Body fluids monitor

Method and apparatus are described for determining volumes of body fluids in a subject using bioelectrical response spectroscopy. The human body is represented using an electrical circuit. Intra-cellular water is represented by a resistor in series with a capacitor; extra-cellular water is represented by a resistor in series with two parallel inductors. The parallel inductors represent the resistance due to vascular fluids. An alternating, low amperage, multi-frequency signal is applied to determine a subject's impedance and resistance. From these data, statistical regression is used to determine a 1% impedance where the subject's impedance changes by no more than 1% over a 25 kHz interval. Circuit components of the human body circuit are determined based on the 1% impedance. Equations for calculating total body water, extra-cellular water, total blood volume, and plasma volume are developed based on the circuit components.

ORIGIN OF THE INVENTION 
The invention described herein was made by employee(s) of the United States 
Government and may be manufactured and used by or for the Government of 
the United States of America for governmental purposes without the payment 
of any royalties thereon or therefor. 
BACKGROUND OF THE INVENTION 
The invention relates to a process for determining amounts of body fluids 
in a subject using bioelectrical response spectroscopy (BRS). 
Determining amounts of body fluids in a subject and detecting changes in 
the level of fluids is an important clinical and research tool. For 
example, it is documented that athletes show decreases in plasma volume 
after they stop exercise training. Similarly, exposure to real or 
simulated micro gravity may decrease plasma or blood volume in astronauts. 
This decrease may affect the physical performance and safety of the 
astronauts during space flights. Being able to assess blood or plasma 
volumes during flight may help evaluate the effectiveness of measures 
designed to restore or maintain those volumes. 
Prior art FIG. 1 shows a typical BRS method for determining volumes of body 
fluids in a subject. A signal generator 1 applies an alternating, low 
amperage signal through electrodes 2 to a subject 3. The alternating, low 
amperage signal travels through the subject 3 and is measured by an 
impedance analyzer 4 to determine a subject's impedance and resistance. 
The impedance and resistance are used to determine the subject's volumes 
of body fluids. 
One known BRS method assumed that total body resistance was due to a total 
body water and was equivalent to the resistance of a wire. The volume of 
the wire is proportional to the resistance of the wire and directly 
related to the square of the length of the wire and the resistivity of the 
wire: 
EQU volume=.rho..multidot.length.sup.2 /R 
where .rho. is the specific resistivity (ohms.multidot.cm) of the wire and 
R is the resistance. Using this electrical law and statistical regression, 
these investigators were able to develop estimation equations for total 
body water. 
One known BRS method treated the body as a plurality of segmented 
conductors having uniform cross-sectional area. By measuring impedance to 
determine the composition of one or more body segments, a total body 
composition could be determined. 
One known BRS method found that input signals of different frequencies 
would produce different resistances. These resistances were thought to be 
specific to different fluid compartments (e.g. extra-cellular fluid) and 
not to total body water. 
One know BRS method used input signals of multiple frequencies to determine 
volumes of body fluids. These investigators used a Cole-Cole plot and 
iterative curve fitting techniques to determine extra-cellular and total 
body resistance. 
One known BRS method assumed that capacitance was present in the body. This 
was based on a theory that cell membranes in the body acted like 
capacitors. Prior art FIG. 2 shows an electric circuit model of a human 
body that contains a capacitor. A series combination of resistor RI and 
capacitor C represented an intra-cellular impedance. A single resistor RE 
represented an extra-cellular resistance. The intra-cellular and 
extra-cellular branches were parallel to each other. A total impedance of 
the circuit between terminals 5 and 6 represented a total body impedance 
ZT that was thought to be due to a total body water. 
One known BRS method assumed that inductance was also present in the body. 
This was based on a theory that vascular fluids in the body acted like an 
inductor. Prior art FIG. 3 shows a circuit model of the human body that 
included an inductor. A series combination of resistor RI and capacitor C 
represented an intra-cellular impedance. A series combination of resistor 
RE and inductor LE represented an extra-cellular impedance. The 
intra-cellular and extra-cellular branches were parallel to each other. A 
total impedance of the circuit between terminals 7 and 8 represented a 
total body impedance ZT. This model showed an 11% shift in blood volume 
after subjects completed 40 minutes of supine rest while resistance and 
estimates of total body water changed only 0.4-1.5%. These data suggested 
that the change in inductance, not resistance, may relate to known 
increase in blood volume (.sup..about. 10%) that occurs with supine rest. 
Other known methods determined volumes of body fluids using dilution 
techniques that required injecting isotopic tracers into the subject's 
body. .sup.51 Cr-labeled hematocrit, .sup.125 I-labeled albumin, carbon 
monoxide, and inert dyes (e.g. Evans Blue) are examples of tracers used to 
assess blood, red cell, or plasma volumes. Most of these methods required 
multiple blood samples and sufficient time for the tracers to equilibrate 
within the vascular compartment. Also, repeat assessments must wait until 
the level of tracer in the blood decreased. 
