Potassium per kilogram fat-free mass and total body potassium: predictions from sex, age, and anthropometry

Am J Physiol Endocrinol Metab 284: E416 E423, 2003. First published October 15, 2002; 10.1152/ajpendo.00199.2001. Potassium per kilogram fat-free mass and total body potassium: predictions from sex, age, and anthropometry INGRID LARSSON, ANNA KARIN LINDROOS, MARKKU PELTONEN, AND LARS SJÖSTRÖM Department of Body Composition and Metabolism, The Sahlgrenska Academy at Göteborg University, SE-41345 Goteborg, Sweden Submitted 9 May 2001; accepted in final form 6 October 2002 Larsson, Ingrid, Anna Karin Lindroos, Markku Peltonen, and Lars Sjöström.Potassium per kilogram fat-free mass and total body potassium: predictions from sex, age, and anthropometry. Am J Physiol Endocrinol Metab 284: E416 E423, 2003. First published October 15, 2002; 10.1152/ ajpendo.00199.2001. Total body potassium (TBK) is located mainly intracellularly and constitutes an index of fat-free mass (FFM). The aim was to examine whether TBK and the TBK-to-FFM ratio (TBK/FFM) can be estimated from sex, age, weight, and height. A primary study group (164 males, 205 females) and a validation group (161 and 206), aged 37 61 yr, were randomly selected from the general population. TBK was determined by whole body counting, and FFM was obtained by dual-energy X-ray absorptiometry (DEXA; FFM DEXA ). The primary study group was used to construct sex-specific equations predicting TBK and TBK/FFM from age, weight, and height. The equations were used to estimate TBK and TBK/FFM in the validation group. The estimates were compared with measured values. TBK in different age ranges was predicted, with errors ranging from 5.0 to 6.8%; errors for TBK/FFM ranged from 2.7 to 4.8%, respectively. By adding FFM DEXA as a fourth predictor, the error of the TBK prediction decreased by approximately two percentage units. In conclusion, TBK and TBK/FFM can be meaningfully estimated from sex, age, weight, and height. body composition; dual-energy X-ray absorptiometry; potassium-40; total body potassium-to-fat-free mass ratio; randomly selected study groups BECAUSE 98% OF THE TOTAL BODY POTASSIUM (TBK) is located intracellularly (27), TBK is an excellent indicator of the respiratory cell mass of the body. TBK has therefore been the subject of intensive research during the last 50 years. In a classic paper from 1956 (9), Forbes and Lewis reported the potassium (K) content of two male corpses, (9, 11), one female corpse previously examined by Widdowson et al. (26) in 1951, and one adult carcass of unknown sex examined by Shol (20) already in 1939. The potassium content of these cadavers was 66.5 (male), 66.6 (male), 72.6 (female), and 66.8 (adult) mmol/kg fat-free mass (FFM), or an average of 68.1 mmol K per kg FFM. In a follow-up paper from 1961, Forbes et al. (7) reported TBK in 42 males and 8 females measured by means of a whole body counter. FFM was estimated as TBK/68.1, and body fat (BF) was calculated as body weight minus FFM. In males, percent BF was correlated with skinfold (r 0.80) and with the weight-toheight ratio (r 0.56). Although Forbes et al. did not specifically conclude that the potassium content of FFM is constant, the subsequent literature often interpreted these data as evidence that it was. More recently, several reports have indicated that the potassium content of the body is dependent not only on FFM but also on sex (8, 12), age (6, 13) and body build (asthenic vs. athletic) (5, 15, 18). Also, some studies based on underwater weighing (28) or computed tomography (CT)-based body composition (14, 21) have indicated that the potassium content per kilogram FFM may be lower than 68.1 mmol/kg. Taken together, these studies suggest that the relation between TBK and FFM is not as straightforward as previously assumed and that more sophisticated conversion procedures are required. FFM estimates based on TBK are dependent on a valid assumption of the potassium content per kilogram FFM. Therefore, our primary aim was to examine whether potassiumbased FFM determinations could be improved by using individual rather than fixed TBK-to-FFM ratio (TBK/ FFM) estimates. The individual TBK/FFM ratios were predicted from age, weight, and height by using the measured ratio as the dependent variable. TBK was determined using whole body counting and FFM by means of dual-energy X-ray absorptiometry (DEXA). Our secondary aim was to examine whether TBK could be predicted from age, weight, and height alone or with the addition of FFM determined by DEXA (FFM DEXA ). Such estimates are potentially important, because relatively few whole body counters are available worldwide. METHODS The Swedish Obese Subjects reference study. The Swedish Obese Subjects (SOS) reference study is an ongoing study including randomly selected middle-aged inhabitants of the Address for reprint requests and other correspondence: L. Sjöström, Dept. of Body Composition and Metabolism, The Sahlgrenska Academy at Göteborg Univ., SE-41345 Goteborg, Sweden (E-mail: lars.sjostrom@medfak.gu.se). 