Abstract
The maintenance of body cell mass (BCM) is critical for survival in human immunodeficiency virus (HIV) infection. Accuracy of bioimpedance for measuring change (Δ) in intracellular water (ICW), which defines BCM, is uncertain. To evaluate bioimpedanceestimated ΔBCM, the ICW of 21 weightlosing HIV patients was measured before and after anabolic steroid therapy by dilution (total body water by deuterium − extracellular water by bromide) and bioimpedance. Multiplefrequency modeling and dilutiondetermined ΔICW did not differ. The ΔICW was predicted poorly by 50kHz parallel reactance, 50kHz impedance, and 200 − 5kHz impedance. The ΔICW predicted by 500 − 5kHz impedance was closer to, but statistically different from, dilutiondetermined ΔICW. However, the effect of random error on the measurement of systematic error in the 500 − 5kHz method was 12–13% of the average measured ΔICW; this was nearly twice the percent difference between obtained and threshold statistics. Although the 500 − 5kHz method cannot be fully rejected, these results support the conclusion that only the multiplefrequency modeling approach accurately monitors ΔBCM in HIV infection.
 human immunodeficiency virus
 acquired immunodeficiency syndrome
 weight loss
 extracellular water
 intracellular water
a measurement of the central, energyexchanging mass of working tissue has long been sought as a standard for assessing nutritional status (40). The core reference for the central tissues of the body has, in the past, been identified as fatfree mass (FFM). However, the FFM is too broad, including extracellular water (ECW) and the structural bone matrix, which are largely involved with support and not direct oxidative energy turnover. On the other hand, body cell mass (BCM) consists of cellular components minus ECW and support tissue. The ability to measure BCM would provide a reference basis for the measurement of oxygen consumption, caloric requirements, basal metabolic rate, and work performance (51). From an ideal point of view, the intracellular water (ICW) most closely approximates the BCM (40,51). This is because acute changes in body protein occur mainly in the cellular compartment (23), and changes in body protein are generally accompanied by changes in ICW (2).
The depletion of BCM and involuntary weight loss are common in human immunodeficiency virus (HIV) infection and are closely associated with morbidity and mortality (1, 26, 42). In fact, BCM loss has been observed to precede overt weight loss even in the early stages of HIV infection (42), and a critical level of BCM must be maintained for survival (26). Therefore, the ability to accurately monitor changes in BCM is essential to the successful treatment of individuals with HIV infection and acquired immunodeficiency syndrome. BCM can be estimated from total body potassium (TBK) measured with whole body counting, from ICW measured by dilution methods, or from total body nitrogen measured by neutron activation (16). However, whole body counting and neutron activation are expensive, and dilution methods are tedious and time consuming.
Theoretically, bioimpedance measurements can be used to estimate BCM noninvasively by measuring ICW; however, there is considerable debate concerning the best bioimpedance method to use. One group of investigators believes that ECW, ICW, and total body water (TBW) are best predicted using a bioimpedance spectroscopy (BIS) approach (11,58). Others continue to advocate the approach first proposed by Thomasset in 1963 (53; see also Refs. 14, 19). Although various frequency combinations have since been used, Thomasset proposed the use of a fixed, single lowfrequency (1kHz) bioimpedance approach to measure ECW and a fixed, single highfrequency (100kHz) bioimpedance approach to measure TBW. The ICW was computed as TBW minus ECW. A third group of investigators proposes that BCM can be adequately measured by a fixed, singlefrequency 50kHz measurement of impedance (Z) (43) or reactance (X) transformed into parallel X (X_{P}) (7, 25, 31). Whereas the latter two approaches rely on the derivation of prediction equations for TBW, ECW, and ICW using statistical methods, BIS provides a more direct measure of body water components. In fact, BIS is the technique from which all underlying theories of the bioimpedance method evolved and implies fitting measured spectral data to a biophysical model (44).
Basic theoretical and analytic bioimpedance principles.
Biological cell membranes behave as capacitors (C _{m}), and Z is frequency dependent (9) (Fig.1). With direct current or at the zero frequency, there is theoretically no conduction through biological cells, and Z is purely resistive (R) and a function of ECW [R at 0 frequency (R_{0}) or R_{E}]. With alternating current, C _{m} charges and discharges the current at the rate of the frequency; therefore, as frequency increases, the amount of ICW measured increases. At some infinitely (∞) high frequency (>10,000 kHz or 10 MHz; Fig. 1), the charge and discharge of current through the cells become so fast that the effects ofC _{m} become insignificant, Z becomes purely resistive (R_{∞}), and both ECW and ICW are fully measured. Once R_{0} or R_{E} and R_{∞} are determined, ICW resistance (R_{I}) can be computed as 1/R_{I} = 1/R_{∞} − 1/R_{0} (Fig. 2). At R_{0} and R_{∞}, the overall Z is independent ofC _{m}; whereas, at the middle or characteristic frequency (f _{c}), the dependence on the value ofC _{m} is at a maximum (Fig. 2). Thef _{c} can also be defined as the frequency of maximum X (9). The f _{c} is an important term because it is computed from R_{E}, R_{I}, andC _{m} and thus changes with changes in ECW, ICW, or the cell membranes, respectively (30). The equation forf _{c} is 1/[2πC _{m}(R_{E} + R_{I})].
Comparison of BIS and singlefrequency approaches.
Some studies comparing the BIS and singlefrequency approaches report no advantage of BIS in predicting ECW, TBW, and ICW (43). These conclusions, however, are based on the prediction of absolute volume using correlation, standard error of estimate (SEE), and bias statistics. It is well known that ECW, ICW, and TBW are highly intercorrelated and that Z measured at any frequency can equally predict the absolute volume of each body water compartment (11, 43,58). This intercorrelation would be expected because ECW and ICW are generally tightly regulated and comprise TBW. Detection of any systematic error (E_{sys}) that would impair the measurement of change in fluid compartments by a particular bioimpedance method would be obscured by the high intercorrelation of the variables when only absolute volume is predicted. For this reason, the ability to measure change should be the test of the validity of a bioimpedance method. Furthermore, correlation and SEE statistics should not be used to assess change, because neither of these statistics is sensitive to scaling; thus the predicted change could be significantly different from the actual change. For example, the correlation and SEE for the set of numbers 10, 15, 20, and 25 compared with the set 5, 7.5, 10, and 12.5 would be a perfect 1 and 0, respectively, despite the 50% difference between the sets.
