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J Appl Physiol 82: 1542-1558, 1997;
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Journal of Applied Physiology
Vol. 82, No. 5, pp. 1542-1558, May 1997
METABOLISM

Predicting body cell mass with bioimpedance by using theoretical methods: a technological review

A. De Lorenzo1, A. Andreoli1, J. Matthie2, and P. Withers2

1 Department of Physiology, University of Rome "Tor Vergata," 1-00173 Rome, Italy; and 2 Xitron Technologies, Inc., San Diego, California 92121

ABSTRACT
INTRODUCTION
SUBJECTS AND METHODS
RESULTS
DISCUSSION
APPENDIX
FOOTNOTES
REFERENCES

ABSTRACT

De Lorenzo, A., A. Andreoli, J. Matthie, and P. Withers. Predicting body cell mass with bioimpedance by using theoretical methods: a technological review. J. Appl. Physiol. 82(5): 1542-1558, 1997.---The body cell mass (BCM), defined as intracellular water (ICW), was estimated in 73 healthy men and women by total body potassium (TBK) and by bioimpedance spectroscopy (BIS). In 14 other subjects, extracellular water (ECW) and total body water (TBW) were measured by bromide dilution and deuterium oxide dilution, respectively. For all subjects, impedance spectral data were fit to the Cole model, and ECW and ICW volumes were predicted by using model electrical resistance terms RE and RI in an equation derived from Hanai mixture theory, respectively. The BIS ECW prediction bromide dilution was r = 0.91, standard error of the estimate (SEE) 0.90 liter. The BIS TBW prediction of deuterium space was r = 0.95, SEE 1.33 liters. The BIS ICW prediction of the dilution-determined ICW was r = 0.87, SEE 1.69 liters. The BIS ICW prediction of the TBK-determined ICW for the 73 subjects was r = 0.85, SEE = 2.22 liters. These results add further support to the validity of the Hanai theory, the equation used, and the conclusion that ECW and ICW volume can be predicted by an approach based solely on fundamental principles.

bioimpedance spectroscopy; extracellular water; total body water

INTRODUCTION

THE FIRST SUCCESSFUL VALIDATION of extracellular water (ECW), TBW (total body water), and intracellular water (ICW) by using bioimpedance spectroscopy (BIS) methods was reported in 1992 (30). BIS, which implies fitting complex impedance (Z) data measured at multiple frequencies to a biophysical model, has been used extensively in biophysics and is the technique from which derive all the underlying theories for body impedance analysis (BIA) (48). Although a number of studies have been reported that used the methods employed in this study, the BIS principles and the rationale for the methods employed remain poorly understood. Partly because of the complex nature of BIS, there has been very little cross-transfer of BIS information to the field of human body composition; furthermore, these methods have not been fully reported by the investigators responsible for their development (30). As a result, these methods have been only partially reported with insufficient underlying discussion.

Several single-frequency Z studies have reported a prediction of body cell mass (BCM; Refs. 3, 42), but the scientific bases of the approaches used were not well supported, and the relationships reported may have simply been a result of high intercorrelation between variables (48). Results should be associated with ICW or total body potassium (TBK) rather than BCM, because BCM is a concept that can only be defined by ICW or TBK (33). Any relationship between Z and BCM can only emerge from the relationship between Z and cell volume. What becomes important then is the best approach of predicting cell volume with Z.

This study reports the relationship between a BIS-predicted ICW and a TBK-predicted ICW, and the relationship between a BIS-predicted volume of ECW, ICW, and TBW compared with dilution-determined volumes. This manuscript also provides a description of the principles of BIS and a discussion of the simplified single- and dual-frequency methods relative to well-known BIS principles.

Physical Principles

Variations in heterogeneous tissues cause interfaces, separating regions of different properties, to trap or release electrical charge as a stimulus potential is changed. The time lag between the stimulus potential and the change in charge in these interfaces creates a frequency (f)-dependent Z (i.e., dispersion). The dispersion found in the low-frequency (LF) radio range (1 kHz to 100 MHz), which is of interest for predicting ECW and ICW volume, is known as beta -dispersion and is caused by cell membrane capacitance (Cm) (40) (Fig. 1). With direct current (DC), there is no conduction through a capacitor. Thus, in the LF range of beta -dispersion, there is minimal conduction through the cells because of the high Z of the Cm, and conductivity is governed primarily by the properties of the ECW. As f increases into alternating current (AC), the Z of the Cm decreases, allowing more current to flow into the ICW compartment. Because of the change in polarity that occurs with AC current, the cell membrane charges and discharges the current at the rate of the f. The Z decreases with f, because the amount of conducting volume is increasing. At higher frequencies (HF), the rate of charge and discharge becomes such that the effect of the Cm diminishes to insignificant proportions, and the current flows through both the ECW and ICW compartments in proportions dependent on their relative conductivity and volumes (5) (Fig. 2). Thus, at both very low and very high frequencies, the overall Z is essentially independent of the Cm, whereas at the mid- or characteristic frequency (fc), the dependence on the value of the Cm is at a maximum.
Fig. 1. Log dielectric constant of muscle tissue vs. log frequency in the alpha -, beta -, and gamma -dispersion regions. Recreated in vitro data from H. Schwan, Electrical properties of tissue and cell suspensions. In: Advances in Biological and Medical Physics, edited by J. H. Lawrence and C. A. Tobias. New York: Academic, 1957, vol. 5, p. 147-209. Used by permission.
[View Larger Version of this Image (20K GIF file)]

Fig. 2. Diagram representing high-frequency and low-frequency current distribution in cell suspensions.
[View Larger Version of this Image (31K GIF file)]

If the complex Z [resistance (R) and reactance (X)] of skeletal muscle tissue is measured, and the f varies from low to high, a series of values is derived that can be represented by complex points. The curve formed by these points is called an impedance locus, and its shape is a result of the electrical and structural characteristics of the tissue (5). The mathematical model that is used most often to describe both theoretical and experimental data on skeletal muscle tissue is known as the Cole model. It produces a semicircular relationship between R and X, with a depressed center when plotted (5) (Fig. 3). Modeling is considered essential, because it is the only means of independently analyzing the individual components of a heterogeneous material system (5, 25). The Cole model can be viewed as the equivalent electrical circuit shown in Fig. 4.

Fig. 3. Impedance locus: reactance vs. resistance in beta -dispersion region. R infinity  and Ro, resistances at 100 MHz and 1 Hz, respectively; fc, characteristic frequency.
[View Larger Version of this Image (7K GIF file)]

Fig. 4. Equivalent electrical circuit analogous to Cole model. RE is component value in ohms; RI is aggregate component value in ohms; and membrane capacitance (Cm) is aggregate component value in farads.
[View Larger Version of this Image (14K GIF file)]

To accurately predict volume, the mixture effects need to be accounted for, because the relationship between R and body water volume is nonlinear (9, 17). These mixture effects are greater at LF because the conductor (i.e., ECW) represents only 25% of the total body volume compared with a concentration of nonconductor of 75%. At HF, the concentration of nonconductor is much less (e.g., 40%). Good examples of the mixture effects are the change in resistivity (rho ) that occurs with a change in hematocrit (14) and that plasma (i.e., ECW) is four- to sixfold more conductive than is skeletal muscle tissue measured at 1 kHz (14). At 1 kHz, there is little conduction through the cells; thus the rho should be similar to that of plasma. It is dramatically increased because the cells are nonconductive at LF and restrict the flow of current. Hanai (17) developed a theoretical equation that describes the effect on the apparent conductivity of a conducting material having a restricting concentration of nonconductive material in suspension. Hanai postulated that the theory could be applied to tissues with nonconductive concentrations ranging from 10 to 90%. To employ his theory, we have constructed an equation that considers the ECW to be such a medium at LF, where the ECW is the conductive material, and all remaining items (including ICW because it is surrounded by cell membrane) in the body are the restricting nonconductive material. At HF, the combination of both ECW and ICW forms the conductive medium, and all remaining items in the body form the restrictive material. Previous results have supported that this theory can be used in vivo to predict ECW, TBW, and ICW volume (35, 47).

SUBJECTS AND METHODS

A group of 87 healthy Italian men (n = 77) and women (n = 10), ages 21-57 yr, volunteered to participate in this study. Written informed consent was obtained from all participants. The study protocol was approved by the Medical Ethical Committee of the University of "Tor Vergata" in Rome.

On arriving in the morning in an overnight-fasted state, subjects were weighed in swimming clothes, and body weight (Wt) was measured with a standard balance to the nearest 0.05 kg. Body height (Ht) was measured with a stadiometer to the nearest 1 mm. After the measurements of Wt and Ht were made, and still in the fasting state, all 87 subjects had their 40K measured by a whole body counter, formed by a cell 2.5 m wide and 3 m high of 10-cm-thick lead bricks, the door to which was formed by a 22-cm-thick iron slab. The room was continuously ventilated. A single 20.3 × 10.2 thallium-activated sodium iodine crystal was positioned above the subject, who was measured in a sitting position and dressed in only paper pajamas. TBK was calculated as 40K * 8,474.6 (11). The correlation of variation (CV) for TBK was found to be between 2 and 3%. ICW was computed from TBK, assuming that potassium is only present in the intracellular fluid and assuming a potassium concentration in the intracellular fluid of 150 mmol/l (11).

For 14 of the men, out of the total sample of 87 men and women, TBW and ECW were measured by dilution methods. Deuterium oxide (D2O) was used for the determination of TBW, and sodium bromide (NaBr) was used for the determination of ECW. While still in a fasted state and after the Z measurements were taken, the subjects drank 50 g of a solution containing 10 g of D2O (99.8%; Carlo Erba) and 1.3 g of NaBr (Carlo Erba) in 38.7 g of tap water. After a 3-h equilibration time, urine was collected for the determination of D2O, and a venous blood sample was taken for determining plasma NaBr. The subjects remained in a fasted state throughout the equilibration period and refrained from voiding. No baseline measurement samples of either urine or plasma were taken. Enrichment of D2O in the urine sample was measured after sublimation with infrared spectrophotometry, as described by Lukaski and Johnson (24). A correction of 5% for nonaqueous dilution was used (11). The venous blood sample was centrifuged (3,000 revolutions/min for 15 min) to separate the plasma. The plasma was then stored in sealed plastic tubes at -20°C until analysis. Bromide enrichment was measured in the plasma by high-pressure liquid chromatography (32). The accuracy of the NaBr measurements by this technique is considered to be within 1% (50). ECW was calculated by using a 10% correction for nonextracellular distribution and 5% for the Donnan equilibration (11, 50). ICW was calculated as the difference between TBW and ECW.

After the measurement of Wt, Ht, and TBK; before ingestion of the D2O and NaBr solution; and with subjects still in a fasted-state; single wrist-to-ankle (i.e., whole body) complex Z measurements were taken in all 87 subjects by using a BIS analyzer (model 4000B, Xitron Technologies, San Diego, CA). R and X were measured, and the corresponding Z, phase (theta ), was computed from R and X at 21 f ranging from 1 kHz to 1.248 MHz. The measurements were taken within the first several minutes after the subjects assumed a supine position. No correction was made for orthostatic fluid shifts. The measurements were taken on the left side of the body, with the use of disposable electrocardiogram electrodes (5 cm2; 3M, Minneapolis, MN) and in accordance with the standard wrist-to-ankle protocol (47). Data were transmitted directly from the analyzer into an ASCII format file via an RS232 interface to a personal computer and controlled by the software program supplied with the device.

