Cardiovascular Research 38 Ž1998. 668–675
The effect of changing excitation frequency on parallel conductance in
different sized hearts
Paul A. White a , Carl I.O. Brookes b, Hanne B. Ravn c , Elizabeth E. Stenbøg c ,
Thomas D. Christensen c , Rajiv R. Chaturvedi a , Keld Sorensen d , Vibeke E. Hjortdal c ,
Andrew N. Redington a,)
a
Department of Paediatric Cardiology, Royal Brompton Hospital, Sydney Street, London SW3 6NP, UK
b
Department of Adult Cardiology, Royal Brompton Hospital, Sydney Street, London SW3 6NP, UK
c
Institute of Experimental Clinical Research, Aarhus UniÕersity Hospital, Aarhus, Denmark
d
Department of Cardiology, Aarhus UniÕersity Hospital, Aarhus, Denmark
Received 10 September 1997; accepted 3 February 1998
Abstract
Objective: An important component of the ventricular volume measured using the conductance catheter technique is due to parallel
conductance ŽVc., which results from the extension of the electric field beyond the ventricular blood pool. Parallel conductance volume is
normally estimated using the saline dilution method ŽVcŽsaline dilution.., in which the conductivity of blood in the ventricle is transiently
increased by injection of hypertonic saline. A simpler alternative has been reported by Gawne et al. w12x. VcŽdual frequency. is estimated
from the difference in total conductance measured at two exciting frequencies and the method is based on the assumption that parallel
conductance is mainly capacitive and hence is negligible at low frequency. The objective of this study was to determine whether the dual
frequency technique could be used to substitute the saline dilution method to estimate Vc in different sized hearts. Methods: The
accuracy and linearity of a custom-built conductance catheter ŽCC. system was initially assessed in vitro. Subsequently, a CC and
micromanometer were inserted into the left ventricle of seven 5 kg pigs Žgroup 1. and six 50 kg pigs Žgroup 2.. Cardiac output was
determined using thermodilution Žgroup 1. and an ultrasonic flow probe Žgroup 2. from which the slope coefficient Ž a . was determined.
Steady state measurements and Vc estimated using saline dilution were performed at frequencies in the range of 5–40 kHz. All
measurements were made at end-expiration. Finally, Vc was estimated from the change in end-systolic conductance between 5 kHz and
40 kHz using the dual frequency technique of Gawne et al. w12x. Results: There was no change in measured volume of a simple insulated
cylindrical model when the stimulating frequency was varied from 5–40 kHz. VcŽsaline dilution. varied significantly with frequency in
group 1 Ž8.63 " 2.74 ml at 5 kHz; 11.51 " 2.65 ml at 40 kHz. Ž p s 0.01.. Similar results were obtained in group 2 Ž69.43 " 27.76 ml at
5 kHz; 101.24 " 15.21 ml at 40 kHz. Ž p - 0.001.. However, the data indicate that the resistive component of the parallel conductance is
substantial ŽVc at 0 Hz estimated as 8.01 ml in group 1 and 62.3 ml in group 2.. There was an increase in a with frequency in both
groups but this did not reach significance. The correspondence between VcŽdual frequency. and VcŽsaline dilution. methods was poor
Žgroup 1 R 2 s 0.69; group 2 R 2 s 0.22.. Conclusion: At a lower excitation frequency of 5 kHz a smaller percentage of the electric
current extends beyond the blood pool so parallel conductance is reduced. While parallel conductance is frequency dependent, it has a
substantial resistive component. The dual frequency method is based on the assumption that parallel conductance is negligible at low
frequencies and this is clearly not the case. The results of this study confirm that the dual frequency technique cannot be used to substitute
the saline dilution technique. q 1998 Elsevier Science B.V. All rights reserved.
Keywords: Pig; Neonatal; Adult; Left ventricle; Conductance catheter; Saline wash-in; Parallel conductance; Dual frequency excitation
1. Introduction
The conductance catheter technique has successfully
been used to study ventricular pressure volume relation)
Corresponding author. Tel: q44 Ž171. 351 8546; Fax: q44 Ž171.
