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Am J Physiol Heart Circ Physiol 285: H1774-H1785, 2003. First published May 22, 2003; doi:10.1152/ajpheart.00048.2003
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Right ventricular volume measurement by conductance catheter

Mark H. D. Danton,1 Gerald F. Greil,3 John G. Byrne,1 Michael Hsin,1 Lawrence Cohn,1 and Stephan E. Maier2

Departments of 1Cardiac Surgery and 2Radiology, Brigham and Women's Hospital, and 3Department of Cardiology, Boston Children's Hospital, Harvard Medical School, Boston, Massachusetts 02115

Submitted 21 January 2003 ; accepted in final form 5 May 2003


    ABSTRACT
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 DISCLOSURES
 REFERENCES
 
Continuous ventricular volume measurement by the conductance method assumes a homogeneous electrical field dispersed throughout and contained within the ventricle. Because of dense trabeculation and complex geometry, right ventricular (RV) volume description by this method may be seriously compromised. This study sought to determine the accuracy and limitations of RV volume measurement by conductance, with magnetic resonance (MR) imaging (MRI) used as a reference, in the porcine RV. Anesthetized pigs (n = 5, 45–55 kg) were placed in a 1.5-T magnet, and ECG-gated transverse MR images (5-mm slices) were acquired during the complete cardiac cycle. RV cavity volumes were subsequently determined by Simpson's technique. Animals were then instrumented with an RV conductance catheter and an ultrasonic pulmonary artery flow probe. Conductance catheter signals were recorded using single- and dual-field (SF and DF) excitation, and the saline-dilution technique was used to correct volumes for parallel conductance. The gain factor ({alpha}) was calculated as the ratio of conductance- to MRI-derived stroke volume ({alpha}SV). Variation of {alpha} during the cardiac cycle was computed by comparing RV conductance volumes with 1) MRI volumes at isochronal time points within the cardiac cycle [{alpha}(t)] and 2) the pulmonary flow integral during ejection. After calibration, the conductance-MRI volume relation was modeled linearly with good correlation [r = 0.96 (SF) and r = 0.94 (DF)], close to the line of identity. Individual conductance-MRI plots displayed a slight curvilinear relation that was concave toward the MRI axis. Consistent with this finding, {alpha}(t) varied significantly during the cardiac cycle (0.49 and 0.39 by SF for end systole and end diastole, respectively, P = 0.011). DF excitation resulted in improved volume measurement [{alpha}SV = 0.41 (SF) and 0.96 (DF)], with less variation in {alpha}(t) (1.0 and 0.92 by DF for end systole and end diastole, respectively, P = 0.66). These results indicate that, with calibration, the conductance method can measure absolute RV volume under steady-state conditions. However, the curvilinearity and {alpha}(t) variation would indicate the potential for nonlinearity when RV volumes are varied over a wider range.

magnetic resonance imaging; conductance catheter


THE ABILITY TO MEASURE CONTINUOUS real-time right ventricular (RV) volume would be valuable in assessing RV function. However, the anatomic complexity of the RV chamber has essentially precluded volume description in the clinical setting. Imaging techniques such as cineangiography and two-dimensional echocardiography rely on mathematical modeling, which may be invalidated by pathologically induced changes in ventricular geometry. Sonomicrometry can provide accurate, instantaneous RV volume, but because the technique requires an open-chest preparation for piezoelectric crystal placement, its application has been limited. Presently, MRI, using tomography and Simpson's rule, is considered the "gold standard" method for deriving RV volume in the intact animal (11). However, long acquisition times preclude real-time volume measurement, and beat-to-beat changes in volume cannot be assessed by this method.

The conductance catheter technique has emerged as a method capable of providing a real-time continuous assessment of ventricular volume by measuring the electrical conductivity of blood within the chamber (3). Previous studies have analyzed the accuracy of conductance in measuring left ventricular (LV) volume (3, 4, 7); the signal has been demonstrated to be linear and highly correlated to LV volume measured by an alternative method. However, inasmuch as the relation between real and conductance volume does not fall on the line of identity, the conductance signal must first be calibrated for parallel conductance and gain to derive absolute volume.

