Introduction. N.J. Fuller, M.B. Sawyer and M. Elia

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1 lntemdonlll Journal of Obesity (1994) 18, ~12 C Macmillan Press Ltd 1994 Comparative.evaluation of body. composition methods and predictions, and calculation of density and hydration fraction of fat-free mass, in obese women N.J. Fuller, M.B. Sawyer and M. Elia MC Dunn Clinical Nutrition Centre, Hills oad, Cambridge CB2 2DH, UK The objective of this study was to apply a three-component model of body composition to a group of obese women In order to (a) establish the relative value of a number of readily available prediction equations by comparison of the extent of agreement between these predictions and body composition estimated by the model and other reference methods and (b) evaluate density and hydration of fat-free mass. Estimation of body composition was carried out by reference methods and prediction equations and the usefulness of these prediction equations for application speclflcally to obese women was evaluated. The subjects were 15 obese, otherwise healthy, Caucasian women (body mass Index> 30kg/m 2 and body fat> 40% of body weight, as orlglnally determined using densitometry). Body composition was estimated using three established reference methods (deuterium dilution which primarily measures total body water, densitometry for body fat and fat-free mass and total body potassium) and the three component model constructed from deuterium dilution and densitometry. Density and hydration fraction of the fatfree mass were calculated from appropriate values obtained as Integral parts of the three-component model. In addition, body composition was predicted from various prediction equations Incorporating weight and height (some of which Include a factor for age), from a number of prediction equations utilizing different terms Involving the same whole-body blo-electrlcal Impedance measurement and from measurements of sklnfold thickness and near Infrared lnteractance. The extent of agreement between methods was assessed using bias and 95% limits of agreemenl Mean density of fat-free mass was found to be kg/i (s.d kg/I) with a range of to kg/i, and mean hydration fraction was (s.d ) with a range of hydration from 88.2% to 75.1% (all values were calculated from the three-component model). In general, the reference methods (densitometry, deuterium dilution, the three-component model and total body potassium) demonstrated better agreement with each other than with the prediction methods or equations. In these obese women, sklnfold thickness measurements are apparently less reliable (large bias and 95% limits of agreement) than In the lean subjects of a variety of other studies. A majority of'lnterpretatlons of weight and height measurements and predictions Incorporating Impedance/resistance measurements are apparently not applicable to this group of obese women, due to large values for both bias and 95% limits of agreemenl For body fat estimation (% body weight), for example, the bias between reference methods and weight/height prediction equations ranged from-12.5% to 8.4%, with 95% limits of agreement up to 15.8%; and the bias between reference methods and predictions incorporating whole-body bio-electrlcal Impedance ranged from -7.6% to 8.1%, with 95% limits of agreement up to 24. 7%. The results of this study suggest that there Is no compelling reason, on the basis of the threecomponent model, to change the traditional value of 1.1 kg/i for use In densitometry with obese female lndlvlduals. It fs also suggested that, there Is apparently a large and unacceptable variability In estimates of body composition obtained by the various prediction equations applied here, and that there Is a particular risk Involved In applying prediction equations, orlglnally derived In lean Individuals, to obese women., Keywords: body fat, total body water, bias and 95% limits of agreement Introduction There are many different simple or convenient methods and prediction equations available which claim to predict reference method assessments of body composition accurately and reproducibly.' A series of body composition studies in non-obese individuals carried out in our laboratory, have shown that there is a large range of possible predictions of body composition through the use of different methods, or even different interpretations of the same measurements, for example weight, height and whole-body bio-electrical impedance. 1 ~ However, a comprehensive comparative assessment of the extent of agreement between these predictions and reference methods or multi-component reference models has yet to be established. With few exceptions 7 there is also a paucity of information regarding the relative value of these predictions in groups of obese subjects. 5 Moreover, since some measurements may be difficult to obtain accurately and precisely in the obese (e.g. skinfold thicknesses), the application of the apparently reproducible whole-body bio-electrical impedance measurement may prove to be more appropriate in this group. However, since the numbers of overweight or obese individuals have been included to a varying extent in the derivation of prediction equations, the use of those equations based on weight, height and bio-electrical impedance may be inappropriate in the obese and lead to substantial errors in assessment of body composition. In addition, there is quite often a lack of basic information provided by the manufacturers of certain commercially available bio- Correspondence to: N.J. Fuller. eceived 13 October 1993; accepted 12 January 1994