351 8545; E-mail: [email protected]
0008-6363r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
PII S 0 0 0 8 - 6 3 6 3 Ž 9 8 . 0 0 0 5 2 - 2
Time for primary review 27 days.
P.A. White et al.r CardioÕascular Research 38 (1998) 668–675
ships in vivo in animals w1–3x, and humans w4,5x, in both
the left and right ventricles w6–8x. The calculation of
ventricular contractility from these volume measurements
has become increasingly popular in humans both perioperatively and in the cardiac catheterisation laboratories, but a
potential drawback of this technique is the complexity of
absolute volume determination. The volume signal obtained includes a proportion of the actual volume Žreflected
by the dimensionless gain constant, a , and an element of
additional volume measured beyond the ventricular blood
pool Žparallel conductance.. Alpha is measured by calibration against a known ventricular volume, e.g. thermodilution w4,5,8x, flow probe stroke volume w4,8x, or angiographic assessments w4x. Parallel conductance needs to be
measured directly.
The conductance volumetric principle is based on the
assumption that the electric field is homogenous and parallel to the longitudinal axis of the ventricle and that all
current is contained within the ventricular cavity. However, parallel conductance ŽVc. occurs because cardiac
muscle is not a perfect insulator and a component of the
volume signal arises from the conductance of structures
extrinsic to the ventricular blood pool. Several investigators have chosen not to quantify the parallel conductance
w3,9–11x and have instead presented relative volumes.
While still useful for some applications calibration to
absolute volume markedly strengthens the utility of measurements made with the catheter system.
Parallel conductance ŽVcŽsaline dilution.. is normally
estimated by injection of hypertonic saline, which transiently changes the conductivity of the blood in the ventricle w4x. This technique has the disadvantage of inappropriate saline loading with multiple measurements and cannot
be performed during transient changes in the loading conditions of the ventricle, such as snaring of the inferior vena
cava.
To overcome these weaknesses, Gawne proposed a
method that exploits the difference in conductivity in
muscle and blood at different frequencies w12x. The standard saline dilution technique is usually performed at an
excitation frequency of 20 kHz w1,2,4,6x. However, blood
has essentially a constant conductivity over the range of
frequencies from 2 to 100 kHz w13x. Muscle, is more
conductive at frequencies higher than 12 kHz w14x. Thus it
might be possible to eliminate or reduce the myocardial
component by altering the stimulating frequency. Indeed,
Gawne w12x using a swine model, suggested that a dual
frequency method could reliably substitute the saline dilution technique in potentially determining species specific
parallel conductance, assuming that parallel conductance is
mainly capacitive and hence negligible at low frequencies.
This study further investigates and develops the use of a
multiple frequency excitation technique over the range of
5–40 kHz in neonatal and adult pigs. We examined the
changes in Vc with increasing frequency and determined
whether a dual frequency technique could be used as an
669
alternative to the saline dilution technique in different
sized hearts.
2. Conductance catheter
The principles and techniques of the conductance
catheter to estimate left ventricular volume are described
in detail elsewhere w4,15x. Briefly, the conductance catheter
method is based on the measurement of the electric conductivity of blood in a ventricular cavity. A custom built
signal conditioning and processing unit ŽCardiodynamics,
The Netherlands. was constructed in order to allow for a
variable excitation frequency while at the same time maintaining a constant electrical current of 30 mA. An alternating current of 5–40 kHz and 30 mA is applied between the
two outermost electrodes Želectrodes 1 and 8. to generate
an intracavity electric field. The remaining electrodes are
used to measure the potential difference and therefore
derive the time varying ventricular conductance ŽGt. as the
sum of five segments. Total left ventricular conductance is
calculated as the sum of the segmental conductances. The
relationship between time varying volume ŽVt. and time
varying conductance ŽGt. is given by the simple formula:
Vt s 1ra .L2 .r Ž Gt y Gp . .
Ž 1.
Where a is the slope of the relation between conductance derived volume and true volume, r is the blood
resistivity, L is the interelectrode distance and Gp is
parallel conductance. The offset volume Vc, caused by the
parallel conductance, Gp is equal to:
Vc s 1ra .L2 .r.Gp.
Ž 2.