The Z and theta  spectra data were fit to an enhanced Cole model (5) to account for any time delay (Td) effects (see APPENDIX a), using the nonlinear curve-fitting software developed for the device. The ECW and ICW volumes were predicted by using modeled RE and RI values in equations formulated previously (47) from Hanai mixture theory (17) (APPENDIX b). The BIS TBW was calculated as ECW + ICW. The constants used for kECW (i.e., men = 0.306, women = 0.316) and krho (men = 3.82, women = 3.40) had been scaled to D2O and NaBr data collected in a previous study (47). Although only the constants for men were used in this study, the constants for women were included for discussion purposes because a previous study discovered a gender difference (47). When reference ECW and TBW data are available for only one gender, the software automatically and arbitrarily scales the other gender's constant by the same percentage difference discovered previously. Further research needs to be done to determine whether there truly is a gender difference in these terms. Expressing the above kECW and krho terms as apparent ECW and ICW resistivity (rho ECW and rho ICW, respectively), they become 214 and 206, and 824 and 797 for rho ECW and rho ICW in men and women, respectively. These terms will be expressed as apparent rho  in the remainder of the document. The male constants from a previous study (47) listed above were used to predict the dilution ECW, TBW, and ICW of the 14 men. The TBK-determined ICW of these 14 men was also predicted by both BIS- and dilution-ICW volumes. Then, new constants for men were computed from the dilution volumes measured on the sample of 14 men, as described in APPENDIX b. The new rho ICW constant was then used to predict the BIS-ICW volume for the other 73 men and women and cross-validated against their TBK- determined ICW.

The Excel program was used for the statistical analysis. In addition to the descriptive statistics, the Pearson's product moment correlation (r) and standard error of estimate (SEE) statistics were computed. Bland-Altman plots were also constructed to display the individual subject differences between the BIS-predicted water volumes and those determined by TBK and dilution methods.

RESULTS

Table 1 displays the physical characteristics of the two subject groups. Table 2 provides the Cole modeling results for the two subject groups. Of the 87 subjects, according to the criteria rating the fit to the Cole model (APPENDIX a), 21 subjects were rated as 0, 64 were rated as 1, and the remaining 2 were rated as 2. The mean correlation of fit to the Cole model, using scalar Z, was 0.998. With the use of the constants for men from a previous study (47), the dilution ECW was predicted as r = 0.91, SEE = 0.90 liters, with a mean of 21.03 liters and a mean difference of 2.69 liters. Dilution TBW was predicted as r = 0.95, SEE = 1.33 liters, with a mean of 41.02 liters and a mean difference of -4.46 liters. Dilution ICW (as TBW - ECW) was predicted as r = 0.87, SEE = 1.69 liters, with a mean of 19.99 liters and a mean difference of -7.14 liters (Table 3).

Table 1. Descriptive characteristics of TBK and dilution study groups

TBK
Dilution, Men
Men Women Combined
n 63 10 73 14
Age, yr 37.92 ± 9.60  25.33 ± 3.29  36.20 ± 9.99  28.57 ± 6.64 
Height, cm 174.23 ± 7.43  164.55 ± 7.88  172.91 ± 8.20  175.25 ± 6.50 
Weight, kg 74.99 ± 8.71  56.40 ± 4.86  72.44 ± 10.47  74.80 ± 8.83 
TBK-ICW, liters 25.08 ± 3.19  17.54 ± 2.60  24.05 ± 4.06  28.35 ± 3.19 
Potassium, g 147.13 ± 18.72  102.90 ± 15.23  141.07 ± 23.78  166.30 ± 18.71 
ECW, liters 18.34 ± 2.04 
TBW, liters 45.48 ± 3.87 
ICW, liters 27.13 ± 2.63
Values are means ± SD. TBK, total body potassium; n, no. of subjects; ICW, intracellular water; ECW, extracellular water; TBW, total body water.

Table 2. Cole modeling characteristics of TBK and dilution study groups

TBK
Dilution, Men
Men Women Combined
n 63 10 73 14
r of fit 0.9978 ± 0.001  0.9974 ± 0.001  0.9978 ± 0.001  0.9970 ± 0.001 
RE, Omega   582.09 ± 47.86  742.81 ± 44.56  604.13 ± 72.81  577.71 ± 44.87 
RI, Omega   1,109.04 ± 138.72  1,504.73 ± 209.42  1,163.20 ± 202.79  1,020.42 ± 81.33 
Cm, nF 2.32 ± 0.43  1.27 ± 0.26  2.18 ± 0.55  2.24 ± 0.30 
 alpha 0.70 ± 0.02  0.68 ± 0.03  0.70 ± 0.03  0.68 ± 0.01 
fc, kHz 57.02 ± 8.39  80.14 ± 17.22  60.19 ± 12.83  61.96 ± 5.95 
Td, ns 20.66 ± 8.46  32.40 ± 9.43  22.26 ± 9.49   -3.27 ± 4.37
Values are mean ± 1 SD. n, No. of subjects; r, correlation of fit; RE and RI, Cole model electrical resistance terms used to predict volume of ECW and ICW, respectively; Cm, membrane capacitance; alpha , exponent; fc, characteristic frequency; Td, time delay.

Table 3. ECW, TBW, and ICW determined by D2O, NaBr, and BIS

Subject Br BIS-ECW D2O BIS-TBW D2O-Br BIS-ICW
1 20.61 22.93 49.29 43.96 28.68 21.03
2 16.47 18.99 43.9  38.09 27.43 19.10
3 17.86 18.84 42.7  40.36 24.84 21.52
4 22.81 24.45 48.84 45.91 26.03 21.45
5 16.91 20.39 44.33 41.05 27.42 20.66
6 17.41 19.96 43.71 40.18 26.30 20.21
7 16.22 19.53 42.60 38.46 26.38 18.93
8 20.21 23.73 49.40 44.70 29.19 20.97
9 17.19 20.38 43.43 37.87 26.24 17.49
10 15.23 17.83 40.28 35.05 25.05 17.23
11 20.52 22.31 51.42 45.26 30.90 22.95
12 18.71 20.79 41.19 36.00 22.48 15.21
13 17.25 20.97 42.81 40.15 25.56 19.18
14 19.41 23.33 52.78 47.30 33.37 23.97
Mean ± SD 18.34 ± 2.11  21.03 ± 2.02  45.48 ± 4.01  41.02 ± 3.84  27.13 ± 2.73  19.99 ± 2.34
BIS, bioimpedance spectroscopy.

The new rho ECW and rho ICW constants computed from the dilution sample of 14 men were 174.32 and 1,177.94, respectively. For discussion purposes, the computed contants for women became 167.8 and 1,139.34 for rho ECW and rho ICW, respectively. Using the new rho ICW constant for men, the prediction of the TBK ICW for the 73 subjects with BIS ICW was r = 0.85, SEE = 2.22 liters, with virtually no mean difference (i.e., 0.08 liter). When the TBK ICW was predicted by gender (men = 63, women = 10) the correlations and SEE were similar to that of the total group, but there was a slight mean difference (i.e., 0.15 and -0.38). For the 14 men, the correlation and SEE values for the BIS- and dilution-predicted ICW and the TBK-predicted ICW were r = 0.56 and 0.57, and SEE = 2.68 and 2.32 liters, respectively.

To determine the effect that scaling of rho ECW and rho ICW had on the correlation and SEE, the new constants for men were used to repredict the dilution ECW, TBW, and ICW on the 14 male subjects. The correlation and SEE remained identical for ECW (i.e., r = 0.91, SEE = 0.90 liter) with no mean difference. For TBW, the correlation decreased slightly (i.e., r = 0.95-0.94) and the SEE increased slightly (i.e., 1.33-1.41 liters) with no mean difference. For ICW, the correlation decreased slightly (i.e., r = 0.87-0.80) and the SEE decreased very slightly (i.e., 0.01 liter) with no mean difference. Thus, rho ECW is purely a scalar and has no affect on correlation or SEE for ECW. Similarly, rho ICW is effectively a scalar, since changing it only slightly alters the prediction of ICW because the nonlinearity is slight. Figures 5-7 display the plotted differences between the BIS-predicted ECW, ICW, and TBW volumes and the dilution-predicted volumes. Figure 8 displays the plotted differences between the BIS and the TBK-predicted ICW. The ECW prediction was achieved by using the exponent 1.5 predicted by Hanai theory.

Fig. 5. Residual extracellular water (ECW) values plotted against mean values for bioimpedance spectroscopy (BIS) prediction and reference method (sodium bromide). Heavy horizontal line, mean difference (bias); lighter lines, mean ± 2 times SD of differences.
[View Larger Version of this Image (14K GIF file)]

Fig. 6. Residual total body water (TBW) values plotted against mean values for BIS predictions and reference method (deuterium oxide). Heavy horizontal line, mean difference (bias); lighter lines, mean ± 2 times SD of differences.
[View Larger Version of this Image (13K GIF file)]

Fig. 8. Residual ICW values plotted against mean values for BIS predictions and reference method [total body potassium (TBK)] by whole body counting. Heavy horizontal line, mean difference (bias); lighter lines, mean ± 2 times SD of he differences.
[View Larger Version of this Image (15K GIF file)]

DISCUSSION

Effects of mixture, scaling, and reference methods. We constructed an equation from Hanai theory (17) because we wanted to account for as many error sources as possible, and we believed the relationship between R and volume should be explained scientifically rather than randomly through multiple-regression analysis. rho  is dependent on the concentration of nonconductor present in a mixture, giving rise to an empirical exponent ranging from 1.43 for very small spheres to 1.53 for packed cylinders (7, 17). Hanai theory predicts an exponent, 1.5. The exponent 1.5 was recently confirmed in vitro in human blood (9). A linear equation computed from multiple-regression analysis is not well suited to nonlinear effects. Thus it did not seem prudent to solve for a five-dimensional nonlinear biophysical model (i.e., Cole) and then use an overly simplistic volume theory (i.e., Ht2/R) that assumes only one material is being measured. Predicting volume with an equation formed by scientific principles would enhance its utility and address the error sources directly rather than accounting for them statistically, which offers no scientific explanation.

Although the successful prediction of ECW and ICW volume with the equation used in this study has been reported (35, 47), it had not been reported that when we regressed an exponent against NaBr space (47), the highest correlation was achieved by using the exponent 1.5 predicted by Hanai theory. This finding strongly suggests the presence of mixture effects, and the strong predictions by using the exponent 1.5 (10, 35, 47) support the validity of Hanai's theory. As a spherical theory developed in the emulsion sciences, the reasons why Hanai's theory should not work are many, but they do not explain the strength of prediction this theory provides or the emergence of the exact theoretical exponent. In the absence of a more applicable theory, we use the developed equation, because we believe the errors of not accounting for mixture effects are greater than the inadequacy of the theory.
Fig. 7. Residual intracellular water (ICW) values plotted against mean values for BIS predictions and reference methods (deuterium - bromide). Heavy horizontal line, mean difference (bias); lighter lines, mean ± 2 times SD of differences.
[View Larger Version of this Image (14K GIF file)]

Because the strength of the BIS prediction (r and SEE) is independent of scaling, and TBW is determined by ECW + ICW, a good prediction of a dilution TBW would suggest a strong ECW and ICW prediction. This would only not be the case if there were exactly offsetting errors in the ECW and ICW prediction. Thus it is probable that the BIS prediction of ICW was better than that of dilution because the r and SEE were better for the BIS prediction of TBW than that of ICW. The inaccuracies of determining ICW by dilution have not been adequately discussed, nor is it clear whether the errors are additive or propagated. For the 14 subjects, both the dilution and BIS-predicted ICW were poorly correlated to the TBK-ICW. That the TBK-ICW prediction improved substantially for the larger sample of 73 subjects suggests that the poor correlations were caused by outlying data in a small sample. That both BIS and dilution ICW were highly correlated with each other, as well as both poorly correlated to the TBK ICW in the 14 subjects, suggests that the lower correlation between BIS ICW and TBK ICW in the entire sample was due to the error in TBK rather than BIS. Nevertheless, the strength of the discovered relationships among the BIS ICW and dilution and TBK ICW suggests that BCM can be determined by BIS.