2 504 electrical impedance instruments regarding their calibration procedures and the origins of their equations. Furthermore, ' although some manufacturers claim that their particular technique is applicable to a wide variety of individuals or groups, including lean and obese adults, extending their use beyond the range over which they were derived may be inappropriate. The primary aim of this study was to evaluate the validity and reproducibility of a large number of different prediction equations for body composition assessment in a specific group of obese, otherwise healthy, Caucasian women by comparison with a three-component (fat, water, and protein plus mineral 4 ) model and other traditional reference methods. These particular prediction equations incorporate terms involving weight and height only or have additional terms involving bio-electrical impedance/resistance mea ~urements, and were assessed irrespective of whether or not they were intended for use exclusively in females or in the obese. Ultimately, it was intended to identify those that are most suitable for use with obese women. The secondary aim of the study was to establish both mean values and extent of variation in the density and hydration fraction of fat-free mass using the three-component model. These values have major implications for the interpretation of measurements obtained by two-component models of body composition (densitometry and deuterium dilution) which has been a matter for some debate in lean 4 8 and, especially, in obese subjects Methods Subjects The characteristics (mean ± s.d.) of the fifteen obese, otherwise healthy, Caucasian female subjects who volunteered for the study are shown in Table 1. The criterion for inclusion of subjects in the study were that each should be 40% fat or more, as estimated bv densitometry (see below). All measurements were performed on all subjects within about a six hour period following an overnight fast. Approval for the study was granted by the Ethical Committee of the Dunn Clinical Nutrition Centre, and all subjects gave their informed consent. Weight and height Body weight (Wt - kg) was determined using a Sauter Type El210 electronic scale with digital readout, accurate to O.lg (Todd Scales, Unit 4, Studlands Park Industrial Estate, Newmarket, Suffolk, UK), and height was measured to the nearest 0.5 cm using a wall mounted stadiometer (Holtain Ltd., Crosswell, Crymych, Dyfed, Wales SA41 3UF). Densitometry Body volume (BV = body weight - under-water weight) and body density (d = Wt I BV) were obtained using the under-water weighing technique of Akers and Buskirk with a modified helium dilution technique to account for lung volume. 2 Fat(% body weight) and fat-free mass (FFM - kg) were calculated from body density using the equation of Siri 11 : Fat (% body weight) = 4 ~ 5-450, which assumes constant mean densities of these gross body components (0.9kg/l and l.lkg/l, for fat and fat-free mass, respectively). Fat mass (kg) %Fat x Wt FEM (kg) = Wt - Fat mass Total body water was calculated from the densitometric estimate of fat-free mass by assuming that the hydration fraction of fat-free mass is 0.72,1 1 or 72%. Deuterium dilution Total body water (TBW) was measured using deuterium dilution space. 3 Fat-free mass was estimated by assuming that the hydration fraction of fat-free mass is 0.72,1 1 and body fat mass (kg) was determined by difference between body weight and fat-free mass. Fat mass (kg) = Wt (kg) - FEM (kg) Fat (%Wt) _ Eat mass 2!' Wt Table 1 Characteristics of the subjects (mean, standard deviation and range, unless otherwise stated) Age (years) Weight (kg) Height (mj Body density (kgll) Total body water 0) Total body potassium (mmol) Lean body mass (leg) Body fat (% body weight) Whole bqdy impedane!! (Ohms) Mean : s.d. Estimated using the thru-component model. 43 Jmedlan) :I: 29.6 l.63:t :t :t :t 1.S.O.S6.6 :t :I: ± 45 ange S - 16.S l.(j!) I.Oil S J - 5.S6 Three-component model Body composition, in terms of body fat and fat-free mass, was assessed using a three.component model, 4 which assumes that the body can be divided into fat, water and fat free dry mass (protein plus mineral), and that utilises direct measurement$ of body weight (Wt), body volume (BV - from densitometry) and totaj body water (TBW from deuterium di lution pacq); Fat mass (kg) :::::: 2.220BV (1 ) TBW (1) Wt (leg) Fat(% Wt) and fat-free mass (kg) were calculated as above. Calculation of the density of fat-free mass (Dffei): Elements of the three-component model were combined to

