Vol. 85, Issue 2, 497-504, August 1998
Dynamics of segmental extracellular volumes during changes in
body position by bioimpedance analysis
Fansan
Zhu2,
Daniel
Schneditz1,
Erjun
Wang2, and
Nathan W.
Levin1
1 Renal Research Institute and
2 Division of Nephrology and
Hypertension, Department of Medicine, Beth Israel Medical Center,
New York, New York 10128
 |
ABSTRACT |
Extracellular
volume (ECV) of arms, trunk, and legs determined from segmental
bioimpedance data in 11 healthy men (31.6 ± 7 yr) obtained at the
end of a 30-min equilibration phase in the supine body position was
compared with ECV determined from whole body measurements
(ECVWB). ECV was calculated from
extracellular resistance
(RECV)
identified from the bioimpedance spectrum for a range of 10 frequencies. Whole body
RECV (527.6 ± 55.6 
) was equal to the sum of
RECV in the arms,
trunk, and legs (241.6 ± 36.3, 49.2 ± 5.1, and 236.3 ± 25.5 , respectively). The sum of equilibrated ECV in arms (1.31 ± 0.25 liters), trunk (10.08 ± 1.65 liters), and legs (2.80 ± 0.82 liters) was smaller than
ECVWB (20.90 ± 2.59 liters).
In six subjects who changed from a standing to a supine body position,
ECV decreased in arms (
2.59 ± 2.51%, P = NS) and legs (10.96 ± 3.02%, P < 0.05) but increased in
the trunk (+4.2 ± 3.2%, P < 0.05). ECVWB also decreased
(4.98 ± 1.41%, P < 0.05). However, the sum of segmental extracellular volumes remained
unchanged (0.06 ± 0.07%, P = NS). The sum of segmental ECVs is not sensitive to changes in body
position, which otherwise interferes with the estimation of ECV in
bioimpedance analysis when ECVWB
is used.
segmental extracellular resistance; multifrequency
bioimpedance analysis; automatic digital switch; fluid shifts; whole
body impedance
| |
INTRODUCTION |
ONE APPROACH TO DETERMINE body composition and
body hydration in humans is based on the measurement of electrical
characteristics of biological tissue (12, 14, 23, 35, 37). However, recent studies have shown that changes in body position lead to changes
in whole body bioimpedance (28, 31, 33) and to apparent changes in
extracellular volume (ECV) of up to 3.8 liters (32). This is a
significant error for many clinical applications, such as the
restoration of fluid balance during treatments with the artificial
kidney, where the measurement of changes in ECV is of value in the
estimation of adequate body hydration (1, 2, 5-7, 11, 15-18,
20, 22, 27, 30, 34, 36). It has been suggested that the apparent
changes in ECV calculated from whole body bioimpedance measurements
were related to erroneous model assumptions (31), which are outlined as
follows: It was assumed that the geometry of the body could be
approximated by a single equivalent cylinder and that the ECV was a
homogeneous compartment. Usually, measurements were taken from one body
segment with well-characterized geometry, such as the lower leg or the upper arm (segmental bioimpedance measurement), or from the whole body,
for which electrodes were placed on the wrist and the ankle (so-called
whole body bioimpedance measurement). With the assumption of
homogeneous distribution of ECV, data obtained in one segment or in the
whole body were then extrapolated for total ECV computation. Because
measures in the limb segments do not adequately reflect total ECV with
changes in body position, paradoxical results, such as an apparent
increase in ECV with orthostasis and a decrease with supine body
position, have been obtained (31). Although the distribution between
intra- and extracellular fluid volumes is known to be unaffected by
changes in body position (25), there are considerable changes in the
regional distribution of ECV (24, 29), so that the ECV is heterogeneous
with respect to local tissue resistance.
A stable measurement of ECV is the prerequisite for bioimpedance
monitoring in applications with variations in regional fluid distribution because of changes in body position. Local changes in ECV
require considerable time and a constant body position to equilibrate
between different parts of the body. A technique that can account for
changes in regional fluid distribution would be of great advantage in
clinical applications, such as hemodialysis, where considerable amounts
of fluid are removed from the body by ultrafiltration. It was the aim
of this study to observe differences in ECV estimation between whole
body and segmental analysis after changes in body position. It was
hypothesized that estimation of ECV via segmental analysis would be
less sensitive to changes in body position, because it is not based on
the assumption that the body can be treated as a uniform, equivalent
cylinder with a homogeneous distribution of ECV throughout the body.
