduced the precision error by half. Estimates from TBW (two-

Percent body fat estimated by two-, three-, and four-com- compartment model) produced the highest variability in the

partment models is shown in Table 3. Reliabilities were slightly measurements.

higher with correction for day-to-day variation in TBW in thethree-compartment model (0.994) than for UWW alone (0.991);the four-compartment model did not further increase this reli- Discussionability with correction for TBBM. Fat mass from the variousmodels gave the same pattern of reliabilities reflected in the ret- The data from this study indicate that the multicompartmentative fat estimations (Table 4). The individual day-to-day vari- model, which includes measurements ofTBW and TBBM, can

ations in the difference of the fat weight measured by UWW be used to improve the accuracy ofbody-fat measurement fromand the two-compartment model is shown in Figure 1; its corn- UWW without being invalidated by the sum of errors from the

TABLE 4Fat mass estimated by various methods reported in this study

Three-compartment Four-compartment

Subject DEXA TBW UWW method method

kg

1 6.1 ± 0.2 4.1 ± 0.2 6.7 ± 1.8 5.2 ± 0.9 5.0 ± 1.0

2 6.1 ± 0.4 5.5 ± 0.7 6.4 ± 0.1 5.9 ± 0.4 6.0 ± 0.43 14.0 ± 0.4 13.7 ± 0.8 14.2 ± 0.7 13.9 ± 0.7 13.8 ± 0.8

4 18.9 ± 0.4 20.3 ± 1.6 19.6 ± 0.3 20.0 ± 1.0 20.0 ± 1.05 10.9 ± 0.1 1 1.6 ± 0.3 10.6 ± 0.6 1 1.2 ± 0.2 1 1.2 ± 0.2

6 22.3 ± 0.2 20.9 ± 0.1 19.3 ± 0.9 20.2 ± 0.4 20.7 ± 0.5

7 23.5 ± 0.8 23.4 ± 2.1 20.2 ± 0.7 22.1 ± 1.2 22.6 ± 1.18 12.4 ± 0.2 14.0 ± 2.0 1 1.0 ± 0.6 12.7 ± 1.2 12.8 ± 1.1

9 11.5±0.3 15.7±2.1 11.9±0.4 14.1±1.1 14.0±1.110 1 1.1 ± 0.4 16.0 ± 0.6 1 1.1 ± 0.6 13.9 ± 0.6 14.0 ± 0.6

.�±SD 13.7±0.4 14.5± 1.3 13.1 ±0.8 13.9±0.8 14.0±0.8Cronbach’s a 0.999 0.989 0.992 0.995 0.995

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1 2 3 4 5 6

Subject

7 8 9 10

Difference in fat weight (kg)

.3-i -�.J -

FFM d.nafty (k�t):

1.056 1.OQS 1.008 1.101 1.102 1.106 1.107 1.106 1.108 1.110

1 2 3 4 5 6

768 FRIEDL ET AL

FIG 1. Fat weight estimated from density and the two-compartment

equation of Siri in 10 healthy young subjects whose weight was studiedin three separate experiments within I wk.

multiple measurements. The largest error in this model appears

to come from the procedure ofUWW itself. UWW was no morereliable than ± 1.0% body fat or ±0.002 g/cm3, as previouslyreported (18-2 1). The precision of this measurement is largely

dependent on how well gas spaces are accounted for, which is

affected by methodological differences in the method of residual-

volume measurement (22), biological variations in intestinal gas

(23, 24), and the ability of the subjects to consistently match

their exhalation performances from the residual-volume mea-

surement to their efforts underwater. The method of trial selec-

tion also varies from study to study and, in this study, averaging

trials in a fixed sequence (eg, first 6 or last 3 of the 10 trials)

instead ofselecting best trials produced an additional difference

in density of -0.003 ± 0.002 g/cm3 (P < 0.001) or > + 1% body

fat. We believe that, because ofthe greater difficulty encounteredby subjects in exhaling to residual volume underwater, the best-

trials approach is the more accurate reflection of the residual-volume measurements used in the calculation of density. This

difference between in-water and out-of-water exhalation perfor-

mance is illustrated by the learning effect between experiments

for half of the subjects in this study, whereas residual-volume

measurements remained unchanged.

Siri (2) estimated that the standard deviation in fat estimated

by UWW was ±4.6% body-fat units and, with no errors in mea-

suring density, the error would still be ±3.8% body-fat units

“because of the normal variability in body constituents.” He

estimated the degree of hydration to be the next largest error in

fat estimation, with variations of ±6.5% of TBW in normally

hydrated individuals; thus, with the combination of UWW andTBW, Siri suggested that the estimate could be reduced to ± 1.5%

body-fat units ifthe error in body-water measurement could be

reduced to ± 1% of body weight. The error of the technique we

used is slightly better than ± 1% of body weight.

Adjustments for hydration produced sizeable changes in thefat estimates for some of our subjects and these adjustments

appeared to be more important than corrections for fractional

bone mass. This was indicated by the difference in fat-weight

means between those calculated from UWW and those fromthe three-compartment model of Siri, with little additional

change from the correction for TBBM (Table 4). Normal vari-

ations in the TBW of our 10 subjects ranged between 71% and

74% of FFM. These ranges are significant departures from the

assumed value of 73.2%, decreasing the fat estimate by UWW

by 2.2% body fat and increasing it by 3.4% body fat at the cx-

tremes of hydration (Table 3). Hydration, as a key determinant

of the departures from the assumed density of 1. 100 g/cm3 forthe FFM, progressively decreased throughout our subjects or-dered by increasing FFM density (Table 2).