Although it has been reported that the Kotler et al. (25) X_{P} equation detected direction of change in 89% of the subjects with a BCM change (ΔBCM) ≥5%, the accuracy of the prediction of the actual ΔBCM was not reported. A method that predicts direction of change (i.e., positive or negative) but is in error by 50% would have little clinical value. To assess change, multiple measurements must be made, and this greatly increases the effect of random error. At the same time, that which is being measured (change) is significantly less than absolute volume, often by a factor of 10 (e.g., 2 vs. 20 liters). To accurately measure ICW change (ΔICW) in an individual, a method must have small E_{sys}and random errors. How well a method measures what it purports to measure is the major uncontrollable contributor to E_{sys}. Thus the closer the theory underlying a method matches reality, the smaller the E_{sys} and the better the measurement of change.
Van Loan et al. (55) recently reported that, after gonadal hormone replacement therapy in HIVpositive men, the BIS method accurately predicted change in FFM (ΔFFM) compared with the estimated accretion of lean tissue from nitrogen balance measured daily for 21 days with the use of 24h urine and fecal collections. It was also reported that the BIS method predicted ΔFFM better than did dualenergy Xray absorptiometry or deuterium (^{2}H) dilution. Because the cellular compartment would have retained most of the increased nitrogen (23), the results of this study strongly suggest that the BIS method is sensitive to ΔBCM. Given that BCM is most closely related to ICW, the aim of the present study was to determine which bioimpedance method would provide the most accurate estimate of ΔICW compared with ΔICW measured by dilution (difference between ^{2}H dilution for TBW and bromide dilution for ECW). It was hypothesized that BIS would provide valid measures of ICW (BCM) and would estimate ΔICW with better accuracy than would other bioimpedance methods. To accomplish this aim, measures of ICW by bioimpedance were compared with criterion dilution measures of ICW in patients with HIV infection receiving anabolic steroid therapy for treatment of weight loss.
SUBJECTS AND METHODS
Study design.
This study was part of a larger clinical evaluation of HIVinfected individuals who were undergoing treatment for weight loss with the anabolic steroid oxandrolone (Oxandrin, BTG Pharmaceuticals, Iselin, NJ). Oxandrolone is an orally administered testosterone derivative (2oxa analog of 17αmethyldihydrotestosterone) that was approved by the FDA more than 30 years ago “as adjunctive therapy to promote weight gain after weight loss following extensive surgery, chronic infections, or severe trauma, and in some patients who without definite pathophysiologic reasons fail to gain or to maintain normal weight” (3). Dosedependent anabolic effects of oxandrolone in normal healthy subjects were demonstrated by decreased nitrogen excretion and increased protein synthesis with an anabolic potency 6.3 times that of methyltestosterone (17). Oxandrolone has been used successfully to treat growth failure (Turner's syndrome) in children (48) and has been safely used to treat proteinenergy malnutrition in alcoholic liver disease (4, 5, 35, 36). Oxandrolone has also been shown to significantly increase body weight (Wt) and muscle function after burn injury (12).
In the present study, measurements of TBW and ECW were taken on 21 subjects at baseline and postOxandrin therapy. Time on the study averaged 20 wk; only four subjects deviated from this mean, with final measurements at 6, 28, 35, or 40 wk.
Subjects.
Subjects were recruited from an outpatient clinic with a population of ∼600 HIVinfected patients. Any individual with a history of weight loss, who was receiving standard antiretroviral therapy and whose primary care physician prescribed Oxandrin therapy, was recruited to participate in the study. Twentyone subjects (20 men, 1 woman) between the ages of 27 and 56 yr, with a mean age of 41 ± 7.7 yr, completed this study. Of these, 20 subjects (19 men, 1 woman) were maintained on an Oxandrin dose of 20 mg/day, whereas one subject's dose was reduced to 10 mg/day after 1 mo. At the time of baseline assessment, the subjects had experienced an average weight loss of 9%. Ethnic distribution of the subject population was 72% (15 subjects) Caucasian, 14% (3 subjects) Hispanic, and 14% (3 subjects) AfricanAmerican. The study protocol was approved by the Human Subjects Committee of The University of Arizona, and written, informed consent was obtained from all participants.
Procedures.
Subjects came to the Metabolic Monitoring Laboratory at The University of Arizona for comprehensive assessment of body composition before initiation and after termination of Oxandrin therapy. To standardize testing conditions and to avoid acute changes in hydration status, subjects were instructed to abstain from vigorous exercise for at least 12 h and to abstain from alcohol and caffeine consumption for 48 h before assessment. Subjects reported to the laboratory on test days in the morning, after an 8 to 12h fast.
Anthropometric assessment.
At each visit, Wt was measured to the nearest 0.1 kg with a digital platform scale [Kubota model K10–300LA, Chugai Boyeki (America), Commack, NY]. Subjects were instructed to wear the same lightweight clothing at each visit. Standing height (Ht) was measured to the nearest 0.5 cm with a stadiometer (Narragansett Machine, Providence, RI).
Dilution volume.
Criterion estimates of TBW and ECW were derived from ^{2}H and bromide dilution, respectively. While still in a fasted state and after baseline urine and venous blood samples were collected, subjects were given a weighed dose of deuterium oxide (^{2}H_{2}O; 99.8 atom percent; Isotec, Miamisburg, OH) equivalent to 0.15 g/kg TBW. To calculate the dose, an estimate of TBW was obtained by singlefrequency bioimpedance analysis by using the Kushner et al. (29) equation. Immediately afterward, the subjects drank a measured dose of a sodium bromide (NaBr; Sigma Chemical, St. Louis, MO) solution, providing 1.0 ml of 3% (wt/vol) solution/kg body wt. Dose solutions were administered from paper cups and were followed by a 30ml wash with deionized, distilled water. A 3h equilibration period, during which subjects did not ingest anything, was allowed for ECW determination by bromide dilution. A second blood sample was drawn at 3 h postbromide dosing, and a light snack was provided immediately after the second blood draw. At 5 and 6 h after dosing with^{2}H_{2}O, urine samples were collected for TBW determination by ^{2}H dilution. Blood samples were collected in 10ml tigertop vacutainer tubes and centrifuged at 3,000 rpm for 20 min to separate serum. Two 2.5ml aliquots of each serum sample and three 5ml aliquots of each urine sample were stored frozen at −80°C in airtight cryogenic vials until analysis.