3 505 enable a simple calculation of the density of fat-free mass 4 : Mass of body water (kg) + Mass of fat-free dry matter (kg) DITm (kg/i) =-v-o_l_u_m_e_o_f_b_o_d_y~w-a-te_r_(_l_) -+~V-o...,1-um-e of fat-free dry matter (1) Calculation of the hydration fraction of fat-free mass (HFffin): Hydration of the fat-free mass was calculated from body water and fat-free mass 4 : HF _ Mass body water (kg) ffm - Fat-Free mass (kg) Hrtm (%) = HFrtm x 100 Total body potassium measurement Total body potassium (TBK) was determined from whole body measurement of radioactive potassium ( 4 K) in a whole body counter (Department of Nuclear Medicine, Addenbrooke's Hospital, Cambridge), by assuming a constant proportion (0.0012% 12 ) of 4 K existing in all naturally occurring potassium. The effect of attenuation was accounted for by applying an (unpublished) equation, originally derived in a sample consisting mainly of obese subjects using 42 K. Fat-free mass was estimated from TBK assuming that the fat-free mass of women contains a constant 2.34g/kgFFM or 60mmol/kgFFM. 13 Total body water and body fat (as % body weight) were calculated from fat-free mass, as above. Weight/height/age prediction equations Body composition was estimated from a number of published prediction equations incorporating simple anthropometric measurements. Those equations incorporating a measure of body mass index (Wt/Ht 2 - also known as BMI or Quetelet's Index):- (1) (2) % Fat= 1.48Wt _ 7.0 (derived by T.P. Eddy 14 ) Ht 2 (m) % Fat = Ht2 (m}_ Wt (rearrangement of the equations relating body fat to a combination of density, deuterium dilution and total body potassium estimations of fat, derived mainly from women attending an obesity clinic reported by Garrow and Webster) 15 (3) % Fat =.L.20Wl _ 0.23A Ht 2 (m) Those equations incorporating separate tenns involving weight, height and age: (4) FFM (kg)= 0.069Wt Ht A (unpublished equation derived from data of Pullicino et al. )3 (5) TBW (1) = 0;236Wt Ht ~ 0.027A (derived from anti-pyrine distribution volume) 17 (6) TBW (kg)= 0.24Wt Ht- 0.03A-13.9 (tritiated water space) 18 (7) FFM (kg) = O. l 50Wt Ht A (rearrangement from equations derived from total body potassium measurements reported by Boddy et al.) 19 Equations incorporating terms containing weight and height only:- (8) FFM (kg)= 0.035Wt Ht (unpublished equation derived from data of Pullicino et a/.)3 (9) TBW (I) = O. l 84Wt Ht ( 10) TBW (I) = O. I07Ht Wt And, an equation with weight and age terms only:- (11) TBW (kg)= 0.698Wt Wt A.Wt (rearrangement of equations reported by Moore et a/.) 22 where; Ht = height (cm, unless otherwise indicated as m), Wt= weight (kg) and A= age (years). Assessment of gross body components was obtained directly from these specific equations. However, where this was not possible, fat (or fat-free mass) was obtained from the difference between body weight and fat-free mass (or fat); and body water was obtained from fat-free mass (or vice versa) assuming that the hydration fraction of fat-free mass is Wherever necessary, the appropriate conversion was applied to ensure consistency between the different estimates of total body water (equations use the units 1 or kg) assuming that the density of water is lkg/l at 36oC.4 Impedance/resistance Whole body resistance (with a small correction to obtain the appropriate impedance value, by accounting for reactance )2 23 was measured for all subjects in this study using a Valhalla model l 990b instrument (Valhalla Scientific, 9955 Mesa im oad. San Diego Ca USA). The accuracy and reproducibility of measurements obtained by this and all other instruments used in this study, to measure both standard resistors and whole-body resistance, had been established previously. 6 With the exception of Holtain Ltd.. none of the manufacturers of instruments used here had released details of their particular equations. Therefore, body composition was assessed (according to manufacturers' instructions) using the E-Z Comp 1500 (Cranlea and Co, The Sandpits, Acacia oad, Boumeville, Birmingham B30 2AH) and the Maltron Model BT-905 (Maltron Ltd.; PO Box 15, ayleigh, Essex SS6 9SN) by effecting an exact reproduction of the appropriate impedance/resistance

