# Body composition estimates from multicomponent models using BIA to determine body water

##### Abstract

EVANS, E. M., S. A. ARNGRIMSSON, and K. J. CURETON. Body composition estimates from multicomponent models using BIA to determine body water. *Med. Sci. Sports Exerc.*, Vol. 33, No. 5, 2001, pp. 839–845.

Purpose: The purpose of this study was to compare estimates of body fat (%BF) from three- and four-component models with total body water (TBW) determined by single-frequency bioelectrical impedance analysis (BIA; %BF_{3C-BIA} and %BF_{4C-BIA}) to %BF estimates from densitometry (%BF_{2C-D}) and from three- and four-component models with TBW determined using deuterium dilution (%BF_{3C-D2O} and %BF_{4C-D2O}), the criterion methods.

Methods: Measures of body density by hydrostatic weighing, TBW by BIA and D_{2}O dilution, and bone mineral by dual energy x-ray absorptiometry (DXA) were obtained in 40 men and 93 women, 18–42 yr. TBW was estimated from BIA resistance (RJL analyzer) using an equation developed and cross-validated in two independent samples. Body fat was estimated using the three-component model of Siri (1961) and a four-component model modified from Lohman (1986).

Results: There was a strong relation and no significant difference between TBW estimated by BIA and D_{2}O [r = 0.94, SEE = 2.4; T̄×_{Diff} = 0.0 ± 2.4 L (SD), *P* > 0.05]. There were strong relations between methods for estimating %BF, with deviations from %BF_{4C-D2O} (errors) for %BF_{3C-BIA} [r = 0.99, SEE = 2.4% BF, T̄×_{Diff} = −0.4 ± 2.4% BF (SD)] and %BF_{4C-BIA} [r = 0.99, SEE = 2.3% BF, T̄×_{Diff} = 0.2 ± 2.3% BF (SD)] being nonsignificant (*P* > 0.05) although greater than for %BF_{3C-D2O} [r = 1.00, SEE = 0.5% BF, T̄×_{Diff} = −0.6 ± 0.5% BF (SD)], and comparable or slightly worse than for %BF_{2C-D} [r = 0.99, SEE = 2.3% BF, T̄×_{Diff} = 0.4 ± 2.3% BF (SD)].

Conclusions: We conclude that because estimates of %BF from multicomponent models with TBW estimated from BIA are not more accurate than from body density alone using a two-component model, estimates of %BF from three- and four-component models using TBW_{BIA} are not acceptable substitutes for estimates from the same models using TBW_{D2O}.

##### Author Information

Department of Exercise Science, University of Georgia, Athens, GA 30602-6554

January 2000

August 2000

Estimates of body fatness (%BF) from body density based on a two-component model assume a constant density of fat-free mass (FFM; 1.1 g·mL^{-1}) which, in theory, is based on the assumption that the proportions and densities of the constituents of FFM (water, mineral, and protein) are uniform across individuals ^{(23)}. Estimates of %BF from three- and four-component models in which body water, or body water and mineral, are measured in addition to body density are more accurate than estimates from body density alone based on a two-component model, because variation in the water, or water and mineral, content of the body is measured and not assumed to be constant ^{(16)}.

However, measurement of total body water (TBW) using a dilution method is time consuming, technically demanding, and relatively expensive. If body water could be estimated with sufficient accuracy from bioelectrical impedance analysis (BIA), this would facilitate the use of multicomponent models to estimate body composition. Alternatively, it is possible that the theoretical advantage of measuring TBW for use in multicomponent models to estimate %BF could be negated by the additional error introduced by estimating TBW rather than measuring it using a dilution method.

The purpose of this study was to compare %BF estimates from three- and four-component models with TBW determined by single-frequency BIA (TBW_{BIA}) to %BF estimates from densitometry (%BF_{2C-D}) and from three- and four-component models with TBW determined by deuterium dilution (TBW_{D2O}), the criterion methods. The primary questions were: Can estimates of TBW_{BIA} be substituted for estimates of TBW_{D2O} in estimating body fatness from multicomponent models without significant loss in accuracy? And, are estimates of %BF from three- and four-component models with TBW estimated from BIA more accurate than estimates of %BF from densitometry alone, using estimates of %BF from a four-component model with TBW determined by deuterium dilution as the criterion? It was hypothesized that: 1) estimates of %BF from three- and four-component models with TBW estimated from BIA are less accurate than estimates of %BF from three- and four-component models with TBW determined by deuterium dilution; and 2) estimates of %BF from three- and four-component models with TBW estimated from BIA are more accurate than estimates of %BF from densitometry alone, using estimates of %BF from a four-component model with TBW determined by deuterium dilution as the criterion.