The degree ofhydration also markedly affected the fat estimate

by the other two-compartment model in this study, based on

TBW. The differences between fat estimates from UWW andTBW in our 10 subjects ranged between +3.8% and -5.9% body-

fat units; however, the differences were smaller between TBWor UWW fat estimates and estimates made by three- and four-compartment models. Because the fractional bone mass also

tended to be higher in our subjects with lower degrees of meanhydration, this greater difference between fat estimates by thetwo two-compartment models suggests that TBW incorrectlyaccentuates differences when the fractional bone mass also de-parts from the 7% TBBM-FFM reference value. Thus, the two-

compartment model using TBW underestimates fatness whenthere is less bone mineral and overestimates fatness when thereis more than the assumed fraction of bone mineral, as a con-

sequence of the increased body mass, which is not consideredin the TBW-determined estimate of FFM. The error produced

by deviations in the assumed TBBM in fat estimation from

UWW is in the opposite direction. This may explain the puzzling

overestimate of the fractional bone mineral in black subjects

encountered by Schutte et al (25) when they tried to estimate

FFM density from a comparison of TBW and UWW fat esti-mates.

The 2% correction that we applied to the isotope-dilution

method is nothing more than a best guess at the magnitude ofthe exchange that is known to occur. This value was recom-mended as the upper limit by Pinson (12) but others estimateda higher theoretical maximum of 5.2% (26). Whatever the upperlimit is, equilibrium is reportedly not achieved until 24 h (27),

3

2

0

-1

-2

-4

Sublect

7 8 9 10

FIG 2. Difference in fat weight estimated from density by the two-compartment equation compared with the estimate from the four-com-partment equation, including assessments of TBW and TBBM. The re-

producibility of the four-compartment model is illustrated by the dif-ferences obtained in three separate experiments performed within 1 wk

for each of 10 subjects. Subjects are ordered by their mean FFM density(1. 100 is the assumed value in the two-compartment model).

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RELIABILITY OF BODY-FAT ESTIMATIONS 769

and on this basis we chose not to apply the higher correction

factor to samples equilibrated in vivo for only 3 h.

Our estimates of TBW from electrical impedance were also

remarkably similar to our values for TBW determined by deu-

terium dilution and they actually yielded smaller day-to-day

variations than did our measurements by deuterium. This finding

suggests either greater precision by electrical impedance than by

the deuterium method or a decreased sensitivity to small differ-ences. These measurements would have been even closer (0.24

± 2.2 L; � ± SD) if we had made no adjustment for proton

exchange, just as no adjustment was made in the original deri-

vation of this equation (9). This suggests the possibility thatimpedance could become a useful substitute for estimations of

TBW, offering the convenience ofimmediate results. Estimationofbody fat by using electrical impedance currently suffers from

the same limitations encountered with fat estimation from TBW,

namely the variation in hydration. However, this problem may

be overcome with multifrequency impedance measurements (28)

iffat estimation is based on intracellular water instead of TBW,as suggested by Keys and Brozek (29).

The other significant error in the assumptions of the two-

compartment models is the effect of the bone. This error was

well recognized in the earliest presentation ofbody-density mea-surements, when Behnke et al (30) noted that “excess fat is

viewed as the prime factor governing the level ofspecific gravity,”

but “precise measurements ofthis excess fat will necessarily await

a knowledge of the relative percentage variation of the weight

of the skeleton in lean persons.” This variable component cannow be more reliably measured than either body density or TBWand the measurement of TBBM is important because it varieswith ethnicity (3 1), physical training (32), and even total weight

(33), although in our subjects TBBM was of lesser importancethan TBW. A 20% increase in the average TBBM of 6.8% ofFFM in this study would produce an approximate correction of

+0.7 kg offat, an error ofunderestimation that might be typically

observed when these assumptions are applied to the average

black subject by using UWW. Nevertheless, this technology still

remains to be validated when, for example, subject hydration

and subject size are varied; subject size may artifactually reducethe bone measure with increasing body thickness (34).

The four-compartment-model approach to percent-body-fat

estimation improves upon the two-compartment models of Siri

(2) and Brozek et al (3) in terms of accuracy, by accounting for

the bone mineral and water components, which are otherwise

assumed to be of fixed proportions when they can be quite vari-able. The largest remaining error, the precision error of ±0.002

g/cm3 measured in our three UWW sessions, coupled with theerror in the TBW-measurement technique (±0.5 L), makes the

four-compartment model estimates offat no better than ± 1 per-

cent, but probably the accuracy is within Sin’s goal of 1.5%.

Further improvements in precision will probably only occur

when a technique that is easier for subjects to perform is adopted.

Thus, passive methods that do not require subjects to forciblyexhale underwater (eg, DEXA soft tissue analyses) may be pref-erable because of their superior reproducibility, particularly if

they are found to be accurate when compared with the four-

compartment model. 0

We thank Sherryl Kubel, Maijorie Harp, Sonja Moore, and Robert

Mello for their care and expert technical assistance in data collection.We are grateful to Henry Lukaski (USDA, Grand Forks, ND) for his

timely suggestions that led to this line of investigation and to John F

Patton for his helpful suggestions concerning this manuscript.

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