Frozen urine samples, diluted dose (1:5 wt/wt), and tap water were packed on dry ice in a sealed, insulated biomailer, shipped overnight, and analyzed for ^{2}H enrichment by the National Institute of Diabetes and Digestive and Kidney Diseases laboratory in Phoenix, AZ. After treatment with activated charcoal, enrichment of ^{2}H was determined by using an isotope ratio mass spectrometer (model Delta S; Finnigan MAT, Bremen, Germany) and hydrogen equilibration with Pt catalyst (250 μm diameter of 3% by weight Pt beads; Shoko, Minatoku, Tokyo, Japan), as described by Coplen and Harper (10). The reproducibility of this method is superior to the zinc reduction method. With 28 runs, the 841 δ‰ standard measured 840.1 ± 1.9 (SD) δ‰ and the −73 δ‰ standard measured −72.9 ± 1.4 δ‰. Appropriate dilutions of the doses were also used as internal controls. Stock dose solution was prepared twice during the study; dose 1 was measured as 759.8 ± 1.1 (SD) δ‰ (n = 20) and dose 2A was 733.5 ± 1.4 δ‰ (n = 21). The TBW was calculated by using a twopoint method as described by Schoeller et al. (47) using the^{2}H enrichment of the urine sample collected 5 h postdose that had, in all cases, greater ^{2}H enrichment than did the sample collected at 6 h.
Frozen serum samples were shipped overnight to the Pennington Biomedical Research Center, Baton Rouge, LA, for bromide analysis. Serum bromide enrichment was determined by the HPLC method of Miller and Cappon (38) by using an HPLC (model 1090M; Hewlett Packard, Palo Alto, CA) equipped with autosampler and diodearray detector. The analytic precision of the bromide measurements by this technique is ∼2% (38). The coefficient of variation (CV) for the bromide assay in this study was ∼5%. The ECW was calculated by using a correction of 10% for nonextracellular distribution and 5% for Donnan equilibration (39). The ICW was estimated as the difference between TBW and ECW. The accuracy of a dilutiondetermined ICW volume is unknown because ECW is impossible to measure directly. Nonetheless, the bromide dilution method for ECW is estimated to have an accuracy of 5% (54). Although in animal studies there is found to be some variability in the^{2}H dilution method for TBW, it is reported to be accurate within 1.5% (22). Most laboratories do not report accuracy, but rather mean intraassay CV, which is an indication of repeatability (43). For estimating the propagation of ICW error, we assumed the ^{2}H and bromide dilution methods to have accuracies of 1.5 and 5%, respectively.
The preOxandrin therapy dilutiondetermined fluid compartments were as follows: TBW, 39.9 liters; ECW, 17.4 liters; and ICW, 22.5 liters (Table 1). A 1.5% error for ^{2}H dilutionmeasured TBW is 0.60 liter, and a 5% error for bromide dilutionmeasured ECW is 0.87 liter. Squaring and adding these two terms (0.60^{2} + 0.87^{2}) equals 1.12. The square root of 1.12 is 1.06. Because volume change is being assessed, 1.06 was multiplied by 1.414 (square root of 2) and is 1.50 liters. This is a 6.7% error in 22.5 liters of ICW, assuming that the errors in the dilution methods are not correlated.
Bioimpedance measurements.
After the measurement of Wt and Ht and ingestion of the^{2}H_{2}O and NaBr doses, fasting subjects assumed a supine position for 30 min. The effects of orthostatic fluid shifts on Z can be considerable (i.e., 3% on recumbence, an additional 2% after 10 min, and an additional 4% after 4 h) (28). Thus the duration of recumbency before bioimpedance measurements are performed will affect the prediction of absolute volume, but, for estimation of fluid volume changes, the important thing is that repeated measurements be performed at identical time points during the recumbent period. This error was minimized by taking all measurements at the same 30min mark after recumbence. With the use of the standard wristtoankle measurement protocol (27), a Z measurement was made with a multiplefrequency bioimpedance device (model 4000B or 4200; Xitron Technologies, San Diego, CA). The multiplefrequency devices were confirmed to be in calibration according to manufacturer instructions. Three patients had baseline measurements taken with the 4000B device. All subsequent measurements were performed with the newer 4200 device. Comparison of R and X measurements by the two devices for seven subjects and 35 data points (frequencies 5, 50, 100, 200, and 500 kHz) showed no significant differences. Data were transmitted directly from the analyzer to a personal computer and controlled by the software programs supplied with the devices. All measurements were taken on the right side of the body by using disposable electrodes (IS4000; Xitron Technologies).