Glossary
| RECV |
Modeled resistance of the extracellular compartment
|
| RSSR |
Sum of segmental extracellular resistance
|
| RWBR |
Whole body extracellular resistance
|
| ECV |
Extracellular volume of the whole body
|
| ECVWB |
Extracellular volume estimated from whole body (wrist to
ankle) extracellular resistance
|
| ECVSSV |
ECV estimated from sum of segmental ECV
|
| ECVarm,(trunk,leg) |
ECV in arm, trunk, or leg determined from segmental extracellular
resistance
|
| Whole body bioimpedance |
Bioimpedance measured between the ipsilateral wrist and ankle
|
| Segmental bioimpedance |
Bioimpedance measured in one segment of the body such as arm, trunk, or
leg
|
| |
MATERIALS AND METHODS |
Theory.
The electrical resistance (R) of a
body segment is given by
|
(1)
|
where
L is the length and
A is the cross-sectional area of the
cylinder and 
is the specific resistivity of the tissue. At low
frequencies, the resistivity is equal to the resistivity of
extracellular volume (ECV),
which is assumed to be 47 · cm (10). Expansion of
the right side of Eq. 1 yields an
expression that relates R to volume
(V)
|
(2)
|
However, A must be uniform
over the distance L. This condition is
violated for whole body bioimpedance measurements when electrodes that
inject the current (I) and electrodes that sense (S) the voltage are
mounted on the wrist and on the ankle. To obtain a uniform
A, the parts of the body measured by
whole body bioimpedance can be divided into three segments: the arm,
the trunk, and the leg. Usually, spot electrodes are used to inject the
current from the body surface. Therefore, the distribution of current
in the segment depends on the ratio of
L to
A. This ratio must be large to obtain
a homogeneous distribution of the current. The ratio is large in the
arm and in the leg, but not in the trunk. Estimation of trunk volume by
use of Eq. 2 leads to much smaller
values than expected. However, the nonuniform distribution can be
corrected using a weighting factor
(k).
In a distributed model, ECV is given by
|
(3)
|
where
ECVSSV is the sum of all segmental
ECVs
|
(4)
|
|
(5)
|
|
(6)
|
|
(7)
|
and
where ECVhead,neck,hands,feet
refers to the ECV in the head, neck, hands, and feet. This volume is
not measured by bioimpedance analysis but can be obtained from
anthropometric relations, where the head accounts for ~5.6% and the
hands and feet for ~1.8% of the body weight (9). In this study,
k = 4 was assumed for the calculation
of ECVtrunk from symmetrical
considerations. This is similar to using a higher specific resistivity
of the trunk (4).
Measurements.
Bioimpedance was measured for a logarithmic spectrum of 10 frequencies
ranging from 5 to 500 kHz (model 4000B analyzer, Xitron Technologies,
San Diego, CA) with use of disposable electrodes (7.7 × 1.9 cm2) supplied with the
instrument. Two injecting electrodes for applying the alternating
current were placed on the dorsal surfaces of the hand (I1) and the
ankle (I2) on the same side of the body. Sensing electrodes were placed
on the wrist (S1), the shoulder (acromion, S2), the upper anterior
iliac spine (S3), and the ankle (malleolus, S4) (Fig.
1).
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Fig. 1.
Measurement system and arrangement of electrodes. DS, digital switch;
I1 and I2, injecting electrodes; S1-S4, sensing electrodes; 4000B,
bioimpedance measuring system; PC, personal computer.
|
|
To make use of current technology that derives the bioimpedance signal
from only two sensing electrodes, electrodes S1-S4 were connected
to a digital switch that was developed for the purpose of segmental
measurements (39). The switch automatically controlled and transferred
the signal measured between electrodes to the bioimpedance-measuring
device (model 4000B, Xitron). A personal computer was used for data
acquisition and data storage. The different positions of the switch
permitted the measurement of body segmental bioimpedance between S1 and
S2 ("arm"), S2 and S3 ("trunk"), and S3 and S4
("leg") and whole body bioimpedance between S1 and S4 ("whole
body") (Fig. 1). After data acquisition had been completed in one
segment, the connection of the sensing electrodes was automatically
switched to the next position. Thus sequential measurements of three
body segments (arm, trunk, leg) and of the whole body were
obtained. The duration for a sweep of frequencies for the measurement
of bioimpedance in one segment was 15 s. The duration for a complete
cycle of measurements was 1 min.