SUMMARY OF THE INVENTION 
In some embodiments, the invention relates to a process for determining a 
volume of body fluid in a subject, comprising the steps of applying a 
signal to a subject, increasing the frequency of the signal by 
predetemined increments, measuring an impedance and a resistance of the 
subject at each frequency increment, determining a total body frequency 
FT, wherein the total body frequency FT is the frequency at which the 
impedance decreases by a predefined percent over a predefined frequency 
interval, determining circuit components of a human body circuit model, 
wherein the circuit components comprise a total body impedance ZT, a total 
body resistance RT, an extra-cellular resistance RE, an intra-cellular 
resistance RI, a capacitance C, a self-inductance L, and a 
mutual-inductance M, and determining the volume of body fluid from the 
circuit components. 
In some embodiments, the invention relates to an apparatus for determining 
a volume of body fluid in a subject, comprising of means for applying a 
signal to a subject, means for increasing a frequency of the signal by 
predetermined increments, means for measuring an impedance and a 
resistance of the subject at each frequency increment, means for 
determining a total body frequency FT, wherein the total body frequency FT 
is the frequency at which the impedance decreases by a predefined percent 
over a predefined frequency interval, means for determining circuit 
components of a human body circuit model, wherein the circuit components 
comprise a total body impedance ZT, a total body resistance RT, an 
extra-cellular resistance RE, an intra-cellular resistance RI, a 
capacitance C, a self-inductance L, and a mutual-inductance M, and means 
for determining the volume of body fluid from the circuit components. 
In some embodiments, the invention relates to an apparatus for determining 
a volume of body fluid in a subject, comprising of a signal generator 
configured to apply a signal to a subject and increase a frequency of the 
signal by predetermined increments, an impedance analyzer configured to 
measure an impedance and a resistance of the subject at each frequency 
increment, and a data processing unit configured to determine a total body 
frequency FT where the impedance decreases by a predefined percent over a 
predefined frequency interval, determine circuit components of a human 
body circuit model including a total body impedance ZT, a total body 
resistance RT, an extra-cellular resistance RE, an intra-cellular 
resistance RI, a capacitance C, a self-inductance L, and a 
mutual-inductance M, and determine the volume of body fluid from the 
circuit components. 
Advantages of the invention include one or more of the following: a fast, 
repeatable, non-invasive, and non-radioacive method for determining a 
volume of body fluid in a subject; and an accurate electrical circuit 
representation of the human body. Other advantages and features will 
become apparent from the following description and from the claims.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Preferred embodiments will now be described with reference to FIGS. 4-13. 
Referring to FIG. 4, a block diagram shows a system for determining volumes 
of body fluids in a subject. A signal generator 9 generates an 
alternating, low amperage signal, which may be a square wave of about 250 
uA amplitude. The signal generator 9 is connected to the subject by 
electrodes 10 which are attached to distal portions of a subject 11, e.g. 
ventral surface of the hand and end of the foot. The electrodes 10 may be 
Ag/AgCl pre-gelled electrodes such as those available from Classical 
Medical Products, Inc., Muskego, Wis. The signal generator 9 also 
increases the frequency of the signal, which may be from 0 to 300 kHz, by 
predetermined increments. The predetermined increments may include, but 
are not limited to, 5, 50, 67, 85, 100, 150, 166, 200, 250, and 300 kHz. 
An impedance analyzer 12 measures an impedance and a resistance of the 
subject 11 at each frequency increment. Frequencies above 300 kHz were not 
used because changes in impedance or resistance at those frequencies were 
due to "skin effect" and did not represent penetration of fluid 
compartments. The impedance analyzer 12 is connected to the subject 11 by 
electrodes 10 that are attached to distal portions of the subject 11, e.g. 
the upper wrist and ventral surface of the foot. The signal generator 9 
and impedance analyzer 12 may be, for example, a Hewlett Packard Model 
4284A Precision LCR Meter. The Hewlett Packard Model 4284A Precision LCR 
Meter uses an auto-balancing bridge technique to assess impedance and 
phase, and is therefore suitable for human application so long as the 
electrodes 10 have a mutual ground and the meter is optically isolated 
from the AC source. Comparisons between the HP impedance meter, a Valhalla 
meter (Scientific Incorporated, Valhalla, Calif.) and a Xitron Model 4000B 
meter (Xitron Technologies, San Diego, Calif.) using standardized subjects 
showed equivalence for resistance (.+-.1 ohms) during near simultaneous 
measurements. A data acquisition unit 13, which may be a computer, 
acquires and stores the impedance and resistance for processing. A data 
input unit 14, which may be a keyboard, allows manual entry of the 
subject's physical and anthropometric data into the data processing unit 
15 for processing. The data processing unit 15, which may also be a 
computer, is configured to process the impedance and resistance and the 
physical and anthropometric data to determine volumes of body fluids, 
including an amount of total body water TBW, an amount of extra-cellular 
water ECW, a total blood volume TBV, and a plasma volume PV. The total 
body water TBW, extra-cellular water ECW, total blood volume TBV, and 
plasma volume PV can be determined by solving step-wise multiple 
regression equations that have been developed for each quantity. The 
results are viewed or displayed via a data output unit 16. 