To evaluate the BIS method, Z and phase (θ) spectral data were fit to the Cole model (9) by using nonlinear least squares curvefitting software supplied with the devices. The Cole model consists of R_{E}, R_{I}, C _{m}, and exponent α. Because it is not possible to measure Z at sufficiently low or high frequencies, the ends of the semicircle that is formed when R and X are plotted are extrapolated to R_{0} and R_{∞} by using mathematical curvefitting techniques (Fig.2). Then, as discussed, R_{I} is computed. In practice, R_{E}, R_{I}, C _{m}, α, and time delay (T _{d}) are simultaneously computed. The termC _{m} is related to the thickness of the cell membrane (9). Exponent α is a Cole model term that represents the suppression of the semicircle below the R axis (Fig. 2) (9). The suppressed semicircle is thought to be a result of a distribution effect caused by the different sizes and shapes of cells (49). The termT _{d} is used to account for any error introduced by a frequencyinvariant time delay and allows for an improved fit to the Cole model. The T _{d} is caused by the interaction between contact R, stray capacitance, and transmission line effects. A detailed review of T _{d} and the method by which Z data are fit to the Cole model has been published by De Lorenzo et al. (11). The ECW and ICW volumes were predicted by using the values of Cole model terms R_{E} and R_{I} in equations developed by Xitron Technologies from mixture theory (11, 34). The TBW was calculated as ECW plus ICW. The resistivity constants used to predict ECW and ICW were developed by De Lorenzo et al. These constants (scalars) were selected because they previously predicted the expected sized ECW and TBW spaces [i.e., a TBWtoWt ratio of 0.60 and an ECWtoTBW ratio (ECW/TBW) of 0.40 for healthy young men] (11). It is important to note, however, that differences in dilution methods makes calibrating the scaling of the Z method (zero bias) extremely difficult (11, 32, 57, 59). Fortunately, any bias between methods has less of an effect on volume change because it is smaller than absolute volume by a factor of 10.
The Ztobody water volume relationship is not 1:1; therefore, reliability tests should be applied to both Z measurements and predicted water volume. Chumlea et al. (8) described reliability analyses using estimates of interobserver mean absolute difference (MAD) and technical error (TE). The MAD was computed as the difference between the mean of Z measurements taken at two time points by one observer and the mean of corresponding measurements by a second observer. The TE provides an estimate of the magnitude of the error for individual measurements and was computed as the square root of the sum of d^{2}/2N, where d is the difference between paired measurements for an individual and N is the number of individuals. Because the sameday interobserver MAD and TE have been reported to be only 1% for R up to 1 MHz and X up to 100 kHz for the Xitron 4000B device (8), no further analyses of precision were performed. For the BIS method, no differences (P > 0.05; paired ttest) were found for repeat measurements taken on 10 healthy subjects (with no change in electrodes) or on a simulated electronic circuit (34). The CV for the BIS method was 1.3% for ECW and 1.9% for TBW after repeat measurements (with repositioned electrodes) taken using the Xitron 4000B device on 29 patients with edema and 11 patients with gastrointestinal cancer (20). Because the present study used a new multifrequency bioimpedance device (Xitron 4200), additional measurements were taken to assess the MAD, TE, and CV. A total of 90 measurements was obtained by taking two consecutive measurements each day over 5 consecutive days (4 consecutive days for 3 subjects) plus the day following a weekend on eight subjects (6 men, 2 women; ages 26–50 yr) for the computation of MAD. To compute TE, the day 1 and day 2 measurements were paired for each subject. The CV for ECW, ICW, and C _{m} was calculated by using the first measurement for each subject on each day (45 measurements). To simulate field conditions, the subjects performed the measurements on each other after instructions were given on the first day. Measurements were taken at the same time each day to minimize biological variation. Subjects were asked to wear similar clothing each day and were instructed to refrain from eating large meals for several hours before the test and to void immediately beforehand. Ht was measured on the first day, and Wt was measured daily. Bioimpedance measurements were obtained as described above at the 4 to 6min mark after the recumbence. The raw data were fit to the Cole model, and ECW and ICW volumes were computed.
The interday, interobserver TE with the use of the Xitron 4200 device, with electrode repositioning, was 0.072 liter for ECW and 0.110 liter for ICW. The average MAD for daily consecutive measurements was 0.022 liter for ECW and 0.066 liter for ICW. The mean MAD for the entire period was 0.56 liter (0.28 − 1.02 liter) for ECW and 1.08 liter (0.76 − 1.50 liter) for ICW. Relative to the dilutiondetermined ECW and ICW volumes obtained in this study (Table 1), this represents 2.8 and 3.8% maximum variation (including normal biological variation) in the ECW and ICW, respectively. The interday, interobserver CVs for ECW and ICW measurements with electrode repositioning were 1.28% (0.013 liter) and 1.72% (0.017 liter), respectively.
To evaluate the validity of the single lowfrequency method for predicting ECW volume, the following 5kHz equations were used: the Deurenberg et al. (14) Z [ECW_{5 Z (D)}], Hannan et al. (20) R [ECW_{5 R (H)}], and Segal et al. (50) R [ECW_{5 R (S)}]. The ECW was also estimated by subtracting the predicted ICW from the predicted TBW by using the Kotler et al. (25) 50kHz X_{P}[ICW_{50 X (K)}] and Z [TBW_{50 Z (K)}] equations, respectively. To evaluate the single highfrequency method for predicting TBW, the following equations were used: TBW_{50 Z (K)} (25), Deurenberg et al. (14) 100kHz R [TBW_{100 R (D)}], Segal et al. (50) 100kHz R [TBW_{100 R (S)}], Hannan et al. (20) 200kHz R [TBW_{200 R (H)}], and Hannan et al. (19) 500kHz R [TBW_{500 R (H)}]. For the three subjects whose baseline measurements were made using the 4000B device, R measured at 204 and 488 kHz was used to compute TBW. Because the average differences for seven subjects between R measured at 200 and 204 kHz and between R measured at 488 and 500 kHz were only 0.3 ± 0.5 and 0.8 ± 0.7%, respectively, no further analyses were performed.
To evaluate the singlefrequency method for predicting ICW, the ECW predicted by the 5kHz equations was subtracted from the TBW predicted by the 100, 200, and 500kHz equations. Two published 50kHz equations developed specifically from subjects with HIV infection were also evaluated (25, 43). For the ICW_{50 X (K)} method, X was transformed as suggested into X_{P} and used in published male and female exponential equations to predict TBK (25). To obtain ICW volume, predicted TBK was divided by 150 mmol. This is valid because potassium is primarily distributed in ICW, and the relation between TBK and BCM is through the TBKtoICW relationship (40). The Paton et al. (43) 50kHz Z equation [ICW_{50 Z (P)}] was also used. For 17 subjects and 38 measurements, no difference was observed between R and X (α = 0.05; P = 0.063 and P = 0.139, respectively) measured at 50 kHz by the Xitron 4000B or 4200 devices and the RJL model 101A device (RJL Systems, Clinton Township, MI).