3. Method
3.1. In Õitro: the effect of excitation frequency on Õentricular Õolume measurements
Preliminary in vitro measurements were obtained with
the modified conductance catheter system to check the
accuracy and linearity in glass cylinders containing 0.9%
NaCl solution ŽAbbott Laboratories.. The resistivity of this
solution was measured using the four electrode cuvette
integral to the Sigma 5 signal conditioning and processing
unit. The mean of three estimates was used as the resistivity of the 0.9% NaCl for that experiment and was entered
into the custom software along with the interelectrode
distance of the catheter.
The relationship between conductance volume, known
volume and frequency was initially investigated using
three glass cylinders of differing diameter. A 7 French 8
electrode conductance catheter with a total interelectrode
distance of 7 cm ŽWebster. was positioned in the central
670
P.A. White et al.r CardioÕascular Research 38 (1998) 668–675
long axis of the cylinder. The cylinder was initially filled
until all electrodes were just covered by fluid with a
known volume of 7 ml, 22.5 ml and 62 ml. Measurements
of conductance volume were recorded after changing the
catheter excitation frequency by 5 kHz increments between
5 and 40 kHz.
the main pulmonary artery, just distal to the pulmonary
valve, in order to measure pulmonary flow.
3.2. In ÕiÕo study
The conductance catheter was connected to our custom
built Sigma 5 DF signal conditioning and processing unit
ŽCardiodynamics, The Netherlands.. Analogue signals representing the five segmental conductances, left ventricular
pressure, and ECG were digitised Ž12 bit, 250 Hz., using a
DT 2821 A–D convertor ŽData Translation, Marlboro,
MA., monitored on line and stored on a microcomputer for
later analysis using custom software. Having obtained an
optimum conductance catheter position, a 4 ml blood
sample was taken to measure blood resistivity Žr . and
entered into the custom software. This software allows the
analysis of multiple indices of ventricular performance
Žend systolic pressure volume relationship, end diastolic
pressure volume relationship, preload recruitable stroke
work, etc.., but in this study we only used end systolic
volume ŽESV., end diastolic volume ŽEDV. and stroke
volume ŽSV. in order to calculate VcŽsaline dilution.,
VcŽdual frequency. and a Žsee below.. Measurements of r
were repeated after each injection of saline.
Cardiac output was measured in the neonatal group
Žgroup 1. by thermodilution. The mean of four measurements was taken as the cardiac output for that specific time
point. In group 2, cardiac output was determined on a beat
by beat basis from the flow probe around the pulmonary
artery. The conductance catheter gain factor Ž a . was calculated as the ratio of conductance derived cardiac output to
that measured by thermodilution in group 1, and by
flowmeter in group 2. Two measurements were made at
steady state at each excitation frequency over the range of
5–40 kHz during suspended ventilation at end expiration.
To calculate VcŽsaline dilution., a small volume 0.7 ml of
10% hypertonic saline Žgroup 1. and 7 ml of 10% Žgroup
2. was then injected into the pulmonary artery and the
superior vena cava respectively during continuous data
acquisition. If changes in heart rate or ventricular pressure
were apparent during the saline injection, the run was
repeated with a smaller injectate volume. End diastolic
volume ŽEDV. was plotted against the subsequent end
systolic volume ŽESV. of each beat during the ascending
limb of the saline wash-in. The points are linearly regressed by the least squares method. When this regression
line is extrapolated to the line of identity ŽEDV s ESV.
the blood conductivity is zero and all the current goes
through the ventricular wall. The volume at this point is
due to parallel conductance ŽVcŽsaline dilution... Two
measurements were made per animal at each excitation
frequency in both group 1 and group 2 from which the
mean was obtained to determine VcŽsaline dilution.. If
ectopy occurred during the saline dilution data collection,
The investigation conformed with the Guide for the
Care and Use of Laboratory Animals published by the US
National Institute of Health w16x.