Data analysis.
Acquisition, storage, and analysis of data were performed with the
software supplied with the bioimpedance analyzer. Resistance of the
extracellular compartment
(RECV) for each
segment and for the whole body was identified by fitting the spectrum
of bioimpedance data to the Cole-Cole model by use of the software
supplied with the bioimpedance device (8, 10). The correlation
coefficient of the data fit was better than 0.99 for all measurements.
Noise in the resistance data related to physiological processes such as
breathing and movements and other noise related to the interface between the electrode and the skin were reduced by a digital low-pass filter.
ECV in the different segments and
ECVSSV were calculated from
Eqs. 4-7.
Extracellular volume (ECVWB) was
also calculated from whole body extracellular resistance
(RWBR) measured
between the wrist and the ankle with use of relations that have been
derived elsewhere (10)
|
(8)
|
where
RWBR is whole
body extracellular resistance, W is
body weight (in kg), H is body height
(in cm), and kECV
is a function of ECV (in
· cm), body density (D, in
kg/m3), and
KB, which relates
H to limb and trunk size
|
(9)
|
Subjects and procedure.
Eleven male subjects (31.6 ± 7 yr, 74.3 ± 13.4 kg, 178.6 ± 5.9 cm) who had given informed consent were studied. The study protocol
was approved by the Committee on Scientific Activities of Beth Israel
Medical Center. Body weights were measured to the nearest 0.1 kg with
an electronic scale. Body heights, limb lengths, and limb
circumferences were measured by flexible tape to the nearest 0.1 cm.
All limb measurements were taken on the right side of the body with the
subject standing erect and the arms hanging freely. The mean of
duplicate circumference measurements was used. The room temperature was
22 ± 1°C.
Bioimpedance was measured in the 11 subjects during an equilibration
phase of 30 min, while they rested in a relaxed supine body position
with arms and legs slightly abducted and with forearms pronated. In 6 of 11 subjects, measurements were also obtained during a 30-min
standing phase, which preceded the subsequent supine phase. Each phase
lasted at least 30 min. Arms were kept in a dependent position during
the standing phase.
Statistical analysis.
Values are means ± SD. Paired
t-tests were used for comparison of
extracellular resistance and ECV during the different phases. P < 0.05 was assumed to reject the
null hypothesis. Equilibrated extracellular resistance data were
obtained by fitting serial data measured during the duration of the
equilibration phase to exponential functions and extrapolating the
value of the dependent variable to the end of the equilibration phase.
The precision of the resistance measurements and of the volume
calculations was obtained from the SD and from the coefficient of
variation (CV) of fitted and raw data.
| |
RESULTS |
Physical and electrical characteristics of subjects.
Physical characteristics of the 11 subjects are summarized in Table
1. A summary of extracellular resistance
for the different segments and for the whole body obtained from the
bioimpedance spectrum is given in Table 2.
For Table 2, extracellular resistance was obtained at the end of each
observation phase with subjects standing or lying down. In all subjects
the resistance of the arm (241.6 ± 36.3 ) was larger than the
resistance of the leg (236.3 ± 25.5 ). Among all segments, the
trunk had the lowest resistance (49.2 ± 5.1 ). The CV of serial
data in different segments was comparable in the arm, leg, and whole
body and higher in the trunk (Table 3). An important
theoretical identity was validated: the sum of resistance measured in
the arm (45.7%), trunk (9.4%), and leg segment (44.9%) was equal to
99.9% of the whole body resistance measured between the wrist and the
ankle. This strong correlation may be attributed to the measuring
technique in which leads are switched automatically and where the four
different segments are measured within a short period of time.
ECV estimation.
ECV of different segments (Eqs.
5-7),
ECVSSV (Eq. 4), and ECVWB
(Eq. 8) are given in Table 2. Data
were obtained after 30 min in the supine body position. The precision
in the measurement of ECV was highest for the sum of segmental volumes,
followed by a lower and comparable precision for arm, leg, and whole
body volumes and a reduced precision in the estimation of trunk volumes (CV = 1.63 ± 2.62%; Table 3).