4 506 measurement (obtained from the Valhalla instrument) on the display of both these instruments, as described previously.6 In addition, the Bodystat-500 technique (Bodystat Ltd., PO Box 50, Douglas, Isle of Man, British Isles) enables whole-body impedance to be obtained manually, before interpretation in terms of body composition by means of a discrete computer program available on disk. This same impedance/resistance value was incorporated into a number of previously published equations. Those equations which are specific for females:- (12) FFM (kg)= 0.475Ht Wt (Lohman, 1988; reported by Graves et al. 24 ) (13) FFM (kg)= 0.821Ht (14) FFM (kg)= Ht Wt (JL Systems Incorporated, Detroit, MI USA 26 ) (15) FFM (kg)= Ht Wt A (Segal et al equation derivation included a number of obese women) ( 16) FFM (kg) _ 0.698Ht s -. (17) FFM (kg)= Ht Wt A (Gray et al equation for non-obese women) ( 18) FFM (kg) = o. 3 ~Ht Wt (Ht - 100) !3 (19) FFM (kg)= Ht Wt A (20) TBW (l) = 0. 3 ~ 2 Ht Wt + 8._ (21) TBW (kg) = il.24ht 2 + O. I 72Wt + O. I 65Wt Equations which are fat~ spec ifi c for obese women:- (22) FFM (kg)= Ht Wt A (Segal et al equation for obese women) (23) FFM (kg) = Ht Wt A (Gray et al equation for obese women) Miscellaneous -equation_s, some of which are non-sex or non-fat specific or were originally derived in men:- and; (24) TBW (l) = o Ht z (Holtain Ltd 2 ) (25) TBW (I)= Ht (calculated from data in men provided by Hoffer et al. 33 ) (26) TBW (I) = Q,Qlli (Lukaski et al equation derived in men) (27) Body density (d) = Wt. 34 Ht 2 % Fat= fil d (28) % Fat= CZ. WO Ht2 where; Z =impedance (Ohms), =resistance (Ohms), Ht =height (cm) and Wt= weight (kg). Wherever possible, assessment of body composition was obtained directly from available instruments or from specific equations. However, where this was not possible, fat (or fat-free mass) was obtained from the difference between body weight and fat-free mass (or fat); and total body water was obtained from fat-free mass (or vice versa) assuming that the hydration fraction of fat-free mass is Again, the appropriate conversion was applied to ensure consistency between the different estimates of total body water (equations use the units I or kg) assuming that the density of water is kg/I at 36 C. 4 Skinfold thickness measurements Skinfold thicknesses were measured using standard calipers (Holtain Ltd.) at four sites (biceps, triceps, supra-iliac and subscapular) following the method of Durnin and Womersley. 36 Body density was predicted from the sum of the four skinfolds, and body fat calculated from body density (as above). Near infra-red interactance Body fat was estimated from measurement of near infra-red interactance (NII) at the biceps, as previously described by Elia et al. 37 Statistics The biitii lilld 95% limit of 1agreement between ferenc_ methods and the al ternative prediction technique or equations were calculated according to the method described by Bland and Altman 38 - please note that this statistical method indicates whether or not an alternative assessment can acceptably repr-uduce estimates that would have been

5 507 obtained by using an existing assessment method; although, in this study, reference methods were selected as the basis for comparison, this statistical approach does not involve any preconceived assumptions about which method is correct, neither does it assess potential relationships which might exist between estimates obtained by different assessments. Possible relationships between the magnitude of the estimate and the difference between methods were scrutinized.38 esults Comparisons of methods (bias and 95% limits of agreement) for estimates of body fat (% body weight), fat-free mass (kg) and total body water (l), are presented in Tables 2, 3 and 4 for reference methods, weight/height prediction equations and whole body impedance/resistance prediction instruments and equations and skinfold thickness and near infra-red interactance measurements, respectively. In general, wherever there was a positive or a negative bias between a particular reference method and its prediction from specific measurements, this was also found to be true for all the alternative reference methods and the same interpretation or prediction (see Tables). eference methods (three-component model, densitometry, deuterium dilution and also total body potassium) provided better estimates of the body composition assessments obtained by other reference methods than predictions based on alternative bedside methods (equations incorporating weight and height, whole-body bio-electrical impedance or resistance, skinfold thicknesses and near infra-red interactance). Tables 3 and 4 show the bias and 95% limits of agreement between the reference assessments of body composition and equations incorporating various combinations of weight and height (Table 3), bio-electrical impedance/resistance measurements (Table 4) and skinfold thickness and near-infra-red interactance measurements (Table 4). These Tables also indicate which reference method was used to derive the particular prediction equation and the sample type or population on which it was originally based. Clearly, application of the vast majority of these interpretations to the obese subjects in this study is associated with substantial errors. This is demonstrated by large limits of agreement between methods, irrespective of the magnitude of the particular bias. In a majority of instances this poor agreement was demonstrated despite the presence of very good associations between estimates (correlation coefficients of associations between methods were all very high, often in excess of not shown). In many instances (indicated in the Tables by a superscript + or -) the difference between methods became more positive (+) or more negative (-) with increasing magnitude of the estimate. However, in no instance did the difference between methods become obviously larger or smaller with increasing magnitude of the estimate and so the use of log plots was not indicated. 