4. Preparation
Studies were performed in seven 5 kg Žgroup 1. and six
50 kg Žgroup 2. Danish Landrace pigs. The neonatal pigs
Žgroup 1. were sedated and paralysed with Midazolam Ž0.1
mgrkg i.v., Fentanyl Ž5 mgrkgrh i.v. and Pancuronium
Ž0.1 mgrkg i.v.. The adult pigs Žgroup 2. were paralysed
with Pancuronium Ž0.04 mgrkgrh i.v., while anaesthesia
was maintained with Propofol Ž8–10 mgrkgrh i.v. and
Fentanyl Ž0.3 mgrh i.v.. All animals were intubated and
mechanically ventilated with positive pressure ventilation
using a Siemens Servo 900 C ŽSiemens Elema, Solna,
Sweden.. Serial blood gas measurements were performed
to maintain a physiological level of oxygenation and ventilation. The right and left carotid arteries and the internal
jugular vein Žin group 2. were cannulated. Access to the
heart was obtained through a standard median sternotomy,
the pericardium was opened, and the heart was suspended
in a pericardial cradle.
4.1. Group 1: 5 kg neonatal pigs
A 2.5 French micromanometer ŽMillar Instruments,
Houston, TX. was inserted through the left ventricular
apex. A 5 French custom built 8 electrode conductance
catheter ŽNumed, Hopkinton, NY. with a total interelectrode distance of 3 or 4 cm to match the longitudinal axis
of the ventricle was advanced through the right carotid
artery sheath into the left ventricle using fluoroscopic
guidance. Confirmation of correct positioning was obtained from typical waveforms. A thermodilution catheter
Ž5.5 French. was placed into the pulmonary artery via the
right internal jugular vein, again guided by fluoroscopy.
4.2. Group 2: 50 kg adult pigs
The preparation of these larger animals was similar to
group 1 except that a 6 French 8 electrode conductance
catheter ŽWebster. with a total interelectrode distance of 6
cm was placed in the left ventricle, and a 24 mm transit
time flow probe ŽTransonic, Ithaca, NY. was placed around
5. Protocol
P.A. White et al.r CardioÕascular Research 38 (1998) 668–675
we performed another injection in order to obtain at least
two acceptable recordings. Each dataset was acquired for
approximately 20 s during suspended ventilation.
671
8. Results
8.1. In Õitro: the effect of excitation frequency on Õolume
measurements
6. Gawnes dual frequency technique to determine Vc
There was no volume variation with frequency. The
mean gradient of the regression lines for all frequencies
was 0.83 " 0.007 suggesting little frequency dependence.
The y-intercept ranged from y0.3 ml at 5 kHz to y0.69
ml at 40 kHz. The mean y intercept for all frequencies was
y0.61 ml " 0.16 ml. The mean value of R 2 for each
frequency was 1.00.
This method uses a dual frequency technique w12x to
measure VcŽdual frequency.. VcŽsaline dilution. was first
measured at an excitation frequency of 5 kHz. This value
was expressed as a percentage of end systolic volume
measured at 5 kHz. These values were plotted against the
percentage rise in end systolic volume as the excitation
frequency was increased from 5 to 40 kHz. A linear
regression analysis was performed on the data with the y
intercept set at or close to zero, which is similar to that
used by Gawne reflecting the original theoretical basis on
which the technique was proposed. The reciprocal of this
regression slope is used to determine a constant which
when multiplied by the absolute rise in ESV which occurred between the measurements at 5 and 40 kHz would
estimate VcŽdual frequency.. A standard least squares
regression analysis was also performed on the data for
further comparison.
8.2. In ÕiÕo study
8.2.1. Group 1: 5 kg neonatal pigs
Group data for parallel conductance ŽVcŽsaline dilution..
and ventricular volumes are presented in Table 1. Parallel
conductance volume ŽVcŽsaline dilution.. varied significantly with frequency Ž5 kHz s 8.63 " 2.74 ml; 20 kHz s
9.43 " 3.25 ml; 40 kHz s 11.51 " 2.65 ml. Ž p s 0.01.
ŽFig. 1.. There was no detectable difference in stroke
volume ŽSV. over the range of excitation frequencies; The
mean SV at 5 kHz s 4.13 " 1.45 ml demonstrated a nonsignificant rise to 4.75 " 1.52 ml at 40 kHz Ž p s 0.19..
