Calibrating volume measurements made using the dual-field conductance catheter

doi:10.4236/jbise.2009.27070

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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.

Email: [email protected]

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:

))](([)(

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:

)]([)(

2tGLtQ









(2)

The volume estimated using the conductance catheter

technique was then calculated:

)(

)( 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:

tV V



)(



(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:





QQESED







(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).

 



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:



( )0.630.06( )559,

(0.90, 0.001)

QtV t











(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.





( )0.270.01( )1045,

(0.96, 0.001)

QtVt











(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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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

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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