J. Biomedical Science and Engineering, 2009, 2, 484-490
doi: 10.4236/jbise.2009.27070 Published Online November 2009 (http://www.SciRP.org/journal/jbise/
JBiSE
).
Published Online November 2009 in SciRes. http://www.scirp.org/journal/jbise
Calibrating volume measurements made using the dual-field
conductance catheter
Simon P. McGuirk1,2, David J. Barron1, Dan Ewert3, John H. Coote2
1Department of Cardiac Surgery, Birmingham Children’s Hospital, Birmingham, UK; 2School of Clinical and Experimental Medicine,
University of Birmingham, Birmingham, UK; 3Department of Electrical and Computer Engineering, North Dakota State University,
Fargo, USA.
Received 1 February 2009; revised 24 June 2009; accepted 16 July 2009.
ABSTRACT
The conductance catheter technique allows real-
time measurements of ventricular volume based on
changes in the electrical conductance of blood
within the ventricular cavity. Conductance volume
measurements are corrected with a calibration coef-
ficient, α, in order to improve accuracy. However,
conductance vo lume measurements are also affect ed
by parallel conductance, which may confound cali-
bration coefficient estimation. This study was un-
dertaken to examine the variation in α using a
physical model of the left ventricle without parallel
con duc tan ce. Calibration coefficients were calculated
as the conductance-volume quotient (αV(t)) or the
stroke conductance-stroke volume quotient (αSV).
Both calibration coefficients varied as a non-linear
function of the ventricular volume. Conductance
volume measurements calibrated with αV(t) estimated
ventricular volume to within 2.0 ± 6.9%. By contrast,
calibration with αSV substantially over-estimated the
ventricular volume in a volume-dependent manner,
increasing from 26 ± 20% at 100ml to 106 ± 36% at
500ml. The accuracy of conductance volume meas-
urements is affected by the choice of calibration coef-
ficient. Using a fixed or constant calibration coeffi-
cient will result in volume measurement errors. The
conductance-stroke volume quotient is associated
with particularly significant and volume-dependent
mea- surement errors. For this reason, conductance
volume measurements should ideally be calibrated
with an alternative measurement of ventricular vol-
ume.
Keywords: Conductance Catheter; Calibration; Volume
Measurement
1. INTRODUCTION
The conductance catheter technique is an established
method to measure the ventricular volume in real-time,
based on the electrical conductance of blood within the
ventricular cavity [1,2,3]. Conductance volume meas-
urements are based on the assumption that the electric
field produced by the conductance catheter is homoge-
neously distributed within the ventricular cavity [1].
However, theoretical and experimental studies have
demonstrated that this assumption is not valid [4,5,6]. As
a result, the conductance catheter tends to overestimate
the volume in small ventricles and underestimate the
volume in larger ventricles [2,3].
The dimensionless calibration coefficient, α, was in-
troduced by Baan et al. [3] in order to account for the
non-uniform conductance-absolute volume relationship
[3]. This calibration coefficient represents the slope of
the relationship between the conductance-derived vol-
ume and the true volume. The calibration coefficient, α
may also vary with ventricular volume. It is relatively
high in small animals [7], lower in humans [3] and in-
termediate values are found in dogs [3,8,9]. Experimen-
tal studies demonstrate that α also varies during inferior
vena caval occlusion [9] and may even fluctuate during
the normal cardiac cycle [10,11].
The tissues and fluid surrounding the ventricular cav-
ity also contribute to the measured conductance signal
[3]. This creates a volume offset called parallel conduc-
tance. Parallel conductance also varies according to the
ventricular volume [4,7,8,9,12,13]. This volume- de-
pendent parallel conductance may confound the calibra-
tion coefficient estimation.
This study was undertaken to examine the variation in
the calibration coefficient, α, over a range of volumes
pertaining to clinical studies, in a physical model of the
left ventricle without parallel conductance.