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. E416 0193-1849/03 $5.00 Copyright 2003 the American Physiological Society http://www.ajpendo.org

E417 city of Molndal, Sweden. The main purpose of the study is to obtain a reference sample for the SOS project (22). Other purposes of the study are to examine body composition, risk factors of cardiovascular disease, habitual dietary intake, and various aspects of quality of life in relation to age. The subjects were randomly selected from a population registry by use of a computer-based procedure. Each subject received a written invitation to a health examination along with an explanation of the purpose of the investigation. Between August 1994 and December 1998, 360 men and 452 women were examined (response rate: 52% in men and 57% in women). Of these individuals, 349 men and 423 women were examined with both DEXA and TBK techniques. Individuals showing large differences between measured body weight and the sum of DEXA compartments (see RE- SULTS and Fig. 1) were excluded. Thus 325 males and 411 females remained available. After allocation to age groups, these individuals were randomized to a primary study group (164 men and 205 women) and a validation group (161 men and 206 women). Anthropometry. All anthropometric measurements in this study were performed with the subjects dressed in underwear after an overnight fast. Body height was measured to the nearest 0.01 m with the subject standing back to a wall-mounted stadiometer in bare feet. Weight was measured to the nearest 0.1 kg with calibrated scales. Body mass index (BMI) was calculated as weight in kilograms divided by height in meters squared (kg/m 2 ). The following anthropometric measurements were also performed: waist and hip circumferences, sagittal trunk diameter, and thigh, neck, and upper-arm circumferences (22, 23). DEXA. Body composition by means of DEXA results in a three-compartment model consisting of bone mineral content (BMC), BF, and lean tissue mass (LTM) (25). BMC plus LTM corresponds to FFM with the TBK technique and several other two-compartment methods. The DEXA scanner used was a LUNAR DPX-L scanner (system no. 7156; Scanexport Medical, Helsingborg, Sweden) with software version 1.31 and with the extended analysis program for total body analysis (LUNAR Radiation, Madison WI). This scanner uses a constant potential X-ray source and a K-edge filter to achieve a congruent beam of stable dual-energy radiation. A quality assurance test was conducted on a daily basis, as recommended by the manufacturer (16). DEXA determines BMC, BF, and LTM without using body weight. Therefore, one way to validate the method is to compare the sum of the three body compartments with body weight. The manufacturer does not recommend examinations of individuals heavier than 120 kg, because the sum of BMC, BF, and LTM gradually lags behind weight at higher body weights. Precision errors of the scanner were determined by comparing results from two separate examinations of 10 healthy subjects. They were 1.7% for BF, 0.7% for LTM, 1.9% for BMC, and 1.5% for bone mineral density (BMD). One total body scan exposes the subject to a radiation dose equivalent to 0.5 Sv, which is in the lower range of radiation exposure measurements (17). For comparison, the radiation from one chest radiography is 80 times higher than a total body DEXA Fig. 1. Body weight minus the sum of bone mineral content, lean tissue mass, and body fat by DEXA (DEXA SUM) by body weight in the total study group. On the y-axes, the differences between body weight and DEXA SUM are shown as a function of body weight. A (men) and B (women): all available subjects. C (men) and D (women): the same relation after exclusion of subjects with body weights 100 kg or beyond 2 SD., Regression coefficient.