Parallel conductance results from electrical conductivity beyond the blood pool, which results in an offset volume [i.e., parallel conductance volume (Vp)] that must be determined and subtracted from total conductance volume. In the LV, under steady-state conditions, there is minimal variation in Vp; therefore, it can be described by a single value (7, 29). However, studies in which the LV volume was varied over a broad range have shown that Vp may have a volume dependency (2, 6), and employing a single value of Vp in such circumstances would result in significant inaccuracies.

As a consequence of nonhomogeneous dispersion of the electrical field within the ventricular cavity, the conductance method leads to an underestimation of true volume, which is corrected by applying a gain factor ({alpha}). Theoretical and experimental studies have indicated that {alpha} may also vary with large changes in LV volume (2, 16, 20, 23, 24) and may even vary significantly with the volume changes within the cardiac cycle (28). Significant variation of gain (and parallel conductance) with changing ventricular volume would introduce nonlinearity into the conductance-actual ventricular volume relation. An advancement in the conductance method has been the use of dual-field (DF) excitation. DF conductance employs two frequencies and, therefore, generates a more homogeneous electrical field with flatter equipotential planes in the ventricle and has been shown to improve the accuracy and potential nonlinearity in the conductance-volume relation with respect to LV volume determination (10, 26, 30). The effectiveness of DF excitation for RV volume measurement has not been previously evaluated.

The RV cavity has a more complex geometry than the LV cavity, and there are theoretical reasons for greater error associated with conductance-derived RV volume. The thinner free wall will provide less resistance to conduction and will potentially increase the magnitude and error associated with Vp. Furthermore, in contrast to the LV cavity, the RV cavity comprises an inlet and an outlet compartment traversed by dense trabeculation. Such architecture is likely to further limit homogeneous dispersion of the electrical field within the ventricular cavity and cause different current densities in different areas of the chamber. Previous assessments of RV conductance have been limited to excised preparations (8, 22, 32) or have used stroke volume as a reference volume for comparison (25). No study has compared conductance with an alternative method of assessing absolute RV volume in the intact circulation.

The present study was designed to evaluate the accuracy of the conductance method for quantifying absolute RV volume in the intact animal under steady-state conditions, with MRI-derived RV volumes used as a reference. The RV conductance signal was calibrated for absolute volume by determining parallel conductance by a saline-washin technique and by deriving gain by comparing conductance stroke volume with MRI stroke volume. Calibrated conductance RV volumes were then compared with MRI volumes at 20 isochronal time points throughout the cardiac cycle. Variation in {alpha} was determined by comparing 1) ventricular volumes obtained by conductance with those obtained by MRI at isochronal time points throughout the cardiac cycle and 2) conductance-derived ejected volume with electromagnetic pulmonary flow probe-derived volume. The potential variation in parallel conductance during the cardiac cycle was determined by deriving multiple estimates for Vp during systole. Studies were performed with single-field (SF) and DF excitation for comparison.


    METHODS
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 DISCLOSURES
 REFERENCES
 
Protocol

The study was conducted on five adult Yorkshire pigs (45–55 kg). The animals were cared for according to the National Institutes of Health Guide for the Care and Use of Laboratory Animals. After induction of anesthesia with Telazol (tiletamine hydrochloride and zolazepam hydrochloride, 5 mg/kg im), the pigs were intubated and ventilated with 40% O2 in air. Intravenous access was established, and anesthesia was maintained with continuous intravenous infusion of propofol. Saline infusion was established to maintain hydration. The animals were monitored with continuous ECG and an arterial saturation probe and placed in a transport cage for transfer to the MRI facility.

Animals were placed on the MRI delivery table and carefully positioned in a lateral position within the magnetic coil. Limb and chest ECG electrodes were placed, and the animals were covered with an insulating blanket to reduce heat loss. Propofol infusion was adjusted to maintain a deep level of sedation, in which there was no spontaneous respiratory movement; muscle relaxants were not used. After a period of stabilization, MR images were acquired with ventilation temporally suspended. MR images were stored on an optical disk for later analysis.

After image acquisition, a short superior-midline sternotomy was performed, and the pericardium was opened to expose the main pulmonary artery. A 5-Fr 12-electrode conductance catheter (Cordis Webster, division of Johnson & Johnson, New Brunswick, NJ) was introduced via the pulmonary artery and positioned within the RV cavity. A 5-Fr pressure-tip micromanometer (model PC350, Millar Instruments, Houston, TX) was positioned similarly. Correct catheter position was determined by monitoring individual segmental pressure-volume loops. An electromagnetic flow probe (model 105, Caroline Medical Electronics, King, NC) was placed around the pulmonary artery and positioned until an optimum flow signal was achieved. When instrumentation was complete, the sternum was reapproximated.