ECVSSV was 32 ± 1% smaller
than ECVWB. This corresponds to a
mean difference of 6.7 liters. Part of this difference is due to the
exclusion of head, neck, hands, and feet from bioimpedance
measurements. However, whole body bioimpedance measurements make use of
anthropometric relationships to calibrate ECVWB to ECV, as determined by
gold standard techniques such as indicator dilution
(Eq. 8).
Figure 2 shows the relationships between
ECVSSV determined from the sum of
segmental volumes, ECVWB
determined from whole body bioimpedance analysis, and body weight. An
excellent linear relation and a high correlation coefficient were
obtained for both relationships.
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Fig. 2.
Extracellular fluid volume (ECV) and body weight. ECV was calculated
from sum of segmental volumes (solid line,
ECVSSV, Eq. 3) and from whole body bioimpedance analysis (dashed
line, ECVWB, Eq. 8). Linear regressions between ECV and body weight
(W) are as follows:
ECVSSV = 0.20W + 0.68 (r2 = 0.86) and
ECVWB = 0.18W + 7.65 (r2 = 0.79).
|
|
Changes in body position.
The change from a standing to a supine body position led to a marked
increase in RWBR
and in sum of segmental resistance
(RSSR; Fig.
3A). Linear
regression showed that
RWBR and
RSSR were
identical throughout the observation phase (Fig.
3B). However, when analyzed for
different segments, leg and arm resistance increased whereas trunk
resistance decreased during the supine phase (Fig.
3C).
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Fig. 3.
Resistance and changes in body position. Continuous recording of
segmental and whole body resistance is shown for
subject 7. At 30 min, subject changed
from a standing to a supine body position.
A: sum of segmental
(RSSR) and
whole body
(RWBR)
resistance of extracellular compartment
(RECV).
B: linear relationship between
RWBR and
RSSR:
RSSR = 1.07RWBR 32 (r2 = 0.97).
C: segmental
RECV in arm, leg,
and trunk.
|
|
A representative time course of the changes in
ECVWB and
ECVSSV is shown in Fig.
4. Whereas ECVSSV
remained virtually constant throughout the entire observation phase,
ECVWB increased during the
standing phase and sharply decreased when the subject changed from a
standing to a supine body position. In this study the amplitude of the
ECV change was 1.5 liters, and no steady state was reached within 30 min of the supine observation phase. The mean change of ECV in all
subjects was 
ECVSSV = 0.06 ± 0.07 liter, with ECVtrunk = +0.38 ± 0.26 liter, ECVarm = 0.03 ± 0.03 liter, and ECVleg = 0.35 ± 0.12 liter (Table
4).
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Fig. 4.
ECV and changes in body position. Registration of changes in
ECVSSV (see Eq. 3) and ECVWB
(see Eq. 8) is shown for
subject 7. At 30 min, subject changed
from a standing to a supine body position.
|
|
Analysis of the time course in the different segments is shown in Fig.
5. Relative changes in the three segments were
calculated as
(ECVt /ECV0 1) × 100%, where indexes 0 and
t refer to initial and subsequent
measurements, respectively. The relative change was especially large in
the leg. In both phases the trunk change was opposite to the change in
the leg. A summary of changes in ECV with changes in body position is
given in Table 5.
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Fig. 5.
Relative changes of segmental ECV
(ECVrel) and whole body ECV with
changes in body position. Experiment is the same as that shown in Fig.
4 but was separated for arm, trunk, and leg segments.
|
|
| |
DISCUSSION |
In this study, ECVWB was compared
with ECVSSV. Bioimpedance was
continuously measured over a 1-h period, during which subjects changed
from a standing to a supine body position. The change in body position
caused significant changes in whole body and segmental bioimpedance.
ECVWB significantly changed by as
much as 1.5 liters in a single subject (1.1 ± 0.67 liters, P < 0.05), whereas
ECVSSV remained unchanged
(0.06 ± 0.07 liter, P = NS) during the change in body position.
Even though ECV must be assumed to remain unchanged during a change in
body position (25), ECVWB is
apparently very sensitive to changes in body position:
ECVWB increases with orthostasis and decreases with supine body position (31). These changes can be
explained by changes in regional fluid distribution in different parts
of the body, which lead to changes in whole body bioimpedance and,
hence, to spurious estimations of
ECV.