E418 scan, and the daily background radiation in Goteborg is 3 Sv (source: Department of Radiation Physics, Göteborg University). TBK counting. With the TBK method, body weight is compartmentalized into FFM and BF. The natural abundance of the potassium-40 isotope ( 40 K) is a constant fraction ( 0.012%) of all natural potassium (6). The 40 K isotope emits a 1.46-MeV -ray that can be counted using a detection system with appropriate shielding. The measurements took place in a high-sensitivity, 3 whole body counter containing four plastic scintillators with a total volume of 700 liters (24). The standard deviation of a single TBK determination (usually between 2,000 and 4,000 mmol) was 80 mmol (3). The conversion of TBK into FFM is traditionally based on the assumption that 1 kg FFM contains 68.1 mmol K (FFM 68.1) (9). We constructed TBK-to-FFM DEXA ratios (TBK/FFM DEXA) in the primary study group and regressed these by weight (W), height (H), and age (A) separately for men and women. In the validation group, we used the resulting equations to predict individual [TBK/FFM] WHA ratios. FFM K was calculated from TBK either by using Forbes ratio (68.1 mmol K/kg FFM) or by using the individually determined [TBK/FFM] WHA. In this study, FFM K and BF K designate FFM and BF determined with the TBK method without specifying which TBK/FFM ratio was used, whereas FFM 68.1 indicates FFM determined from TBK and the assumption of 68.1 mmol K/kg FFM. FFM WHA indicates FFM determined from TBK and the individually estimated [TBK/FFM] WHA. BF(BF 68.1 or BF WHA) was calculated as the difference between body weight and FFM 68.1 or FFM WHA. Human subjects. The protocol was approved by the ethics committee of the Medical Faculty of Göteborg University, and written informed consent was obtained from all subjects before the examinations. Statistical procedures. Age, height, weight, and body composition measurements are presented as means SD for men and women separately. To describe age-related differences in body composition, the subjects were divided into one of five age groups: 37 41, 42 46, 47 51, 52 56, and 57 61 yr of age. Age-trend calculations were also performed using age, TBK, and TBK/FFM as continuous individual variables. Subjects were allocated to either a primary study group or a validation group by means of the Microsoft Excel (Microsoft, 1998) random function within each sex and age group. In the primary study group, multiple linear regression analysis was performed to develop sex-specific predictive equations to estimate individual TBK/FFM from age, weight, and height. Measured TBK/FFM were used as dependent variables. Similarly, TBK was estimated from age, weight, and height with or without FFM DEXA, and measured TBK was used as a dependent variable. Measurements of sagittal diameter and circumferences of waist, hip, thigh, neck, upper arm, age squared, weight squared, and height squared were also considered and tested as predictors (independent variables) in the regression analyses. P values were considered significant when 0.05 in two-sided tests. Equations obtained from the primary study groups were then applied on the validation groups, and errors between measured and estimated TBK or TBK/FFM were calculated as the within-subjects coefficient of variation (2) d2 2n 100 X where d is the difference between measured and estimated value, n the number of paired observations, and X the grand mean. The statistical analyses were conducted with a JMP statistical software package, version 3.2.1 (SAS Institute, Cary, NC). RESULTS Because the main purpose of this study