## METHODS

##### Subjects

Because it was desirable to include subjects with a broad range of body fatness and TBW to investigate the question, the data from a diverse group of men and women were utilized. The sample (*N* = 133) included: 40 men, 93 women; and 3 Blacks, 14 Hispanics, and 116 Whites. Physical characteristics of the subjects are presented in Table 1. The subjects were free from any known medical or nutritional conditions or medication use known to affect body composition measures. The study was approved by the University’s Institutional Review Board, and written consent was obtained before data collection.

Reliability of the body composition methods was evaluated in an independent group of nine subjects (4 female, 5 male, 24 ± 3.8 yr, 16.6 ± 11.6%BF_{4C-D2O}) who were tested on two occasions 1 wk apart (see Table 2).

##### Data Collection Protocol

Physical characteristics, body density, total body water, total body bone mineral, and body composition from DXA, body resistance from BIA, and anthropometric measures were measured during a single test session (∼3.5 h). Subjects were asked to arrive at the laboratory well hydrated after a 12-h fast. Water consumption was encouraged based on personal preference and habit. A baseline urine sample, from the second void of the morning indicated that, on average, the subjects were adequately hydrated with a urine specific gravity of 1.020 ± 0.01 g·mL^{-1}^{(2)}. No food or beverages, including water, were consumed during the testing session.

##### Body Composition Measures

##### Anthropometric measures.

Body mass (BM) in air was determined using an electronic scale to the nearest 0.01 kg with subjects wearing the same attire as when weighed under water. Barefoot standing height was measured to the nearest 0.1 cm using a stadiometer.

##### Densitometry.

Body density was measured using underwater weighing and Archimedes’ principle to determine body volume. Body mass under water was determined using a Chatillon (Greensboro, NC) autopsy scale to the nearest 0.25 kg, with residual lung volume measured simultaneously using a closed-circuit oxygen-rebreathing, nitrogen-dilution technique modified from Goldman and Buskirk ^{(11)}. Volume of gas in the gastrointestinal tract was assumed to be 0.1 L.

##### Body water.

Total body water was measured using deuterium oxide dilution ^{(7)}. After a baseline blood sample was taken, subjects ingested a known quantity of D_{2}O [0.3 g D_{2}O·kg^{-1} BM] in 100 mL of distilled water. Another 100 mL of distilled water was used as a rinse and then consumed to insure complete ingestion of the tracer. After a 3-h equilibrium period during which all urine was collected, another blood sample was taken. Blood samples were centrifuged at 3000 rpm and plasma was stored at −70°C. Plasma samples were purified by diffusion by incubating equal volumes of plasma and deionized water at 37°C for 48 h in incubation dishes (Bel-Air Products, Pequannock, NJ). Isotope abundance in the purified plasma sample was determined in duplicate with an isotope-ratio mass spectrometer (*N* = 44; Finnigan MAT 251, Bremen, Germany) or in triplicate by single-beam infrared spectrophotometer (*N* = 90) as previously described ^{(19)}.

TBW_{D2O} was corrected for D_{2}O loss in urine and decreased 4% to account for hydrogen exchange with protein and carbohydrate during the 3-h equilibrium period ^{(22)}. Agreement between the two methods for analyzing deuterium was close as determined using 50 TBW samples [T̄×_{Diff} = −0.06 ± 0.9 (SD) L].

##### BIA resistance.

Determination of body resistance was made using a standard four-surface electrode bioimpedance analyzer (RJL Systems, Inc., Clinton TWP, MI) on the right side of the body after 10–15 min of supine rest utilizing standardized procedures ^{(14,18)}.