S. P. McGuirk et al. / J. Biomedical Science and Engineering 2 (2009) 484-490 485
2. METHODS
2.1. Model Ventricle
This study used a physical model of the left ventricle
previously described by this laboratory [14]. This model
consisted of an ellipsoid latex balloon enclosed in a
pressurised Perspex chamber (Figure 1). The chamber
was filled with distilled water and hydraulically pressur-
ised with an intra-aortic balloon pump (IABP; Datascope
Medical Co. Ltd, Huntingdon, UK) with a paediatric
volume-limiting chamber. The IABP console was con-
nected to two 25ml intra-aortic balloon catheters in par-
allel. The IABP circuit was filled with helium gas to
ensure a rapid pneumatic response.
The electrocardiogram (ECG) from a patient simulator
(Bioma Research Inc, Quebec, Canada) was used to
trigger the IABP console at a predetermined rate (60
beats·min-1). Inflation of the IABP balloon catheters
caused a rise in the ventricular pressure. This displaced
saline from the latex balloon through a 2/2-way solenoid
valve (Bürkert GmbH, Ingelfingen, Germany) into a
calibrated measuring cylinder at the top of the model
ventricle. Deflation of the IABP balloon catheters caused
ventricular pressure to fall, which allowed the latex bal-
loon to refill. Electronic circuitry was used to control the
opening and closure times of the solenoid valve in order
to simulate different contraction patterns.
For the purposes of this study, the solenoid valve re-
mained open throughout the model ventricular cycle to
produce isobaric contractions. Each inflation of the
IABP balloon catheters displaced a fixed stroke volume
(SV) of 50ml. The stroke volume was independently
quantified before each experiment. The IABP balloon
catheters were manually inflated and the displaced vol-
ume was measured in the measuring cylinder.
Three separate latex balloons were used to simulate
the change in volume that may be observed during infe-
rior vena caval occlusion. Each balloon was 13 cm in
length and had a maximal volume at atmospheric pres-
sure of 125ml, 215ml and 500ml, respectively. The
shape of the balloons was ellipsoid at low volumes and
became increasingly spheroid as the volume increased.
The length-diameter ratio at maximal filling decreased from
3.03 for the smallest balloon to 1.52 for largest balloon.
Figure 1. Schematic diagram of the model heart consisting of a model ventricle and outflow tract. The position of the conductance
catheter is also illustrated.
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S. P. McGuirk et al. / J. Biomedical Science and Engineering 2 (2009) 484-490 486
During each experiment, the model ventricle was
filled with a known volume of 0.9% normal saline at
room temperature. The end-diastolic volume (VED) was
varied between 100–125ml for the 125ml balloon; 160–
215ml for the 215ml balloon; and 410–500ml for the
500ml balloon. The resistivity (conductivity-1) of this
solution was measured before each test using a dedicated
measuring cuvette (CD Leycom, Zoetermeer, The Neth-
erlands). The mean ± SD resistivity was 68.3 ± 0.5
Ω·cm.
2.2. Conductance Catheter
The principle of the conductance catheter technique for
measuring LV volume has been described elsewhere [3].
In this study, a 7-French 12-electrode high-fidelity dual
pressure-volume conductance catheter (Millar Instru-
ments, Houston, TX, USA) was used. The electrodes
were mounted at 10 mm intervals near the tip of the
catheter. One alternating current (20 kHz, 30 µA RMS)
was applied between the two outermost electrodes (elec-
trodes 1 and 12) and a second alternating current (20
kHz, -10 µA RMS) was applied between the two adja-
cent electrodes (electrodes 2 and 11). This dual-field
configuration was used in all studies [15]. A signal proc-
essor unit (CFL-512; CD Leycom) was used to measure
the potential difference between seven consecutive pairs
of the remaining eight electrodes (electrodes 3–10).
These measured voltages were converted into seven
time-varying segmental conductance signals, Gi(t).
The conductance volume, Q(t), was measured using
the following formula:
))](([)(
7
1
2
P
i
iGtGLtQ  


(1)
where ρ is the blood resistivity, L is the inter-electrode
distance, and GP is parallel conductance.
By assuming that parallel conductance is negligible (i.e.
GP = 0), this formula can be simplified to:
)]([)(
7
1
2tGLtQ
i
i


 
(2)
The volume estimated using the conductance catheter
technique was then calculated:
)(
1
)( tQtV g

(3)
where α is the dimensionless calibration coefficient [3].
2.3. Experimental Data
Analogue signals representing 7 segmental conductance
volumes within the model ventricle and the ECG were
digitised at 12-bit accuracy and a sample frequency of
250 Hz. End-diastole and end-systole were retrospec-
tively identified. End-diastole was defined as the R wave
on the ECG and end-systole was defined as the point
immediately prior to IABP circuit deflation.
Each experiment was conducted three times and, in
each, data from 10 consecutive cycles were analysed.
The estimated within-experiment standard deviation was
0.45 ml. The standard deviation was not significantly
correlated with the mean conductance volume (Kendall’s
τ coefficient = -0.72), and so subsequent analyses were
based on the average data from each experiment [16].
Two separate calibration coefficients were calculated.
Firstly, the calibration coefficients, αV(t) was calculated
by dividing the conductance-derived volume measure-
ment by the absolute ventricular volume at either
end-diastole or end-systole:
ED
ED
tV V
Q