The only other equation derived from Hanai theory, or any mixture theory for that matter, was never validated, and its sensitivity to change was poor (9). We believe the results achieved in this and other studies can be attributed to viewing the body as having three compartments (i.e., ECW, ICW, and the remainder) rather than only the two used previously (i.e., ECW, ICW) (9). We also believe this to be attributed to the fact that the Hanai equation describes the effect on conductivity of the material, not the overall conductance. Thus, its use is volume dependent. To apply mixture theory, total volume must be known and is provided by body Wt/body density (Db). Db varies between individuals, but the range is generally within 1-1.07 kg/l (20). The effect on rho ECW in this range is ±1%, because it is only dependent on the cube root of Db. We do not use body Wt as a fudge factor to improve the correlation (8) but rather as a theoretically required term to measure of total body volume. Like Db, body Wt is expressed in cube root form; thus its contribution to the prediction of body water is reduced by 2/3.

The fact that changing rho ECW had no effect on correlation or SEE for ECW, and only slightly for ICW when rho ICW was changed demonstrates the scaling nature of these constants and that they have no effect on the scientific relationship between the BIS and dilution volumes. Large offsets were observed when the constants derived from a previous study were used (47), but these constants, which were derived from D2O and NaBr (47), have been cross-validated (10, 35). As such, it is troubling that rho ECW would decrease by 19% and rho ICW increase by 30%. This difference could have been caused by error in the BIS method. However, the high correlations and low SEE values observed, and the fact that the sample studied was similar to those samples used to calibrate (47) and cross-validate (35) these terms, suggest otherwise. Because subjects were healthy, it is unlikely that there were any major differences in ion concentration. Even so, a 5 mmol change in ion has been found to affect ECW only 1-2% and ICW only 4-5% (38).

Different dilution methods produce differently sized ECW and TBW spaces, e.g., sulfate (35SO4) space being typically 20% smaller than NaBr space (11). Thus, a rho ECW calibrated to NaBr would predict an ECW space scaled 20% larger than 35SO4 space. We have noted (28) that Van Marken Lichtenbelt et al. obtained slightly higher r2 and lower SEE values by using the methods described in this study, but D2O space was underpredicted by -6.3 liters, and the NaBr space overpredicted by 3.0 liters. The NaBr-to-D2O space ratio was in the expected range of 0.40 and 0.42 in this study (Table 1) and the study reported by Van Marken Lichtenbelt (48), respectively. In contrast, the BIS ECW-TBW ratio predicted in this study by the previous constants was 0.51 (Table 3). This supports that the rho ECW constant computed previously (47) may be scaling ECW too large, but this would equally occur if ICW were underestimated. That ICW, and thus TBW, may have been scaled too low was supported by the finding that the percent TBW of body Wt was 61% by dilution and 55% by BIS (Tables 1 and 3). Further evidence that the new rho ICW constant may have validity was that TBK-ICW, which was independent from dilution, was predicted with very little mean difference. It is of concern that the previously determined constants are predicting ECW and TBW with little mean difference at some laboratories but not others. There is nothing apparent in the dilution methods used in this study, by Van Marken Lichtenbelt et al. (48) or Van Loan et al. (47). For D2O, each used accepted protocols (e.g., fasted state, dosage, and equilibration time). Both we and Van Loan et al. (47) analyzed D2O enrichment with an accepted infrared spectrophotometry method and Van Marken Lichtenbelt et al. (48) with an accepted isotope-ratio mass spectrometry approach. All three laboratories corrected for isotope fractionation. The only variable identified was that we did not make a baseline measure of D2O, which potentially could lead to an underprediction of TBW space. However, this is unlikely to explain such a large scaling difference. We also did not account for D2O lost in the urine, but the subjects were measured in a fasted state and refrained from drinking or eating; thus, this is unlikely to explain such offset. Similarly, for NaBr, all three laboratories used accepted administration and analytical protocols, including 10% corrections for nonextracellular distribution and 5% Donnan equilibration. As did Van Marken Lichtenbelt et al. (48), we measured NaBr concentrations with the accepted anion-exchange chromatographic method (32, 50), and Van Loan et al. (47) used a fluorescent-excitation technique. The only variables not accounted for were basal NaBr concentrations and NaBr lost in the urine during the equilibration. However, over such a short period of time and with the subjects being in a fasted state, the loss in NaBr in the urine would be small, as would be the error caused by not subtracting baseline NaBr from the plasma after administration (32). There are other variations (such as hydration status and metabolic rates) (11), but these also would not explain such large offsets. As such, there was little difference in the methods used. The offset could be attributed to the small sample size (n = 24) originally used to compute rho ECW and rho ICW (47), but if correctly determined there should not be such large deviations between individuals or samples. The validity of these terms is supported by their correspondence to biophysics results and cross-validation.

If BIS or even the same dilution methods have such variation, it will be difficult to completely standardize the BIS prediction of ECW and ICW. To establish whether this variability is BIS or dilution based, rho ECW and rho ICW should be computed from D2O and NaBr collected from a large, well-standardized, multiple-laboratory study. Later studies could then use the same methods to judge how well these terms hold up. However, if constants can be derived that allow ECW and ICW to be predicted close to an accepted reality, the change in volume may become the most relevant clinically. The change in BIS-predicted volume has been reported to be quite good (10, 18). Despite the small gender difference discovered in rho ECW and rho ICW (35, 47), this may be only a sample-specific phenomenon. Isolating rho ECW and rho ICW will allow investigation of the specific effects of temperature and ion concentration on ECW and ICW, rather than using a gross single-frequency tissue measurement.

Effects of geometry on rho . A wrist-ankle measurement would be inappropriate for patients with ascites, but the vast majority of subjects do not have such conditions (29). The good predictions of body water reported by this and many other studies using a wrist-ankle measurement supports that body water is evenly distributed in healthy subjects. If not, good predictions of body water would not be possible. To evaluate the error caused by making a wrist-ankle measurement and determine the validity of rho ECW and rho ICW computed previously (47), we compared the values of these terms to results reported in biophysics for plasma and ICW. First, we used standard anthropometric values for the ratios of arm, leg, and trunk lengths and girths (45) in the equation listed in APPENDIX c to compute a geometry constant KB and remove the geometry effects on rho . Albeit a rough approximation, because the arms, legs, and trunk are not perfect cylinders and the fraction of ECW and ICW is not constant between segments, an approximation should be possible. The value for KB was computed to be 4.3. The longitudinal rho  of human skeletal muscle tissue measured at 1 kHz has generally been reported to be 200-300 Omega  · cm. (14). These reported measures for apparent rho  were obtained from direct measurements on skeletal muscle tissue (14) and thus were corrected for the mixture effects caused by the ICW contained in that muscle. Assuming the fluid distribution found in a previous study (47) to be representative of healthy adults (45% ECW in TBW and 73% TBW in FFM), the concentration of nonconductive material in the skeletal muscle tissue was estimated to be 67.2%. By using Eq. C4, this yielded a rho  for ECW of nominally 250 · (1 - 0.672)1.5 or rho ECW of 47 Omega  · cm. Our results indicated that kECW was nominally 0.311; by using a nominal Db of 1.05 kg/l, this relates to a rho ECW of 41 Omega  · cm, which is in reasonable agreement with both the rho calculated from skeletal muscle tissue measurements and to the rho  for pure ECW reported (50-60 Omega  · cm)(14). Thus the distribution of ECW throughout the body was very consistent, and there was no significant error caused by making a wrist-ankle measurement. Similarly, the values found for krho (i.e., 3.6) and alpha  (i.e., 0.7; Table 2) were in reasonable agreement with the values of 0.3 and 0.6 previously reported in biophysics (5, 14), respectively. These findings have been replicated in a pediatric sample where the computed rho ECW was within 5% (49) of the value discovered in healthy adults (47). It is uncertain how the mixture effects will be adequately accounted for with a segmental measurement.

Principles of fitting data to a biophysical model. Plots are used to construct an applicable physical or mathematical model. Once a model has been constructed, computing the components of the model becomes the focus (5, 25, 40). The Cole model can be computed graphically or mathematically by drawing or fitting the best fitting curve through the data and extrapolating each end of the curve to where it intercepts the resistance axis (known as R0 and Rinfinity ) (Figure 3). R0 equals RE; thus, once R0 an Rinfinity are known, RI can be determined by 1/Rinfinity  - 1/R0 = 1/RI. Fitting is generally performed mathematically because it is far more precise (25). Modeling can also be performed either manually or mathematically by simply fitting a circle through the measured R and X data (6, 43) but this approach does not include f and thus is two dimensional, using one-third less data to determine and cross-check the best fit. This method also provides no estimate of Cm but most importantly does not allow for the effects of Td to be removed. Network analysis is a well-known analytical technique, and the common method used for fitting data to a network model is to simultaneously fit f and weighted Z and theta  data, using nonlinear least squares curve fitting (25). The important data are not at LF and HF but in the middle surrounding fc because these data have greater certainty. To accurately fit and extrapolate a curve requires adequate data on either side of fc. Properly weighting the raw data is essential for obtaining the most accurate fit to the model (25) because measurements may have greater uncertainties at LF and HF. By weighting, the data with more certainty (i.e., middle) make a greater contribution to the overall fit to the model (25). Determining what weights to use is not easily decided (25), and simultaneously fitting a multidimensional nonlinear equation is an art, with the raw data having a very complicated relationship to the final fitted parameters. Evaluating the accuracy of fit should be determined by comparing the offset to fit to the expected measurement uncertainty at each f (25). Because of weighting and the Cole model being multidimensional, evaluating the fit with a two-dimensional statistical analysis [e.g., root mean square error (RMSE) of R and X] would be meaningless (8, 27, 43). Weighting can be determined by measuring the range of error at each f, according to the expected error in the measured quantities (e.g., accuracy specifications of the device), or as we use by weighting the error rather than the data by comparing the expected error with the actual error (25). Limitations must be enforced to prevent the software from forcing a fit. As many frequencies as possible should be used because solving for five unknowns requires at least five data, and all data are potentially contaminated with error (e.g., interference) and thus are uncertain (25). The ability to delete data that are significantly decreasing the overall accuracy of fit is a highly desirable capability (25). The accuracy of resolving a model is a function of the square root of the number of extra data pairs (i.e., Z and theta ) over the number of variables in the model. A 16:1 increase in data provides a 4:1 improvement. However, processing time is effectively the square of the number of data pairs. Thus, a 16:1 increase in data takes 256 times longer to compute. We presently measure at 50 frequencies logarithmically spaced from 5 kHz to 1 MHz to balance between accuracy and processing time. It is important to space the frequencies logarithmically to ensure a proper density of data. We fit with both Z and theta  (rather than Z alone, or R and X) to ensure the best possible accuracy of fit. If only Z is modeled (8), the overall accuracy is reduced (25). Using Z and theta  provides twice the amount of data, and theta is an extremely important discriminating variable because it has a much broader range of sensitivity to change than Z. However, using theta  requires that the time delay (Td) effects must be accounted for (37). We fit with Z and theta  vs. R and X because the weighting introduced by X would enhance the importance of frequencies furthest away from fc and thus emphasize the opposite to what is needed. Furthermore, fitting against R and X is more complex and considerably slower because X is nonlinear.