38 With the use of the three-component model, the density of fat-free mass was found to be ± kg/i (mean ± standard deviation), with a range of kg/i. The hydration fraction of fat-free mass was ± (i.e. 71.2% ), with a range of l %. Discussion The extent of variability in density and hydration fraction of the fat-free mass of a specific group of obese, otherwise healthy, Caucasian women was assessed using values obtained with the three-component model. Because of the nature of body composition calculations, the apparently narrow ranges of results for the fat-free mass observed here (mean density kg/i, range kg/i to kg/i; mean hydration 71.2%, range 68.2% to 75.l % ) outwardly conceal major implications for individuals using multicomponent models. Small discrepancies in the density of fat-free mass of about kg/i, for example, will result in body fat estimates being in error by about 2.5% fat as % Table 2 Comparison of various body composition assessments obtained using reference methods (see text)*: bias and 95% (± 2 s.d.) limits of agreement"* eference methods Densitometry Deuterium dilution Three-component model (a) Body fat{% body weight) Deuterium dilution (n;: 15) 1bree-component model (n = 15) Total body potassium (n = 13) ± ± ± ± ± ± 8.4 (b) Fat-free mass (kg) Deuterium dilution (n = 15) 1bree-component model (n = 15) Total body potassium (n = 13) 1.2 ± ± ± ± ± 8.s ± 7.9 *eference method/model assessment (top of Table) minus alternative method (left hand side of Table); *To obtain equivalent figures for comparison of estimates of total body water. multiply the values for fat-free mass by a factor of 0. 72; Values for the bias forfat-free mass as % of body weight are equal and opposite to those for % fat. and the 95% limits of agreement are equal for both. Those for bias for kg fat are equal and opposite to those for fat-fru mass, and the 95% limits of agreement are equal for both (see Bland and Altman. 1986); The differena between methods is significantly related to the magnitude of measurement (difference becomes more positive with increasing magnitude - see Bland and Altman, 1986).

6 508. Tllble 3 Comparison of various body composition assessments obtained using equations incol'.j)oratlng weights and heights (with or without a factor for age) against reference methods and three-component model (see text)*: bias and. 95% (:1: 2 s.d.) limits of agreement.. ; n = 15 Prediction equation derived against: Equation number.and source Densitometry Deuterium Three-component (see text) eference method Population dilution model (a) Body fat(% body weight) (I) Black et al. (1983) d Mainly lean/some obese -9.1± ± ± (2) Garrow and Webster (1985) TBW/d!fBK Mainly obese/some lean 0.5 ± ± ± 7.4 (3) Deurenberg et al. (1991) d Mainly lean/some obese ± ± ±11.5- (4) Pullicino et al. (1990) - with age TBW Mainly lean -11.7± ± ± 8.5 (5) Dossing et al. (1982) TBW Mainly lean 7.3 ± ± ±7.3 (6) Bruce et al. (1980) TBW Mainly lean 3.6± ± ± 6.9 (7) Boddy et al. (1972) TBK Mainly lean -5.4 ± ± ± 8.2 (8) Pullicino et al. (1990) - without age TBW Mainly lean -12.5± ± ± II.4- (9) Hume and Weyers (1971) TBW Mainly lean/some obese 0.5 ± ± ± 7.7 (10) Watson et al. (1980) TBW Lean and obese 1.8 ± ± :1: 7.4 (11) Moore et al. (1963) TBW Mainly lean :I: :I: :t: I0.4- (b) Fat-free mass (kg) (I) Black et al. (1983) d Mainly lean/some obese 12.0:t: 23.I 10.8 ± :I: 23.6 (2) Garrow and Webster (1985) TBW/d!fBK Mainly obese/some lean -0.7 ± :I: :I: 8.1 (3) Deurenberg et al. ( 1991 ) d Mainly lean/some obese 9.0± :I: 18.I+ 8.2 :I: 17.4 (4) Pullicino et al. ( 1990) - with age TBW Mainly lean 13.5 :I: :t: 11.? :I: 11.4 (5) Dossing et al. (1982) TBW Mainly lean - 8.1± ± ±9.1 (6) Bruce et al. (1980) TBW Mainly lean -4.3 :I: ± ±9.3 (7) Boddy et al. (1972) TBK Mainly lean 6.5 ± ± :I: 9.o+ (8) Pullicino et al. ( 1990) - without age TBW Mainly lean 14.6 :I: 14.o :I: ± (9) Hume and Weyers (1971) TBW Mainly lean/some obese -0.4 :I: ± :I: 7.8 (10) Watson et al. (1980) TBW Lean and obese -2.3 :t: IO.I ± ±9.4 (I I) Moore et al. (1963) TBW Mainly lean 4.5 :I: :I: ± 14. t *eference method/model assessment (top of Table) minus weight and height prediction equation (left hand side of Table); *To obtain equivalent figures for comparison of estimates of total body water, apply a factor of to the values shown for iat-free mass; **Values for the bias for fat-free mass as % of body weight are equal and opposite to those for % fat. and the 95% limits of agreement are equal for both. Those for the bias for Kg fat are equal and opposite to those for fat-free mass, and the 95% limits of agreement are equal for both (see Bland and Altman. 