1Exercise and Health Laboratory, Faculty of Human Movement-Technical University of Lisbon, 1495-688 Lisbon, Portugal; 2New York Obesity Research Center, St. Luke's-Roosevelt Hospital, Columbia University Institute of Human Nutrition, College of Physicians and Surgeons, New York City 10025; 3Department of Medicine, Winthrop-University Hospital, Mineola, New York 11501; and 4John Hancock Center for Physical Activity and Nutrition, Friedman School of Nutrition Science and Policy at Tufts University, Boston, Massachusetts 02111
Submitted 1 June 2004 ; accepted in final form 1 June 2004
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ABSTRACT |
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body composition models; obesity; total body water; underwater weighing
Although approach of Behnke et al. (2) filled a critical methodology gap for body fat measurement, workers in the following two decades noted model concerns, notably the assumption that FFM density is constant across all subjects in health and disease, including in patients with severe obesity (8). The FFM component at the molecular body composition level includes total body water (TBW), protein (TBPro), soft tissue minerals (Ms), bone minerals (Mo), and glycogen (G) (25). Any actual subject differences in the proportions of these components from those assumed stable on the basis of cadaver studies by early two-component model developers (2, 3) will lead to fat and FFM estimation errors.
Siri in 1956 (22) and later in 1961 (23) derived a three-component (3C) model that accounted for variation in subject hydration by adding a TBW estimate to Behnke's two-component model (2). On the basis of data available at the time for five chemically analyzed human cadavers (11, 16, 26), Siri assumed that FFM consisted of two molecular level components, TBW, and a combined TBPro and total mineral (M, i.e., the sum of Ms and Mo) residual component. To complete the model, Siri suggested an M-to-TBPro ratio (i.e., ) of 0.35, as estimated from the five cadavers, with a corresponding density of 1.565 kg/l.
In recent years, Siri's 3C model (23) has been supplanted by more complex four- and six-component models as estimation of Ms and Mo became possible with in vivo neutron activation (IVNA) analysis (4, 6) and dual-energy X-ray absorptiometry (DEXA) (19). However, most DEXA and IVNA systems cannot accommodate subjects with severe or morbid obesity, leaving underwater weighing or the recently introduced air-plethysmography methods for body volume measurement, along with TBW measurement by isotope dilution, as viable means by which to quantify fat and FFM. Therefore, renewed interest is now directed to Siri's 3C model with the rising prevalence of obesity (29). This led us in the current study to critically evaluate Siri's 3C model (23) as it applies across sex, age, weight, and racial groups. We specifically focused our attention on the assumed value of and the related density of the combined compartment including M, TBPro, and G. IVNA analysis and DEXA techniques, unavailable during Siri's era, allowed us to evaluate Ms, Mo, TBPro, and G in a large sample of healthy adults.
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METHODS |
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The primary aim of this study was to compare the classical 3C model value (0.35) and related density (1.565 kg/l) proposed by Siri with the corresponding estimates provided by combined IVNA and DEXA measurements. After the initial health examination of each subject, a DEXA scan was performed at St. Luke's-Roosevelt Hospital in New York City. On the next study day, subjects underwent delayed-
and prompt-
IVNA analysis and whole body 40K counting at Brookhaven National Laboratory (BNL) in Upton, Long Island.
Subjects were a convenience sample of 323 healthy adults participating in other unrelated investigations. A physical examination and routine blood studies indicated that each of these individuals was in good health. The sex and racial distribution of this sample was dictated by the original planned studies.
In a second phase of our study, we examined potential biological errors inherent in the Siri formula compared with the new models developed in the initial study group. These errors were modeled for illustrative purposes in a second convenience sample of 293 healthy adults who had body volume and TBW measured by underwater weighing and deuterium dilution (2H2O), respectively, on the same day. These subjects participated in other ongoing investigations (18) and did not complete neutron activation analysis studies. The sample includes subjects at the extreme upper range of body weight, whose size necessitates the development and improvement of alternative practical evaluation methods. The investigation was approved by the Institutional Review Boards of St. Luke's-Roosevelt Hospital and BNL.
Body Composition Measurements
TBK.
TBK was estimated from the measured 1.46 MeV -ray decay of naturally occurring 40K, as TBK = 40K/0.000118 (17). Naturally occurring 40K was determined with the BNL whole body counter, which has a between-measurement coefficient of variation (CV) of 1% (4, 5).
TBN, TBCa, TBNa, and TBCl.