Effects of f invariant Td. As published (30) and provided in Xitron's product literature since 1992, we recommend investigators extend the HF range of the measurement by removing the effects of Td by multiplying the Cole equation by the factor e-jwTd, where e is natural number, j is radical -1, and w is f in radians/s. Despite the confusion this parameter has caused (8, 43), all conductors exhibit a Td that causes a linear theta  shift with f. Conductor length would be an obvious cause for Td (copper wire having a Td of ~1.2 ns/ft), whereby an 8-ft conductor length (e.g., wrist to ankle) would produce 10 ns of delay (37). However, a longer Td of 32.4 ns was observed in the female subjects (Table 2). This is because Td can also be caused by interaction between contact R, stray capacitance and transmission line effects, with the latter including conductor length (wrist to ankle) and the conductor (i.e., body) position relative to ground (floor, bed, table, and so on) (15). Only conductor length is a true Td effect, but in the 1 kHz-1 MHz f range the other effects also give rise to a linear theta  shift with f and thus can be approximated as a Td. For simplicity, all effects will be labeled as Td throughout the discussion. The various causes of Td were simulated by using the widely available SPICE circuit-simulation software program (Intusoft, San Pedro, CA) and using the SPICE file shown in Table 4. Td were modeled by a high-Z transmission line with conductor length set by Td, and the body Z was modeled by a simple three-element model (no alpha ) using an RE = 680, RI = 900, and Cm = 2.8 nF. Figure 9 shows a plot of theta  vs. f in the 1 kHz-1 MHz f range for body Td of 0, 15, and 30 ns of Td and a characteristic transmission line impedance (Zc) of 300 Omega . Because the body is usually suspended some distance from a ground plane, the body behaves like a transmission line (15). Figure 10 shows theta  vs. f by using the same three-element values for RE, RI and Cm, a fixed conductor length Td of 15 ns, and a Zc of 150, 300, 450, and 600 Omega , respectively.

Table 4. SPICE file for simulating circuit time delay effects

Fig. 9. SPICE plot of phase (theta ) vs. frequency ( f ), simulating effects of time delay Td of 0 ns (1), 15 ns (2), 30 ns (3) caused by different conductor lengths on 3-element model consisting of RE in parallel with series RI and Cm and fixed transmission line characteristic impedance of 300 Omega .
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Fig. 10. SPICE plot of theta  vs. f, simulating effects of Td caused by different transmission line characteristic impedances of 150 (1), 300 (2), 450 (3) and 600 Omega  (4) on 3-element model consisting of RE in parallel with series RI and Cm and fixed conductor length Td of 15 ns.
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For convention, theta  in these plots is expressed as having positive polarity. As shown in Figs. 9 and 10, there is a significant linear theta  shift with f caused by both conductor length (wrist to ankle) and conductor (body) relative to ground. Adjustment of the various parameters (e.g., distance from ground plane) in the simulation circuit changed the magnitude and frequency at which Td effects emerged. As shown in Figs. 11 and 12, there can be considerable variations in Td between subjects. Different devices, subjects, and environments will cause different responses to the variables causing Td (15). The interaction between variables resulted in an effect larger than their sum and begin to affect Z slightly over 1 MHz. As shown in Fig. 10, the effects caused by conductor relative to ground can cause a negative Td and opposite effect on theta , thus explaining the negative Td shown in Table 2. Although less accurate than modeling, the Td effects can be removed manually by the methods described in APPENDIX d.
Fig. 11. Plot of theta  vs. f of measured data (raw) and data fit to Cole model on 1 subject with calculated Td of -1.3 ns.
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Fig. 12. Plot of theta  vs. f of measured data (raw) and data fit to Cole model on subject with calculated Td of 36.1 ns.
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It is disappointing that several investigators would not use or even mention our suggested methods and information on Td, then cause undue confusion by reporting an intermediate result and incorrectly attributing the deviation in the raw X data from the Cole model to measurement error (8, 43), particularly when these methods had been disclosed and used to successfully predict ECW and ICW volumes for the first time using Cole model terms RE and RI (30, 47). The effects of Td are linear on theta  not on X, and in the f range of interest Td only significantly affects HF theta  shifts not Z (37). If Td were not a valid term, the correlation of fit of Z (which is the radical R2 + X2) would also be seriously reduced, whereas it is not (i.e., 0.998; Table 2). Stroud et al. (43) should have questioned their conclusions, because if the measurement was poor, the data would not have corresponded so well to an electronic circuit. Similarly, Deurenberg et al. (8) should have questioned their conclusions when there was no deviation of Z from the model at HF (8), and as stated, the final fit to the model included data up to 500 kHz. To review APPENDIX a, it can readily be seen that any f significantly affecting the overall fit will be deleted.

The practical reasons for modeling for Td are simple. There are Td effects in all raw data to varying degrees (15); thus as much of the Td effects as possible should be removed from the analysis. Fortunately, in the f range of interest, all the effects of Td cause a linear theta  shift with f. Because the Cole model (i.e., Cm) causes a nonlinear theta  shift with f, the effects of Td can be effectively modeled and significantly removed. Our modeling program and information on Td were widely distributed in 1992. As such, it would not be difficult to adjust the various parameters to push out to higher frequencies where the effects of Td become dominant. However, as discovered by Stroud et al. (43), without removing the effects of Td, only useful data up to 500-600 kHz will be obtained (43). Table 5 is an output file (.MDL file) generated from our fitting software on one of the subjects of this study. As shown, few data were deleted from the final fit, and frequencies up to 1 MHz were included. Without removing the effects of Td, inclusion of such HF data would not be possible. The problem with not modeling for Td is that there are variations in the environment in which measurements will be performed, and it is not uncommon, particularly in the clinical setting, to observe fcs >500 kHz. With usable data only to 500-600 kHz, it would not be possible to accurately fit for RI. Although the physics underlying Td is important, what is important to the prediction of ECW and ICW is to remove the effects of Td so the highest possible f range can be included. Even with lower fc, the closer the actual data are to Rinfinity , the better the calculation of RI will become.

Table 5. Modeling software output file (MDL) displaying measured versus calculated data fit to the Cole model

Dual- and single-frequency measurements. Biophysicists have been fitting Z data to models since the early 1920s. However, before 1963 when a dual LF-HF Z approach was first introduced as a measure of ECW and TBW (44), measuring Z was much more difficult. Additionally, solving a five-dimensional nonlinear equation by hand without a microprocessor would have been extremely tedious. Although pragmatic at the time, it can readily demonstrated (Figs. 1 and 13) that for some subjects where the current is fully conducting through the ICW does not occur until >10 MHz. A f of 10 MHz is 100-fold away from 100 kHz. Thomasset (44) reported in 1963 that 100 kHz was too low a f. Even if higher frequencies could be measured, the effects of gamma dispersion must still be avoided (Fig. 1). Similarly, the effects of alpha -dispersion become dominant near 1 kHz and must be avoided (Fig. 1). Most importantly, the proportion of current conducting through the cells at "any" single f is not fixed but varies with fc, and fc varies between individuals, as well as in the same individual when RE, RI, Cm, or alpha  is altered (5, 22, 26, 40; Figs. 1, 13, and 14). By fitting the data to the R0 and Rinfinity , the above error sources are removed. Jaffrin (19) reported that the overestimation of RI can be as high as 200% by not using Rinfinity (19).
Fig. 13. Resistance vs. frequency of 3 patients pre- and postdialysis. Data provided by and used with permission of Krassimir Katzarski, Dept. of Renal Medicine, Karolinska Institute, Stockholm, Sweden.
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Fig. 14. Impedance locus of 1 patient pre- and postdialysis. Data provided by and used with permission of Krassimir Katzarski, Dept. of Renal Medicine, Karolinska Institute, Stockholm, Sweden.
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As shown in Figs. 1 and 13, a 50-kHz measurement is neither a measure of ECW or TBW but rather some of both. No single HF measurement is a measure of TBW, including Rinfinity and Z at fc as promoted by Cornish et al. (6, 27), but rather a measure of two significantly different fluids. The rho ECW has been reported to be 50-60 Omega  · cm (14) and the rho ICW to be 200-300 Omega  · cm (5). It has been previously assumed that the rho  of TBW is constant. Obviously this assumption is invalid because a simple change in the ECW-ICW ratio would dramatically change it. This error can be reduced, as we have done, by using the measured RE and RI with the previously established constants rho ECW and rho ICW to determine the actual relative proportions of ECW and ICW. From this, one can establish the rho  of TBW. The equation shown uses a linear mixture effect; however, in practice a nonlinear ECW-ICW mixture effect was used. The difference is insignificant in healthy subjects or when small changes are not of concern.

The prediction of ECW is inherently better than ICW and TBW for both technical and theoretical reasons. The prediction of ECW is achieved directly from model term RE, whereas ICW is predicted effectively by the difference between two large numbers (Rinfinity and R0). Thus, a 0.1% error in Rinfinity is approx 0.5% error in the predicted ICW. Although there is a call for a return to a HF and LF approach because Rinfinity is more variable than a fixed HF (8), the above error sources can never be resolved with a fixed-f nonmodeling approach; thus, it is fraught with error. On the other hand, the repeatability and accuracy of solving for Rinfinity and thus ICW is technical rather than theoretical in nature. Improvements in the measurement should reduce the variability in predicting ICW.

Parallel reactance, phase angle, and cell membrane capacitance. Series reactance at 50 kHz (Xs) had been proposed as a measure of ECW (41) and as a measure of the extracellular mass/BCM ratio (42). A 50-kHz parallel X model (Xp) has now been proposed as a measure of BCM (3, 23). To support this proposal, Lukaski (23) performed a progressive potato study to demonstrate the f dependence of biological tissue (23) and drew on the statement by Foster et al. (12) that Z can be interpreted as either a parallel or series circuit and both resulting in two final elements (real and imaginary). The later is absolutely true for any single f measurement, but biological tissue consists of more than two elements. Z at any single f can be interpreted as a parallel or series circuit, but the field is concerned with how to interpret the Z of biological tissue. According to Fricke (13), Schwan (40), and Cole (5), single biological cells can be represented as a series-parallel network having three elements: RE in parallel with a series Cm and RI. Cole (5) added an exponent (alpha ) to the model to represent the distribution effects observed on biological cell suspensions and tissues. The Cole model is used most often to interpret Z measured on biological tissue and consists of four elements (31). Based on the belief that how biophysicists interpret Z measurements has merit, we use the Cole model. To do this, we fit all real and imaginary data (i.e., corresponding Z and theta ) to the Cole model to discriminate the component parts of the tissue.

If previous work in biophysics does have validity, the use of R and X at any single f to predict ECW or ICW would be an oversimplification and is dependent on the elements in the tissue having relative uniformity between individuals. Any relationship between BCM and X is likely a function of the relationship between X and Cm because ICW is a resistive not capacitive medium. It has been suggested that as the cell swells, the membrane becomes thinner and Cm increases, and the opposite occurs when the cell shrinks (16). However, X at any single f is not merely Cm, and Cm can only be computed by modeling for all the elements in the Cole model (5, 25, 40). Which variable is affecting X at any single f cannot be determined. However, since RE, RI, and alpha  tend to be tightly regulated and vary within narrow limits, X would tenuously reflect Cm and give rise to a correlation to cell volume.