Referring to FIG. 5, an electrical circuit model of a human body according 
to one embodiment of the present invention is shown. A series combination 
of resistor RI and capacitor C represents an intra-cellular impedance. A 
series combination of resistor RE and parallel inductors L1 and L2 
represents an extra-cellular impedance. The intra-cellular and 
extra-cellular branches are in parallel to each other. The total impedance 
between terminals 15 and 16 represents a total body impedance ZT. Parallel 
inductors L1 and L2 were added to the extra-cellular branch to represent 
vascular fluids in the body. The vascular tree has many branches that are 
interwoven, similar to the windings or coils of an inductor. Electrical 
current flowing within these branches produces an inductance called 
self-inductance L that must be comprehended in the human body circuit 
model. The vascular tree also has two main branches, arterial and venous, 
in which fluids flow in basically opposite directions. These two main 
branches act like two parallel inductors to produce an inductance called 
mutual-inductance M that must also be comprehended in the human body 
circuit model. The opposite direction of flow in the arterial and venous 
branches makes the mutual inductance M negative. Inductors L1 and L2 
represent the self- and negative mutual-inductance. 
Referring to FIG. 6, a graph of impedance versus frequency is shown. 
Impedance is seen to decrease as frequency increases. However, at a 
certain frequency, the impedance is seen to decrease by no more than 1% 
over a 25 kHz increase in frequency. This 1% frequency is a total body 
frequency FT, and the 1% impedance is a total body impedance ZT. The total 
body impedance ZT is theoretically related to a true total body water TBW. 
An extra-cellular resistance RE is the resistance which corresponds to a 
frequency of 0 kHz. 
The total body frequency FT, total body impedance ZT, total body resistance 
RT, extra-cellular resistance RE, intra-cellular resistance RI, 
self-inductance L, mutual-inductance M, and capacitance CI can be 
determined as follows: 
(1) Determine a 3rd order polynomial regression equation for impedance 
(ordinate) versus frequency (abscissa) in Hertz using statistical 
regression methods known to those skilled in the art, i.e. 
EQU y=.beta..sub.0 +.beta..sub.1 .multidot.x+.beta..sub.2 .multidot.x.sup.2 
+.beta..sub.3 .multidot.x.sup.3. 
(2) Repeat (1) for resistance versus frequency. 
(3) Determine the total body frequency FT by solving the following 
equations in order: 
EQU p=(0.01.multidot..beta..sub.2 
+7.5E4.multidot..beta..sub.3)/(0.01.multidot..beta..sub.3); 
EQU q=(1.875E9.multidot..beta..sub.3 +5E4.multidot..beta..sub.2 
+0.01.multidot..beta..sub.1)/(0.01.multidot..beta..sub.3); 
EQU r=(0.01.multidot..beta..sub.0 +1.5625E13.multidot..beta..sub.3 
+6.25E8.multidot..beta..sub.2 
+2.54E4.multidot..beta..sub.0)/(0.01.multidot..beta..sub.3); 
EQU a=(3.multidot.q-p.sup.2)/3; 
EQU b=(2.multidot.p.sup.3 -9.multidot.q.multidot.p+27.multidot.r)/27; 
EQU m=2.multidot.SQRT(-a/3); 
EQU .O slashed.=(a cos(3.multidot.b/a.multidot.m))/3; 
EQU y=m.multidot.cos(.O slashed.); and 
EQU FT=m.multidot.cos(.O slashed.+4.multidot..pi./3)-p/3. 
(4) Determine a total reactance X.sub.1 at FT, X.sub.2 at FT+25 kHz, and 
X.sub.3 at FT+50 kHz by solving the following equation: 
EQU X=SQRT(Z.sup.2 -R.sup.2) 
where Z=impedance at the specified frequency and R=resistance at the 
specified frequency. To find Z and R solve the 3rd order polynomial 
regression equations for impedance and resistance respectively using the 
specified frequencies. 
(5) Determine a radian frequency .omega..sub.1 at FT, .omega..sub.2 at 
FT+25 kHz, .omega..sub.3 at and FT+50 kHz by solving the following 
equation: 
EQU .omega.=2.multidot..pi..multidot.frequency in Hz. 
(6) Determine a numerical constant K by solving the following equation: 
EQU K=(X.sub.2 -(.omega..sub.1 .multidot.X.sub.1 
/X.sub.2))/(.omega..sub.1.sup.2 /.omega..sub.2)-.omega..sub.2). 
(7) Determine the self-inductance L by solving the following equation: 
EQU L=-(X.sub.3 .multidot..omega..sub. 
/(2.multidot..omega..sub.1.sup.2))-(.omega..sub.3.sup.2 
.multidot.K/(2.multidot..omega..sub.1.sup.2))-(K/2)-(X.sub.1 
/((2.multidot..omega..sub.1)). 
(8) Determine the mutual-inductance M by solving the following equation: 
EQU M=K+L 
(9) Determine the capacitance C by solving the following equation: 
EQU C=1/((L.multidot..omega..sub.1.sup.2)-(M.multidot..omega..sub.1.sup.2)-(X1. 
multidot..omega..sub.1)) 
(10) Determine the total body resistance RT by using FT in Hz to solve the 
3rd order polynomial regression equation for resistance in (2). 