Although the end systolic volume rose with frequency Ž5
kHz s 12.55 " 2.96 ml; 20 kHz s 13.70 " 3.83 ml; 40
kHz s 14.72 " 4.43 ml., the difference was not significant
when the ESV at 5 kHz and 40 kHz were compared
Ž p s 0.16.. Pressure volume loops demonstrating this
change in end systolic volume between the different excitation frequencies are shown in Fig. 2. Similarly the
end-diastolic volume demonstrated a non-significant rise
Ž5 kHz s 16.69 " 3.55 ml; 20 kHz s 18.29 " 4.49 ml; 40
kHz s 19.47 " 5.40 ml. Ž p s 0.12.. Nonetheless an analysis of variance for repeated measures throughout the group,
at all frequencies does show a highly significant dependence of volumes on frequency. In this group as a was
measured by thermodilution we were unable to assess the
variability of a over the excitation frequency range.
7. Data analysisr
r statistics
Data are expressed as mean Ž" 1SD.. A Bland Altman
methods comparison was used to compare VcŽsaline dilution. and VcŽdual frequency.. The variability of stroke
volume, end systolic volume, end diastolic volume, parallel conductance volume ŽVcŽsaline dilution.. and conductance gain factor Ž a . were assessed over the excitation
range of 5–40 kHz by using an analysis of variance. The
relationship between VcŽsaline dilution. as a percentage of
end systolic volume with the percent rise in end systolic
volume with frequency was assessed by a linear regression
using the least squares method with the y intercept set at or
close to zero. A standard least squares regression analysis
was also performed on the data for further comparison.
The null hypothesis was rejected when p - 0.05.
Table 1
Group data for neonatal pigs over the excitation frequency range of 5–40 kHz
Frequency ŽkHz.
VcŽsaline dilution. Žml.
ESV Žml.
EDV Žml.
SV Žml.
5
10
15
20
30
40
ANOVA Ž5 vs. 40 kHz.
8.63"2.74
8.75"3.07
9.21"2.76
9.43"3.25
9.88"3.07
11.51"2.65
ps 0.01
12.55"2.96
12.91"3.34
13.01"3.59
13.70"3.84
13.81"3.91
14.72"4.43
ps 0.16
16.69"3.55
17.40"3.67
17.55"4.18
18.29"4.49
18.43"4.74
19.47"5.40
ps 0.12
4.13"1.45
4.49"1.65
4.54"1.54
4.6 "1.55
4.62"1.55
4.75"1.52
ps 0.19
VcŽsaline dilution.: Parallel conductance volume; ESV: End systolic volume; EDV: End diastolic volume; SV: Stroke volume. Data is expressed as
mean"SD. Significant difference was determined at p- 0.05.
P.A. White et al.r CardioÕascular Research 38 (1998) 668–675
672
Fig. 1. The relationship between frequency ŽkHz. and parallel conductance ŽVcŽsaline dilution.. for neonatal pigs using the saline dilution
technique. There is a good correlation between frequency and VcŽsaline
dilution.. As the frequency is reduced VcŽsaline dilution. also decreases.
A similar relationship was also evident in the adult pigs Žgroup 2..
8.3. Gawnes dual frequency technique to determine Vc
Due to technical difficulties it was not possible to
estimate VcŽsaline dilution. in one pig. However, results
for the remaining six pigs are reported accordingly. From a
graph of parallel conductance ŽVcŽsaline dilution.. as a
percentage of end systolic volume ŽESV. plotted against
the rise in end systolic volume as the excitation frequency
was increased from 5–40 kHz a constant was derived. The
derivation of this constant Ž1rŽ a G y1.., found to be 4.55
for the neonatal group, when multiplied by the percent
change in end systolic volume from 5–40 kHz would yield
an estimate of parallel conductance volume ŽVcŽdual frequency... However, the relationship of VcŽsaline dilution.
and VcŽdual frequency. produce a poor correlation Ž R 2 s
0.69..
A standard regression analysis using the least squares
method was performed on the graph of parallel conductance ŽVcŽsaline dilution.. as a percentage of end systolic
volume ŽESV. plotted against the percent rise in esv as the
frequency was increased from 5–40 kHz for comparative
purposes. A negative slope Ž Y s 24.56–0.14 X. and a poor
correlation coefficient Ž R 2 s 0.064. were obtained.