During orthostasis, extracellular fluid is shifted from the upper to
the lower parts of the body (3, 24). First, there is a rapid
translocation of blood volume to the venous system of the lower body.
Second, the increase in intravascular pressure in the lower extremities
causes a change in the Starling equilibrium. The pressure gradient for
fluid filtration increases because of the rise in capillary pressure,
and fluid is shifted from the intravascular to the extravascular space
in the lower body. Thus extracellular fluid increases in the leg but
decreases in the trunk.
Extracellular resistance.
In this study the extremities accounted for 90.6% of whole body
resistance, and 44.9% of this value was due to the high resistance of
the legs (Table 2). These ratios were almost identical to data reported
for a group of 51 normal and overweight women (4) and to results from a
detailed study of segmental bioimpedance in 200 healthy, white adult
subjects (26). The contribution of the trunk to whole body
extracellular resistance was only 9.4%. The change from a standing to
a supine body position led to an increase of both whole body and sum of
segmental extracellular resistance (Fig. 3,
A and
B).
RECV increased in
the arm and in the leg but decreased in the trunk (Fig.
3C).
The change in whole body resistance can be clarified in a thought
experiment with use of two cylindrical segments
(indexes a and
b) where volume is shifted from
segment a to segment
b (see APPENDIX).
Assume that the volume change in segment
a (Va) is
|
(10)
|
where
indexes 0 and t refer to conditions
before and after the fluid shift, respectively. The sum of volumes in
both segments remains constant. If L
remains constant in both segments, then
|
(11)
|
where
RS is the sum of
resistance in both segments.
If A is larger in
segment a
(Aa) than in
segment b
(Ab) before
and after the fluid shift, the expression in parentheses in Eq. 11 is positive. Thus the change in
resistance
(RS) is
negative for a volume shift from segment
a to segment b;
otherwise it is positive (see
APPENDIX).
Extracellular volume.
In contrast to the small contribution of the trunk to whole body
RECV, 48.2% of
the extracellular fluid computed from Eq. 8 was located in the trunk (Table 2). In other words,
48.2% of the extracellular fluid located in the trunk only contributed to 9.4% of whole body resistance. When 0.35 ± 0.12 liter of fluid was shifted from the leg to the trunk when body position was changed from standing to supine, trunk resistance changed by 2.2 ± 1.5 , but leg resistance changed by 28.7 ± 12.1 and arm
resistance changed by 11.0 ± 5.5 (Table 4). As a consequence,
whole body resistance decreased and
ECVWB computed from
Eq. 8 increased during orthostasis
(Fig. 4). Because ECV change in segments contributes to whole body
resistance with different weights, segments must be measured separately
and segmental volumes must be calculated for each segment with use of
Eqs. 5-7.
ECVSSV is the sum of segmental ECVs (Eq. 4).
During changes in body position, changes in
ECVSSV are much smaller than
changes in ECVWB. This is
important from a practical and a theoretical point of view. When ECV is
calculated from the sum of segmental volumes, neither rigorous control
of body position nor an equilibration phase may be required for the
assessment of fluid status.
In applications such as hemodialysis, during which patients change from
a standing to a sitting and often to a head-down tilt position,
regional fluid shifts are likely to affect the ECV as measured by
conventional whole body technique. Such a change in body position will
lead to considerable redistribution of blood and ECV between peripheral
and central body compartments. If measured by whole body bioimpedance
technique, this redistribution will lead to an apparent change in ECV.
Peripheral sequestration of blood and extracellular fluid is likely to
contribute to an apparent increase in
ECVWB during hypotension (38). On
the other hand, sequestration of ECV in the trunk leads to an
underestimation of ECVWB by whole
body impedance technique (7).
Others have used one segment, such as the lower leg (19, 21) or the
forearm (13), to measure bioimpedance and to relate changes in
segmental measurements to changes in body hydration during hemodialysis
and ultrafiltration. It follows from the data presented in this study
that measurements in one segment will be subject to the same
inaccuracies as measurements for which the whole body technique is used
(Fig. 5). Measurements in the leg can be assumed to be especially
susceptible to changes in body position.