(11) Determine the extra-cellular RE by using a frequency of 0 Hz to solve 
the 3rd order polynomial regression equation for resistance in (2). 
(12) Determine the intra-cellular resistance RI by solving the following: 
EQU RI=1/((1/RT)-(1/RE)). 
Referring to FIG. 7, the flow chart shown is a process for determining 
volumes of body fluids in a subject according to the embodiment of FIG. 4. 
In ST1, the subject's physical and anthropometric data is entered. In ST2, 
the subject is connected to a signal generator and an impedance analyzer. 
In ST3, an alternating, low amperage signal is applied to the subject. In 
ST4, the frequency of the alternating, low amperage signal is increased 
within a predetermined range, which may be from 0 to 300 kHz, by 
predetermined increments, which may include 5, 50, 67, 85, 100, 150, 166, 
200, 250, and 300 kHz. In ST5, a subject's impedance and resistance are 
measured at each frequency increment. In ST6, the subject's impedance and 
resistance are acquired and stored. In ST7, a total body frequency FT is 
determined. In ST8, a total body impedance ZT that corresponds to the 
total body frequency FT is determined according to a human body circuit. 
In ST9, a total body resistance RT that corresponds to the total body 
frequency FT is determined according to the human body circuit. In ST10, a 
total body water TBW is calculated using the step-wise multiple regression 
equation for TBW. In ST11, an extra-cellular resistance RE that 
corresponds to a frequency of 0 Hz is determined according to the human 
body circuit. In ST12, an extra-cellular water ECW is calculated using the 
step-wise multiple regression equation for ECW. In ST13, a 
mutual-inductance M that corresponds to the total body frequency FT is 
determined according to the human body circuit. In ST14, a total blood 
volume TBV is calculated using the step-wise multiple regression equation 
for TBV. In ST15, a self-inductance L that corresponds to the total body 
frequency FT is determined according to the human body circuit. In ST16, a 
total plasma volume PV is calculated using the step-wise multiple 
regression equation for PV. 
The equations for calculating total body water TBW, extra-cellular water 
ECW, total blood volume TBV, and plasma volume PV were developed using 
step-wise multiple regression of impedance, resistance, and body fluids 
data obtained in laboratory studies. 
Two studies were conducted: one to determine TBW and ECW, the other to 
determine TBV and PV. All subjects who participated in the studies passed 
an Air Force Class III physical and were divided randomly into two groups, 
a development group and a validity group. For subjects in the development 
group, impedance and resistance were obtained using the embodiment of FIG. 
4, and TBW, ECW, TBV, and PV were obtained using dilution. These data were 
used in step-wise multiple regression to develop equations to predict TBW, 
ECW, TBV, and PV. For subjects in the validity group, TBW, ECW, TBV, and 
PV were obtained using dilution. The equations developed using subjects in 
the development group were applied to subjects in the validity group, and 
the results thereof were compared to the results obtained using dilution. 
In the study to develop the equations to calculate total body water TBW and 
extra-cellular water ECW the following subjects participated: 23 subjects 
in the TBW development group and 31 subjects in the TBW validity group; 17 
subjects in the ECW development group and 9 subjects in the ECW validity 
group. Table 1 shows the characteristics of the subjects. 
TABLE 1 
______________________________________ 
TBW and ECW Subject Characteristics 
Development Group 
Validity Group 
TBW ECW TBW ECW 
______________________________________ 
Age, yr 32.0 .+-. 6.6 
33.8 .+-. 5.8 
35 .+-. 6.4 
34.0 .+-. 7.0 
Height, cm 
168 .+-. 6 
170 .+-. 11 
170 .+-. 10 
170 .+-. 9 
Mass, kg 67.8 .+-. 13.0 
64.7 .+-. 11.4 
69.2 .+-. 14.0 
72.9 .+-. 17.1 
TBW, kg 38.8 .+-. 7.7 
34.6 .+-. 6.3 
36.8 .+-. 7.8 
38.6 .+-. 9.6 
ECW, kg N/A 15.4 .+-. 2.9 
16.0 .+-. 3.4 
16.2 .+-. 3.8 
Sex 10M/13F 6M/11F 16M/15F 6M/3F 
______________________________________ 
The subjects in the TBW development group had their TBW evaluated with 
.sup.18 O-labeled water. The subjects in the TBW validity group were 
evaluated with deuterium oxide (.sup.2 H.sub.2 O). The unavailability of 
.sup.18 O-labeled water and the desire to demonstrate the robust nature of 
the present invention led to the use (.sup.2 H.sub.2 O) for the validity 
group . Prior investigators have reported a 0.3 kg difference between mean 
TBW values determined by .sup.18 O-labeled water H.sub.2 O) from urine 
samples. In addition, these investigators showed that TBW measurements 
from saliva samples were equivalent to those measured from urine samples. 
This difference was within the expected measurement error (precision of 
&lt;1%) of either method used in this study. It was assumed that the bromide 
space of the subjects in the development and validity groups represented 
the ECW. 
After an overnight fast, subjects reported to the Exercise Physiology 
Laboratory at the Johnson Space Center in the morning for collection of 
baseline saliva (development group) or urine (validity group) samples. 