To investigate the strength of the relationship between Cm and the variables related to Cm and BCM as defined by TBK, we investigated their correlation to TBK. As shown in Table 6, weight was strongly correlated to TBK, but variables other than BCM can cause a change in weight. Cm alone was strongly correlated to TBK and improved when expressed as Ht2 × Cm. There was a poor direct relationship between Xs and Xp and TBK and Cm, respectively. Xs and Xp were moderately correlated to TBK when expressed as Ht2/Xs or Ht2/Xp, respectively, but Ht alone was highly correlated. fC was also correlated to TBK, but mathematically fc is dominated by Cm and RE, and since this healthy population would have a narrow range in RE in relation to the other model parameters, the relationship between fc and TBK was most likely dominated by Cm. As shown in Table 6, there was a strong relationship between fc and Cm. Use of fc cannot be supported, because it is affected by all the variables in the model, but as expected, fc predicted TBK better than X at 50 kHz. The mean fc for this healthy sample was approx 60 kHz (Table 2); thus, X would approximate fc. However, fc was more highly correlated than X simply because fc more closely reflects Cm, whereas the strength of the relationship between X and Cm varied with fc, which ranged in this sample from 43 to 110 kHz. The strong relationship between Cm and TBK was expected because Cm is a function of cell surface area. The moderate relationship between Cm and weight reflects this dependence. However, Cm is also affected by the aspect ratio (length to cross-sectional area) of the body's conductor. With an identical total cell volume, a greater conductor length would cause less Cm, whereas a greater conductor cross-sectional area would cause higher Cm. Although error caused by aspect ratio is removed by length2 × Cm, this is only true for a uniform cylinder. Further refinements in Cm would need to be made by accounting for KB (APPENDIX c). As discussed above, Cm is also affected by the thickness of the cell membrane. With the errors caused by aspect ratio and cell membrane thickness, it is unclear why a surface measurement (i.e., Cm) would be used to reflect what is inside the cells when it can be determined more directly by a resistive-predicted ICW (ICWR).

Table 6. Correlation between various variables in total TBK study group (n = 73)

Ht Wt Cm fc Ht2 * Cm Ht2/fc Ht2/Xs Ht2/Xp
TBK 0.58 0.64 0.50  -0.39 0.73 0.62 0.43 0.69
Cm 0.33  -0.81
Ht, height; Wt, weight; Xs, series reactance; Xp, parallel reactance.

A single 50-kHz-frequency measure of X and theta , and an R-X graph have been proposed as measures of fluid distribution and discriminating indexes of health and disease (2, 36). Recently, theta -angle spectrum analysis (that is, theta  vs. f) has been proposed as descriptive of body water and body composition (4). theta  angle is a function of the ratio of R and X; thus, both theta  and an R-X graph would be sensitive to the same errors and uncertainties as any single frequency of R and X. The sensitivity of theta  is extremely dependent on X, which in turn is extremely dependent on the relationship between the frequency of measurement and fc, and is symmetrical about fc. X and theta  at 50 kHz change dramatically when fc changes, simply because 50 kHz is a fixed point on the changing curve (22, 26) (Fig. 14). X simply changes more than R because X is only 5% of the total Z; thus, a slight change in fc causes a greater percentage change in X. In 1974 (Fig. 14; see Ref. 34), it was observed that dialysis patients had a lower X and theta  measured at 50 kHz predialysis and that it returned to that observed in healthy subjects postdialysis. Lofgren (22) attributed the cause of this to the change in fc 23 yr previously. The change in X and theta  with a change in fluid distribution has given the incorrect impression that X and theta  are somehow directly related to fluid distribution. A change in fluid distribution does change fc, which in turn changes X and theta , but this is principally caused by a change in ECW (and Cm, as discussed above). Again, the problem with using X, theta , or fc to reflect any body composition parameter is that these variables are affected by all the elements in the tissue (APPENDIX a). One can question the utility or need for X, theta , fc, or an R-X graph when which variable is causing their change cannot be determined and they have no theoretical basis. On the other hand, RE and RI at least relate in theory to a physical object (i.e., ECW and ICW).

On the same individual, Cm is determined by total cell volume and membrane thickness and porosity (5). Thus, any Ht2 × Cm relationship would be a function of these three parameters. An ICWR can be used to predict total cell volume, and then if removed from the KB corrected Ht2 × Cm relationship by using Ht2 × Cm/ICWR, the remaining index would reflect cell membrane thickness and porosity. Such a measure might have several applications. Scheltinga et al. (39) observed that as the severity of sepsis increased, Cm decreased to the point where there was virtually no beta - dispersion. This corresponds to what Lukaski (23) observed on a cooked potato. It is well known that with cell death or cell destruction, the cell membrane loses its high resistive properties. During dialysis, ECW changes are on the order of 20-30%, RI varies little, but both Fc and Cm can change by as much as 2:1 (1, 19) (Fig. 14). As shown in Table 2, the mean Cm for the male subjects of this study was 2.32 nF. Bestoso et al. (1) discovered a mean increase of Cm in men from pre- to postdialysis of 64% (1.64-2.47 nF), with the postdialysis Cm being quite close to that measured in the men in this study. Thus, if Scharfetter's (38) estimates are correct that a 5-mmol change in ion affects the ICW 4%, the error caused by ion on ICWR, as well as the error in predicting ICW, would be insignificant compared with the percentage change in Cm. Use of Cm for studying cell membrane health is an exciting area of research that awaits further investigation.

In conclusion, there has been very poor crosstransfer of information from the fields of physics and engineering to the field of human body composition. It does not help that the principles of BIS and mixture theory are rather complicated for many investigators. However, Z is an engineering- and physics-based technique, and the principles and merits of modeling and mixture theory have been known for a very long time. Multiple-frequency devices safe for human studies and modeling programs have now been available for >4 yr; thus, the lack of appropriate equipment is no longer a valid reason for not using modeling. Due to the high intercorrelation (48) among ECW, ICW, and TBW, one can always correlate a limited single- or dual-frequency measurement to body water, but this leads to population-specific equations and a reduced sensitivity to change, which is why Z measurement has not yet reached its full potential. Until investigators begin using the proven and accepted fundamental techniques used in other fields of science (i.e., modeling) that use Z measurements (e.g., biophysics, advanced materials research, and chemical engineering), the use of Z in clinical medicine will remain what it is today---a technique that generates many papers but has no real clinical application.

FOOTNOTES

Address for reprint requests: J. Matthie, Medical Dept., Xitron Technologies, Inc., 6295 Ferris Sq., Suite D, San Diego, CA 92121 or A. De Lorenzo, Dept. of Human Physiol., Univ. of Rome "Tor Vergata," via O. Raimondo 1, I-00173, Rome, Italy.

Received 23 May 1996; accepted in final form 13 November 1996.

APPENDIX a

Modeling

The Z and theta  spectra data were fit to the Cole-Cole model (5), Eq. A1, using iterative nonlinear curve-fitting software. The modeling program evaluated the weighted least square error of both Z and theta , where the weighting is established by the published accuracy specifications of the instrument, and removed any f that would significantly decrease the total weighted least square error. In addition to the correlation of fit using scalar Z, the program established the accuracy of fit to the model as follows:

1) Mean offset to fit <1/2 the instrument measurement specifications.

2) Mean offset to fit less than the instrument measurement specifications.

3) Mean offset to fit <2 × the instrument measurement specifications.

4) Mean offset to fit <5 × the instrument measurement specifications.

5) Mean offset to fit >5 × the instrument measurement specifications.

To prevent the program from deleting frequencies solely to "force" a fit to the model, the following limitations were enforced in the software

1) A maximum of 25% of the frequencies (f) may be deleted.

2) Within any 3:1 range of f, at least one f must remain.

3) Only f whose Z and theta  lay more than the instrument specification from the curve may be deleted.

4) Only one f is deleted per iteration of fitting.

5) A f is only deleted if it results in the maximum improvement in resultant fit; this is not necessarily the f whose Z and theta  lay farthest from the fit.

The Cole model was extended to allow for the f invariant time delay (Td) caused by the speed at which electrical information is transferred through a conductor (15, 37). The error introduced by this fixed Td was modeled as a theta  error that increases linearly with f. This linear theta  error was mathematically modeled by multiplying Eq. A1 by the factor e-jwTd. Thus the overall modeled equation was
Z<SUB>obs</SUB> = <FENCE><FR><NU>R<SUB>E</SUB></NU><DE>R<SUB>E</SUB> + R<SUB>I</SUB></DE></FR></FENCE> <FENCE>R<SUB>I</SUB> + <FR><NU>R<SUB>E</SUB></NU><DE>1 + [ <IT>j</IT>w<IT>C</IT><SUB>m</SUB>(R<SUB>E</SUB> + R<SUB>I</SUB>)]<SUP>&agr;</SUP></DE></FR></FENCE> (e<SUP>−<IT>j</IT>wT<SUB>d</SUB></SUP>) (A1)
where Zobs is the observed complex Z; RE, RI, and Cm are the component values of this circuit; w is f in radians/s (= 2pi × f ); and j is radical -1.

fC was computed after the model components (RE, RI, CM, Td, and alpha ) had been determined by solving the equation
<FR><NU>∂X(<IT>f</IT><SUB>c</SUB>)</NU><DE>∂&ohgr;</DE></FR> = 0 (A2)
where X(fc) is the imaginary part of Eq. A1 at fc.

APPENDIX b

Theoretical Volume Equations

The ECW and ICW volumes were predicted from the modeled RE and RI by using equations formulated from Hanai's theory, which describes the effect that a concentration of nonconductive material has on the apparent resistivity (rho ) of the surrounding conductive fluid, and is
&rgr; = <FR><NU>&rgr;<SUB>0</SUB></NU><DE>(1 − C)<SUP>3/2</SUP></DE></FR> (B1)
where rho  is the apparent rho  of a conductive material; rho 0 is the actual rho  of a conductive material; and C is volumetric concentration of the nonconductive material contained in the mixture.

From Eq. B1, with the following assumptions, we derived a set of equations as follows
V<SUB>ECW</SUB> = <IT>k</IT><SUB>ECW</SUB><FENCE><FR><NU><IT>L</IT><SUP>2</SUP><RAD><RCD>W t</RCD></RAD></NU><DE>R<SUB>E</SUB></DE></FR></FENCE><SUP>2/3</SUP> (B2)
where VECW is the predicted total extracellular fluid volume (in liters)
<IT>k</IT><SUB>ECW</SUB> = <FR><NU>1</NU><DE>1,000</DE></FR> <FENCE><FR><NU><IT>K</IT> <SUP>2</SUP><SUB>B</SUB>&rgr;<SUP>2</SUP><SUB>ECW</SUB></NU><DE>D<SUB>b</SUB></DE></FR></FENCE><SUP>1/3</SUP> (B3)
Wt is body weight (kg); L is height (cm); RE is the value from the model fitting (Omega ); KB is a factor correcting for a whole body measurement between wrist and ankle, relating the relative proportions of the leg, arm, trunk, and height (see APPENDIX c). rho ECW is the rho  of extracellular water (Omega  · cm); Db is body density (kg/l)
<FENCE>1 + <FR><NU>V<SUB>ICW</SUB></NU><DE>V<SUB>ECW</SUB></DE></FR></FENCE><SUP>5/2</SUP> = <FENCE><FR><NU>R<SUB>E</SUB> + R<SUB>I</SUB></NU><DE>R<SUB>I</SUB></DE></FR></FENCE> <FENCE>1 + <FR><NU><IT>k</IT><SUB>&rgr;</SUB>V<SUB>ICW</SUB></NU><DE>V<SUB>ECW</SUB></DE></FR></FENCE> (B4)
where
<IT>k</IT><SUB>&rgr;</SUB> = <FR><NU>&rgr;<SUB>ICW</SUB></NU><DE>&rgr;<SUB>ECW</SUB></DE></FR> (B5)
RI is the value from the model fitting (Omega ).

The following assumptions were made:

1) The volumetric concentration of nonconductive elements in the body at low frequencies (LF) is given by
1 − <FR><NU>V<SUB>ECW</SUB></NU><DE>V<SUB>Tot</SUB></DE></FR>
where VTot is the total body volume.