1986); The difference between methods is significantly related to the magnitude of measurement (difference becomes more positive with increasing magnitude - see Bland and Altman, 1986). -The difference between methods is significantly related to the magnitude of measurement (difference becomes more negative with increasing magnitude - see Bland and Altman, 1986). Abbreviations: d = densitometry TBW = Total body water TBK = Total body potassium Table 4 Comparison of various body composition assessments obtained using alternative prediction methods incorporating bio-electrical impedance (with or without weights and heights), skinfold thickness and near infra-red interactance measurements against reference methods and three-component model (see text)*: bias and 95% (:1: 2 s.d.) limits of agreement*"; n = 15 Equation number and source (see text) Prediction equation derived against: eference method Population Densitometry Deuterium dilution Three-component model (a) Body/at(% hotly weight) Bio-electrical impedance instruments (a) Valhalla I 990B (see Elia, 1992) Cbl Bodyst!t-500 (c) Maltron model BT-905 (d) E-Z comp ± l.9±7.6-6.i ± ± ± :I: ± :t: ± ± 6 Z ± ± 9.5- Equation number and source (see text) Prediction equation derived against: eference method Population (12) Lohman (see Graves et al. 1989) (13) Lukaski et al. (1986) d d Unreported Mainly lean/some obese (14) JL (see Van Loan and Mayclin, 1987) d Unreported (15) Segal et al. (1988) for non-obese d Lean (16) Deurenberg et al. (1989) d Unreported (17) Gray et al. (1989) for non-obese d Lean (18) Hodgdon and Fitzgerald (1987) d Mainly lean/some obese (19) Van Loan and Mayclin (1987) d Mainly lean/few obese (20) Kushner and Schoeller (1986) TBW Lean and obese (21) Heitmann (1990) TBW/TBK Lean and obese (22) Segal et al. (1988) for obese d Obese 6.9 ± :I: :I: ± :I: ± :I: :I: :I: 9.9 I.I :I: :I: :I: :I: :I: :I: ± :I: :I: :I: 8.s+ 2.0± :I: :I: :I: :I: ± :I: :I: ± ± :I: :I: :I: :I: 6.8

7 509 Table 4 Continued Prediction equation derived against: Equation number and source Densitometry Deuterium Three-component (see text) eference method Population dilution model (23) Gray et al. ( 1989) for obese d Obese -6.7 ± ± ±6.3 (24) Holtain (see Fuller and Elia, 1989) TBW Unreponed ± ± ± 9.0 (25) Hoffer (data from Hoffer et al. 1969) TBW Mainly lean/few obese -7.3 ± ± ±9.1 (26) Lukask.i et al. (1985) d Mainly lean/few obese -4.0± ± ± (27) Segal et al. (1985) d Lean and obese 3.2 ± ± ± 9.6- (28) Khaled (1988) d Mainly lean/few obese -4.1± ± 18.J ± Miscellaneous methods Sk.infold thickness (n = 15) 5.9 ± 10.J+ 7.1 ± ± 10.2 Near infra-red interactance (n = 11) 8.9 ± 7.7' 9.7 ± ±8.1 (b) Fatjree mass (kg) Bio-electrical impedance instruments (a) Valhalla 1990B (see Elia, 1992) 11.4 ± ± ± 34.9 (b) Bodystat ± ± 7.7 l.6 ± 7.2 (c) Maltron model BT ± I t ± ± 11.1 (d) E-Z comp ± ± I ± 10.2' Prediction equation derived against: Equation number and source (see text) eference method Population (12) Lohman (see Graves et al. 1989) d Unreponed ± ± ± 9.7- (13) Lukask.i et al. (1986) d Mainly lean/some obese 6.2 ± o ± ± 10.5 (14) JL (sec Van Loan and Mayclin, 1987) d Unreponcd -3.3 ± ± ±7.2 (15) Segal et al. (1988) for non-obese d Lean 0.8 ± ± ±7.1 (16) Deurenberg et al. (1989) d Unreponed 8.7 ± ± 11.5' 7.8 ± I t.4 (17) Gray et al. (1989) for non-obese d Lean 3.9 ± ± ±6.9 (18) Hodgdon and Fitzgerald (1987) d Mainly lean/some obese -6.I ± ± ± 9.8- (19) Van Loan and Mayclin (1987) d Mainly lean/few obese -6.6 ± ± ± (20) Kushner and Schoeller ( 1986) TBW Lean and obese ± l.7 ± ± 7.5 (21) Heitmann (1990) TBWrrBK Lean and obese - l.4 ± ± ± 7.7 (22) Segal et al. (l 988) for obese d Obese 0.0 ± ± ± 8.5 (23) Gray et al. (l 989) for obese d Obese 7.4 ± ± ± 7.0 (24) Holtain (see Fuller and Elia, 1989) TBW Unreponed 9.0 ± J J ± 10.s+ 8.2 ± 10.5 (25) Hoffer (data from Hoffer et al. 1969) TBW Mainly lean/few obese 8.7 ± ± ± 10.s+ (26) Lukask.i et al. (l 985) d Mainly lean/few obese 5.2 ± ± ± 10.1 (27) Segal et al. (l 985) d Lean and obese -2.6 ± ± ± 9.8 (28) Khaled (1988) d Mainly lean/few obese 6.9 ± ± ±24.2 Miscellaneous methods Sk.infold thickness (n = 15) ± ± ± Near infra-red interactance (n = 11) ± ± i.5 ± *eference method/model assessment (top of Table) minus alternative method (left hand side of Table); *To obtain equivalent figures for comparison of estimates of total body water, apply a factor ofo. 72 to the values shown for fat-free mass; **Values for the bias for fat-free mass as % of body weight are equal and opposite to those for % fat, and the 95% limits of agreement are equal for both. those for the bias for Kg fat are equal and opposite to those for fat-free mass, and the 95% limits of agreement are equal for both (see Bland and Altman, 1986); The difference between methods is significantly related to the magnitude of measurement (difference becomes more positive with increasing magnitude - see Bland and Altman, 1986). -The difference between methods is significantly related to the magnitude of measurement (difference becomes more negative with increasing magnitude - see Bland and Altman, 1986). Interprets impedance in terms of body density and then to estimates of body