was to examine relationships between TBK and FFM DEXA, it was important to exclude individuals with erroneous values on these variables. It was not possible for us to check the potassium measurements independently. However, the sum of the DEXA-determined BMC, LTM, and BF (DEXA SUM ) could be compared with the simultaneously measured body weight. Figure 1, A and B, shows the difference between body weight and DEXA SUM as a function of body weight in those 349 men and 423 women in whom both DEXA and TBK were measured. The slopes were positive and significant in both sexes, and most observations above 100 kg body wt were located above the regression line, indicating an increasing difficulty of the DEXA equipment to detect the total body mass with increasing body weight. Some outliers with 100 kg body wt were also observed. To minimize the effects of systematic and random errors on the final TBK/FFM DEXA ratios, all individuals with body weights 100 kg or with [body weight DEXA SUM ] beyond 2 SD shown in Fig. 1, A and B, were excluded in Fig. 1, C and D. The excluded individuals were 24 men [age: 51.9 5.6 (40.9 61.1) yr; height: 181.6 5.5 (174.0 194.0) cm; weight: 97.2 13.0 (74.5 115.0) kg] and 12 women [age: 48.6 7.4 (37.9 60.9) yr; height: 169.3 4.7 (162.0 178.0) cm; weight: 77.6 13.8 (60.0 107.0) kg]. The excluded subjects represented 6.8 and 2.8%, respectively, of the men and women who were examined with both DEXA and the TBK technique. After the exclusions, the difference between body weight and DEXA SUM was 0.1 0.5 kg in men and 0.2 0.4 kg in women, which was not significantly different from zero in either sex (Fig. 1, C and D). In women, the slope for [body weight DEXA SUM ] vs. body weight was reduced from 0.0061 to 0.0017 and was no longer significant. In men, the corresponding slope dropped from 0.013 to 0.006 and the significance level from P 0.0002 to P 0.03. The men and women of Fig. 1, C and D, were first divided into age groups, and within each age group individuals were randomized to a primary study group or a validation group, as described in Statistical procedures. Table 1 shows age, height, weight, BMI, TBK, FFM, and BF of all men and women within the primary study group and the validation group. There were no significant differences between the primary study group and the validation group either in men or in women. All measurements in Table 1, except age and BF, were lower in women than in men. Although women had a lower BMI than men, they had

E419 Table 1. Age, height, weight, BMI, TBK, FFM, and BF in the primary study group and the validation group Primary Study Group Validation Group Variables Men Women P value Men Women P value Numbers 164 205 161 206 Age, yr 49.3 6.9 49.0 6.8 0.60 49.4 7.0 49.1 7.0 0.65 Height, cm 179.2 6.0 166.5 5.6 0.0001 178.7 6.6 165.6 6.1 0.0001 Weight, kg 80.7 9.4 66.6 10.0 0.0001 80.5 9.8 66.5 9.7 0.0001 BMI, kg/m 2 25.1 2.7 24.0 3.4 0.001 25.2 2.8 24.2 3.5 0.01 TBK, mmol 4,216 473 2,927 359 0.0001 4,172 540 2,910 359 0.0001 FFM DEXA 61.2 5.8 43.3 4.3 0.0001 61.0 6.5 43.0 4.3 0.0001 FFM 68.1 61.9 6.9 43.0 5.3 0.0001 61.3 7.9 42.7 5.3 0.0001 BF DEXA 19.6 5.9 23.0 8.0 0.0001 19.6 6.3 23.3 7.4 0.0001 BF 68.1 18.7 5.9 23.6 8.1 0.0001 19.2 7.3 23.8 7.4 0.0001 Values are means SD. BMI, body mass index; TBK, total body potassium; FFM DEXA, fat-free mass determined by dual-energy X-ray absorptiometry (DEXA); FFM 68.1, FFM determined by the TBK method based on the assumption of 68.1 mmol K/kg FFM according to Forbes et al. (7); BF DEXA, body fat determined by DEXA; BF 68.1, BF calculated as the difference between