After a 30-min stabilization period, specific blood conductivity was measured, and steady-state RV pressure-volume and pulmonary flow data were digitally acquired (200 Hz) with the ventilator temporarily suspended at end expiration. This procedure was carried out with the conductance catheter first in the SF excitation mode and then in the DF mode. Then six injections (3 in the SF mode and 3 in the DF mode) of hypertonic saline (0.02 ml/kg saturated solution) were delivered into the external jugular vein; during these injections, pressure-volume data were continuously acquired for assessment of Vp. If ectopic beats occurred or if heart rate or systolic arterial blood pressure changed during the saline-washin period, the injection was repeated with a smaller volume and a slower rate of delivery.

Animals were then euthanized by barbiturate overdose.

MRI

MRI experiments were conducted on a 1.5-T cardiac whole body unit (General Electric Medical Systems, Milwaukee, WI) with version 8.2.5 software release. The magnetic field gradients of this system are capable of up to 40 mT/m gradient amplitude and up to 150 mT · m1 · ms1 gradient slew rate. The standard phased-array cardiac radio-frequency coil was used for imaging. A segmented gradient-echo–echo-planar imaging sequence (Fastcine) was applied to obtain shortaxis cine loops of the heart. ECG-gated sagittal and oblique multislice scans were used to determine the optimal planes for the short-axis cine scan. Images were acquired at a quadratic field of 320 x 320 mm and a scan matrix size of 256 x 160, which, for the final image data, was extrapolated to 256 x 256. The effective section thickness was set at 5 mm with 0-mm gap between slices. The radio-frequency flip angle was set to 15°. Together with a pulse repetition of 9.6 ms, this setting appeared to provide optimal contrast among myocardium, blood pool, and lung tissue. Examples of an end-diastolic and an end-systolic image for a midventricle slice are shown in Fig. 1.



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Fig. 1. MRI transverse section of porcine heart at end systole (A) and end diastole (B).

 

The standard ECG device provided by the manufacturer of the MRI system was used for cardiac gating. MR image acquisition was triggered on the R wave of the ECG, and single excitation cine loops of 20 images were obtained for each slice, with temporary suspension of ventilation of ~25 s. A total of 12–14 cine loops of contiguous slices covering the entire RV were recorded in multiple breath holds. The total scan time for the RV cine loops was ~10 min.

MR images were analyzed with the aid of Mass software (Magnetic Resonance Analytical Software System, MEDIS, Leiden, The Netherlands). The endocardial edge of the RV free wall and septum for all transverse slices were manually outlined, and the surface area of the cavity was determined by counting the number of pixels enclosed by the endocardial edge. Segmental volume was calculated by multiplying slice area by slice thickness (5 mm), and total RV cavity volume was determined by summation of the segmental volumes.

Conductance Catheter

The conductance catheter technique for measuring LV volume is described in detail elsewhere (3, 4). The conductance catheter used in this study was a 5-Fr 12-electrode catheter with 6-mm electrode spacing that could be employed in SF or DF mode, depending on the box setting. The catheter was placed in the RV long axis with the electrode tip at the apex and the most-proximal electrode above the pulmonary valve. An alternating current (20 kHz, 30 µA) was applied to the outer electrodes (1 pair for SF mode and 2 pairs for DF mode), and a Sigma-5 signal conditioner (Cardiodynamics, Rijnsburgerweg, The Netherlands) was used to measure voltage between five successive pairs of intervening electrodes. The measured voltages were related to five segmental conductances, the sum of which gave a total time-varying conductance [G(t)]. The instantaneous volume [V(t)] was given by

(1)
where {alpha} is a dimensionless constant, L is the interelectrode spacing, and {sigma} is the specific resistivity of blood measured at body temperature by means of a specially designed curette. Vp was determined by a saline-dilution technique described by Baan et al. (5), whereby the conductivity of the blood was transiently increased by a bolus injection of hypertonic saline administered into the jugular vein. Linear regression performed between end-systolic and end-diastolic volume and the intersection with the line of identity determined Vp.