composition. Abbreviations: d = densitometry 1HW = Total body water TBK =.Tota/body potassium body weight (in a reference man of 15% fat as body weight, this represents a relative error of about 17% ). The ranges of values obtained reflect, in part, biological variation and, in part, precision of methodology (precision for the reference methods used here has been reported previously4). In this study, methodological imprecision 4 in estimating the density (s.d kg/i) and hydration (s.d. 0.7%) of fat-free mass accounts for less than one half of the measured variability (s.d kg/i and s.d. 1.6%, respectively). Therefore, biological variation makes an important contribution to variability in these estimates. However, despite this variability, the calculated mean value (1.104 kg/i) for the density of fat-free mass is close to that constant (1.1 kg/i) traditionally used in densitometry and also close to the mean value (l.097 kg/i, s.d kg/i) obtained for a group of non-obese women (calculated, using the threecomponent model, on the data of Fuller et al. 4 ) Therefore, we feel that there is no compelling reason to change the classic assumptions or calculations pertaining to estimation of body composition in obese women by densitometry.

8 510.. Deurenberg et al. 9 had previously proposed such a revision based on the assumption that additional water (protein and mineral is assumed to remain constant) associated with excess adipose tissue deposition would increase the mean hydration fraction of fat-free mass (not observed in this study) and consequently decrease its density (also not observed here). The hydration of fat-free mass obtained in this study (71.2%) was close to that traditional value (72%) proposed by Siri, 1 1 and that calculated from data presented previously (73.0%) in lean women. 4 However, the suggestion that there may be a need to change the traditional assumptions and calculations used in the obese was not based on actual estimates of the hydration fraction and density of the fat-free mass, but on speculative assumptions. Fuller and Elia 10 argued that obesity is not only associated with excess water, but it may also be associated with additional protein and mineral which would tend to increase the density of fat-free mass and counteract the effect of the extra water. (Despite the observed differences between obese and lean women being apparently of little material importance, it should be noted that the mean density of fatfree mass was significantly higher, P < 0.01, and the mean hydration significantly lower, P < 0.01, in this group of obese women: and, although small, this trend is in the opposite direction to that proposed by Deurenberg et al.) 9 The outcome of any debate surrounding the extent of these changes, and their concomitant effect on the density of the fat-free mass, 10 is the apparent need for more detailed measurements using the four (or more) - component modei 1.4 which incorporates direct measurements of total body bone mineral. Although the four-component model is limited by an assumed constant ratio of total body bone mineral to total body mineral, its use negates the need for assuming a constant ratio of protein to total body mineral (a central assumption of the three-component model) which may not be universally applicable and, in particular, this ratio may differ between lean and obese women. Nevertheless, if the ratio of protein to mineral was to change by about 20%, this would only effect the estimated density of fat-free mass by about kg/l to kg/l. Of the body composition techniques that were not incorporated into the construction of the three-component model, total body potassium appeared to provide the best agreement with the established reference methods. This is despite the poor precision (> 5% 39 ) associated with total body potassium counting which may be due to the two relatively insensitive sodium iodide crystals used for detecting 40 K emissions. Furthermore, the extent of attenuation of these emissions is probably greater in the obese than in lean subjects, and so geometric considerations assume greater significance in this group. The better agreement between total body potassium and reference method estimates of body composition obtained in this group of obese subjects, compared to the non-obese group studied previously, 4 may be explained, in part at least, by the fact that calibration of the AOK counter was achieved against 42 K in a group consisting predominantly of obese individuals. Furthermore, there is some debate surrounding the most appropriate value to apply as constant for the potassium content of fatfree mass (discussed by Burkinshaw and Cotes 40 ). In this study, an assumed constant value for females of 60 mmol/kgffm 13 was applied. A slight discrepancy of only 2 mmol/kgffm could contribute a mean systematic error of 2.1 % fat (as body weight) in this particular group of obese women (mean weight 112kg and 48% fat). In contrast, skinfold thicknesses are notoriously more difficult to obtain and interpret in the grossly