8.4. Group 2: 50 kg adult pigs
Parallel conductance ŽVcŽsaline dilution.. increased with
frequency by 31.42% from 69.43 " 27.76 ml at 5 kHz to
Fig. 2. Pressure volume loops demonstrating the increase in end-systolic
volume with increasing frequency over the range of 5–40 kHz. Note also,
how there is an apparent increase in stroke volume in this animal Žsee text
for details..
101.24 " 15.21 ml at 40 kHz Ž p - 0.001.. Unlike in the
neonatal group Žgroup 1., there was a significant difference
in stroke volume ŽSV. over the range of excitation frequencies ŽSV at 5 kHz s 30.82 " 3.70 ml; 40 kHz s 38.44
" 5.24 ml. Ž p s 0.003.. The end systolic and diastolic
volumes also increased significantly with frequency ŽESV5
kHz s 140.17 " 13.36 ml; ESV40 kHz s 170.53 " 21.44 ml
Ž p s 0.002.; EDV5 kHz s 170.98 " 14.04 ml; EDV40 kHz s
208.84 " 23.07 ml. Ž p - 0.001. Žsee Table 2.. The slope
or gain factor a was determined in this group by comparing conductance derived cardiac output to that obtained on
a beat to beat basis by a transit time flow probe. The mean
a for the group at 5 kHz Ž0.62 " 0.14. increased to
0.75 " 0.16 at 40 kHz Ž p s 0.18.. Correcting EDV and
ESV for both Vc and a produced no change in stroke
volume with frequency Žcorr SV5 kHz s 52.28 " 17.98 ml;
corr SV40 kHz s 53.81 " 19.90 ml Ž p s 0.89...
8.5. Gawnes dual frequency technique to determine Vc
Similar results were obtained in the adult group. The
parallel conductance volume ŽVcŽdual frequency.. as a
percent of end systolic volume for the adult group was
found to be 3.45 times percent rise in ESV with changing
frequency ŽFig. 3.. There was no significant relationship
between VcŽsaline dilution. and VcŽdual frequency. Ž R 2 s
0.22.. The standard least squares regression analysis was
Table 2
Group data for adult pigs over the excitation frequency range of 5–40 kHz
Frequency ŽkHz.
VcŽsaline dilution. Žml.
ESV Žml.
EDV Žml.
SV Žml.
5
20
40
ANOVA Ž5 vs. 40 kHz.
69.43"27.76
86.99"12.57
101.24"15.21
p- 0.001
140.17"13.36
132.75"21.18
170.53"21.44
ps 0.002
170.98"14.04
162.59"25.07
208.84"23.07
p- 0.001
30.82"3.70
29.90"5.45
38.44"5.24
ps 0.003
VcŽsaline dilution.: Parallel conductance volume: ESV: End systolic volume: EDV: End diastolic volume; SV: Stroke volume. Data is expressed as
mean"SD. Significant difference was determined at p- 0.05.
P.A. White et al.r CardioÕascular Research 38 (1998) 668–675
673
VcŽsaline dilution.. Similarly in the adult pigs Žgroup 2.
VcŽdual frequency. maybe y63.66 ml below or 94.50 ml
above that estimated by VcŽsaline dilution.. Thus, the dual
frequency estimation of Vc cannot be used to reliably
substitute the saline dilution technique.
10. Discussion
Fig. 3. ŽA. Graph of parallel conductance volume ŽVcŽsaline dilution.. as
a percentage of end-systolic volume ŽESV. plotted against the percent
rise in ESV with frequency, for adult pigs. VcŽsaline dilution. as a
percent of end-systolic volume was found to be 3.45 times percent rise
with a change in frequency. Solid line – Regression line. Dotted line,
95% confidence limit for regression line. ŽB. Graph of parallel conductance determined by the saline dilution method against parallel conductance determined by the Gawne technique for adult pigs. R 2 s 0.22.
Dashed line – Regression line.
performed as in group 1. Again a poor correlation coefficient was obtained Ž Y s 14.18 q 0.05 = R 2 s 0.067..