)(

or
ES
ES
V
Q
(4)
where SVVV EDES


.
Including a “phase of measurement” (i.e. ED or ES) in
this equation did not improve the goodness of fit of the
model. The effect of “phase of measurement” was not
significant (P=0.38) and was therefore not included in
the model used to predict αV(t).
The conductance-stroke volume quotient, αSV, was
calculated by dividing the conductance-derived stroke
volume by the absolute stroke volume:


SV
QQESED
SV

 
(5)
Finally, the measurement error, ζ was calculated as a
percentage of the absolute ventricular volume:
100
)(
)(  tV
tVg

(6)
The terms ζV(t) and ζSV were used to denote the meas-
urement error associated with αV(t) and αSV, respectively.
2.4. Data Analysis
Data were analysed using SPSS for Windows (v12,
SPSS Inc., Chicago, IL, USA). Conductance volumes,
calibration coefficients and measurement errors were in
turn examined as functions of the known volume of the
model ventricle. These relationships were evaluated by
least squares linear regression based on fractional poly-
nomials of the ventricular volume. The standard error
for the regression coefficients and intercept were also
calculated. A probability, P<0.05, was taken to represent
statistical significance in these analyses. Correlation
coefficients between the variables were also calculated.
3. RESULTS
3.1. Relationship between Conductance and
Absolute Volume
The simultaneous conductance volume, Q(t), and abso-
lute volume measurements, V(t) for the three balloons
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S. P. McGuirk et al. / J. Biomedical Science and Engineering 2 (2009) 484-490 487
are illustrated in Figure 2. There was a non-linear rela-
tionship between these two volume measurements.
When analysed as a whole, the conductance-absolute
volume relationship was best approximated by the fol-
lowing relationship (Eq. 7).
 

2
14.2 0.39
0.17 0.02,(0.90,0.001)
Qt volume
volume rP



 

(7)
Compared with the line of identity (i.e. x = y), con-
ductance volume measurements predicted using this
model were equal to ventricular volume at approxi-
mately 150 ml; slightly overestimated ventricular vol-
ume when the absolute volume was less than 150 ml; but
underestimated ventricular volume at volumes over 150
ml.
The volume measurements formed two distinct sub-
sets. Data from the small and medium balloons were
clustered on the left-hand side of the plot while data
from the large balloon was clustered on the right-hand
side. When considered individually, the conduc-
tance-absolute volume relationship was well approxi-
mated by linear regression (Eq.s 8 and 9). In neither
case was the quadratic term significant. For the small
and medium-sized balloons, the linear regression was:

2
( )0.630.06( )559,
(0.90, 0.001)
QtV t
rP
 



(8)
while for the large balloon, the corresponding equation
was:
Figure 2. Conductance volume measurements, Q(t) versus
absolute volume, V(t) at end-diastole (●) and end-systole (○)
for each of the three latex balloons. The curve (dashed line)
represents the regression analysis of the conductance-absolute
volume relationship. The curve (dotted line) representing the
line of identity (x=y) is also illustrated.