Differences of 7.38 ± 1.6 and 6.36 ± 1.7 liters were found
between ECVWB and
ECVSSV during the standing and
supine phases, respectively (Table 4). The reasons for the difference
in estimated volumes may be as follows:
1)
ECVWB has been found to
overestimate ECV measured by indicator-dilution technique by 2.7 ± 2.02 liters (10). 2) Neither method
includes head, neck, hands, and feet by direct measurement. However,
the contribution of these segments is included in the
ECVWB value with anthropometric
relations built into the derived results. The contribution of these
segments to the ECV is ~1 liter for a body weight of 70 kg.
3)
ECVWB may not have reached a
steady state within 30 min in the supine body position (31). If the
ECVWB is corrected for these
effects, the difference between
ECVSSV and ECV determined by
indicator-dilution technique reduces to less than 6.4 2.7 1 = 2.7 liters. Because the sum of segmental resistance was
identical to whole body resistance, the difference between
ECVWB and
ECVSSV must have been related to
differences in the calculation of ECV from
RECV in segmental (Eqs. 5-7) and whole body
calculations (Eq. 9). The segmental
technique also needs to be calibrated, which requires measurements of
ECV in different body segments and introduction of correction factors in Eqs. 5-7. Unfortunately,
standard approaches such as the inulin-distribution technique cannot be
used for the measurement of segmental and regional extracellular
volumes. The measurement of regional volumes with radiolabeled tracers
and body scanning techniques surpasses the scope of this contribution
but remains to be considered should segmental measurements gain wider
interest.
The advantage of the new technique is an improved spatial resolution of
ECV, i.e., separation of ECV in the limbs from ECV in the trunk, and
the fact that ECVSSV is relatively
independent of changes in body position. However, the new
approach requires two more electrodes, an automatic switch (39), and
more anthropometric measures such as segmental lengths and
circumferences. The additional sensing electrodes on the trunk (S2 and
S3 in Fig. 1) could be replaced by electrodes on the contralateral
wrist and ankle (26). Our results are obtained with the assumption that
the resistivity of the extracellular fluid is constant (47 · cm) and that the trunk can be approximated by
four normal cylinders with uniform current distribution. ECVs are then
calculated from simple equations (Eqs.
4-7).
In conclusion and in contrast to measurements using whole body
bioimpedance technique, ECVSSV is
almost independent of changes in body position. This is a considerable
improvement in the application of bioimpedance technique. It also is a
prerequisite for clinical applications such as continuous fluid
monitoring in hemodialysis patients, in whom orthostatic fluid shifts
have obscured changes in regional fluid distribution. Such changes in
regional fluid distribution may be caused by cardiovascular
compensation and by osmotic transcellular gradients. The analysis of
these processes should be possible in future studies with the new
segmental technique.
| |
APPENDIX |
Assume two cylindrical segments a and
b with cross-sectional areas
Aa and
Ab and with
constant lengths
La and
Lb. Also assume that Aa > Ab before and
after the volume shift and that
La < Lb. The
resistance in each segment before the shift (index 0) is
|
(A1)
|
and
|
(A2)
|
In a serial arrangement of segments, the resistance of both
segments (RS)
is given by the sum of the individual resistances. Therefore
|
(A3)
|
before
the shift (index 0), and
|
(A4)
|
after
the shift (index t).
A change in volume in segment a
(Va) is defined as
|
(A5)
|
The
volume changes in segments a and
b are given by
|
(A6)
|
The
change in resistance
(RS) after
the fluid shift is
|
(A7)
|
Because
of the initial assumption
|
(A8)
|
Therefore, RS
depends on the direction of the fluid shift. If
Va is negative (from
a to
b), comparable to a fluid shift in
an upright body position,
RS is also
negative. If Va is positive
(from b to
a), comparable to a shift from the
leg to the trunk in the supine body position,
RS is also
positive (Fig. 3A).
Because RS
changes with fluid shifts between segments, an apparent change in
volume is computed if segments are lumped into a single compartment.
| |
ACKNOWLEDGEMENTS |
The authors thank Raphael Recanati for support of the Renal
Research Fellowship for the Division of Nephrology and Hypertension of
Beth Israel Medical Center and Xitron Technologies (San Diego, CA) for
supplying the bioimpedance analyzer.
| |
FOOTNOTES |
Address for reprint requests: D. Schneditz, Renal Research Institute,
Yorkville Dialysis, 1555 3rd Ave., New York, NY 10128.
Received 8 September 1997; accepted in final form 27 March 1998.
| |
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Abstract
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