They then ingested a dose of water containing 40 g of 10.6 atom percent 
H.sub.2.sup.18 O or 4 g of 99.8 atom percent .sup.2 H.sub.2 O (Icon 
Services, Summit, N.J.) diluted to 100 g total volume with tap water. 
Samples collected 3, 4, and 5 h after administration of the dose were 
stored frozen in cryogenically stable tubes at -20.degree. C. until 
analysis. Samples were prepared according to the procedures for .sup.18 
O/.sup.16 O or .sup.2 H/.sup.1 H isotope-ratio measurements by 
gas-isotope-ratio mass spectrometry. 
Dilution space was calculated from baseline, 4-h, and 5-h sample 
collections by using the following equation: 
EQU N(mol)=((W.multidot.A)/18.02.multidot.a)).multidot.((.delta.a-.delta.t)/(.d 
elta.s-.delta.p)) 
were N is the pool space; W is the amount of water used to dilute the dose; 
A is the amount of dose administered; a is the dose diluted for analysis; 
and .delta. is enrichment of dose A, tap water t, peak postdose sample s, 
and predose baseline sample p. To account for incorporation of tracer into 
nonaqueous tissue, a correction factor of 1.04 (deuterium) or 1.01 
(.sup.18 O-labeled water) was used for the relationship between the 
isotope dilution space and TBW. The estimated error of the laboratory for 
this measurement is &lt;1% (based on the difference between 4- and 5-h 
samples). 
It was assumed that ECW was the bromide dilution space. Baseline bromide 
levels were determined from an initial blood sample. Subjects then 
ingested an oral dose of bromide (1.2 g of NaBr). Additional blood samples 
were collected 3 and 4 h after administration of the dose. All samples 
were centrifuged, and the plasma was stored at -20.degree. C. Plasma 
proteins were removed from the sample before ion chromatography by adding 
0.3 mL of the sample to Ultra-free-PF Filter units (10,000 nominal mol 
mass limit; Millipore, Bedford, Mass.). Pressurizing the filter assembly 
with 10 mL of air from a plastic syringe activated the units. The 
protein-free filtrate (60 .mu.L) was diluted 1:100 with ion chromatography 
eluant (1.8 mM Na.sub.2 CO.sub.3 /1.7 mM NaHCO.sub.3). Recovery of 
bromide-spiked plasma samples was &gt;90%. 
Bromide concentration in the samples was determined by using ion 
chromatography (Dionex model 2000i suppression-based system; Dionex, 
Sunnyvale, Calif.). Samples (500 .mu.L) were automatically injected onto 
the AS4A column (Dionex) by using the Dionex autosampler module with a 
flow rate set at 1 ml/min. Bromide was determined by suppression-based 
conductivity detection and quantified by using a calibration curve (least 
squares linear regression). 
ECW volumes were determined from the difference in plasma bromide 
concentrations between the baseline and 3-h samples. ECW was calculated as 
follows: 
EQU ECW=Brdose/[Br].multidot.0.90.multidot.0.95.multidot.0.94 
where Brdose was the amount of bromide orally administered to the subject, 
[Br] was the plasma bromide concentration obtained from the difference 
between the 0- and 3-h blood samples, 0.90 was the fraction of the bromide 
assumed to be extracellular, 0.95 was the Donnan equilibrium factor, and 
0.94 was the assumed water content of plasma. 
Impedance and resistance were measured using the embodiment of FIG. 4. The 
impedance analyzer 12, may be a Hewlett-Packard model 4284A Precision LCR 
Meter. Electrodes 10 were placed on the hand, wrist, ankle, and foot at 
standard locations before subjects 11 assumed the supine position. An 
input signal of 250 .mu.A at frequencies of 5, 50, 67, 85, 100, 150, 166, 
200, 250, and 300 kHz was applied. Subjects 11 reclined to a supine 
position, and a data acquisition unit 13, which may be a computer, 
recorded the impedance and resistance immediately and after 40 minutes of 
quiet rest. A blanket or extra clothing kept the subjects warm during the 
rest period and reduced possible variation in impedance and resistance 
caused by skin temperature changes. The difference between the impedance 
and resistance measured at 0 and 40 minutes evaluated the effects of 
shifting fluids between interstitial and vascular spaces. Prior 
investigators showed an association between the increases in total body 
resistance RT (measured at a set frequency) and decreases in hematocrit 
that accompany a change in posture. 