9. Comparison of methods
It is possible to compare VcŽsaline dilution. to that
obtained by a dual frequency excitation technique ŽVcŽdual
frequency.. using a Bland Altman comparison w17x. Using
this, VcŽsaline dilution. and VcŽdual frequency. did fall
within the 95% limits of agreement, for both the neonatal
group Žgroup 1. or the adult group Žgroup 2.. However,
there is no obvious relation between the difference and the
mean. Under these circumstances we can summarise the
lack of agreement by calculating the bias, estimated by the
mean difference and the standard deviation of the differences. Thus for the neonatal pigs Žgroup 1. VcŽdual frequency. maybe y9.88 ml below or 16.56 ml above
The conductance technique has widely been applied to
the study of left ventricular pressure volume relationships.
However, a drawback of the conductance catheter method
is its inability to determine absolute volume without calibration factors. Calculation of absolute left ventricular
volume from conductance measurements requires the estimation of parallel conductance volume ŽVc. and a slope
factor Ž a .. Parallel conductance volume accounts for a
substantial portion of the total conductance signal, ranging
from approximately 50% to as much as 70% of the total
signal w18x. Thus Vc is not small and should not be
ignored. Parallel conductance volume is normally determined by injecting a small amount of hypertonic saline
into the pulmonary artery which transiently increases the
conductivity of blood in the ventricle w4x. The disadvantage
of this technique is that measurements have to be performed during steady state, and it is not possible to
determine whether parallel conductance changes during a
loading manoeuvre such as transient snaring of the inferior
vena cava. In addition it is subject to the variability
inherent, at best 10%, to indicator dilution methods. As the
parallel conductance volume can be as much as twice the
actual ventricular volume, small errors in parallel conductance volume will have a larger impact on subsequent
estimation of absolute left ventricular volume w18x.
This study investigated the effect of changing excitation
frequency over the range of 5–40 kHz on left ventricular
volume measurement according to the technique described
by Gawne w12x, who described a species specific substitute
to the saline dilution method in the estimation of parallel
conductance volume.
In vitro there was no significant relationship between
frequency and volume, confirming the linearity and accuracy of our custom-built hardware. However, in both the 5
kg neonatal Žgroup 1. and 50 kg adult pigs Žgroup 2. we
observed a significant change in VcŽsaline dilution. with
frequency. In group 1 VcŽsaline dilution. increased by
25.02% between 5 kHz and 40 kHz. Similarly in group 2 a
difference of 31.42% was observed. These findings suggest that the lower the excitation frequency, the lower the
dissipation of current beyond the blood pool. These data
indicate that the resistive component of Vc is substantial.
For instance, estimated Vc at 0 Hz in group 1 is 8.01 ml
compared with 11.51 ml at 40 kHz.
At frequencies of 20 kHz or greater, the resistivity of
the myocardium is less than 400 V P cm which is only 2.5
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P.A. White et al.r CardioÕascular Research 38 (1998) 668–675
times greater than that of blood Ž150 V P cm. w10x. However, by reducing the excitation frequency to 5 kHz the
resistivity of the myocardial tissue is considerably greater
and thus a much smaller percentage of the measuring
current extends beyond the blood pool. For this excitation
frequency, cardiac tissue and blood are predominantly
resistive w19–21x. Similar results were observed by
Steendijk who, using a novel approach to measure
anisotropic myocardial resistivity, showed a reduction in
both longitudinal and transverse fibre measurement with
increasing frequency. These results show that over the
range of 5–60 kHz both transverse and longitudinal resistivity decreased by approximately 25% w22x, which was
similar to that obtained by Sperelakis w23x. A discrepancy
can be seen between our data and those obtained by Duck
w19x, Rush w20x and Schwan w21x which maybe explained
by Ži. differences in preparation, e.g. the difference in
resistivity between blood and Tyrode solution; Žii. the
condition of the preparation e.g. ischaemia; and Žiii. the
excitation frequency at which the resistivity measurement
has been performed.