To assess variability of Vp within the cardiac cycle, multiple volume estimates of Vp were obtained during systole using a method previously described for LV parallel conductance assessment (13). Briefly the systolic portion (from dP/dtmax to dP/dtmin) of the volume signal of each beat during saline delivery was divided into 20 equal time intervals. Isochronal volumes were linearly regressed against the corresponding index of the relative blood conductivity for each beat. The volume intercepts of each of the 20 regression lines (Vp) corresponded to Vp at each time interval.

DF excitation. The conductance catheter employed in these experiments could be used in SF or DF excitation mode, depending on the setting on the Sigma-5 generator. In the SF mode, the outermost electrodes supply a single excitation current (IS). DF excitation is established by generating a second current (IC) from the adjacent electrodes. The two currents have the same frequency and phase, but the two intracavity fields are generated with opposite polarity. The ratio of the two currents (f = –IC/IS) was constant at 0.25.

Data Analysis

Conductance catheter- and MRI-derived volumes were determined as described above. Conductance catheter-derived data are based on an average of 10 consecutive cardiac cycles. Because MRI acquisitions were triggered on the R wave of the ECG, conductance end-diastolic volume was defined as the volume at the time of the R wave. The conductance volume data were then linearly interpolated to provide volume data at 20 equal time intervals per cardiac cycle, commencing at end diastole. Isochronal conductance and MRI volumes were then compared.

Variability in {alpha}: comparison with MRI. After correction of the conductance volumes for Vp measured by saline dilution, {alpha} was determined. A single value of {alpha}, representing the complete cardiac cycle, was determined by dividing conductance-derived stroke volume by MRI-derived stroke volume ({alpha}SV). Variation in {alpha} within the cardiac cycle was determined by dividing conductance-derived volume by MRI-derived volume at each of 20 isochronal time points during the cardiac cycle [{alpha}(t)]. The variation in {alpha}(t) within the cardiac cycle was assessed using analysis of variance (ANOVA), and the difference between {alpha} at end diastole ({alpha}ED) and {alpha} at end systole ({alpha}ES) was assessed with a paired t-test.

Variability in {alpha}: comparison with pulmonary flow probe. Conductance-derived volume was compared with pulmonary flow probe-derived volume over 10 consecutive cardiac cycles. To study the instantaneous relation between pulmonary flow and conductance measurements, only data obtained during the RV ejection phase of the cardiac cycle were compared (defined as positive pulmonary flow). Ejected volume determined with the flow probe was estimated by summation of the digitally integrated flow signal using the trapezoidal rule with a 5-ms interval. The simultaneous ejected volume measured using the conductance catheter was defined as the difference between the volume at the onset of ejection and the volume at each 5-ms interval. The instantaneous ejected volume from the flow probe was then plotted against that obtained by conductance. The slope of the linear regression of the plot represented another estimate of {alpha} ({alpha}PF). To determine whether {alpha}PF changed during the cardiac cycle, the relation between flow probe- and conductance-derived ejected volume was divided into two equal time periods, and linear regression analysis was performed for each. A paired t-test was then used to compare the slope corresponding to early ejection with that corresponding to late ejection.

Vp variability. The significance of variation from a mean of the 20 isochronal values of Vp obtained during systole was assessed using ANOVA. The values obtained at dP/dtmax were compared directly with those obtained at dP/dtmin using a paired t-test.


    RESULTS
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 DISCLOSURES
 REFERENCES
 
Numerical data are presented as means ± SD and graphical data as means ± SE. Statistical significance is assumed at P < 0.05.

Overall Correlation: MRI vs. Conductance

After calibration of conductance for {alpha}SV and Vp, conductance-derived volumes were linearly regressed against MRI-derived volumes in the SF and the DF mode (Fig. 2, Table 1). In general, there was good correlation between conductance- and MRI-derived RV volumes (r = 0.96 ± 0.03 in SF mode and r = 0.94 ± 0.02 in DF mode), with the relation falling close to the line of identity. However, each individual conductance-MRI relation displayed a slight curvilinear appearance that was concave toward the MRI axis.



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Fig. 2. Right ventricular (RV) volume measured by conductance catheter (RV volumeCond) vs. MRI-derived RV volume (RV volumeMRI). A: single-field linear regression in 5 animals after correction for parallel conductance (Vp) and stroke volume gain factor ({alpha}SV). Linear regression values are given in Table 1. B: dual-field regression in 5 animals after correction for Vp and {alpha}SV.