Determination of circuit components of the human body circuit model was 
made according to the body circuit model of FIG. 5. The determination of 
circuit components used the 1% impedance method illustrated by FIG. 6 
instead of the Cole--Cole method used by prior investigators. The results 
of the 1% impedance method produced resistances similar to graphic 
techniques based on the Cole--Cole method. Each subject's impedance and 
resistance were regressed versus frequency using 3rd-order least square 
regression. Referring to FIG. 6, the extra-cellular resistor RE was the 
resistance at a frequency of 0 Hz. At a frequency of 0 Hz, the current 
preferentially flows through the extra-cellular side of the circuit 
because the capacitor acts as a gap on the intra-cellular side of the 
circuit. The resistance of the total circuit RT was the resistance at the 
frequency where impedance changed by only 1% with a frequency increase of 
25 kHz. The 1% limit was used because it is an industry standard for 
high-precision resistors. Impedance was used because it incorporated 
resistance, capacitance, and inductance. The 25 kHz frequency increment 
was previously shown to be sufficient to identify the 1% impedance. This 
analytical approach uses the theory that, at very low frequencies, the 
electrical current does not enter cells, whereas at high frequencies, the 
current enters both the intracellular and extracellular fluid spaces. The 
intra-cellular resistor RI is the difference between one divided by the RT 
and one divided by RE. 
The method of determining circuit components illustrated by FIG. 6 
discussed above is a teleological approach and is different from the 
traditional Cole--Cole method. The Cole--Cole method solves for 
resistances when reactance is zero. The Xitron BIS 4000B analyzer (Xitron 
Technologies, San Diego, Calif.) uses a modified Cole--Cole approach with 
iterative curve fitting. Unlike the Cole--Cole method, the modified 
Cole--Cole method allows for the removal of 25% of the data to increase 
the fit of the resistance and reactance values. The method of the present 
invention uses all the data. A high correlation (r=0.987-0.994) was 
observed between the analysis techniques for the RE and RT resistors. 
However, the main predictor of TBW, Ht.sup.2 /RT, had a significantly 
weaker correlation and larger standard error of the estimate (SEE; 
r=0.693.+-.5.6 kg) for the Cole--Cole analysis than that observed from 
present invention (r=0.945.+-.2.6 kg). 
Stepwise multiple regression equations to calculate TBW and ECW were 
developed from the RT and RE values of the human body circuit model. The 
TBW equation used Ht.sup.2 /RT and body mass m, whereas ECW only used 
Ht.sup.2 /RE. The validity of these equations were evaluated with four 
statistical tests: mean differences (analysis of variance, Newman-Keuls 
post hoc testing), strength of linear relationship (Pearson product-moment 
correlations), SEE, and Bland-Altman pairwise comparisons. These 
statistical tests are standard statistical methods known to one having 
ordinary skill in the art. 
The Bland-Altman pairwise comparison evaluates the validity of a new method 
to an accepted technique. This comparison was a graphical representation 
of the difference (absolute or % .DELTA. from accepted method) between 
methods and the average of these methods. Bland-Altman suggests that if 
all values are within .+-.2 SD (standard deviation) of the averaged values 
and there is no correlation between the differences versus the averaged 
values, then the methods are clinically equivalent. Validity of a new 
method decreases if the mean difference is greater than the measurement 
error, the Bland-Altman plot shows date points outside confidence 
intervals, and there is a significant relationship indicating that one 
method overestimates or underestimates the other as a function of size. 
The stepwise multiple regression for TBW yielded the following equation for 
TBW with a multiple R of 0.987 and SEE of 1.26 kg: 
EQU TBW(kg)=2.584+0.379.multidot.Ht.sup.2 /RT+0.1686.multidot.m 
where RT is the resistance (ohms) of the circuit and m is the body mass 
(kg). The mean .+-. SD of RT for the development group was 465.+-.83 ohms. 
The stepwise multiple regression for ECW yielded the following equation 
for ECW with a multiple R of 0.858 and SEE of 1.72 kg: 
EQU ECW(kg)=2.854+0.2877.multidot.Ht.sup.2 /RE 
where RE is the resistance (ohms) of the circuit at a frequency of 0 Hz. 
The mean .+-. SD of RE for the development group was 683.+-.88 ohms. No 
other independent variables (age or gender) significantly improved the 
strength of the ECW equation. 
The TBW and ECW calculations were evaluated for validity. TBW had high 
correlations (r=0.956-0.964) and low SEE (2.08-2.28 kg) compared with 
results obtained using isotopic dilution in the validity group. The 
calculation of TBW was not significantly different from the dilution 
values for both 0 and 40 minutes (1.3.+-.6.1 and -0.4.+-.5.5% for 0 and 40 
min, respectively). Referring to FIG. 8 and Table 2, the Bland-Altman 
correlations for % change (BRS-dilution) versus averaged TBW were not 
significantly different from zero. FIG. 8, shows a Bland-Altman plot for a 
single-frequency prior art BRS method (SF) and the multi-frequency BRS 
method of the present invention (MF) versus dilution at 0 minutes. The 
solid arrow indicates the mean difference for the SF method versus 
dilution, and the open arrow indicates the mean difference for the present 
invention versus dilution. This indicated there is no trend in the 
calculations for TBW. Values for the TBW calculations were within 2 SD of 
the averaged values. For details of the SF method, see Estimation of Total 
Body Water by Bioelectrical Impedance Analysis, R. F. Kushner and D. A. 
Schoeller, American Journal of Clinical Nutrition, vol. 44 pages 417-424, 
1986. 