body weight and FFM 68.1. higher BF as measured both with the DEXA and the TBK 68.1 methods. Individually determined TBK and FFM DEXA observations were used to calculate TBK/FFM DEXA for all men and women in the primary study group. These ratios were multivariately regressed by age, weight, and height. The resulting sex-specific equations were (see Table 2) Males: TBK/FFM 98.30 0.1594 age 0.1431 weight 0.1849 height Females: TBK/FFM 94.39 0.1735 age 0.1169 weight 0.1567 height where TBK/FFM is given in millimoles per kilogram, age in years, weight in kilograms, and height in centimeters. All three predictors contributed significantly to the explained variances (Table 2). In contrast, the sagittal trunk diameter and circumferences of waist, hip, thigh, neck, and upper arm did not contribute to the explained variances, nor did age squared, weight squared, or height squared when added separately as a fourth variable in these equations (P 0.10 0.97). In addition, Table 2 provides TBK estimates based on age, weight, and height alone and also when FFM DEXA is added. In the former equations, age was negatively related to TBK, whereas weight and height were positively related to TBK. The explained variance was 52% in women and 68% in men. When FFM DEXA was added as a predictor, the explained variances increased to 73 and 88%, respectively. Height became negatively related to TBK in men and tended to be so in women. In the validation group, the correlation between the measured TBK/FFM and the same ratio estimated from age, weight, and height were significant both in men (r 0.48, P 0.0001) and in women (r 0.39, P 0.0001). When TBK was estimated from age, weight, and height, the estimate was closely related to measured TBK both in men (r 0.75, P 0.0001) and in women (r 0.73, P 0.0001). These associations were even stronger when FFM DEXA was added as a predictor (men: r 0.93, P 0.0001; women: r 0.90, P 0.0001; data not shown in figures). In the validation group, the difference between FFM DEXA and FFM 68.1 was not significantly different from zero either in men ( 0.3 3.3 kg) or in women (0.3 2.5 kg) (see Table 1). However, this difference was Table 2. Multiple regression equations of TBK/FFM DEXA and TBK as dependent variables and age, weight, height, and FFM DEXA as independent variables in males and females of the primary study group Independent Variables Dependent Variables Age, yr 1 Weight, kg 2 Height, cm 3 FFMDEXA, kg 4 Intercept Adjusted R 2,% Males (n 164) TBK/FFM DEXA, mmol/kg 0.1594 0.1431 0.1849 98.30 25.5 TBK, mmol 12.04 34.67 13.75 449.6 67.7 TBK, mmol 9.179 7.827 11.95 71.82 1784 88.0 Females (n 205) TBK/FFM DEXA, mmol/kg 0.1735 0.1169 0.1567* 94.39 9.2 TBK, mmol 13.37 18.55 18.97 810.4 52.3 TBK, mmol 8.0107 6.0907 5.743 NS 63.91 1103 72.7 *P 0.01; P 0.001; P 0.0001; NS, not significant;, regression coefficients.

E420 negatively related to body weight in women (P 0.0053) and tended to be so in men (P 0.08) (Fig. 2, A and B); i.e., FFM 68.1 resulted in larger values than FFM DEXA at large body weights but in smaller values at low body weights. This weight bias disappeared completely if FFM K was calculated as TBK/(TBK/FFM DEXA ), since [FFM DEXA TBK/(TBK/FFM DEXA )] is equal to zero (data not shown). However, the bias also disappeared when FFM K was calculated from measured TBK and TBK/FFM individually estimated from weight, height, and age according to the sex-specific equations of Table 2 (Fig. 2, C and D). As indirectly suggested by Table 2, [FFM DEXA FFM 68.1 ] might be biased not only by weight but also by age and height. Usually, this turned out