##### Bone mineral.

Bone mineral ash was determined from whole-body scans by DXA (Hologic QDR-1000W, enhanced whole body analysis software version 5.71, Waltham, MA). Bone mineral ash was multiplied by 1.27 to estimate total body mineral content. The constant 1.27 assumes that 4% of the bone mineral is lost during the ashing process and that nonosseous mineral mass is 23% of bone mineral ash ^{(5)}.

##### Body Composition Calculations

%BF was estimated from body density (D_{b}, %BF_{2C-D}) using the Siri equation ^{(23)} based on a two-component (fat and FFM) model:

Equation 1 assumes the density of the fat is 0.9 g·mL^{-1} and the density of the FFM is 1.1 g·mL^{-1}.

%BF was estimated from body density and body water using the three-component model (fat, water, and residual) modified from Siri ^{(23)} : with w being equal to total body water measured by D_{2}O dilution or estimated by body resistance expressed in relation to body mass (i.e., w/BM). Equation 2 assumes that the mineral-to-protein ratio of the FFM is 0.35 ^{(5)}.

%BF was estimated from body density, total body water, and total body mineral using the following equation from Lohman ^{(16)} based on a four-component model (fat, water, mineral, and protein):MATHwhere Db is body density, w is TBW and m is total body mineral estimated from bone mineral ash expressed relative to body mass (i.e., w/BM and m/BM).

##### Statistical Analysis

Data were analyzed with SPSS for Windows version 7.0 (SPSS Inc., Chicago IL). Reliability and repeatability of the body composition measures were assessed using an intraclass correlation coefficient (ICC) from a one-way ANOVA, the SD of the difference between repeat measures (SD_{Diff}) and the coefficient of variation (CV%;Table 2).

An equation predicting TBW_{D2O} from BIA resistance and other variables was developed and double cross-validated on the present sample. Subjects were randomly assigned to either a model or a validation group. Stepwise multiple regression analysis was applied to each sample to identify the best predictors of TBW_{D2O} utilizing the following independent variables: height squared/resistance, mass, gender (coded as male = 1 and female = 0) and age. In both samples, all variables except age contributed significantly to the prediction. Then, the equation predicting TBW_{D2O} developed on the model group was used to predict TBW in the validation sample, and *vice versa*. Correlations between measured and predicted TBW_{D20}, tests of the deviations of the slope and intercept from 1 and 0, respectively, and a dependent *t*-test of significance of the differences between measured and predicted means in the two samples were used to assess how well the equations cross-validated.

Repeated measures analysis of variance was used to determine the significance of differences among body fatness estimates with planned comparisons (contrasts) used in the event of a significant finding. An experiment-wise alpha level of 0.05 was used for all tests. A Bonferroni adjustment was used for the family of 4 contrasts (0.05/4 =*P* _{fw} < 0.013). Relations between variables were described using simple linear regression analysis. Individual agreement between %BF estimates of interest was assessed using the Bland-Altman approach ^{(1)}. The significance of differences in variance for differences between methods (error) when utilizing the Bland-Altman approach was assessed using a *t*-test for dependent samples.

## RESULTS

The multiple regression equations for the estimation of TBW in the model and validation groups were similar [Equation 1: TBW = 0.283 Ht^{2}/R + 0.180 Mass + 6.137 Gender + 7.029 (R = 0.95, SEE = 2.3 L) and Equation 2: TBW = 0.331 Ht^{2}/R + 0.137 Mass + 5.709 Gender + 7.855 (R = 0.94, SEE = 2.7 L)]. The cross-validation R between the measured TBW in the validation group and TBW predicted in the validation group using the equation developed on the model group was high (R = 0.91). The slope and intercept of the regression prediction equation (TBW_{D2O} = 1.00 TBW_{BIA} + 0.06) were not significantly different from 1 (t = 0.01, *P* = 0.99) and zero (t = 0.04, *P* = 0.97), respectively. There was no significant difference between measured (38.0 ± 7.4 L) and predicted (38.0 ± 7.0 L) TBW means. Likewise, the cross validation R between the measured TBW in the model group and TBW predicted in the model group using the equation developed on the validation group was high (R = 0.88). The slope and intercept of the regression prediction equation (TBW_{D2O} = 0.99 TBW_{BIA} + 0.42) were not significantly different from 1 (t = 0.10 *P* = 0.95) and 0 (t = 0.23, *P* = 0.82), respectively. There was no significant difference between measured (38.1 ± 7.4 L) and predicted (38.2 ± 7.0 L) TBW means.