The calculations for ECW had high correlations (r=0.941-0.949) and low SEE 
(1.27-1.12 kg) compared with results obtained using dilution in the 
validity group. Referring to Table 2, the calculations for ECW were not 
significantly different from dilution at both 0 and 40 minutes (1.2.+-.7.7 
and -1.7.+-.7.6%, respectively). Referring to FIG. 9 and Table 2, the 
Bland-Altman correlations for % A (BRS -dilution) versus averaged ECW were 
not significantly different from zero at 0 or 40 minutes. FIG. 9 shows a 
Bland-Altman plot for two prior art BRS methods, Segal et al (Segal) and 
Lukaski and Bolonchuk (L&B), and the multi-frequency BRS method of the 
present invention (MF) versus dilution at 0 minutes. The open and solid 
arrows indicate the mean differences for the L&B and Segal BRS methods 
versus dilution, and the plain arrow indicates the mean difference for the 
present invention versus dilution. This indicated there was no trend in 
the calculations for ECW. Values for the TBW calculations were within 2 SD 
of the averaged values. For details of the L&B and Segal BRS methods, see 
Estimation of Body Fluid Volumes Using Tetrapolar Biolectrical Impedance 
Measurements, H. C. Lukaski and W. W. Bolonchuk, Aviation Space and 
Environmental Medicine, vol. 59 pages 1163-1169, 1988; Estimation of 
Extracullar and Total Body Water by Multiple-frequency 
Bioelectrical-Impedance Measurement, K. R. Segal, S. Burastero, A. Chun, 
P. Coronel, R. N. Pearson, Jr., and J. Wang, American Journal of Clinical 
Nutrition, vol. 54 pages 26-29, 1991. 
Equations were developed for calculating TBW and ECW from the circuit 
components of the human body circuit model. The calculations for TBW and 
ECW were not affected by fluid shifts that occur after 40 min of supine 
rest. These calculations have good statistical validity, based on the 
strength of the correlations (r=0.941-0.969), low SEE (1.15-2.28 kg), 
nonsignificant mean differences (BRS-dilution; % change=-0.4 to 1.3%) that 
were close to the expected measurement errors for TBW (.+-.1%) and ECW 
(.+-.5%), and Bland-Altman pairwise comparisons that showed no significant 
trend. 
TABLE 2 
__________________________________________________________________________ 
TBW and ECW Validation Results 
Dilution vs. BRS Bland-Altman 
BRS SEE % .DELTA. 
SD 
Mins 
Dilution (kg) 
(kg) r (kg) 
r (mean) 
(%) 
__________________________________________________________________________ 
TBW (n = 31) 
36.55 .+-. 7.83 
BRS 0 37.22 .+-. 7.80 
0.956 
2.28 
0.013 
1.3 6.1 
BRS 40 36.42 .+-. 7.86 
0.964 
2.08 
-0.007 
-0.4 
5.5 
ECW (n = 9) 
17.22 .+-. 4.30 
BRS 0 16.93 .+-. 4.62 
0.941 
1.27 
-0.008 
1.2 7.7 
BRS 40 17.09 .+-. 5.08 
0.949 
1.12 
-0.073 
-1.7 
7.6 
__________________________________________________________________________ 
In developing the equations to calculate total blood volume TBV and plasma 
volume PV, 19 subjects were in the development group and 10 subjects were 
in the validity group. For the 19 subjects (9 males and 10 females, age 
34.6.+-.5.7 yr, weight 65.5.+-.13.2 kg, and height 171.+-.11 cm) in the 
development group, impedance and resistance were assessed using the method 
of the present invention, and TBV and PV were assessed using dilution. For 
the 10 subjects (4 males and 6 females, age 34.1.+-.7.5 yr, weight 
73.9.+-.14.7 kg, and height 170.+-.8 cm) in the validity group, TBV and PV 
were assessed using dilution. The equations developed using the 
development group were then applied to the validity group, and the results 
thereof were compared to dilution results. 
Impedance and resistance were measured using the embodiment of FIG. 4 
discussed above in the explanation of the development of TBW and ECW 
equations. Subjects were reclined in a supine position and impedance and 
resistance were measured after 40 minutes. 
Blood and plasma volume measurements were made using .sup.125 I-labeled 
albumin after subjects rested for at least 30 minutes in the supine 
position. Subjects ingested a small amount of concentrated, nonradioactive 
iodide solution (Lugol's solution, 200 mg iodide in .sup.- 50 mL) before 
isotope injection. This iodide solution saturated the thyroid gland to 
reduce the thyroidal radiation dose due to sequestering of .sup.125 I 
liberated from the catabolism of labeled albumin. Then the subjects were 
injected with a sample of human serum albumin labeled with 10 microcuries 
or less of .sup.125 I. Blood samples (10 mL per sample) were obtained 
before the injection, and at 10 and 20 minutes after the injection for 
analysis of radioactive iodine. Technical error was estimated to be less 
than 1% and biological variation was estimated to be less the 3%. 
Therefore, the estimated propagated error for the three blood samples is 
less than 5.2%. Plasma volume PV was calculated using back extrapolation 
of exponential clearance to zero time. Hematocrit was analyzed from the 
blood samples taken for plasma volume measurement. The hematocrit was 
multiplied by 0.87 to compensate for a difference between the body and 
peripheral venous hematocrit. Red cell volume was estimated from the 
plasma volume PV and hematocrit: 
red cell volume=hematocrit.multidot.PV/(1-hematocrit). Total blood volume 
TBV was calculated by adding the plasma volume PV and the red cell volume. 