to be the case, and these biases disappeared or decreased when individually estimated TBK/FFM was used. (women: [FFM DEXA FFM 68.1 ] vs. age, regression coefficient ( ) 0.070, P 0.01; [FFM DEXA FFM WHA ] vs. age, 0.018, P 0.42; [FFM DEXA FFM 68.1 ] vs. height, 0.066, P 0.02; [FFM DEXA FFM WHA ]vs. height, 0.026, P 0.31; men: [FFM DEXA FFM 68.1 ] vs. age: 0.22, P 0.0001; [FFM DEXA FFM WHA ] vs. age, 0.11, P 0.001; [FFM DEXA FFM 68.1 ] vs. height, 0.016, P 0.69; [FFM DEXA FFM WHA ] vs. height, 0.038, P 0.27). The difference between BF DEXA and BF 68.1 was not significantly different from zero in men in the validation group (0.4 3.4 kg) but was so in women ( 0.5 2.5 kg; P 0.0075) (Table 1). Although [FFM DEXA FFM 68.1 ] was negatively related to body weight (see above), [BF DEXA BF 68.1 ] was positively related to body weight in women (P 0.0053). In men, the slope was also positive but nonsignificant (P 0.14; Fig. 3, A and B). Compared with BF DEXA,BF 68.1 thus resulted in smaller BF values at large body weights and in larger values at low body weights, particularly in women. This body weight bias disappeared when BF K was calculated as the difference between body weight and FFM WHA (Fig. 3). Similarly, the biases of [BF DEXA BF 68.1 ] by age and height disappeared or decreased when the prediction equations of Table 2 were used (data not shown). In Tables 3 (men) and 4 (women), measured values for weight, height, BMI, TBK, and TBK/FFM DEXA are given by age groups in the pooled study group (primary validation groups). In this cross-sectional study, the increase in BMI by age was more dependent on decreasing height than on increasing weight in both sexes. TBK as well as TBK/FFM DEXA decreased with age in both men and women. In addition, Tables 3 and 4 are comparing the anthropometrically estimated TBK and [TBK/FFM] WHA with the measured TBK and TBK/FFM DEXA in the validation group. Fig. 2. Fat-free mass (FFM) measured by dual-energy X-ray absorptiometry (DEXA; FFM DEXA) FFM determined by total body potassium (FFM K) based on the assumption of 68.1 mmol K/kg FFM (FFM 68.1) by body weight in the validation group. A and B: differences between FFM DEXA and FFM 68.1 as a function of body weight in men (A) and women (B). C and D: differences between measured FFM DEXA and FFM K when a TBK-to-FFM ratio (TBK/FFM) is used and estimated from weight (W), height (H), and age (A) (FFM WHA) in men (C) and women (D).

E421 Fig. 3. Body fat (BF) measured by DEXA (BF DEXA) BF K by body weight in the validation group. A and B: differences between BF DEXA and BF determined by TBK (BF 68.1) as a function of body weight in men (A) and women (B). C and D: differences between measured BF DEXA and BF WHA in men (C) and women (D). BF WHA is calculated as the difference between body weight and FFM WHA (see legend to Fig. 2 and METHODS). The [TBK/FFM] WHA estimated from weight, height, and age in the validation group were similar to actually measured TBK/FFM DEXA in all age groups of men and women. The errors based on the squared differences between measured and estimated ratios ranged between 2.7 and 3.8% in men and 3.2 and 4.8% in women. The prediction of TBK from weight, height, and age resulted in errors ranging between 5.3 and 6.6% in Table 3. Body weight, height, BMI, TBK, and measured as well as predicted TBK and TBK/FFM by age in indicated study groups in men Group Men Age groups, yr 37 41 42 46 47 51 52 56 57 61 Age trend, P Age, yr P V 39.4 1.4 44.4 1.4 48.9 1.4 53.9 1.4 58.8 1.4 Numbers P V 61 60 61 79 64 Body weight, kg P V 80.0 9.8 82.0 8.9 80.9 10.0 80.4 9.3 79.6 10.0 