2) The volumetric concentration of nonconductive elements in the body at high frequencies (HF) is given by
1 − <FR><NU>V<SUB>ECW</SUB> + V<SUB>ICW</SUB></NU><DE>V<SUB>Tot</SUB></DE></FR>

3) VTot is body Wt/Db.

4) The total volume of a body fluid can be described by
V<SUB>F</SUB> = <IT>K</IT><SUB>B</SUB>&rgr;<SUB>F</SUB> <FR><NU><IT>L</IT><SUP>2</SUP></NU><DE>R</DE></FR> (B6)
where VF is the total volume of the fluid in the body; KB is a factor relating the relative proportions of the leg, arm, torso, and height; rho F is the rho  of the water; L is body height; and R is the measured resistance between wrist and ankle.

5) The factors Db, KB, and rho F can be considered largely constant.

6) The Hanai equation is applicable at HF and LF to mixtures found in the human body.

By using Eqs. B2 and B4, predicted VECW and VICW were computed, from which predicted TBW was computed by using the following equations
TBW = V<SUB>ECW</SUB> + V<SUB>ICW</SUB> (B7)

Computing the Constants

kECW is established as the mean value of
V<SUB>ECW</SUB><FENCE><FENCE><FR><NU><IT>L</IT><SUP>2</SUP><RAD><RCD>Wt</RCD></RAD></NU><DE>R<SUB>E</SUB></DE></FR></FENCE><SUP>2/3</SUP></FENCE>
using a standard spreadsheet program. The method used to derive krho is to repetitively predict VICW/VECW and adjust krho until a minimum mean error between the predicted and measured ratio is obtained.

APPENDIX c

Derivation of KB

It should be noted that the derivation for KB shown here is only an approximation for the purposes of confirming whether its use results in a rho ECW value that is within the range measured by other investigators.

The resistance (R) of a cylinder, measured longitudinally, is given by
R = &rgr; <FR><NU><IT>L</IT></NU><DE><IT>A</IT></DE></FR> (C1)
where rho  is the resistivity of the material; L is the length of the cylinder; and A is the cross-sectional area of the cylinder.

Restating Eq. C1 in terms of the cylinder length and circumference
R = &rgr; <FR><NU>4&pgr;<IT>L</IT></NU><DE><IT>C</IT> <SUP>2</SUP></DE></FR> (C2)
where C is the circumference of the cylinder. The volume of the cylinder is given by
V = <FR><NU><IT>LC</IT> <SUP>2</SUP></NU><DE>4&pgr;</DE></FR> (C3)

If we consider the body to be formed by five cylinders (the legs, the arms, and the trunk), then the volume of the body is given by
V = 2 <FENCE><FR><NU><IT>L</IT><SUB>a</SUB><IT>C</IT> <SUP>2</SUP><SUB>a</SUB></NU><DE>4&pgr;</DE></FR></FENCE> + 2 <FENCE><FR><NU><IT>L</IT><SUB>l</SUB><IT>C</IT> <SUP>2</SUP><SUB>l</SUB></NU><DE>4&pgr;</DE></FR></FENCE> + <FENCE><FR><NU><IT>L</IT><SUB>t</SUB><IT>C</IT> <SUP>2</SUP><SUB>t</SUB></NU><DE>4&pgr;</DE></FR></FENCE> (C4)
where La and Ca are the length and circumference, respectively, of an arm; Ll and Cl are the length and circumference, respectively, of a leg; and Lt and Ct are the length and circumference, respectively, of the trunk.

When we measure the Z between the wrist and the ankle, the measured value will be
R = <FENCE>&rgr; <FR><NU>4&pgr;<IT>L</IT><SUB>l</SUB></NU><DE><IT>C</IT> <SUP>2</SUP><SUB>l</SUB></DE></FR></FENCE> + <FENCE>&rgr; <FR><NU>4&pgr;<IT>L</IT><SUB>t</SUB></NU><DE><IT>C</IT> <SUP>2</SUP><SUB>t</SUB></DE></FR></FENCE> + <FENCE>&rgr; <FR><NU>4&pgr;<IT>L</IT><SUB>a</SUB></NU><DE><IT>C</IT> <SUP>2</SUP><SUB><IT>A</IT></SUB></DE></FR></FENCE> (C5)
But in Eq. B6 we assumed that R was given by
V = <IT>K</IT><SUB>B</SUB> &rgr; <FR><NU><IT>L</IT><SUP>2</SUP></NU><DE>R</DE></FR> (C6)
where L is the height.

Combining Eqs. C4, C5, and C6 yields
<IT>K</IT><SUB>b</SUB> = <FR><NU>1</NU><DE><IT>L</IT><SUP>2</SUP></DE></FR> <FENCE><FENCE><FR><NU><IT>L</IT><SUB>l</SUB></NU><DE><IT>C</IT> <SUP>2</SUP><SUB>l</SUB></DE></FR> + <FR><NU><IT>L</IT><SUB>t</SUB></NU><DE><IT>C</IT> <SUP>2</SUP><SUB>t</SUB></DE></FR> + <FR><NU><IT>L</IT><SUB>a</SUB></NU><DE><IT>C</IT> <SUP>2</SUP><SUB>a</SUB></DE></FR></FENCE> (2<IT>L</IT><SUB>a</SUB><IT>C</IT> <SUP>2</SUP><SUB>a</SUB> + 2<IT>L</IT><SUB>l</SUB><IT>C</IT> <SUP>2</SUP><SUB>l</SUB> + <IT>L</IT><SUB>t</SUB><IT>C</IT> <SUP>2</SUP><SUB>t</SUB>)</FENCE> (C7)
If we relate Lx and Cx to height by factors Kxl and Kxc respectively (i.e., Lx = KxlL), Eq. C7 becomes
<IT>K</IT><SUB>B</SUB> = <FENCE><FENCE><FR><NU><IT>K</IT><SUB>ll</SUB></NU><DE><IT>K</IT> <SUP>2</SUP><SUB>lc</SUB></DE></FR> + <FR><NU><IT>K</IT><SUB>tl</SUB></NU><DE><IT>K</IT> <SUP>2</SUP><SUB>tc</SUB></DE></FR> + <FR><NU><IT>K</IT><SUB>al</SUB></NU><DE><IT>K</IT> <SUP>2</SUP><SUB>ac</SUB></DE></FR></FENCE> (2<IT>K</IT><SUB>al</SUB><IT>K</IT> <SUP>2</SUP><SUB>ac</SUB> + 2<IT>K</IT><SUB>ll</SUB><IT>K</IT> <SUP>2</SUP><SUB>lc</SUB> + <IT>K</IT><SUB>tl</SUB><IT>K</IT> <SUP>2</SUP><SUB>tc</SUB>)</FENCE> (C8)
Thus KB can be set according to standard anthropometric ratios and is independent of any electrical parameters of the body.

APPENDIX d

Removing the effects of Td

Td can be removed through modeling, but it is only applicable when the actual measured data are used as input to fitting a program against a model. In this case, an additional multiplicative term must be added to the model (Eq. A1), which yields no change in amplitude but instead yields a linear theta  shift with increasing f. As shown, the user will have one more "constant" term (K in this example) in the model
Multiplicative term = 1 + <IT>i</IT>(1 + <IT>Kf</IT> )/1 + <IT>Kf</IT> + 1
where K = constant to be modeled; f = frequency; and i = complex unity.

The modeling approach to removing Td performs the best, allowing the user to extend the usable f range up to ~1 MHz, thus allowing for higher accuracy modeling. However, this technique is the most complex and may take excessive computing knowledge or time. The user can also approximate the observed theta  error manually and recalculate the set of measurement data including a correction for this effect. It should be noted that, without employing the full model as outlined above, it is not possible to separately model this effect alone because the biological effects will "skew" the results. The manual method does offer the advantage of being very fast to implement, and it may be performed either by computer or by hand. The technique does not offer the accuracy of this first method, however, because the correction is only optimized over relatively few data points. These data do, however, increase the useful f range of the measured data up to several hundred kiloherz.

Because there is little biological theta  shift caused by Cm at HF, choose a HF and assume that all the observed theta  shift is caused by Td. If 1-MHz data (as an example) are selected, note the measured theta  shift at 1 MHz as phi 1MHz, then correct the measured theta  shifts by subtracting phi 1MHz × f/1,000 from all measured theta  shifts. The measured Z data need no correction. The final, corrected, resistance (R) and reactance (X) data may be computed as follows
resistance = impedance ∗ cos<SUP>−1</SUP> (corrected phase)
reactance = impedance ∗ sin<SUP>−1</SUP> (corrected phase)
Because this manual method is only an approximation, and the resultant data is dependent on a single measured data point, the user may wish to try varying the f of the measured data point (change the divisor in the theta  correction for the f of the point used) or may wish to try taking the average of several HF data points as shown in the following example of averaging data collected at 700, 800, 900, and 1,000 kHz
phase correction = 0.25 ∗ frequency ∗ [(&PHgr;<SUB>700</SUB>/700) 
+ (&PHgr;<SUB>800</SUB>/800) + (&PHgr;<SUB>900</SUB>/900) + (&PHgr;<SUB>1,000</SUB>/1,000)]
These manual techniques only offer advantages when the user is interested in fitting the measured data to a multi-element "circuit" model or in using the measured theta  or X data within a statistically produced model. If only the Z or R is of significant interest, then these corrections offer little because Td only affects theta  and has no effect on Z. 