Data analysis.
To evaluate the fit to the Cole model, the total weighted least squared error was computed by the modeling routine. The fit error is expressed as a ratio between conformance to model to accuracy specification of the device. A ratio of 1 would indicate that conformance to model was equal to device performance. The expected accuracy at each measured frequency is established as a pair of arrays (Z and θ). The error ratio is then established at each modeling point by dividing the modeling error by the corresponding stored array error. Additional statistical analyses were carried out by using SPSS version 8.0 software (SPSS, Chicago, IL). For descriptive statistics, means and SDs were computed. Repeatedmeasures ANOVA was used to compare pre and postOxandrin therapy Wt and dilutiondetermined TBW, ECW, and ICW volumes.
Pearson's product moment correlation (r) and SEE were computed for absolute ECW, ICW, and TBW volumes measured by dilution and predicted by the various Z methods. It is established that the various Z methods equally predict absolute volume (43, 58) and that an accurate prediction of absolute volume does not validate a method for predicting volume change. In addition, the various Z equations have been calibrated to different dilution methods that yield differently sized ECW and TBW spaces (11, 32, 57, 59). Therefore, any bias between methods could simply be due to differences in the dilution method used for calibration. Because correlation and SEE statistics are insensitive to scaling (32), these are appropriate statistics for evaluating the similarities between equations for predicting absolute volume. No further statistical analysis was performed on absolute volume data.
Volume changes were calculated by subtracting baseline volumes from the volumes obtained postOxandrin therapy. Pearson's product moment correlation for fluid volume change by dilution and each bioimpedance method, the average change, and the root mean squared error (RMSE) were computed (41). The RMSE was computed by subtracting the average error of the measured change (E_{avg} _{chg}; the difference between the predicted and measured average change) from the error of each individual measurement, squaring each value, and then computing the mean and its square root. The RMSE computed in this way serves as a measure of random error in each measure of change. For an infinitely large sample size, E_{avg} _{chg} is equivalent to the E_{sys} of a method. For all other sample sizes, to estimate E_{sys} in a method, the effects of random error on the measurement of E_{sys} must be determined. This was accomplished by dividing the RMSE by the square root of the sample size (RMSE/
BlandAltman plots were not constructed because determining both the random error and E_{sys} is a more indepth analytic approach rather than a simple visual analysis. However, to evaluate how well each method predicted ΔICW at the individual level, the difference between predicted ΔICW by the various Z methods and the dilution method was computed for each subject, and the results were categorized as ≤1.0, 1.5, 2.0, 2.5, or 3.0 and >3.5 liters. The total percent represented by each category and the cumulative percent were computed. This presentation of the data is useful because the prediction accuracy of the individual data points can be categorized.
RESULTS
Study findings of fluid compartment change after Oxandrin therapy indicate that both TBW and ICW increased considerably (P < 0.0005; repeatedmeasures ANOVA), whereas ECW did not change (Table 1). Consequently, ECW/TBW decreased. The data fit the Cole model with high precision as evidenced by the low total least squares fit error ratio (Table 2). The fit error ratio for the preOxandrin therapy data does not include the three subjects measured at baseline with the Xitron 4000B device. The routine that was used to model the 4000B data does not display a fit error ratio. However, the fit was rated as good, which means that the fit error ratio equaled 1, and the correlation of fit for these three subjects was >0.997. Consistent with theory, R_{E} was greater than R at 5 kHz and continued to decrease with increasing frequency. Interestingly,C _{m} increased as would likely occur with an increase in intracellular hydration (44). The data used for evaluating the various bioimpedance equations are shown in Table 2.
Prediction of absolute body water volume.
As reported previously, the prediction of absolute ECW, TBW, and ICW volume was similar for all methods tested. Because all 5kHz ECW equations provided similar predictions, only the ECW_{5 R (H)} equation (20) is reported. Similarly, the two 100kHz TBW equations evaluated (14, 50) resulted in predictions similar to those obtained using 50 and 200 kHz. Thus only the predictions from the TBW_{50 Z (K)} (25), TBW_{200 R (H)} (20), and TBW_{500 R (H)} (19) equations are reported. The singlefrequency equations used for the predictions being reported are shown in Table 3. Correlation and SEE for ECW estimates by all methods ranged from 0.78 to 0.92 and 1.04 to 1.70 liter, respectively (Table 4). Subtraction of the ICW_{50 X (K)}predicted ICW from the TBW_{50 Z (K)}predicted TBW produced the best correlation and SEE for ECW (Table 4). For the prediction of absolute TBW volume, correlation and SEE for all methods ranged from 0.90 to 0.97 and 1.15 to 2.09 liter, respectively (Table 4). The TBW_{50 Z (K)} equation predicted TBW with the highest correlation and lowest SEE.
The prediction of absolute ICW volume was similar for all five methods evaluated, with correlation and SEE ranging from 0.76 to 0.88 and 1.70 to 2.31 liters, respectively (Table 4). Although the ICW_{50 Z (P)} equation was developed for men, it is unlikely that its use for the one female subject in this study altered the overall results. This would be particularly true for change data because the measurement of change is far less sensitive to scaling differences between methods.
Prediction of body water volume change.
The correlation of ΔECW was similar for the BIS and ECW_{5 R (H)} methods and slightly higher for the TBW_{50 Z (K)} − ICW_{50 X (K)}approach (Table 5). The bromidedetermined ΔECW was small, and all methods detected this. The ΔECW predicted by BIS was different (P = 0.022) from that estimated by the dilution method. All methods exhibited E_{sys}, because zero (a perfect answer) was not a possible outcome. For every method, the error was of positive polarity (Table 5; Fig.3).