Because the equations strongly cross-validated in each group of subjects, a prediction equation predicting TBW_{D2O} from BIA resistance and other variables based on the total sample was used for the remainder of the data analysis:MATH MATHwhere R = resistance measured in Ohms, Ht is in cm, mass is in kilograms and gender is 1 = male and 0 = female.

The density of the FFM (D_{FFM}; 1.101 ± 0.001) did not differ from that assumed by densitometry based on the cadaver data summarized by Brozek et al. ^{(5)}, [D_{FFM} = 1.100 g·mL^{-1}, water fraction of the FFM (W/FFM) = 73.8%, mineral fraction of the FFM (M/FFM) = 6.8%, and protein fraction of the FFM (P/FFM) = 19.4%]; however, the W/FFM and M/FFM were significantly lower (72.3 ± 2.2 and 6.2 ± 0.6%) and the P/FFM was significantly higher (21.5 ± 2.3) than assumed (*P* < 0.05). Because D_{FFM} did not significantly differ from 1.100 g·mL^{-1}, mean %BF_{2C-D} was not significantly different from mean %BF_{4C-D2O} (Table 3). However, individual differences between %BF_{4C-D2O} and %BF_{2C-D} ranged from −5.3 to 7.8% BF [T̄×_{Diff} = 0.4 ± 2.3% BF (SD);Table 4, Fig. 1]. As expected, there was a strong relation of the difference in estimates of body fatness from a four-component model and densitometry (%BF_{4C-D2O} − %BF_{2C-D}) with D_{FFM} (r = 0.98, *P* < 0.05) and with W/FFM (r = 0.91, *P* < 0.05; data not shown).

Taking into account individual differences in body water greatly increased the accuracy of predicting the criterion measure of body fatness from body density, indicating that most of the difference between %BF_{4C-D2O} and %BF_{2C-D} was due to variability in W/FFM. Despite the statistically significant difference between means (Table 3), the agreement between %BF_{4C-D2O} and %BF_{3C-D2O} was very close (Table 4, Fig. 2). Individual differences ranged from −1.8 to 1.1% BF [T̄×_{Diff} = −0.6 ± 0.5%BF (SD)].

A strong relation existed between the D2O and BIA estimates of TBW (r = 0.94, SEE = 2.4 L;Fig. 3). Individual differences ranged from −5.5 to 6.5 L [T̄×_{Diff} = 0.0 ± 2.4 L (SD)]. Substituting TBW_{BIA} for TBW_{D2O} in estimating body fatness using the three- and four-component models resulted in similar mean values for %BF_{3C-BIA} and %BF_{4C-BIA} compared with %BF_{4C-D2O} (Tables 3). However, individual differences were substantial, with differences between %BF_{4C-D2O} and %BF_{3C-BIA} ranging from −7.1 to 5.0%BF and between %BF_{4C-D2O} and %BF_{4C-BIA} ranging from −5.6 to 5.5%BF (Table 4, Figs. 4 and 5).

Compared with the criterion method, %BF_{4C-D2O}, the accuracy of estimating %BF from three- and four-component models that included TBW_{BIA} was comparable to the accuracy of estimating %BF from body density alone and much poorer than the accuracy of estimates from a three-component model including TBW_{D2O}. The SD_{Diff} between %BF_{4C-D2O} and %BF_{3C-BIA} (2.4% BF) was similar to the SD_{Diff} between %BF_{4C-D2O} and %BF_{2C-D} (2.3% BF, *P* > 0.05, Table 4). In addition, the SD_{Diff} between %BF_{4C-D2O} and %BF_{4C-BIA} (2.3% BF) was comparable to the SD_{Diff} between %BF_{4C-D2O} and %BF_{2C-D} (2.3% BF, *P* > 0.05, Table 4). The SD_{Diff} between %BF_{4C-D2O} and %BF_{3C-BIA} (2.4% BF) and between %BF_{4C-D2O} and %BF_{4C-BIA} (2.3% BF) were much greater than the SD_{Diff} between %BF_{4C-D2O} and %BF_{3C-D2O} (0.5% BF, *P* < 0.05, Table 4).