Most studies have used an excitation frequency of 20
kHz, 30 mA, but a few investigators have used lower
excitation frequencies to reduce the effect of parallel conductance w5,10x. At a frequency of 1.3 kHz the resistivity
of the myocardial tissue is greater than 1000 V P cm and a
much smaller percentage of the measuring current dissipates beyond the ventricle w10x. McKay concluded that the
decrease in current leakage that occurs at a reduced excitation frequency may be responsible for both the improved
accuracy of volume measurements reported in his study as
well as a tendency slightly to overestimate stroke volumes.
The dual frequency technique described by Gawne et al.
w12x uses the change in conductance with frequency to
estimate parallel conductance and it has been argued that
this technique could obviate the need for the saline dilution
technique altogether. When parallel conductance ŽVcŽsaline
dilution.., is expressed as a percentage of end-systolic
volume at 3.3 kHz and plotted against the percent rise in
end-systolic volume with frequency he obtained a highly
linear relationship. From this he calculated a species specific calibration factor w12x. Gawne therefore assumes that
the parallel conductance is a simple linear function with
frequency. This implies that the coupling between parallel
conductance and left ventricular volume is wholly capacitive. However, our results are not consistent with a capacitively coupled parallel conductance with a break frequency
of 12 kHz. Our results have shown that parallel conductance has a significant resistive component which cannot
be estimated from the frequency dependence measured
with the conductance catheter.
A linear regression analysis was performed on the data,
for both the neonatal Žgroup 1. and adult Žgroup 2. pigs,
with the y intercept set at or close to zero, which is similar
to that used by Gawne reflecting the original theoretical
basis on which the technique was proposed. In Gawne’s
paper w12x the regression analysis Žwe presume with an
independent y intercept. produced a remarkably linear
result with a y intercept essentially at zero. Our data
clearly does not support this. Indeed a standard least
squares analysis in group 1 gives a negative slope, further
undermining this technique.
In our study, using an excitation frequency of 5 and 40
kHz, there was the expected increase in parallel conductance at the higher frequency with no significant change in
measured stroke volume in the neonatal pigs Žgroup 1..
However, in adult pigs Žgroup 2. both parallel conductance
volume and stroke volume increased significantly with
frequency, which probably reflected a change in a with
frequency. Comparison of SV, corrected for a and Vc, at
5 kHz showed no significant difference to that obtained at
40 kHz Žcorr SV5 kHz s 52.28 " 17.98 ml; corr SV40 kHz s
53.81 " 19.90 ml. Ž p s 0.89.. However, by comparing the
total corrected end-systolic volume ŽESV-Vc. for both
groups an increase was observed when frequency was
varied from 5–40 kHz. The results obtained in group 2 can
theoretically still be used to show the failure of the dual
frequency technique to substitute for the saline dilution
method.
Thus we have shown why the results in this study
contradict those obtained by Gawne w12x. The fundamental
difference between our study and those of previous investigators is that both the neonatal pigs Žgroup 1. and the adult
pigs Žgroup 2. were studied with an open chest and open
pericardium. Furthermore, we have shown a direct relationship between excitation frequency and alpha, in adult
animals, and inferentially also in group 1 ŽFig. 2.. This
unexpected finding probably relates to changes with field
density patterns and uniformity in these larger hearts.
Alpha was not measured in Gawnes study Žusing mid-sized
pigs. and this finding alone undermines the theoretical
basis of his multiple frequency technique.
In conclusion, while parallel conductance is frequency
dependent it has a substantial resistive component. At a
lower excitation frequency of 5 kHz the resistivity of the
myocardium is considerably greater than that of blood.
Therefore a smaller percentage of measuring current extends beyond the blood pool Žreduced Vc.. The dual
frequency technique is based on the assumption that parallel conductance is negligible at low frequencies and this is
clearly not the case. The results of this study confirm that
the dual frequency technique cannot reliably be used to
substitute the saline dilution technique in different sized
hearts.
Acknowledgements
This work was supported by the Scott Rhodes Research
Fund, Garfield Weston Research Fund, Clinical Research
Committee ŽRoyal Brompton Hospital NHS Trust., The
Institute of Experimental Clinical Research and the Danish
P.A. White et al.r CardioÕascular Research 38 (1998) 668–675
Heart Foundation. Thanks must also be given to Dr R
Szwarc ŽBioMetrics, Las Vegas. for provision of the analysis software used in this paper.
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