The correlation of ΔTBW was similar for all methods, ranging from 0.73 to 0.82 (Table 5). However, for the TBW_{50 Z (K)}and TBW_{200 R (H)} approaches, the predicted ΔTBW was different (P = 0.008 and P = 0.003, respectively) from that determined by the dilution method. In addition, the random error (RMSE) was almost as large as the ΔTBW predicted by these methods (Table 5). There was no difference between the ΔTBW predicted by BIS and TBW_{500 R (H)} (P = 0.109 and P = 0.429, respectively). The RMSE and the predicted average change were better for the TBW_{500 R (H)} approach compared with the BIS method (Table 5). Additionally, TBW_{500 R (H)}had less E_{sys} than did the other methods, because only for this method was zero (a perfect result) a possible outcome (Table 5; Fig. 3).
The correlation of ΔICW was similar for all methods, ranging from 0.59 to 0.68 (Table 5). The RMSE was also similar among methods. Only the ΔICW predicted by BIS did not differ (P = 0.570) from the dilution method (Table 5). In addition to being statistically different from criterion, ICW predicted by ICW_{50 X (K)}, ICW_{50 Z (P)}, and TBW_{200R (H)} − ECW_{5 R (H)} had a random error (RMSE) that was larger than the predicted ΔICW. The BIS method had far less E_{sys}than did all other methods. The E_{avg} _{chg} was small (0.22 liter), and only for the BIS method was zero a possible outcome (Table 5; Fig. 3). The predicted average ΔTBW by TBW_{500 R (H)} had an error of −0.24 liter, and the predicted average ΔECW by ECW_{5 R (H)} had an error of +0.30 liter. Because ICW is computed by the high and lowfrequency method as TBW minus ECW, the error in the predicted average ΔICW is determined by subtracting the ECW error from the TBW error. It is important to note that this resulted in virtually twice the error (−0.54 liter) in the predicted average ΔICW by TBW_{500 R (H)} − ECW_{5 R (H)}(Table 5). As shown in Table 6, for all but the BIS and TBW_{500 R (H)} − ECW_{5 R (H)} methods, approximately onethird or more of the predictions had an error as large as the mean criterion ΔICW of 2.4 liters (Table 5). The ICW_{50 X (K)}, ICW_{50 Z (P)}, and TBW_{200 R (H)} − ECW_{5 R (H)}methods predicted ΔICW very poorly. Although the TBW_{500 R (H)} − ECW_{5 R (H)}method performed slightly better than the other singlefrequency methods, 33% of the predictions of ΔICW were only within 2.0 liters of criterion. The TBW_{500 R (H)} − ECW_{5 R (H)} method either predicted ΔICW very well or only moderately. Such a disproportionate distribution of results suggests the emergence of error under certain conditions. On the other hand, the distribution of the BIS results suggests that this method is primarily affected only by random error.
DISCUSSION
R would be expected to change when ECW and ICW change, but it was of interest that C _{m} increased. In vitro studies have shown C _{m} to be inversely related to cell membrane thickness (9); therefore, an increase in C _{m}suggests swelling of the cells and thinning of the membranes (44). Such a finding appears consistent with the theory of Häussinger et al. (21) that an increase in cellular hydration acts as an anabolic proliferative signal. However, not only are there many factors that can affect C _{m}, but it can change when there is no change in ICW. For example, C _{m} increased 45% from pre to posthemodialysis with virtually no change in ICW (32). De Lorenzo et al. (11) discussed the difficulties of usingC _{m} to estimate ICW (BCM). Furthermore, its use appears unnecessary because ICW can be determined. Although repeat measurements of C _{m} on healthy adults and a simulated circuit showed no significant differences (34), the accuracy of determining C _{m} is dependent on the accuracy of the model fit. Evaluation of the accuracy of fit to the Cole model has been fully discussed by De Lorenzo et al. For repeated measures, the CV for C _{m} in this study was 5%.
Because it is difficult to relate f _{c}, defined as the frequency of maximum X, to a Z plot, it is useful to conceptualizef _{c} as defined by Schwan (49). He definedf _{c} as the frequency corresponding to Z at the midpoint between Z at frequencies zero and infinity (Fig. 1). At any frequency other than zero and infinity, the proportion of ICW volume measured varies with f _{c}, and f _{c}varies when ECW, ICW, or C _{m} change (30, 32). Thus predictions of ECW using anything other than R_{0} should be less sensitive to ΔECW, because a portion of ICW will be included in the measurement. Theory (9), mathematical simulation, and initial in vivo results suggest that this is so (32). In this study, the BIS prediction of ECW was statistically different from the criterion. However, the random error effect on the measurement of E_{sys}was 0.17 liter or 43% of the measured average change of 0.40 liter (Table 5). Furthermore, the random error (RMSE) in each measure of change was, for all bioimpedance methods, larger (0.72–0.82 liter) than the average dilution ΔECW. Therefore, ΔECW was too small to draw any conclusions from the findings of this study (Table 5). It is important to consider that an E_{avg} _{chg} of 0.4 liter (Table 5; Fig. 3) represents only 2% of a total ECW volume of 17.5 liters (Table 1). The BIS method has been used successfully to predict ΔECW in comparison with bromide dilution (15), with net fluid balance during surgery (52), and with volume removed by ultrafiltration during dialysis (60). However, it needs to be clearly established whether it performs better than the fixed lowfrequency (e.g., 5kHz) approach. Gudivaka et al. (18) reported that only an equation using Cole model term R_{E} accurately predicted ΔECW. All predictions were corrected by 1.6% based on the assumption that change in plasma albumin affects the total ECW volume. Coincidentally, 1.6% was effectively the same as the magnitude of the under and overprediction of ΔECW using the Xitron ECW equation. Because the ECW equation published by Xitron (34) corrects for mixture effects, the additional 1.6% correction applied by Gudivaka et al. was, in effect, a double correction.