## DISCUSSION

The primary objective of this study was to determine whether estimates of body water from bioelectrical impedance analysis could be substituted for estimates of total body water from deuterium dilution in estimating body fatness from multicomponent models without significant loss in accuracy. A related objective was to determine whether estimates of %BF from body density and TBW_{BIA} were more accurate than those from body density alone, using %BF_{4C-D2O} as the criterion. The primary findings of the study are that, despite a strong relation between TBW_{BIA} and TBW_{D2O}, estimates of %BF from three- and four-component models using TBW_{BIA} were considerably less accurate than estimates from the same models using TBW_{D2O} and were not more accurate than estimates from body density alone using a two-component model.

The accuracy of estimating TBW_{D2O} from single-frequency BIA at 50 Hz in our study (r = 0.94, SEE = 2.4 L) was similar to that reported by others. Kushner and Schoeller ^{(15)} reported a multiple correlation of 0.99 and a SEE of 1.37 L for TBW_{D2O} predicted from height^{2}/BIA resistance at 50 Hz, weight and gender in a heterogeneous sample of 40 men and women. Van Loan and Mayclin ^{(24)} obtained a multiple correlation of 0.87 and a SEE of 2.9 L for TBW_{D2O} predicted from BIA resistance at 50 Hz, age, height, weight, and gender in 188 men and women. Lukaski and Bolonchuk ^{(17)} found a multiple correlation of 0.97 and a SEE of 1.5 L for TBW_{D2O} predicted using multiple regression from height^{2}/BIA resistance at 50 Hz, gender, weight, and age in 110 men and women. Heitmann ^{(12)} reported a multiple R of 0.92 and a SEE of 3.48 L in predicting TBW measured by deuterium dilution from height ^{2}/BIA resistance at 50 Hz, weight, gender, and age in 139 men and women. The strength of the relation of TBW_{D2O} and TBW_{BIA} in our data and in the studies discussed above indicate that TBW_{D2O} can be predicted quite accurately from BIA.

There was a strong relation of %BF_{2C-D} to the criterion %BF_{4C-D2O} (r = 0.99) with no systematic difference between the two estimates. However, the SD_{Diff} between the two estimates (2.3% BF) indicated substantial individual variation, as reported by others ^{(9,10,20,25,26)}. Taking into account differences in TBW_{D2O} by predicting %BF from body density and TBW_{D2O} using a three-component model substantially decreased this individual variation, reducing the SD_{Diff} to 0.5% BF. This reduction in error indicated that most of the differences between %BF_{2C-D} and %BF_{4C-D2O} were due to individual variation in W/FFM. Others have also reported very high relations between %BF_{4C-D2O} and %BF_{3C-D20}, and, due to the large percentage of FFM that water comprises compared with mineral, variation in W/FFM is more important than variation in M/FFM in contributing to differences between estimates of %BF_{4CD2O} and %BF_{2C-D}^{(3,4,6,19,25,26)}.

Substitution of TBW_{BIA} for TBW_{D2O} in estimating %BF using a three-component model significantly increased the error relative to the criterion (%BF_{4C-D2O}) and produced error comparable to that between the criterion and %BF_{2C-D}. The SD_{Diff} between %BF_{4C-D2O} and %BF_{3C-BIA} (2.4% BF) was comparable to the SD_{Diff} between %BF_{4C-D2O} and %BF_{2C-D} (2.3% BF), and much larger than the SD_{DIFF} between %BF_{4C-D2O} and %BF_{3C-D2O} (0.5% BF).When TBW_{BIA} was substituted for TBW_{D2O} in estimating %BF using a four-component model, the error was comparable to that between the criterion and %BF_{2C-D}. The SD_{DIFF} between %BF_{4C-D2O} and %BF_{4C-BIA} (2.3% BF) was the same as the SD_{DIFF} between %BF_{4C-D2O} and %BF_{2C-D} (2.3% BF), and it was much larger than the SD_{DIFF} between %BF_{4C-D2O} and %BF_{3C-D2O} (0.5% BF).