 

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Table 1. Overall linear regression results for conductance vs. MRI RV volumes after correction for parallel conductance and gain

 

Variation in {alpha}(t)

The {alpha}SV (ratio of conductance- to MRI-derived stroke volume) was 0.41 for SF and 1.13 for DF conductance. In SF excitation, a significant increase in {alpha}(t), reaching a maximum at end systole, was observed (Fig. 3A). SF {alpha}ES was 0.49 ± 0.16 and {alpha}ED was 0.39 ± 0.09 (P = 0.011 by ANOVA) with mean maximum variation of ~20%. With DF excitation, although the variation during the cycle was similarly described (Fig. 3B), the magnitude was less (mean maximum variation ~10%) and not significant: {alpha}ES was 1.0 ± 0.93, and {alpha}ED was 0.92 ± 0.99 (P = 0.66).



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Fig. 3. A: deviation from the mean of the gain factor at isochronal time points during the cardiac cycle [{alpha}(t)] with single-field (SF) excitation. Values are means ± SE of 5 pigs. {alpha}(t) was maximum at end systole (ES) and decreased to a minimum at end diastole (ED). B: variation in {alpha}(t) with dual-field (DF) excitation.

 

Variation in {alpha}PF

The plot of flow probe- vs. conductance-derived instantaneous ejected volume is given in Fig. 4. In all animals, the relation was curvilinear, concave toward the conductance axis. The gradients in the first half of the ejection were compared with those in the second half. There was a small but significant increase in {alpha}PF in late systole: 0.47 ± 0.12 and 0.52 ± 0.09 in early and late ejection, respectively, in the SF mode (P = 0.02) and 0.98 ± 0.46 and 1.12 ± 0.40 in early and late ejection, respectively, in the DF mode (P = 0.01; Table 2).



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Fig. 4. Instantaneous ejected volume measured by pulmonary artery (PA) flow probe plotted against that measured by conductance catheter with SF (A) and DF (B) excitation, with onset of ejection at the origin. Values are means ± SE of 5 animals. There was a small but significant increase in gradient in late ejection with SF excitation. There was a similar increase with DF excitation.

 

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Table 2. Summary of {alpha}PF as determined by slope of linear regression of ejected volume by conductance vs. pulmonary flow probe in SF and DF modes

 

Vp and Systolic Variability

VP was significantly higher for DF than for SF excitation: 56.3 ± 14.3 vs. 138.0 ± 63.1 ml (P < 0.001). When the 20 isochronal values of Vp measured during systole were analyzed, a temporal variation from the mean was found. In the SF mode, the initial value (at dP/dtmax) of –1.30 ± 1.85 ml below the mean increased to a maximum of 1.01 ± 1.62 ml above the mean at midsystole (P = 0.2 by t-test) and then returned to –1.53 ± 1.74 ml by end systole (dP/dtmin; Fig. 5A). Overall, the variation was small and not significant (P = 0.282). In the DF excitation mode, a similar pattern of Vp variation was observed (Fig. 5B). The initial value at dP/dtmax, –1.80 ± 1.70 ml below the mean, increased to a maximum of 3.98 ± 1.65 ml above the mean at midsystole (P = 0.07) and then returned to –3.47 ± 2.02 ml by end systole (dP/dtmin). Overall, the variation was significant (P = 0.028).



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Fig. 5. Deviation from the mean of 20 isochronal values of parallel conductance (Vp) obtained during systole with SF (A) and DF (B) excitation. Values are means ± SE of 5 pigs. Similar increases in Vp were observed at midsystole with SF and DF excitation.

 

In SF and DF conductance, the value at dP/dtmax was not significantly different from that at dP/dtmin.

MRI Accuracy

Accuracy of the MRI methodology (and stability of the model between the two acquisition periods, because ventricular volume measurement was not performed simultaneously) was evaluated by comparing MRI-derived stroke volume with pulmonary flow probe-derived stroke volume. Mean stroke volume for each of the five animals measured by MRI was 49 ± 10 ml, which was not significantly different from 48.6 ± 9.5 ml measured by pulmonary flow probe. Excellent correlation was obtained: linear regression analysis of flow probe- vs. MRI-derived stroke volumes (Fig. 6) yielded a slope of 1.06 with an intercept of –2.6 ml and r = 0.98.