These elements were quantified using the IVNA analysis facilities at BNL (4, 10). Nitrogen was measured with 3.5 MeV neutrons provided by the prompt-
system from a collimated 238PuBe source positioned beneath the recumbent subject. Sodium iodide detectors quantify produced
-rays, H at 2.223 MeV and N at 10.83 MeV. Hydrogen is used as an internal standard to estimate TBN. The CV for repeated phantom measurements is 2.8% for TBN (10).
The BNL delayed- neutron activation system was used to measure TBCa, TBNa, and TBCl (10). Fast neutrons of
3.5 MeV are produced with 14 encapsulated 238PuBe sources positioned below and above the recumbent subject who is resting inside the irradiation chamber. The subject is irradiated with fast neutrons for 5 min and then moved to a counting area, where the following reactions are monitored for TBCa, TBNa, and TBCl: 48Ca + n
49Ca*
49Ca +
(3.10 MeV); 23Na + n
24Na*
24Na +
(2.75 MeV); and 37Cl + n
38Cl*
38Cl +
(2.17 MeV). The CVs for repeated phantom measurements of TBCa, TBNa, and TBCl are 1.5, 1.6, and 1.7%, respectively (9).
The subjects were scanned with a whole body DEXA system (Lunar DPX with software version 3.6, Madison, WI) at peak energies of 40 and 70 keV. The DEXA system software first divides pixels into bone mineral content (BMC) and soft tissue compartments. Soft tissue is then further separated by system software into fat-free soft tissue and fat. The BMC measured by DEXA represents ashed bone. One gram of bone mineral yields 0.9582 g of bone ash, because labile components such as bound water and carbon dioxide are lost during heating (12). Bone mineral was therefore converted to total body bone mineral (Mo = BMC/0.9582). The precision of the DEXA system used is 1.3% for bone mineral (14).
TBW. TBW, expressed in kilograms, was measured by deuterium dilution corrected for 4% isotope exchange and water density at 36°C (20).
BV. BV, expressed in liters, was determined by underwater weighing. Body weight during submersion was recorded by platform force transducers during a 5-s maximal expiration. After a series of practice trials, 10 runs were performed, and the density results were averaged. Corrections in density were made for residual lung volume by using a closed-circuit oxygen-dilution system described by Wilmore (27). Residual volume was measured immediately after the underwater weighing procedure. The CV between days for body volume technique is 1.7% body fat on the basis of repeated studies in five weight-stable individuals in this laboratory.
General 3C Model Derivation
Body minerals were quantified from total body amounts of Ca, K, Na, and Cl by a combination of whole body 40K counting and delayed- IVNA methods, and total body bone mineral (Mo) was quantified from DEXA. Specifically, soft tissue mineral (Ms) was calculated from TBK, TBNa, TBCl, and TBCa (all in kg) as (25, 13)
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According to Eq. 2, the M/TBPro ratio was calculated as
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Body mass (BM) and volume (BV) models can be written as
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Updated Siri 3C Model
Siri combined BM, BV, and TBW estimates in developing his 3C model (23). The model requires density estimates for the three components: fat, water, and residual mass. The original Siri 3C equation reported in 1961 (23) (FM = 2.118 x BV 0.780 x TBW 1.354 x BM) uses a value of 0.9000 kg/l for the density of fat and 0.9933 kg/l for the density of water at 37°C. Although body core temperature approximates 37°C, the average body temperature under basal conditions in a comfortable environment is 12°C lower (28). We therefore used 0.9007 and 0.9937 kg/l, respectively, for the densities of fat and water at 36°C (28). We adjusted Siri's original 3C model (23) accordingly:
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Statistical Methods
All group results are expressed as means ± SD. Analyses were carried out using the statistical program SPSS version 11.5 (SPSS, 2002).
The simple linear correlations between M and TBPro were examined, and the group mean TBPro and DRES residual mass density values were compared between men and women. One-sample t-tests were used to compare the mean densities of residual mass and the values between subjects in the present study and the mean values for subjects reported by Siri (23) (1.565 kg/l and 0.35). Independent sample t-tests were used to compare the mean DRES across sex and racial groups.
Multiple regression analysis was then used to develop DRES prediction equations with sex, age, weight, and race, and interactions between these variables as potential covariates. Separate analyses were carried out for males and females. Interactions of race with other variables were included in the models performed for each gender. Final sex and race combined DRES prediction equations were developed, and the normality of the residuals was tested.
Data from the independent subject group were used to compare estimates of %fat by use of adjusted and original 3C models across sex and racial groups and as a function of age and weight. The differences are illustrated with regression modeling and group mean comparisons by paired t-tests.