0.71 Height, cm P V 180.6 6.5 179.1 6.9 180.3 5.9 179.0 5.5 176.0 6.1 0.001 BMI, kg/m 2 P V 24.5 2.8 25.5 2.6 24.9 2.6 25.1 2.7 25.7 2.9 0.06 TBK, mmol P V 4,365 555 4,342 492 4,243 475 4,073 427 3,998 503 0.0001 TBK/FFM DEXA, mmol/kg P V 70.4 3.4 70.1 2.6 68.5 3.1 67.4 3.2 67.1 3.1 0.0001 Numbers V 30 30 30 39 32 TBK/FFM DEXA, mmol/kg V 70.6 4.0 69.9 3.0 68.4 3.3 67.1 3.3 66.2 2.8 0.0001 [TBK/FFM] WHA, mmol/kg V 69.9 1.4 70.1 1.5 68.6 1.2 68.3 1.3 67.7 1.4 0.0001 Error, % V 3.4 2.7 3.2 3.8 3.3 TBK, mmol V 4,382 619 4,250 519 4,215 496 4,163 456 3,875 520 0.001 TBK WHA, mmol V 4,317 346 4,256 351 4,233 394 4,245 374 3,964 441 0.01 Error, % V 6.2 6.2 6.6 6.1 5.3 TBK WHAD, mmol V 4,328 506 4,256 494 4,228 426 4,242 446 3,963 528 0.05 Error, % V 3.7 2.7 3.1 3.9 3.2 Values are means SD. P, primary study group; V, validation group; TBK/FFM DEXA, ratio of measured TBK by whole body counter and measured FFM DEXA; [TBK/FFM] WHA, predicted TBK/FFM based on weight, height, and age according to equation in Table 2; Error, within-subjects coefficient of variation (2) between measured and predicted TBK/FFM or measured and predicted TBK; TBK WHA, predicted TBK from weight, height, and age according to equation in Table 2; TBK WHAD, predicted TBK from weight, height, age and FFM DEXA according to equation in Table 2.

E422 Table 4. Body weight, height, BMI, TBK, and measured as well as predicted TBK and TBK/FFM by age in indicated study groups in women Group Women Age groups, yr 37 41 42 46 47 51 52 56 57 61 Age trend, P Age, yr P V 39.1 1.4 44.2 1.6 49.2 1.4 54.2 1.4 58.8 1.2 Numbers P V 75 87 90 88 71 Body weight, kg P V 64.8 7.8 66.7 10.5 67.0 11.1 66.8 9.9 67.2 9.2 0.12 Height, cm P V 167.9 6.5 166.8 5.2 166.4 5.7 165.2 5.7 163.9 5.8 0.0001 BMI, kg/m 2 P V 23.0 2.5 24.0 3.6 24.2 3.7 24.2 3.4 25.1 3.5 0.001 TBK, mmol P V 3,050 376 3,014 389 2,893 389 2,822 284 2,815 270 0.0001 TBK/FFM DEXA, mmol/kg P V 68.8 4.1 68.6 4.8 66.8 3.8 66.7 3.8 67.1 3.8 0.0001 Numbers V 37 44 45 44 36 TBK/FFM DEXA, mmol/kg V 69.3 4.6 68.0 3.4 66.8 3.4 66.6 3.2 67.4 4.5 0.0001 [TBK/FFM] WHA, mmol/kg V 69.0 1.1 68.5 1.3 67.8 1.4 66.7 1.1 66.4 1.3 0.01 Error, % V 4.2 3.3 3.3 3.2 4.8 TBK, mmol V 3,040 417 2,998 365 2,895 396 2,787 285 2,836 255 0.001 TBK WHA, mmol V 3,028 251 3,023 254 2,931 271 2,799 219 2,755 212 0.0001 Error, % V 6.8 6.0 5.0 5.2 6.7 TBK WHAD, mmol V 3,024 318 3,019 315 2,931 345 2,788 250 2,800 252 0.0001 Error, % V 4.2 3.3 3.3 3.3 4.8 See Table 3 legend for definitions. men and between 5.0 and 6.8% in women. Adding FFM DEXA to the prediction of TBK reduced errors to 2.7 3.9% in men and 3.3 4.8% in women. DISCUSSION There has been a lack of appropriate information on potassium content per kilogram FFM in the literature. This prediction study on body composition, based on a randomly selected sample from the general population, illustrates that TBK/FFM can be predicted from sex, weight, height, and age, with errors being 5% in the age interval 37 61 yr. Thus our equations can improve the estimation of FFM from TBK when whole body counters are available. Our independent measurements of TBK with a whole body counter and of FFM with DEXA made it possible to predict TBK from sex, weight, height, age, and FFM DEXA with errors 5%. Predictions of TBK from sex, weight, height, and age alone resulted in errors ranging between 5.0 and 6.8%. Thus research sites with or without access to DEXA are able to make meaningful estimates of TBK. Such estimates are of importance, since TBK is a valuable indicator of respiratory cell mass (27). In this cross-sectional study, we found that, although