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Fig. 6. Linear regression of mean stroke volume (SV) for 5 animals measured by pulmonary flow probe (during conductance assessment) and that measured by MRI (y = 1.08x – 2.85, r = 0.98). Results validate the model showing that stroke volumes measured by conductance and MRI are comparable.

 


    DISCUSSION
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 DISCLOSURES
 REFERENCES
 
In this study, the use of gated MRI acquisition provided 20 RV volume measurements per cardiac cycle, which, when compared with referenced isochronal conductance volumes, allowed a means to investigate the extent of nonlinearity of the conductance-actual volume relation within the cardiac cycle. We found that, when appropriately calibrated, the conductance-derived RV volumes correlated closely with MRI-derived volumes, suggesting that the conductance method can measure actual RV volumes under steady-state conditions, despite the complexity of the chamber. There was, however, slight curvilinearity evident in the individual conductance-MRI plots and significant variation in {alpha} within the cardiac cycle. Such findings would raise concerns regarding the ability of the conductance method to measure RV volume when larger-volume excursions are experienced, as with rapid change in the loading conditions.

The conductance catheter technique was first introduced by Baan et al. (3, 4) as a method to measure instantaneous continuous ventricular volume, and the accuracy and limitations of the method have been extensively investigated for the LV. Initially, highly linear conductance-volume relations were reported in isolated ejecting canine hearts (7) and the intact circulation (4). After these initial promising reports, canine studies in which conductance-derived ventricular volumes were compared with those determined by biplane angiography (6) and sonomicrometry (2) demonstrated a nonlinear conductance-volume relation with large volume changes associated with changing loading conditions. It followed that, in situations of rapid changing load, as in inferior vena caval occlusion maneuvers necessary for deriving end-systolic pressure-volume relations, the conductance method may not be reliable. Szwarc et al. (28), in an intact porcine model where conductance-derived LV volumes were compared with MRI-derived volumes at end systole and end diastole, demonstrated significant variation in {alpha} occurring with the ventricular volume excursions during the cardiac cycle under steady-state conditions.

The nonlinear conductance-volume relation has been predicted in a number of theoretical studies (18, 23, 24). The conductance method assumes a homogeneous dispersion of current throughout the ventricular cavity. For Eq. 1 to be satisfied, equipotential planes should be parallel and perpendicular to the axis of the catheter. In reality, as a consequence of point sources of current, these lines are curved, particularly in close proximity to the source electrodes. The conductance segments in the vicinity of these deviated lines will, as a result, underestimate true segmental volume. Furthermore, catheter bending, irregularity of the ventricular cavity, and conduction of current beyond the blood pool may further contribute to conductance volume error. Conductance measurement of RV volume may be vulnerable to greater error than conductance measurement of LV volume because of several factors. The thin-walled chamber will provide less resistance to conduction; thus parallel conduction will be expected to be greater. Furthermore, the reduced insulation may allow greater variations in Vp associated with variations in resistivity surrounding the ventricle. The geometry of the RV being more complex than the LV, comprising an inlet and outlet compartments, and orientation of the catheter along a single axis may preclude electrical field dissemination throughout the entire RV cavity. Field dispersion may be further compromised by the dense trabeculations, including the moderator band that traverses the RV cavity.

Ex vivo RV conductance has been assessed using latex human RV casts (32) and excised porcine hearts (8). Both studies demonstrated a strong linear correlation, close to the line of identity, between conductance and true RV volume, indicating that the method could accurately measure RV volume, despite the complex shape of the RV. However, in both studies, the potential error associated with parallel conduction was effectively eliminated because of the nonconductivity of the model.

Within the intact circulation, RV conductance has been evaluated in human and animal studies (15, 22, 25, 27, 34). Stamato et al. (25) compared RV conductance-derived stroke volumes with thermodilution- and ultrasonic pulmonary flow probe-derived volumes over a range of loading conditions. The study demonstrated that, with volume excursions occurring within the cardiac cycle, the conductance and flow probe measurements were linearly related, with only a small, nonsignificant, increase in gradient identified toward the end of ejection. However, when stroke volumes were altered by changing the loading conditions, {alpha} varied inversely with ventricular volume, suggesting a nonlinear relation between conductance and actual RV volume. The study was limited, because no alternative measure for RV volume was employed, and variation in Vp to account for the nonlinearity was not evaluated.