Determination of circuit components of the human body circuit model was 
made using the method represented in FIG. 6 discussed above in the 
explanation of the development of TBW and ECW equations. 
Results from the 19 subjects of the development group were evaluated for 
validity using four statistical tests: mean differences (dependent 
t-ratio, two-tail testing), strength of linear relationship (Pearson 
product-moment correlations), standard error of estimates (SEE), and 
Bland-Altman pairwise comparison. Statistical power (1-.beta.) was 
computed for the regression models and dependent t-tests. These 
statistical tests are standard statistical methods known to one having 
ordinary skill in the art. 
Stepwise multiple regression analysis was used to develop models for total 
blood volume TBV and plasma volume PV for the 19 subjects in the 
development group using the human body circuit model. Prior investigators 
assumed total body resistance RT was due to total body water TBW and was 
equivalent to the resistance of a wire. The volume of the wire can be 
determined from the following equation: 
EQU volume=.rho..multidot.length.sup.2 /R 
where .rho. is the specific resistivity (ohms.multidot.cm) of the wire and 
R is the resistance. The length of the wire is generally the subject's 
height. However, strict application of this equation to assess blood 
volume using previously reported specific resistivity of blood is not 
possible because blood resistivity changed with hematocrit. The present 
invention used ratios of Ht.sup.2 over different electrical components to 
avoid this problem. The equations for TBV and PV are as follow: 
EQU TBV(mL)=-868.9+1.048E-5.multidot.(Ht.sup.2 /M)-4.996.multidot.(Ht.sup.2 
/RE)+3.489E7.multidot.M 
with multiple r=0.915, SEE=358 mL (8.8%), F-ratio (3, 18 df)=25.65, power 
(1-.beta.)=99%; and 
EQU PV(mL)=-1649+4.941E-6.multidot.(Ht.sup.2 
/L)+4.309E7.multidot.L-9.014E6.multidot.M 
with multiple r=0.903, SEE=233 mL (8.9%), F-ratio (3, 18 df)=22.08, power 
(1-.beta.)=99%. 
Total blood volume TBV and plasma volume PV for these 19 subjects measured 
using dilution were 4045.+-.809 mL and 2605.+-.494 mL, respectively. 
The equations for total blood volume TBV and plasma volume PV were then 
applied to the 10 subjects of the second group. Table 3 shows the TBV and 
PV results for the 10 subjects in the validation group. The TBV and PV 
results obtained using the equations and using dilution for these 10 
subjects were not statistically different (P&gt;0.05). The differences were 
less than the estimated propagated error of .+-.5.2%. 
Referring to FIG. 10, Pearson product-moment correlations between TBV 
calculations and dilution is shown (r=0.298). Dashed line represents the 
method of the present invention, solid line represents dilution. Referring 
to FIG. 11, Pearson product-moment correlations between PV calculations 
and dilution is shown (r=0.945). Dashed line represents the method of the 
present invention, solid line represents dilution. These relationships 
were significantly different from zero (P&lt;0.005), and SEE was low for both 
TBV (7.7%) and PV (6.1%) when expressed as a percentage of mean dilution 
values. 
Referring to FIG. 12, a Bland-Altman pairwise comparisons plot is shown for 
TBV. The short dashed line is the mean difference of 67 mL. The long 
dashed line is the regression line of the difference versus averaged 
values of the present invention versus dilution. Referring to FIG. 13, a 
Bland-Altman pairwise comparisons plot is shown for TBV. The short dashed 
line is the mean difference of -69 mL. The long dashed line is the 
regression line of the difference versus averaged values of the present 
invention versus dilution. Both comparisons show all differences except 
one are within .+-.2 SD of averaged values and there are no significant 
relationships that indicate one method over- or underestimates the other 
as a function of size. These results show the equations developed are 
statistically valid for assessing total blood volume TBV and plasma volume 
PV. 
TABLE 3 
______________________________________ 
TBV and PV Validity Results 
Total Blood Volume 
Plasma Volume 
______________________________________ 
r (Dilution vs BRS) 
0.928 0.945 
SEE (mL) 327 167 
SEE (%) 7.7 6.1 
% Change 1.5 .+-. 9.7 -2.3 .+-. 6.9 
BRS 4293 .+-. 805 
2657 .+-. 503 
Dilution 4227 .+-. 878 
2725 .+-. 508 
Power (1 - .beta.) 
96% 94% 
at .alpha. .+-. 0.05 
______________________________________ 
It should be noted that the studies described above used a limited number 
of test subjects. Notwithstanding the limited number of test subjects, the 
equations developed accurately determined total body water TBW, 
extra-cellular water ECW, total blood volume TBV, and plasma volume PV. 
It is to be understood that the embodiments described above is merely 
illustrative of some of the many specific embodiments of the present 
invention, and that other arrangements can be devised by one of ordinary 
skill in the art at the time the invention was made without departing from 
the scope of the invention.