The TBW_{500 R (H)} method predicted ΔTBW well; however, these results need to be qualified. The f _{c}values for the subjects in this study ranged from 30 to 66 kHz and are similar to the 40–60 kHz measured for healthy subjects (11). The range of f _{c} values obtained makes the difference between Z at 500 kHz and infinity small (Table 2; Fig. 1). Had thef _{c} values been higher, less ICW would have been measured, and the sensitivity of 500 kHz to ΔTBW would have been reduced. This is supported by the finding that the 50 and 200kHz methods did not accurately predict ΔTBW. It has long been known thatf _{c} changes considerably when tissue hydration changes (30). For example, f _{c} values >200 kHz have been reported in hemodialysis patients (11), andf _{c} values >500 kHz have been reported in young children with severe diarrheal disease (37). Although it is unsound to fit a theory to a result, the ratio of the measurement frequency tof _{c} may be useful for exploring the cause for the results of this study. For a measurement frequency of 200 kHz and anf _{c} of 50 kHz, the ratio is 4 (200/50). This suggests that, to achieve the same results when f _{c}is 125 kHz, a measurement frequency of 500 kHz would be required. Following this reasoning, if f _{c} is 300 kHz, a measurement frequency of 1.2 MHz would be required to produce the same poor prediction of ΔTBW that 200 kHz yielded in this study. The fact that the 500kHz equation (19) accurately predicted ΔTBW may be due in part to the similarity of f _{c} values for the subjects of this study (Table 2) to the 40 to 60kHz values determined for healthy subjects (11). This suggests that a measurement frequencytof _{c} ratio of 10 (500/50) may be needed to accurately predict ΔTBW by using a singlefrequency measurement. If this were so, a measurement frequency of 2 MHz would be needed iff _{c} were 200 kHz. However, using a very high single frequency to reduce the error introduced by f _{c}would still be problematic, because a twofold increase in frequency increases measurement error by a factor of 4. Thus a measurement at 1 MHz is four times less accurate than a measurement at 500 kHz. This partially explains why multipleregression analyses provide the best TBW predictions at frequencies between 200 and 500 kHz and why accuracy decreases progressively at frequencies >500 kHz (13). Although the BIS method correctly predicted ΔTBW in this study, it did have E_{sys} (Table 5; Fig. 3). Because TBW is predicted as ECW plus ICW, the E_{sys} in the predicted TBW may have simply been carried over from ECW and ICW. The P value for BISpredicted TBW was only 9% above the threshold for considering the results different, whereas the effect of random error on the measurement of E_{sys} was 0.373 liter or 13% of the measured average change of 2.8 liters (Table 5). Although the TBW predicted by BIS was not different from the criterion (P = 0.109), further research is needed to confirm these findings. An E_{avg} _{chg} of 0.65 liter is only a 1.6% error in 40 liters of TBW (Table 1).
Although it has recently been reported that a multipleregression equation including X_{P} accurately predicted ΔICW in healthy, nonobese subjects (18), we found that the ICW_{50 X (K)} and ICW_{50 Z (P)} methods predicted ΔICW poorly. This discrepancy may be at least partly explained by the fact that Gudivaka et al. (18) used an α of 0.05 to test for differences between methods, which can increase the risk of a type II error in a situation in which sample sizes and the changes measured are small. An evaluation of how well a method performed is not possible without the actual P values for each method. Furthermore, from a physics standpoint, at any single frequency, the effect of a change in ECW, ICW, or C_{m} on X cannot be discerned; therefore, any prediction of ICW using X_{P} would be circumstantial (32). The ΔICW predicted by the fixed high and lowfrequency methods [TBW_{200 R (H)} − ECW_{5 R (H)} and TBW_{500 R (H)} − ECW_{5 R (H)}] was also considered statistically different from the criterion. A poor singlefrequency prediction of TBW or ECW would result in a poor prediction in ICW because it is computed as TBW minus ECW by these methods. In addition, a change inf _{c} causes errors in the predicted ECW and TBW in opposite directions, thereby magnifying ICW error (Table 5). Whenf _{c} increases, a fixed low frequency (5 kHz) becomes closer to zero, and a fixed high frequency (500 kHz) becomes further from infinity. The opposite would occur when f _{c}decreases (Fig. 2). In this study, the changes inf _{c} were very small, but f _{c} can change by as much as 50% (11). Such a large change inf _{c} would cause large errors in the predicted ΔICW. Although the ΔICW predicted by TBW_{500 R (H)}− ECW_{5 R (H)} was different (P = 0.093) from that determined by criterion methods, it is important to consider these results carefully. The probability (P = 0.093) that the results achieved were true was only slightly (7%) below the significance level for considering the results equal. On the other hand, the effect of random error on the measurement of E_{sys}was 0.30 liter or 12–13% of the measured average change of 2.4 liters (Table 5). As the P value becomes smaller and the null hypothesis becomes more unreasonable, however, the point at which results are accepted or rejected is subjective. As such, the findings of this study do not lead to a firm rejection of the TBW_{500 R (H)} − ECW_{5 R (H)}method.
Albeit the strong prediction of TBW using 500 kHz suggests otherwise, the prediction of ΔTBW using a single highfrequency measurement should be poor because the R_{E} and R_{I} differ by a factor of 3 (44). To predict TBW volume, it must be assumed that TBW resistivity is constant. Such an assumption seems tenuous considering that a simple change in the ECW/ICW can alter TBW resistivity.
These results support the BIS or modeling approach. The implication is that the BIS method predicted ΔBCM better than the other methods did solely because it is based on the Cole model. To explore if this were true, multipleregression analysis was used to predict ICW preOxandrin therapy by using variables Ht, Wt, and R_{I}. According to the common singlefrequency model used, Ht^{2}/R, not R alone, should correlate to water volume; thus multiple regression was also performed by using variables Ht^{2}/R_{I} and Wt. Wt alone can be predictive of ΔICW, but it is often an additive term in published multipleregression equations (25) and was therefore included. The resulting equations were used to predict ICW pre and postOxandrin therapy. The ΔICW was computed, and twotailed pairedttests were performed (α = 0.10). The equation using Ht^{2}/R_{I} and Wt performed best. The predicted ICW volume was similar to that obtained from the other methods (Table 4) with pre and postOxandrin correlations of 0.77 and 0.88 and SEEs of 2.27 and 1.99, respectively, but the prediction of ΔICW was poor (P = 0.015). We did not log transform R_{I} before running the regression analysis as suggested by Kotler et al. (25). It was not clear from the literature how to replicate the procedure, and it did not appear valid because X_{P} predicted ΔBCM poorly (Table 5). The implication of these findings is that a mathematical modeling approach that solves for R_{0} and R_{∞}and accounts for any mixture effects should be used (11, 33).