The finding that errors in estimating body fat from multicomponent models that included TBW_{BIA} were larger than those from body density alone was particularly surprising and indicates that using TBW_{BIA} apparently introduces new error that offsets any theoretical advantage of taking into account variation in body water when predicting %BF from body density. These data unequivocally indicate that despite the high relation between TBW_{D2O} and TBW_{BIA}, the magnitude of individual differences between TBW_{BIA} and TBW_{D2O} are such that it is not advantageous to substitute TBW_{BIA} for TBW_{D2O} in estimating body composition from multicomponent models. Using TBW_{BIA} in conjunction with body density, or body density and body mineral, in estimating %BF using a multicomponent model is not better than predicting %BF from body density alone.

The interpretation of results of this study are based on the assumption that estimates of TBW from deuterium dilution and estimates of %BF_{4C-D2O} are error-free criterion measures. Although these are among the best estimates of body composition available, this is obviously not the case. Day-to-day biological variation and technical errors contribute to variation in these measures. The coefficient of variation for repeated measures of TBW_{D2O} in our hands and by others is 1–2%, and differences from values determined by desiccation have ranged from 2 to 6%^{(22)}. Of particular concern in validation studies in which the four-component model has been used as the criterion is the possibility that propagation of errors associated with the three measures used in the calculation of %BF_{4C-D2O} may negate the advantage of measuring more of the sources of variability. We ^{(19)} and others ^{(9)}, however, have reported that errors associated with these measures are quite small, with the within-subjects SD for replicate determinations of %BF_{4C-D2O} being approximately 1% BF. Thus, errors in the criterion measures should not comprise our basic conclusions.

We chose to evaluate the accuracy of substituting TBW estimated from BIA for TBW_{D2O} using a regression equation for predicting total body water developed on our sample, instead of using one of the many prediction equations available in the literature ^{(15,17,24)}. This approach provides the most accurate prediction of TBW_{D2O} from BIA, eliminating error due to sample differences, differences between studies in the methodology in measuring deuterium or BIA resistance. Most clinicians or researchers who would like to use TBW_{BIA} to estimate body composition using a multicomponent model will not have a local validation of TBW_{BIA}. If TBW_{D2O} is predicted from BIA resistance with an equation developed at another site with a different BIA analyzer and technician and on a sample with different characteristics, and used to estimate %BF with a multicomponent model, poorer accuracy than the results reported in this study would be expected. For example, we predicted TBW_{D2O} using the equation of Kushner and Scholler ^{(15)} and found that the agreement between our measured TBW_{D2O} and that predicted from their equation [r = 0.93, T̄×_{Diff} = 0.9 ± 2.6 L (SD) vs r = 0.94, T̄×_{Diff} = 0.0 ± 2.4 L (SD)], between %BF_{3C-BIA} and %BF_{4C-D2O} [r = 0.98, T̄×_{Diff} = −1.5 ± 2.7% BF (SD) vs r = 0.99, T̄×_{Diff} = −0.4 ± 2.4% BF] and between %BF_{4C-BIA} and %BF_{4C-D2O} [r = 0.98, T̄×_{Diff} = −0.8 ± 2.5% BF (SD) vs r = 0.99, T̄×_{Diff} = 0.2 ± 2.3% BF] were poorer compared with using TBW_{D2O} predicted from our equation.

The findings of this study have important implications for clinicians and researchers who need accurate estimates of body composition, particularly in individuals who may have alterations in W/FFM from that assumed by densitometry, such as children ^{(21)}, pregnant women ^{(13)}, the obese ^{(8)} or individuals who have edema or who may be on medication or nutritional supplements that alter the water content of the FFM, or certain groups of athletes ^{(19)}. Although estimation of TBW using BIA is attractive because of its ease, speed, and low cost, its accuracy in the general population is insufficient to be of value in providing estimates of body composition using multicomponent models that are more accurate than those from body density alone.

We conclude that, because estimates of %BF using multicomponent models with TBW estimated from BIA are not more accurate than from body density alone using a two-component model, estimates of %BF from three- and four-component models using TBW_{BIA} are not acceptable substitutes for estimates from the same models using TBW_{D2O}.

Address for correspondence: Ellen M. Evans, Ph.D., Washington University, School of Medicine, 660 South Euclid Avenue, Campus Box 8113, St. Louis MO 63110; E-mail: eevans@im.wustl.edu.

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**Keywords:**

BIOELECTRICAL IMPEDANCE ANALYSIS,; TOTAL BODY WATER