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RESULTS |
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Three hundred and twenty-three subjects, 293 females and 30 males, underwent the study protocol. From the female sample, 216 were Caucasian and 77 were African-American. In the male sample, 6 were Caucasians, 13 were African-American, 4 were Asians, and 7 were Hispanics. Subject characteristics for the model development sample are presented in Table 1. The table provides separate information on the Caucasian and African-American female sample, in addition to pooled values for all females combined. The males are presented as a single group due to its smaller size and a small number of subjects in each racial group.
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The model evaluation sample consisted of 264 subjects: 190 females (166 Caucasian and 24 African-American) and 74 males (31 Caucasians, 19 African-Americans, 17 Asians, 7 Hispanics). The characteristics of subjects in this group are presented for Caucasian and African-American females and pooled males in Table 2. The subjects in the evaluation sample ranged in weight from a low of 44.0 to a high of 107.9 kg, with a BMI mean and range of 27.8 ± 4.7 and 17.741.3 kg/m2, respectively. The age of this sample was 41.1 ± 13.5 yr, with a range of 1888 yr.
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Total body M was highly correlated with TBPro, accounting for 52.1 and 50.0% of the variation between individuals in M for the males (P < 0.001) and females (P < 0.001), respectively. The value for of 0.351 ± 0.043 for the whole sample matched closely Siri's proposed
value of 0.35 (P = 0.549) and did not differ significantly from this value in the pooled female sample (P = 0.174) or in the sample of Caucasian females alone (P = 0.116) (Table 1). However, a lower mean
was observed in the male sample (0.333 ± 0.045, P = 0.044), and a higher
(0.375 ± 0.036, P < 0.001) was present in the African-American females compared with Siri's
value of 0.35. Four of the cadavers reported by Siri (22, 23) were males, and one was a female.
The value of varied significantly with age and weight among the groups (Fig. 1). The value of
significantly increased with weight in the male and African-American female samples (r = 0.37, P = 0.045; r = 0.30, P = 0.007) but not in the Caucasian females (r = 0.12, P = 0.082). The
value was significantly lower with greater age in the Caucasian females (r = 0.42, P < 0.001) but not in the males and African-American females (r = 0.10, P = 0.588 and r = 0.11, P = 0.332, respectively).
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Propagated measurement error.
In the present study, we selected IVNA-estimated Ms, TBPro, and G as the criteria, because measurement precision is high for TBK, TBNa, TBCl, and TBCa. The error associated with measurement of the IVNA model components (Ms) can be estimated for the healthy subjects by assuming an average body composition, as shown in Table 1, and measurement precisions as stated in METHODS. Accordingly,
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In vivo observations. The DRES (Table 1) matched closely Siri's (23) proposed value of 1.565 kg/l for the whole sample (1.565 ± 0.023 kg/l) and for the pooled female subjects (1.566 ± 0.023 kg/l). However, the males and the Caucasian females had lower mean values, 1.555 ± 0.024 kg/l (P = 0.031) and 1.562 ± 0.022 kg/l (P = 0.042), respectively, and a higher mean DRES was observed in the female African-American subjects, 1.578 ± 0.019 kg/l (P < 0.001) compared with Siri's (23) value of 1.565 kg/l.
The relationships between DRES and age and weight are presented for males (age: r = 0.09, P = 0.629; weight: r = 0.38, P = 0.040) and females (Caucasian, age: r = 0.42, P < 0.001; weight: r = 0.12, P = 0.073; African-American, age: r = 0.11, P = 0.345; weight: r = 0.30, P = 0.007) in Fig. 2. Thus there were significant simple linear correlations between DRES and weight in males, between DRES and age in Caucasian females, and between DRES and weight in African-American females.
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Application to Independent Sample
TBW and BV were used to calculate FM with our adjusted 3C model coefficients and Siri's 3C model coefficients (23). The results are expressed as percent (%) FM.
The %FM difference was correlated with weight in males, African-American females, and Caucasian females and with age for Caucasian females (all P < 0.001, Fig. 3). There were no differences between the two %FM estimates for males at a weight of 80 kg, however. Siri's model overestimated %FM by 0.5% and underestimated %FM by 0.5% at weights of
60 and 100 kg, respectively.
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DISCUSSION |
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Siri developed his 3C model on the basis of the limited data available at the time (22, 23). We made minor revisions to his formula, as noted earlier (i.e., Eq. 14), for the density of fat and water values adjusted for average body temperature (36°C) rather than core temperature (37°C). Siri assumed residual mass consisted of two components, M and TBPro, that are present in the ratio (M/TBPro, ) of 0.35. This assumption of stable proportionality of M and TBPro then allowed calculation of DRES, an assumed constant in the 3C model. At the time of model development, Siri had values only for bone ash and TBPro on five cadavers, four males and one female. He applied this data with a rough estimate of mineral density (3 kg/l) to derive values for
and DRES. No corrections were made to convert the cadaver bone mineral ash to total mineral or to consider the separate contributions of soft tissue and bone minerals, limitations he acknowledged (22, 23).