2
( )0.270.01( )1045,
(0.96, 0.001)
QtVt
rP
 



(9)
The slope of these two mathematical models are sig-
nificantly different from one another (P<0.05), further
illustrating that a single, common linear relationship
does not hold over the entire range of absolute volumes.
In addition, the intercepts differ significantly from one
another and from zero (P<0.05). Therefore, neither of
these two lines passes through the origin. This intro-
duces a “volume offset”, which in this apparatus cannot
be due to parallel conductance.
3.2. Relationship between Calibration
Coefficients and Absolute Volume
The calibration coefficients, αV(t) and αSV were calculated
using Eq.s 4 and 5, respectively. Neither calibration co-
efficient was constant or linearly related to the ventricu-
lar volume. Instead, both calibration coefficients de-
creased progressively as the ventricular volume in-
creased (Figures 3A an d 3 B ). The calibration coefficient,
αV(t) varied as a function of the square root of the abso-
lute volume (r2=0.97, P<0.001). By contrast, αSV varied
as a function of the inverse absolute volume (r2=0.98,
P<0.001; and r2=0.93, P<0.001 for end-diastolic and
end-systolic measurements respectively).
The relative ratio of the two calibration coefficients
(i.e. αSV / αV(t)) was also examined over the volume range
(Figure 3C). The stroke volume quotient, αSV was lower
than αV(t) at each volume measurement. However, the
slope calibration coefficient ratio was not constant but
became progressively smaller as the absolute volume
was increased. For example, the αSV / αV(t) ratio de-
creased from 0.98 ± 0.52 to 0.43 ± 0.23 as the
end-diastolic volume increased from 100ml to
500ml.The best approximation for this relationship was
that the αSV / αV(t) ratio varied as a function of the inverse
ventricular volume (r2=0.81, P<0.001; r2=0.75, P<0.001
for end-diastolic and end-systolic measurements, respec-
tively).
3.3. Relationship between Calibrated
Conductance and Absolute Volume
and Measurement Error
Calibrated conductance volume measurements, Vg(t)
were calculated using Eq. 3, in which α was either
αV(t)-volume or αSV-volume relationship, as previously
described (Figure 4). Conductance volume measure-
ments calibrated with the αV(t)-volume relation increased
linearly with the absolute volume (r2 =0.99, P<0.001).
Conductance volume measurements calibrated with the
αSV-volume relation also increased linearly with absolute
volume (r2=0.99, P<0.001), but overestimated the abso-
lute volume.
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S. P. McGuirk et al. / J. Biomedical Science and Engineering 2 (2009) 484-490 488
(a)
(b)
(c)
Figure 3. Calibration coefficient, α versus absolute volume,
V(t) at end-diastole (●) and end-systole (○) for each of the
three latex balloons. The calibration coefficient was calculated
as the conductance-absolute volume quotient (αV(t); A) or the
conductance-stroke volume quotient (αSV; B). The calibration
coefficient ratio (C) represented αSV as a proportion of αV(t).
Curves (dashed lines) representing regression analyses of the
calibration coefficient-conductance volume relations are also
illustrated.
The volume measurement error, expressed as a per-
centage of the absolute volume, was calculated for each
calibration coefficient (Figure 5). Conductance volume
measurements calibrated with the αV(t)-volume relation
had a measurement error of 2.0 ± 6.9%, which was rela-
tively constant across the span of volume measurements.
On the other hand, the measurement error associated
with the αSV-volume relation was volume-dependent,
increasing linearly from 26 ± 20% to 106 ± 36% as the
end-diastolic volume increased from 100ml to 500ml
(r2=0.96, P<0.001).
4. DISCUSSION
The non-homogeneous electric field generated by the
conductance catheter results in a non-linear relationship
between conductance and true ventricular volume meas-
urements. Conductance measurements are, therefore,
calibrated using the dimensionless calibration coefficient,
α in order to obtain absolute volume measurements. This
study investigated the accuracy of conductance volume
measurements, and the effect of calibration, in a series of
in vitro experiments that spanned the volume range ob-
served in clinical studies [17]. This model design also
avoided the potential problems associated with parallel
conductance.
This study has confirmed that there is a non-linear re-
lationship between dual-field conductance and absolute
volume measurements, such that the conductance- vol-
ume relation is concave towards the true volume. The
conductance volume measurements underestimated ven-
tricular volume as the volume was increased above
150ml. This finding is in accord with previous experi-
mental studies [4,6].
Conductance volume measurements are generally
calibrated with the dimensionless calibration coefficient
in order to improve the accuracy of ventricular volume
measurements made using this technique [3]. In the iso-
lated post-mortem canine heart, Mur & Baan reported
that the conductance-volume relation was virtually linear
over a finite volume range [2] and the authors predicted
that a similar, virtually linear conductance-volume rela-
tion would be observed for the human left ventricle up to
a volume of 200ml [2].
However, this study has shown that the calibration
coefficient, α is not constant, but varies as a non-linear
function of the ventricular volume. Using a fixed or con-
stant α during acute volume change will inevitably result
in volume measurement errors. These measurement er-