REFERENCES

1. Bestoso, J. T., and R. L. Mehta. Monitoring volume changes in hemodialysis (HD) with bioimpedance spectroscopy (BIS) (Abstract). J. Am. Soc. Nephrol. 4: 333, 1993.
2. Biasioli, S., R. Foroni, L. Petrosino, L. Cavallini, A. Zambello, G. Cavalcanti, and T. Taluri. Effect of aging on the body composition of dialyzed subjects: comparison with normal subjects. ASAIO Trans. 39: 596-601, 1993.
3. Chertow, G., E. Lowie, D. Wilmore, J. Gonzalez, N. L. Lew, J. Ling, M. S. Leboff, M. N. Gottlieb, B. Zebrowiski, J. College, and M. Lazzarus. Nutritional assessment with bioelectrical impedance analysis in maintenance hemodialysis patients. J. Am. Soc. Nephrol. 6: 75-81, 1995 [Abstract] .
4. Chumlea, W., and S. Guo. Bioelectrical impedance and body composition: present status and future directions. Nutr. Rev. 52: 123-131, 1994 [Medline] .
5. Cole, K. S. Membranes, Ions and Impulses: A Chapter of Classical Biophysics. Berkeley, CA: Univ. of Calif. Press, 1972.
6. Cornish, B. H., B. J. Thomas, and L. C. Ward. Improved prediction of extracellular and total body water using impedance loci generated by multiple frequency bioelectrical impedance analysis. Phys. Med. Biol. 38: 337-346, 1993 [Medline] .
7. De la Rue, R. E., and C. W. Tobias. The conductivity of dispersions. J. Electrochem. Soc. 106: 827-833, 1959.
8. Deurenberg, P., A. Andreoli, and A. De Lorenzo. Multi-frequency bioelectrical impedance: a comparison between the Cole-Cole modeling and Hanai equations with the classical impedance index approach. Ann. Hum. Biol. 6: 31-40, 1996.
9. De Vries, P. M. J. M., J. H. Meijer, K. Vlaanderen, V. Visser, P. L. Oe, A. J. M. Donker, and H. Schneider. Measurement of transcellular fluid shift during haemodialysis. Med. Biol. Eng. Comput. 27: 152-158, 1989. [Medline]
10. Finn, P. J., L. D. Plank, M. A. Clark, A. B. Connolly, and G. Hill. Progressive dehydration and proteolysis in critically ill patients. Lancet 347: 654-656, 1996 [Medline] .
11. Forbes, G. B. Human Body Composition: Growth, Aging, Nutrition, and Activity. New York: Springer, 1987.
12. Foster, K. R., and H. C. Lukaski. Whole body impedance-what does it measure? Am. J. Clin. Nutr. 64, Suppl.: 388S-396S, 1996.
13. Fricke, H. A mathematical treatment of the electrical conductivity and capacity of disperse systems. II. The capacity of a suspension of conducting spheroids surrounded by a non-conducting membrane for a current of low frequency. Phys. Rev. 26: 678-681, 1925.
14. Geddes, L. A., and L. E. Baker. The specific resistivity of biological material: a compendium of data for the biomedical engineer and physiologist. Med. Biol. Eng. 5: 271-293, 1967 [Medline] .
15. Gersing, E., M. Schafer, and M. Osypka. The appearance of positive phase angles in impedance measurements on extended biological objects. Innov. Tech. Biol. Med. 16: 71-76, 1995.
16. Gerth, W. A., L. D. Montgomery, and Y. C. Wu. A computer based bioelectrical impedance spectroscopic system for noninvasive assessment of compartmental fluid redistribution. In: Third IEEE Symposium on Computer Based-Medical Systems. Los Alamitos, CA: IEEE Computer Soc., 1990, p. 446-453.
17. Hanai, T. Electrical properties of emulsions. In: Emulsion Science, edited by P. H. Sherman. London: Academic, 1968, p. 354-477.
18. Ho, L. T., R. Kushner, D. A. Schoeller, R. Gudivaka, and D. M. Spiegel. Bioimpedance analysis of total body water in hemodialysis patients. Kidney Int. 46: 1438-1442, 1994 [Medline] .
19. Jaffrin, M. Y., M. Maasrani, B. Boudailliez, and A. le Gourrier. Extracellular and intracellular fluid volume monitoring during dialysis by multifrequency impedancemetry. ASAIO Trans. 42: M533-M538, 1996.
20. Keys, A., and J. Brozek. Body fat in adult men. Physiol. Rev. 33: 245-325, 1953. [Free Full Text]
22. Löfgren, B. The electrical impedance of complex tissue and its relation to changes in volume and fluid distribution. Acta Physiol. Scand. 23, Suppl. 81: 2-51, 1951.
23. Lukaski, H. Biological indexes considered in the derivation of the bioelectrical impedance analysis. Am. J. Clin. Nutr. 64, Suppl.: 397S-404S, 1996.
24. Lukaski, H. C., and P. E. Johnson. A simple, inexpensive method of determining total body water using a tracer dose of D20 and infrared absorption of biological fluids. Am. J. Clin. Nutr. 41: 363-370, 1985 [Abstract/Free Full Text] .
25. MacDonald, J. R. Impedance Spectroscopy: Emphasizing Solid Materials and Systems. New York: Wiley, 1987.
26. Matthie, J., and P. Withers. The ambiguities of predicting total body water and body cell mass with a single frequency (50 kHz) measurement of bioimpedance (Letter to Editor). J. Am. Soc. Nephrol. 6: 1682-1684, 1995 .
27. Matthie, J. R., and P. O. Withers. Bioimpedance, the Cole model equation and the prediction of intra and extracellular water: science or marketing (Letter to Editor). Clin. Nutr. 15: 147-149, 1996; erratum, 15: 217-219, 1996.
28. Matthie, J. R., and P. O. Withers. Impedance measurements of body-water compartments (Letter to Editor). Am. J. Clin. Nutr. 61: 1167-1169, 1995 [Free Full Text] .
29. Matthie, J. R., and P. O. Withers. Segmental versus whole body multifrequency bioimpedance measurements (Letter to Editor). J. Appl. Physiol. 79: 2177-2179, 1995 [Free Full Text] .
30. Matthie, J. R., P. O. Withers, M. D. Van Loan, and P. L. Mayclin. Development of a commercial complex bio-impedance spectroscopic (CBIS) system for determining intracellular water (ICW) and extracellular water (ECW) volumes. In: Proceedings of the 8th International Conference on Electrical Bio-impedance Kuopio Finland 1992 Kuopio, Finland: University of Kuopio, 1992, p. 203-205.
31. McAdams, E. T., and J. Jossinet. Tissue impedance: a historical overview. Physiol. Meas. 16: A1-A7, 1995 [Medline] .
32. Miller, M. E., J. M. Cosgriff, and G. B. Forbes. Bromide space determination using anion-exchange chromatography for measurement of bromide. Am. J. Clin. Nutr. 50: 168-171, 1989 [Abstract/Free Full Text] .
33. Moore, F. D., and C. M. Boyden. Body cell mass and limits of hydration of the fat-free body: their relation to estimated skeletal weight. Ann. NY Acad. Sci. 110: 62-71, 1963.
34. Nyboer, J., and J. A. Sedensky. Bioelectrical impedance during renal dialysis. Proc. Dial. Transplant. Forum 4: 214-219, 1974 .
35. Patel, R. V., J. R. Matthie, P. O. Withers, E. L. Peterson, and B. J. Zarowitz. Estimation of total body and extracellular water using single and multiple-frequency bioimpedance. Ann. Pharmacother. 28: 565-569, 1994 [Abstract] .
36. Piccoli, A., B. Rossi, L. Pillon, and G. Bucciante. A new method for monitoring body fluid variation by bioimpedance analysis: the Rxc graph. Kidney Int. 46: 534-539, 1994 [Medline] .
37. Ramo, S., J. Whinnery, and T. Van Duzer. Fields and Waves in Communication Electronics (2nd ed.). New York: Wiley, 1984.
38. Scharfetter, H., G. Wirnsberger, Z. Laszzlo, H. Holzer, H. Hinghofer-Szalkay, and H. Hutten. Influence of ionic shifts and postural changes during dialysis on volume estimation with multifrequency impedance analysis. In: Proceedings of the 9th International Conference on Electrical Bio-Impedance, Heidelberg, Germany 1995. Heidelberg, Germany: Univ. of Heidelberg, 1995, p. 241-244.
39. Scheltinga, M., E. Jorna, D. Chandi, M. Wust, E. Grep, D. Compas, and R. Wesdorp. Multiple frequency impedance measurements in critically ill patients. Clin. Nutr. 14: 42-44, 1995.
40. Schwan, H. P. Electrical properties of tissue and cell suspensions. In: Advances in Biological and Medical Physics, edited by J. Lawrence, and C. Tobias. New York: Academic, 1957, p. 147-209.
41. Segal, K. R., S. Burastero, A. Chun, P. Coronel, R. N. Pierson, Jr., and J. Wang. Estimation of extracellular and total body water by multiple-frequency bioelectrical-impedance measurement. Am. J. Clin. Nutr. 54: 26-29, 1991 [Abstract/Free Full Text] .
42. Shizgal, H. M. Validation of the measurement of body composition from whole body bioelectric impedance. Infusionstherapie 17, Suppl.: 67-74, 1990.
43. Stroud, D. B., B. H. Cornish, B. J. Thomas, and L. C. Ward. The use of Cole-Cole plots to compare two multi-frequency bioimpedance instruments. Clin. Nutr. 14: 307-311, 1995.
44. Thomasset, A. Bio-electrical properties of tissue impedance measurements. Lyon Med. 209: 1325-1352, 1963. [Medline]
45. United States Army Natick Research, Development, and Engineering Center. Anthropometric Survey of U. S. Army Personal: Summary Statistics Interim Report, 1989. Tech. Report Natick/TR-89/027, AD-209-600.
46. Van Loan, M. D., L. E. Kopp, J. C. King, W. W. Wong, and P. L. Mayclin. Fluid changes during pregnancy: use of bioimpedance spectroscopy. J. Appl. Physiol. 78: 1037-1042, 1995 [Abstract/Free Full Text] .
47. Van Loan, M. D., P. Withers, J. Matthie, and P. L. Mayclin. Use of bio-impedance spectroscopy (BIS) to determine extracellular fluid (ECF), intracellular fluid (ICF), total body water (TBW), and fat-free mass (FFM). In: Human Body Composition: In Vivo Methods, Models and Assessment, edited by K. J. Ellis, and J. D. Eastman. New York: Plenum, 1993, p. 67-70.
48. Van Marken Lichtenbelt, W. D., K. R. Westerterp, L. Wouters, and S. Luijendijk. Validation of bioelectrical-impedance measurements as a method to estimate body-water compartments. Am. J. Clin. Nutr. 60: 159-166, 1994 [Abstract/Free Full Text] .
49. Withers, P. Multi-frequency impedance measurements of extracellular fluid volume (Letter to Editor). Physiol. Meas. 16: 71-76, 1995 . [Medline]
50. Wong, W. W., H. P. Sheng, J. C. Morkeberg, J. L. Kosanovich, L. L. Clarke, and P. D. Klein. Measurement of extracellular water volume by bromide ion chromatography. Am. J. Clin. Nutr. 50: 1290-1294, 1989 [Abstract/Free Full Text] .
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Nephrol. Dial. Transplant., March 1, 2008; 23(3): 808 - 812.
[Full Text] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
A. L Gibson, J. C Holmes, R. L Desautels, L. B Edmonds, and L. Nuudi
Ability of new octapolar bioimpedance spectroscopy analyzers to predict 4-component-model percentage body fat in Hispanic, black, and white adults
Am. J. Clinical Nutrition, February 1, 2008; 87(2): 332 - 338.
[Abstract] [Full Text] [PDF]

Home page
 Nephrol Dial TransplantHome page
M. Essig, B. Escoubet, D. de Zuttere, F. Blanchet, F. Arnoult, E. Dupuis, C. Michel, F. Mignon, F. Mentre, C. Clerici, et al.
Cardiovascular remodelling and extracellular fluid excess in early stages of chronic kidney disease
Nephrol. Dial. Transplant., January 1, 2008; 23(1): 239 - 248.
[Abstract] [Full Text] [PDF]

Home page
 Nutr Clin PractHome page
C. Earthman, D. Traughber, J. Dobratz, and W. Howell
Bioimpedance Spectroscopy for Clinical Assessment of Fluid Distribution and Body Cell Mass
Nutr Clin Pract, August 1, 2007; 22(4): 389 - 405.
[Abstract] [Full Text] [PDF]

Home page
 Anesth. Analg.Home page
T. Tatara and C. Tashiro
Quantitative Analysis of Fluid Balance During Abdominal Surgery
Anesth. Analg., February 1, 2007; 104(2): 347 - 354.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
M. K. Raja, G. H. Raymer, G. R. Moran, G. Marsh, and R. T. Thompson
Changes in tissue water content measured with multiple-frequency bioimpedance and metabolism measured with 31P-MRS during progressive forearm exercise
J Appl Physiol, October 1, 2006; 101(4): 1070 - 1075.
[Abstract] [Full Text] [PDF]

Home page
 J. Clin. Endocrinol. Metab.Home page
J. G. Esposito, S. G. Thomas, L. Kingdon, and S. Ezzat
Comparison of Body Composition Assessment Methods in Patients with Human Immunodeficiency Virus-Associated Wasting Receiving Growth Hormone
J. Clin. Endocrinol. Metab., August 1, 2006; 91(8): 2952 - 2959.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
F. Zhu, M. K. Kuhlmann, G. A. Kaysen, S. Sarkar, C. Kaitwatcharachai, R. Khilnani, L. Stevens, E. F. Leonard, J. Wang, S. Heymsfield, et al.
Segment-specific resistivity improves body fluid volume estimates from bioimpedance spectroscopy in hemodialysis patients
J Appl Physiol, February 1, 2006; 100(2): 717 - 724.
[Abstract] [Full Text] [PDF]