The effect of assuming a constant value for gain throughout the cardiac cycle is demonstrated in Fig. 7. Correcting the conductance signal with a single value, {alpha}SV, results in a stroke volume corresponding to the MRI-derived stroke volume. However, this correction results in an overestimation of end-systolic and end-diastolic volumes and, consequently, an underestimation of the ejection fraction. By respecting the {alpha} variation during the cardiac cycle, stroke volume is still corrected, but the absolute ventricular volumes are not overestimated.



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Fig. 7. Mathematical consequences of {alpha} increasing with ejection. Actual stroke volume is 65 ml, whereas stroke volume measured by conductance is 20 ml ({alpha} = 1). If {alpha} is allowed to vary from 0.4 at end diastole to 0.5 at end systole, stroke volume is corrected and absolute volumes increase. Although adjusting conductance gain with a constant value of {alpha} = 0.31 also corrects stroke volume, absolute volumes are markedly higher than those obtained when {alpha} was allowed to vary.

 

With DF excitation, the conductance-derived volumes were comparable to MRI-derived volumes, as indicated when {alpha} was ~1. Furthermore, the variation in {alpha}(t) was less with DF than with SF excitation (10% vs. 20%), but the same temporal pattern of variability was still evident. DF excitation has been shown to improve field dispersion within the ventricular cavity by correcting the curvature of the equipotential lines close to the excitation electrodes (10, 26, 30). This results in reduced underestimation of segmental volumes and, consequently, {alpha} closer to 1. Despite the reduced variation in {alpha}(t), the conductance-MRI relation still appeared curvilinear, as was the ejected volume conductance-pulmonary flow relation. This may be because the DF mode does not completely correct the nonhomogeneous intracavity current dispersion, or other factors, including complex RV geometry and catheter curvature (9), may cause the continued non-linear relation.

Variation in parallel conduction within the cardiac cycle might account for or contribute to the observed nonlinear conductance-volume relation. Potentially, LV filling would be expected to increase RV parallel conductance at end diastole, and, conversely, RV filling has been shown to significantly increase LV Vp in the excised canine model (7). However, because the conductance catheter underestimation of volume is greater at end diastole than at end systole, it would be necessary for Vp to decrease with ventricular filling to be the reason for an apparent change in gain. In this study, although variation in Vp during systole was identified, such variation was small and not significant, as found by others (33). Furthermore, the pattern of temporal variation in Vp, in which changes occurred in midsystole, was not consistent with the observed conductance-volume nonlinearity. Parallel conduction was greater for DF excitation in terms of magnitude and variability during systole. The consequence of this is that only minor variations in the derivation of DF Vp (due to incomplete mixing of saline solution within the RV cavity) would result in significant error in conductance calibration and absolute RV volume measurement. Furthermore, variation in the resistivity conditions beyond the blood pool, which have been shown to alter LV and RV parallel conductance (1), might have a profound effect on DF Vp. In the present study, all conductance measurements were performed with the lung deflated. Although changes in lung inflation have been previously demonstrated to not affect SF RV parallel conductance (27), this may not be the case for DF excitation.

In this study, MRI was used as the reference method and has been previously demonstrated to be an accurate method for RV volume measurement in explanted porcine hearts (12) and in vivo in dogs (14) and humans (21). However, Pattynama et al. (17) identified significant intra- and interobserver error associated with assessment of MR images indicating that observer subjectivity may limit the reproducibility of RV measurements. A potential source of this error lies with the manual outlining of the endocardial border, particularly with the dense trabeculations within the RV cavity. Furthermore, the high signal of static blood within the endocardial folds may be mistaken for tissue. Nevertheless, there was good agreement between stroke volume determined by MRI and stroke volume determined by pulmonary flow probe, with a high correlation (r = 0.98), slope of 1.06, and intercept close to the origin.