randomly selected women had a lower BMI, they had more BF than randomly selected men, irrespective of the method (DEXA or TBK) used. Also, BMI increased with age in both sexes, primarily due to decreasing height. Similar results have previously been obtained in cross-sectional (3, 19) and longitudinal (6) studies. The TBK content was 30% lower in women than in men across the five age groups. This sex difference, as well as the decline in TBK with age, is consistent with earlier longitudinal (6, 10) and cross-sectional (1, 13, 19) studies. The agreement with longitudinal studies implies that the decline in TBK with age in this study is related more to the biology of aging than to generation differences. The manufacturer of LUNAR s DEXA machines points out that, at body weights 120 kg, DEXA SUM gradually lags behind body weight. Figure 1 indicates that, when observations 100 kg body wt are excluded, the difference between body weight and DEXA SUM is negligible, particularly in women. Our results show that the now-40-yr-old assumption of Forbes et al. (7) on potassium content per kilogram FFM (68.1 mmol/kg) is approximately true in 50-yr-old men and 45-yr-old women. However, between the ages of 39 and 59 yr, TBK/FFM decreases 3.3 mmol/kg in men and 1.9 2.7 mmol/kg in women, suggesting that the potassium content per kilogram FFM is not constant. Because weight, height, and age were related to TBK/FFM (Table 2), it was anticipated that the difference between FFM DEXA, here considered the gold standard, and FFM 68.1 might be biased by these variables. In fact, this was the case. For instance, FFM 68.1 overestimated FFM at large body weights but underestimated FFM at low body weights in both men and women (Fig. 2). When the potassium-determined FFM was calculated from TBK by use of the anthropometrically estimated [TBK/FFM] WHA on an individual basis, the weight, height, and age biases disappeared. The standard deviations for predicted TBK and predicted TBK/FFM were smaller than for actually measured values. Thus our equations are not able to detect the total biological variation in these respects. However, resulting errors were acceptable in all age and sex groups, and the weight, height, and age bias of [FFM DEXA FFM 68.1 ] disappeared when our equations were used. Thus, despite imperfections, our equations appear to be useful. TBK was related negatively to age but positively to weight and height (Table 2). When FFM DEXA was also used to predict TBK, height became negatively related to TBK. Thus, by keeping FFM constant, TBK decreases with increasing height. This is consistent with

E423 the fact that bone and skin contain less potassium per kilogram than the rest of FFM (4, 8). There are a number of factors that limit the generalizability of our results. Our equations have been shown to be valid for the age interval 37 61 yr, the body weight range 45 100 kg, and the height ranges 160 195 cm in men and 150 179 cm in women. Outside these intervals, the errors are unknown. Furthermore, the equations may not be valid for individuals suffering from diseases that influence body composition or for athletic persons. Finally, our calculations of TBK/FFM are dependent on the validity of the DEXA technique. Using underwater weighing, Womersley et al. (28) reported individual FFM density and TBK values for 36 men and 43 women. From this information, we calculated the TBK-to-FFM density ratio and found it to range from 56.5 to 77.8 (mean SD: 66.0 3.9) mmol/kg in men and from 52.9 to 72.1 (61.6 4.9) mmol/kg in women. 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