The underlying basis for the mixture theory equations developed by Xitron (33) is that the relationship between Z and body water should be explained scientifically rather than randomly by using multipleregression analysis. Use of a physical model (the Cole model) is an important first step, but, according to theory, the Ztobody water association is complex and nonlinear because of conductor (ECW and ICW) and nonconductor (fat and bone) interactions. As such, Cole model terms R_{E} and R_{I} are model terms and not simply ECW and ICW R values, respectively. To accurately predict ECW and ICW volume, mixture effects must be taken into account. The results of this study seem to support this premise, because the prediction of ΔBCM solely by the Cole model was poor. The mixture theory equations used in this study have been fully described (11). Gudivaka et al. (18) recently reported that the ICW mixture equation published by Xitron (34) predicted ΔICW poorly, and that only a multipleregression equation, including Cole model term R_{I}, accurately predicted ΔICW. The equation tested was the original equation developed by Xitron, which assumes a linear relationship between ECW/ICW and TBW resistivity, whereas the present equation in the Xitron software, developed in 1993, assumes a nonlinear relationship. De Lorenzo et al. (11) discussed the differences between equations.
It is generally understood that FFM is not an ideal measure of BCM because it includes ECW and solids (40). Van Loan et al. (55) recently reported the successful prediction of ΔFFM using bioimpedance. The ΔFFM determined by BIS accurately reflected the nitrogen balance change in wasted acquired immunodeficiency syndrome patients after gonadal hormone therapy (55). The first successful prediction of ECW, TBW, and FFM with the use of BIS methods was reported in 1992 (34). The BIS FFM equation developed by Xitron is (
The BIS methodology used in this study has been successfully validated in other clinical populations (15, 22, 57), and there is evidence that ECW and ICW differences can be detected between patient groups (24,57). Whereas these previous findings add strength to the findings of this study, it is unknown whether the results of this study are applicable to other populations. Hannan et al. (19) reported that the BIS method did not accurately predict ECW and TBW, but the potential cause was not discussed. Hannan et al. (personal communication) have observed f _{c} values approaching 1 MHz, and this is consistent with the recent report of Meyer et al. (37). With anf _{c} of 1 MHz, which is equal to the highest frequency measured, an accurate determination of R_{∞} would be extremely difficult because there would be data on only one side of the semicircle to fit (Fig. 2). Even with these constraints, however, it appears that ECW can still be predicted accurately (15).
When f _{c} becomes very high, it is doubtful that either BIS or a fixed, single highfrequency measurement will accurately predict ΔICW. If an accurate bioimpedance measurement were possible over a range of frequencies up to 5 MHz, accurate computation of the Cole model might be possible when f _{c} is very high. Without consistent use of good protocol, the bioimpedance technique can also be adversely affected by inaccurate electrode placement, geometry differences, orthostatic fluid shifts, inappropriate limb abduction, changes in ion concentration, changes in core and skin temperature, and changes in vascular perfusion. Whereas many of the above factors can be controlled, there may be instances when they cannot. Clinicians should have a thorough understanding of the sources and magnitude of potential error in the Z method. A detailed description of the error sources in the Z method can be found in the papers by Kushner et al. (28) and Scharfetter et al. (45). Each clinical population presents unique limitations for the method. For example, when body water is not evenly distributed in the body segments, as in ascites, the wristankle approach used in this study would not yield valid results (46). Furthermore, when changes in body water occur faster than equilibration can occur in the body segments, as would be the case with infusion and ultrafiltration, a segmental approach must be used (52, 60).
In conclusion, the results of this study indicate that the ICW_{50 X (K)}, ICW_{50 Z (P)}, and TBW_{200 R (H)} − ECW_{5 R (H)}methods predict ΔICW poorly. The ΔICW predicted by TBW_{500 R (H)} − ECW_{5 R (H)} was different from the criterion. However, the effect of random error on the measurement of E_{sys} was 12–13% of the average measured ΔICW with the use of this method. This was two times larger than the difference between the obtained and critical threshold statistics. Although the TBW_{500 R (H)} − ECW_{5 R (H)} method predicted ΔICW with only marginal accuracy, it can be neither clearly rejected nor accepted by the results of this study. However, because of potential variations inf _{c} and the considerable E_{sys} inherent in this method, the utility of the TBW_{500 R (H)}− ECW_{5 R (H)} method is questionable. E_{sys} indicates a poor underlying basis that will not be corrected by simply regressing equations against larger data sets (6,25). Random error decreases with sample size, but E_{sys} does not. The BIS mixture theory approach convincingly provided the best prediction of ΔICW (ΔBCM). This was particularly evident when individual results were compared. It can be concluded that the BIS measurement is useful as a field method for monitoring ΔBCM in HIVinfected populations.
Acknowledgments
The authors thank the patients, physicians, and staff at El Rio Special Immunology Associates, Tucson, AZ, for assistance with this research. The authors thank Paul O. Withers for ideas on data analysis, and Dr. Jennifer Rood for input on bromide analyses.
Footnotes

Address for reprint requests: C. P. Earthman, Dept. of Human Nutrition, Foods and Exercise, Virginia Tech., Blacksburg, VA 24061–0430.

This study was supported by an American Dietetic Association Foundation Dietitians in Nutrition Support Dietetic Practice Group Research Award, a Kraft Foods Fellowship, a Helen S. Mitchell Nutrition Scholarship, a Kappa Omicron PhiHettie Margaret Anthony Fellowship, and a BTG Pharmaceuticals (Iselin, NJ) gift grant.

Address for other correspondence: W. H. Howell, Department of Nutritional Sciences, The University of Arizona, P.O. Box 210038, Tucson, AZ 85721–0038 (Email:whhowell{at}ag.arizona.edu).

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. §1734 solely to indicate this fact.
 Copyright © 2000 the American Physiological Society