Developments in conductance catheter technology have addressed the error associated with the nonlinear conductance-volume relation. As identified in this study, DF excitation results in improved current dispersion within the RV, as indicated by the raw conductance volumes being closer to actual volume, with less variation in {alpha} through the cardiac cycle. This finding of improved linearity with DF excitation is consistent with LV studies. The 12-electrode catheter design allows one to match the active sensing length of the catheter length with the specific ventricular dimension. Nevertheless, the ventricular volume between the excitation electrode and the adjacent sensing electrode pairs, located at the base and apex, will not be measured by the catheter. The more recent catheter designs have reduced the distance between the excitation electrodes and the adjacent sensing segment to minimize this error. Furthermore, ventricular volume beyond the length of the catheter will not be measured by the conductance, and, with significant ventricular axial shortening during systole, error due to varying catheter-ventricular length mismatch may result. Gopakumaran et al. (9) developed a complex algorithm to compensate for the nonlinear relation between conductance and true ventricular volumes by quantifying an empirical correction factor for each segment on the basis of distance from the excitation electrode and catheter curvature. This resulted in an improved estimation of true ventricular volume. However, the assumptions of this correction have little theoretical basis, and the parameters for the nonlinear relation were not defined. It is likely that ventricular shape and catheter position and curvature may also influence conductance volume measurement; therefore, such correction may not be valid between different hearts. Therefore, optimizing the electrical field represents a more robust solution. Salo (18, 19) developed a mathematical technique of field extrapolation, which attempted to linearize the generated electrical field by mathematically transforming measured potentials into the potential distribution that would result from infinitely distant current sources. This resulted in improvement in linearity and gain ({alpha} ~ 1) of the conductance method, as identified with stroke volume measurements by thermodilution in human studies (19) and by flow probe in canine studies (18).

Study Limitations

Ideally, RV volumes would have been acquired simultaneously using conductance and MRI. This was not possible, because the steel electrodes render the conductance catheter and MRI incompatible. It is possible that the different time periods of volume acquisition and the invasive instrumentation required for conductance placement could have altered the steady-state hemodynamic parameters, including ventricular volumes. However, regression of stroke volume measured by pulmonary flow probe vs. that measured by MRI was strongly linear (r = 0.98), with a slope of 1.08 and an intercept near the origin (2.85), provided validation of the methodology and stability of the preparation.

In this study, a wide interanimal variation of RV volume was observed, with RV end-diastolic volume 2.4 ± 0.46 (SD) ml/kg. Under normal physiological conditions, major volume changes occur in the RV, influenced primarily by alteration in preload status. Stamato et al. (25), in a porcine model, measured a baseline RV end-diastolic volume of 2.1 ± 0.67 (SD) ml/kg, which increased to 3.3 ± 1.71 (SD) ml/kg with volume loading. The results from the present study are consistent with these reported RV dimensions and variation. Human studies have similarly reported major RV volume variation between subjects, although this has predominantly been in patients with structural and/or functionally abnormal RV (31). In the present study, postmortem RV volumes were not measured. Because of alterations in compliance and biventricular geometry, the RV volume excursions of the explanted ventricle would be unlikely to represent the physiological volume changes occurring in vivo.

The study examined the accuracy of the conductance method in measuring RV volume under steady-state conditions. RV volumes were not investigated over changing loading conditions, which are necessary for contractile assessment.

In conclusion, these results indicate that the conductance method can be used to measure RV volume under steady-state conditions, provided the signal is calibrated for parallel conductance and gain. DF excitation produced a more homogeneous field dispersion, with improved volume measurement and less variation in gain during the cycle than SF excitation. This advantage is partially offset by greater magnitude and variation of parallel conductance. However, the study identified a tendency to a nonlinear conductance-volume relation in the porcine RV with the volume excursions that occur within the cardiac cycle. The use of a single value of gain correction ({alpha}) for conductance calibration will result in an overestimation of absolute volume (and an underestimation of ejection fraction). Systolic variations in parallel conductance were small and would not account for this nonlinear relation. For assessment of RV volume by conductance, DF excitation appears superior; however, other design modifications, such as field extrapolation, will be necessary to optimize RV absolute volume measurement by conductance.


    DISCLOSURES
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 DISCLOSURES
 REFERENCES
 
This study funded by the Cardiac Surgical Research Fund of Brigham and Women's Hospital.


    ACKNOWLEDGMENTS
 
We acknowledge the excellent technical support of Rita Lawerence and Sergey Grachov.


    FOOTNOTES
 

Address for reprint requests and other correspondence: M. H. D. Danton, Dept. of Cardiac Surgery, Level 2, East Wing, Royal Victoria Hospital, Grosvenor Rd., Belfast BT12 6BA, Northern Ireland, UK (E-mail: markdanton{at}yahoo.com).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


    REFERENCES
 TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 DISCLOSURES
 REFERENCES
 

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