Home page
 GlycobiologyHome page
M. Bichara, A. Attmane-Elakeb, D. Brown, M. Essig, Z. Karim, M. Muffat-Joly, L. Micheli, I. Eude-Le Parco, F. Cluzeaud, M. Peuchmaur, et al.
Exploring the role of galectin 3 in kidney function: a genetic approach
Glycobiology, January 1, 2006; 16(1): 36 - 45.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
G. A Kaysen, F. Zhu, S. Sarkar, S. B Heymsfield, J. Wong, C. Kaitwatcharachai, M. K Kuhlmann, and N. W Levin
Estimation of total-body and limb muscle mass in hemodialysis patients by using multifrequency bioimpedance spectroscopy
Am. J. Clinical Nutrition, November 1, 2005; 82(5): 988 - 995.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
P. C Papathakis, N. C Rollins, K. H Brown, M. L Bennish, and M. D Van Loan
Comparison of isotope dilution with bioimpedance spectroscopy and anthropometry for assessment of body composition in asymptomatic HIV-infected and HIV-uninfected breastfeeding mothers
Am. J. Clinical Nutrition, September 1, 2005; 82(3): 538 - 546.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
J. R. Matthie
Second generation mixture theory equation for estimating intracellular water using bioimpedance spectroscopy
J Appl Physiol, August 1, 2005; 99(2): 780 - 781.
[Full Text] [PDF]

Home page
 J. Nutr.Home page
Y. C. Luiking, N. E. P. Deutz, M. Jakel, and P. B. Soeters
Casein and Soy Protein Meals Differentially Affect Whole-Body and Splanchnic Protein Metabolism in Healthy Humans
J. Nutr., May 1, 2005; 135(5): 1080 - 1087.
[Abstract] [Full Text] [PDF]

Home page
 Br J AnaesthHome page
P. Strandberg and R. G. Hahn
Volume kinetics of glucose 2.5% solution and insulin resistance after abdominal hysterectomy
Br. J. Anaesth., January 1, 2005; 94(1): 30 - 38.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
B. J Foster and M. B Leonard
Measuring nutritional status in children with chronic kidney disease
Am. J. Clinical Nutrition, October 1, 2004; 80(4): 801 - 814.
[Abstract] [Full Text] [PDF]

Home page
 Nutr Clin PractHome page
A. C. Buchholz, C. Bartok, and D. A. Schoeller
The Validity of Bioelectrical Impedance Models in Clinical Populations
Nutr Clin Pract, October 1, 2004; 19(5): 433 - 446.
[Abstract] [Full Text] [PDF]

Home page
 Nephrol Dial TransplantHome page
C.-C. Wu, Y.-P. Lin, W.-C. Yu, W.-S. Lee, T.-L. Hsu, P. Y.-A. Ding, and C.-H. Chen
The assessment of fluid status in haemodialysis patients: usefulness of the Doppler echocardiographic parameters
Nephrol. Dial. Transplant., March 1, 2004; 19(3): 644 - 651.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
M. Lof and E. Forsum
Evaluation of bioimpedance spectroscopy for measurements of body water distribution in healthy women before, during, and after pregnancy
J Appl Physiol, March 1, 2004; 96(3): 967 - 973.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
C. Bartok and D. A. Schoeller
Estimation of segmental muscle volume by bioelectrical impedance spectroscopy
J Appl Physiol, January 1, 2004; 96(1): 161 - 166.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
P. L. Cox-Reijven, B. van Kreel, and P. B Soeters
Bioelectrical impedance measurements in patients with gastrointestinal disease: validation of the spectrum approach and a comparison of different methods for screening for nutritional depletion
Am. J. Clinical Nutrition, December 1, 2003; 78(6): 1111 - 1119.
[Abstract] [Full Text] [PDF]

Home page
 J. Am. Soc. Nephrol.Home page
S. J. Davies, G. Woodrow, K. Donovan, J. Plum, P. Williams, A. C. Johansson, H.-P. Bosselmann, O. Heimburger, O. Simonsen, A. Davenport, et al.
Icodextrin Improves the Fluid Status of Peritoneal Dialysis Patients: Results of a Double-Blind Randomized Controlled Trial
J. Am. Soc. Nephrol., September 1, 2003; 14(9): 2338 - 2344.
[Abstract] [Full Text] [PDF]

Home page
 HypertensionHome page
C.-H. Chen, Y.-P. Lin, W.-C. Yu, W.-C. Yang, and Y.-A. Ding
Volume Status and Blood Pressure During Long-Term Hemodialysis: Role of Ventricular Stiffness
Hypertension, September 1, 2003; 42(3): 257 - 262.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
C. Bartok, R. L. Atkinson, and D. A. Schoeller
Measurement of nutritional status in simulated microgravity by bioelectrical impedance spectroscopy
J Appl Physiol, July 1, 2003; 95(1): 225 - 232.
[Abstract] [Full Text] [PDF]

Home page
 Am. J. Clin. Nutr.Home page
D. Smith, B. Engel, A. M Diskin, P. Spanel, and S. J Davies
Comparative measurements of total body water in healthy volunteers by online breath deuterium measurement and other near-subject methods
Am. J. Clinical Nutrition, December 1, 2002; 76(6): 1295 - 1301.
[Abstract] [Full Text] [PDF]

Home page
 J. Nutr.Home page
D. A. Elliott, R. C. Backus, M. D. Van Loan, and Q. R. Rogers
Evaluation of Multifrequency Bioelectrical Impedance Analysis for the Assessment of Extracellular and Total Body Water in Healthy Cats
J. Nutr., June 1, 2002; 132(6): 1757S - 1759.
[Abstract] [Full Text] [PDF]

Home page
 J. Nutr.Home page
D. A. Elliott, R. C. Backus, M. D. Van Loan, and Q. R. Rogers
Extracellular Water and Total Body Water Estimated by Multifrequency Bioelectrical Impedance Analysis in Healthy Cats: A Cross-Validation Study
J. Nutr., June 1, 2002; 132(6): 1760S - 1762.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
P. A. Wilkins, R. D. Gleed, N. M. Krivitski, and A. Dobson
Extravascular lung water in the exercising horse
J Appl Physiol, December 1, 2001; 91(6): 2442 - 2450.
[Abstract] [Full Text] [PDF]

Home page
 J. Nutr.Home page
K. Yokoi, H. C. Lukaski, E. O. Uthus, and F. H. Nielsen
Use of Bioimpedance Spectroscopy to Estimate Body Water Distribution in Rats Fed High Dietary Sulfur Amino Acids
J. Nutr., April 1, 2001; 131(4): 1302 - 1308.
[Abstract] [Full Text]

Home page
 Am. J. Clin. Nutr.Home page
H. Valensise, A. Andreoli, S. Lello, F. Magnani, C. Romanini, and A. De Lorenzo
Multifrequency bioelectrical impedance analysis in women with a normal and hypertensive pregnancy
Am. J. Clinical Nutrition, September 1, 2000; 72(3): 780 - 783.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
M. Forro, S. Cieslar, G. L. Ecker, A. Walzak, J. Hahn, and M. I. Lindinger
Total body water and ECFV measured using bioelectrical impedance analysis and indicator dilution in horses
J Appl Physiol, August 1, 2000; 89(2): 663 - 671.
[Abstract] [Full Text] [PDF]

Home page
 J. Am. Soc. Nephrol.Home page
P. STENVINKEL, B. LINDHOLM, F. LÖNNQVIST, K. KATZARSKI, and O. HEIMBÜRGER
Increases in Serum Leptin Levels during Peritoneal Dialysis Are Associated with Inflammation and a Decrease in Lean Body Mass
J. Am. Soc. Nephrol., July 1, 2000; 11(7): 1303 - 1309.
[Abstract] [Full Text]

Home page
 Nephrol Dial TransplantHome page
G. Woodrow, B. Oldroyd, G. Stables, J. Gibson, J. H. Turney, and A. M. Brownjohn
Effects of icodextrin in automated peritoneal dialysis on blood pressure and bioelectrical impedance analysis
Nephrol. Dial. Transplant., June 1, 2000; 15(6): 862 - 866.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
C. P. Earthman, J. R. Matthie, P. M. Reid, I. T. Harper, E. Ravussin, and W. H. Howell
A comparison of bioimpedance methods for detection of body cell mass change in HIV infection
J Appl Physiol, March 1, 2000; 88(3): 944 - 956.
[Abstract] [Full Text] [PDF]

Home page
 J. Clin. Endocrinol. Metab.Home page
S. A. G. Kemink, J. T. M. Frijns, A. R. M. M. Hermus, G. F. F. M. Pieters, A. G. H. Smals, and W. D. Van Marken Lichtenbelt
Body Composition Determined by Six Different Methods in Women Bilaterally Adrenalectomized for Treatment of Cushing's Disease
J. Clin. Endocrinol. Metab., November 1, 1999; 84(11): 3991 - 3999.
[Abstract] [Full Text]

Home page
 J. Appl. Physiol.Home page
R. Gudivaka, D. A. Schoeller, R. F. Kushner, and M. J. G. Bolt
Single- and multifrequency models for bioelectrical impedance analysis of body water compartments
J Appl Physiol, September 1, 1999; 87(3): 1087 - 1096.
[Abstract] [Full Text] [PDF]

Home page
 J. Am. Soc. Nephrol.Home page
E. C.H. VAN DEN HAM, J. P. KOOMAN, M. H.L. CHRISTIAANS, F. H.M. NIEMAN, B. K. VAN KREEL, G. A.K. HEIDENDAL, and J. P. VAN HOOFF
Body Composition in Renal Transplant Patients: Bioimpedance AnalysisCompared to Isotope Dilution, Dual Energy X-Ray Absorptiometry, andAnthropometry
J. Am. Soc. Nephrol., May 1, 1999; 10(5): 1067 - 1079.
[Abstract] [Full Text]

Home page
 J. Appl. Physiol.Home page
P. R. Schloerb;, J. Matthie, G. Pan, P. Withers, B. Zarowitz, A. de Lorenzo, A. Andreoli, and K. Katzarski
Bioimpedance Measurement of Extracellular Water
J Appl Physiol, February 1, 1999; 86(2): 773 - 774.
[Full Text] [PDF]

Home page
 J. Am. Soc. Nephrol.Home page
J. Q. JAEGER and R. L. MEHTA
Assessment of Dry Weight in Hemodialysis: An Overview
J. Am. Soc. Nephrol., February 1, 1999; 10(2): 392 - 403.
[Abstract] [Full Text]

Home page
 J. Appl. Physiol.Home page
K. J. Ellis and W. W. Wong
Human hydrometry: comparison of multifrequency bioelectrical impedance with 2H2O and bromine dilution
J Appl Physiol, September 1, 1998; 85(3): 1056 - 1062.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
F. Zhu, D. Schneditz, E. Wang, and N. W. Levin
Dynamics of segmental extracellular volumes during changes in body position by bioimpedance analysis
J Appl Physiol, August 1, 1998; 85(2): 497 - 504.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
J. Matthie, B. Zarowitz, A. De Lorenzo, A. Andreoli, K. Katzarski, G. Pan, and P. Withers
Analytic assessment of the various bioimpedance methods used to estimate body water
J Appl Physiol, May 1, 1998; 84(5): 1801 - 1816.
[Abstract] [Full Text] [PDF]

Home page
 J. Appl. Physiol.Home page
R. B. Mazess
Letters to the Editor
J Appl Physiol, January 1, 1998; 84(1): 396 - 396.
[Full Text] [PDF]

Home page
 Nutr Clin PractHome page
S. B. Heymsfield, C. Nunez, and A. Pietrobelli
Bioimpedance Analysis: What Are the Next Steps?
Nutr Clin Pract, October 1, 1997; 12(5): 201 - 203.
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