Despite these rough cadaver-based estimates of and DRES, Siri's corresponding values and our own, derived using state-of-the art in vivo methods, are nearly identical. This apparent agreement is fortuitous, because our analysis applied four components of residual mass (i.e., Ms, Mo, TBPro, and G) rather than two as applied by Siri (i.e., Mo ash and TBPro), and our observations indicate that the sex, race, and age mix of a selected sample will significantly influence
and thus DRES.
An important speculation made by Siri was that the SD of in the general population was likely <0.1 (23). With this SD, he estimated the range of biological error to be only 12% of fat expressed as a percentage of body weight. For example, with a 30% change in
, the estimation error in fat mass will be as little as 2.0% of body weight. We confirmed Siri's estimation of M/TBPro variation in our subjects, who had an
range of 28 to 32% and an SD of only 0.043. These considerations, combined with the fortuitous agreement between Siri's DRES estimate and our own, suggest that Eq. 14 should serve, with limitations recognized, as a useful operational 3C model for general use.
Nevertheless, analysis of separate groups in our study revealed that DRES is not actually "constant" across subjects but varies predictably with sex, race, age, and weight. Accordingly, we developed sex- and race-specific DRES formulas to the extent possible given the limiting nature of our evaluated convenience sample. DRES tends to be lower in men (1.555 ± 0.024 kg/l) than in women (1.566 ± 0.023 kg/l), in old compared with young subjects, and in Caucasian (1.562 ± 0.022 kg/l) compared with African-American (1.578 ± 0.019 kg/l) females. Thus the specific features of our study sample, particularly the much larger number of women, ultimately determined the observed "average" DRES of 1.565. The DRES prediction models (Table 3) or these average DRES values (Table 1) could be used to develop more specific 3C fat mass estimation formulas for each of the respective groups.
When the developed sex- and race-specific formulas were applied to estimate the "errors" arising with application of Siri's 3C model, in general we observed deviations of less than 2% fat from those predicted from our "corrected" models. The magnitude of these error estimates can be viewed by taking an extreme example, elderly normal-weight Caucasian women compared with obese African-American women. The %FM estimate in elderly Caucasian women would be high by
1% and in the African-American women low by
1%, a difference of
2%. Although these are not relatively large errors in estimating relative fatness, the biases might become important when questions such as subtle race differences in resting energy expenditure are examined (21).
A related question, one that prompted the current study, is the %FM estimation errors arising when Siri's 3C model is applied in persons with severe obesity. To estimate these errors, we must extrapolate DRES estimates beyond those of the maximum model development group weight of 100 kg. This is a reasonable extension, as no curvilinear components were observed in our developed DRES prediction model in the present study cohort. We can estimate the expected error in %FM for males and African-American females by a simple extension of the regression lines presented in Fig. 3, which illustrates the differences between the original and corrected models when applied to an independent sample of subjects. Siri's model would underestimate %FM by 1.5 to 2.0% in males and African-American females when weights are in the severely obese range of 150200 kg. As noted earlier, these are not extremely large errors, but their significance must be judged in the context of the measurement application.
Study Limitations
The current study applied state-of-the art methods that allowed the first derivation of residual mass density in vivo. Nevertheless, there are some limitations of the present investigation. Our convenience sample did not have an adequate size, racial diversity, and weight variation to accommodate all of the issues surrounding 3C model development, although our findings do reveal potential sources of model error. Our analyses were based on a cross-sectional sample, and the extent to which subjects changing weight over time conform to the model predictions is unknown. We anticipate that our revised 3C model may find application to the study of body composition changes, for example, in subjects undergoing bariatric surgery, but such studies should be viewed with caution pending validation of the revised models on longitudinal data.
Conclusions
In the current study, we critically examined the classic Siri 3C model in living subjects. We corrected Siri's model on the basis of average body temperature values and established that, in general, this model is appropriate for use in adult women and men who range widely in race, age, and weight. More specific 3C models were also developed for use in males, females, Caucasian females, and African-American females. These subject-specific models may reduce body composition measurement bias when studies are aimed at detecting small between-group differences at the extremes of body size. These observations provide critical insights and practical opportunities for continued use of the 3C model in selected populations.
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GRANTS |
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FOOTNOTES |
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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.
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REFERENCES |
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