obese. There may be major practical difficulties (limited size of_ calipers, site location differences, variation in compressibility and so on) that conspire to create poor reproducibility. The inter-observer reproducibility for skinfold thickness measurements in nonobese subjects is known to be relatively poor in comparison with some other bedside techniques, 41 and is probably more so in the obese. In addition, relatively few grossly obese subjects were involved in the original derivation of equations intended to interpret skinfold thickness measurements in terms of body density and body composition, 36 and so some of our subjects may have been outside the reliable range (see Lohman, 42 for a comprehensive review of different interpretations of skinfold thickness measurements). Of the anthropometric prediction equations incorporating body mass index (Table 3), that of Garrow and Webster 15 apparently agrees most closely with body composition estimated by densitometry, deuterium dilution and the threecomponent model. This is not surprising since this equation was derived from a sample population which consisted of a number of women attending an obesity clinic. We are also able to confirm the observation of Deurenberg et al. 16 that their prediction equation actually overestimates body fat when applied to the obese (Table 3), which supports the view that prediction equations should only be applied to appropriate populations. The other exclusively anthropometric prediction equations examined in this study contain terms involving weights and heights as separate entities. In general, those predictions that were derived against measures of total body water using isotope dilution techniques are better predictors of reference methods and the three-component model than those equations attempting to predict fat-free mass and that were derived against densitometry. In fairness, few of these equations were derived in sample groups containing obese subjects, nor was their use in the obese necessarily advocated by these particular authors. The Moore et al. 22 equation does not, involve height, which might explain its lack of agreement with the reference methods (although height in conjunction with weight may provide an index of body fat, height alone should not be considered to be an independent indicator of adiposity) In addition, the equation of Dossing et al. 17 was regressed against antipyrine distribution space, which may not accurately reflect either isotope dilution space or total body water space. Interpretation of bio-electrical impedance measurements in terms of body composition has been advocated for both lean and obese subjects. Previous studies from our laboratory have shown that use of only certain of the many available bio-electrical impedance predietions are valid in nonobese subjects, but obese subjects were not always included in these particular evaluations. In this study, which does compare predictions of body composition in obese females, the Bodystat-500 package appears to agree

9 511 better with the various reference methods, including the three-component model, than other commercial bio-electrical impedance packages, some of which may result in major inaccuracies (see Table 4). The bio-electrical impedance equations derived from studies in the obese (and,. therefore, advocated for use in the obese) appear to be the most promising Although the Gray et al. 29 obese specific equation has a relatively large bias, there is no obvious trend with increasing magnitude of the estimate, and so the bias could conceivably be removed to predict reference method estimates more accurately. 38 It should be noted that the non-obese specific equations of these same authors are almost as good predictors of body composition in this particular group of obese females as are the obese-specific equations. These comparative findings may reflect the relatively large numbers used in the comprehensive derivation of the Segal et al. 27 prediction equations. Wherever the use of particular prediction equations in obese females has not been openly advocated, no criticism of either the female specific, male specific or miscellaneous predictions (or equations derived from published data) is intended. However, if these non-specific equations were to be applied to groups of obese females by extrapolation (beyond the limits of their derivations), substantial errors could occur. Furthermore, for non-obese subjects it has been argued that no great advantage is gained with the inclusion of bio-electrical impedance in prediction equations incorporating weight and height over those that incor- eferences I Elia, M. (1992): Body composition analysis: an evaluation of 2 component models, multicomponent models and bedside techniques. Clin Nutr 11, Fuller, N.J. & Elia, M. (1989): Potential use of bio-electrical impedance of the 'whole body' and of body segments for the assessment of body composition: comparison with densitometry and anthropometry. 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