rors may be relatively small during the normal cardiac
cycle. However, procedures that produce an acute and
substantial change in volume load, like vena caval oc-
clusion, will potentially result in significant measure-
ment errors.
Kornet et al. suggested that the variation in α observed
in vivo might reflect synchronous volume-dependent
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S. P. McGuirk et al. / J. Biomedical Science and Engineering 2 (2009) 484-490 489
Figure 4. Calibrated conductance volume measurements, Vg(t)
versus absolute volume, V(t) at end-diastole (●) and
end-systole (○) for each of the three latex balloons. Conduc-
tance volume measurements were calibrated using either αV(t)
(●, ○) or αSV (▼, ).Curves (dashed lines) representing re-
gression analyses of the calibrated conductance vol-
ume-absolute volume relations are also illustrated.
Figure 5. Calibrated conductance volume measurement error, ζ
versus absolute volume, V(t) at end-diastole (●) and
end-systole (○).Conductance volume measurements calibrated
using either αV(t) (●, ○) or αSV (▼, ). Volume measurement
error was calculated as a percentage of the absolute volume.
Curves (dotted and dashed lines) representing regression
analyses of the measurement error-absolute volume relations
are also illustrated.
changes in parallel conductance during the cardiac cycle
[13]. However, this study used a physical model of the
left ventricle without parallel conductance. Our findings
suggest that parallel conductance is not a comprehensive
explanation for why the calibration coefficient varies as
a function of the ventricular volume.
Although conductance volume measurements can be
calibrated against another synchronous estimate of ven-
tricular volume [3,10,18], they are generally calibrated
with an alternate measurement of stroke volume [6,10].
Calibration with either an alternate measurement of ven-
tricular volume or stroke volume are generally consid-
ered equivalent. This study also identified that the αV(t)
and αSV are different. The stroke volume quotient, αSV
was lower than αV(t) and the calibration coefficient ratio,
αSV / αV(t) became progressively smaller as the ventricular
volume increased. Calibrating conductance volume
measurements with αSV resulted in the significant over-
estimation of end-diastolic and end-systolic volume, and
the degree of overestimation was even more pronounced
at higher volumes. This demonstrates that conductance
volume measurements should ideally be calibrating us-
ing an independent measure of ventricular volume like,
for example, contrast cineangiography, echocardiogra-
phy or magnetic resonance imaging.
The difference between the αV(t)-volume and αSV-
volume relations may be attributed to the non-homoge-
neous electrical field distribution established by the
conductance catheter [4,12]. Conductance volume mea-
surements are disproportionately influenced by the areas
around the longitudinal axis of the ventricle where the
electrical field is strongest. By contrast, changes in vo-
lume that occur during ejection or when loading condi-
tions are varied primarily affect the myocardial boun-
dary where the electrical field density is weakest. Con-
sequently, αSV and αV(t) are not equivalent and cannot be
used interchangeably.
4.1. Study Limitations
The physical model of the isolated left ventricle used in
this study did not allow changes in the volume loading
conditions could not be modelled continuously. Instead,
a series of steady-state experiments were made at incre-
mental end-diastolic volumes in three separate models,
which carries with it the risk of repeated measurement
errors. The changes in ventricular volume resulted from
changes in the short-axis dimension of the model only. It
was not possible to examine any effect of changing ven-
tricular length, such as those that may occur during the
cardiac cycle [19].
Ideally, the volumes within the model ventricle would
have been acquired simultaneously using the conduc-
tance catheter and another independent method. In the
original design, the ejected volume was measured ac-
cording to the pressure generated within the fluid col-
umn [14]. However, preliminary experiments demon-
strated that the fluid-filled micromanometer was not
sufficiently accurate to enable instantaneous volume
measurements throughout the cardiac cycle and, there-
fore, measurements were made with the calibrated
measuring cylinder.
5. CONCLUSIONS
The conductance catheter technique incorporates a cali-
bration coefficient, α, in order to obtain accurate volume
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S. P. McGuirk et al. / J. Biomedical Science and Engineering 2 (2009) 484-490
SciRes Copyright © 2009
490
measurements. This study has demonstrated that this
calibration coefficient varies as a function of absolute
volume, independent of parallel conductance. Assuming
that the calibration coefficient is fixed or constant will
introduce measurement errors. The conductance-stroke
volume quotient, αSV is associated with particularly sig-
nificant and volume-dependent measurement errors. This
limits the value of volume measurements calibrated us-
ing αSV. Conductance volume measurements should ide-
ally be calibrated with an alternative measurement of
ventricular volume, using any one of the techniques that
are now available.
JBiSE
6. ACKNOWLEDGEMENTS
Simon McGuirk was supported by a British Heart Foundation Junior
Research Fellowship (FS/03/102).
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