INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

THE CONDUCTANCE CATHETER METHOD provides a continuous on-line measurement of left ventricular (LV) volume by means of a multielectrode catheter positioned in the LV. In combination with simultaneous measurement of LV pressure through a sensor on the same catheter, this instrument enables quantification of ventricular function by means of pressure-volume relations. Such relations have proven to be particularly useful, because they provide indexes of systolic and diastolic ventricular function that are relatively independent of loading conditions and, as such, mainly reflect intrinsic myocardial properties.

The conductance catheter method is based on the continuous measurement of the electrical conductance of the blood in the LV. This signal is converted to a volume signal on the basis of a stacked-cylinder model and by taking into account the specific conductivity of blood and the catheter electrode spacing. However, the conductive tissues and fluids surrounding the LV cavity [e.g., myocardial wall, blood in the right ventricle (RV), lung] also contribute to the measured conductances and introduce an offset in the relation between true LV volume and conductance-derived volume. Therefore, to obtain an absolute volume signal, this parallel conductance needs to be determined and subtracted from the raw conductance signal.

To assess parallel conductance or the corresponding offset volume, several methods have been used. These methods are based on a direct comparison with an independent method for absolute volume measurement (5, 6, 20) or do not require an independent volumetric measurement, such as the dual-frequency method (12), the suction method (3), or the volume reduction technique (31). However, in most studies, parallel conductance is determined by a method, previously developed in our laboratory, that consists of injecting a small bolus of hypertonic saline through a balloon-flotation catheter in the pulmonary artery (3). The highly conductive saline transiently changes the conductivity of the blood, practically without affecting parallel conductance. The contribution of parallel conductance to the total conductance signal can be derived from a registration of the conductance signal during the passage of the bolus through the LV. A number of studies indicate that the saline method provides reliable estimates of parallel conductance, but generally the evidence is indirect, since these studies were not specifically designed to test the accuracy of the saline method (1, 7, 20, 26, 28, 29). Some studies were more specifically related to the calibration factors of the conductance catheter method, but those studies largely focused on whether parallel conductance remains constant during preload reduction by caval occlusion (2, 5, 27). The present study, in anesthetized sheep, was designed specifically to test the accuracy of assessment of parallel conductance by the hypertonic saline method and used biplane contrast cineangiography as an independent method for absolute volume measurements. In addition, in the present study we used the dual-field excitation mode to generate the electric field required for the conductance measurements. Dual-field excitation, developed by our group, is used in most studies, because it has been shown to improve the accuracy of the conductance catheter method (10, 24, 25, 35). However, most studies regarding parallel conductance have been performed before the introduction of the dual-field excitation method. The more uniform electric field, which is the rationale for using dual-field excitation, improves the linearity of the relation between conductance and true volume (25), and thus, at least theoretically, the possible dependence of parallel conductance on volume could be expected to be reduced. The more uniform electric field implies more uniform intracavitary current density, but the "wider" field is expected to lead to more current flow through external structures and, thus, higher parallel conductance. A possible advantage, however, is that volume dependence and variability of parallel conductance between hemodynamic conditions may be reduced. To investigate the need for repeated assessments, we determined the variability of parallel conductance between animals and between hemodynamic conditions. Measurements were obtained over a wide range of hemodynamic conditions, induced by dobutamine infusion, volume loading, and -blockade. Finally, it is generally (implicitly) assumed that parallel conductance remains constant during the cardiac cycle. This assumption has been tested by analyzing hypertonic saline injections for individual points in the cardiac cycle (19, 33, 34); however, this analysis may be theoretically incorrect (see DISCUSSION). Therefore, we directly compared the time-varying angiographic and conductance-derived volume signals. After subtraction of a (constant) parallel conductance factor, the remaining difference between the two signals can be interpreted as (time-dependent) variations in parallel conductance during the cardiac cycle.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Animals

1

1

Instrumentation

Conductance Catheter

Nomenclature. In the literature, the term parallel conductance is often used loosely for the "physical" parallel conductance (G^P) and for the correction volume (V_C). In the present study, the results are described mainly in terms of G^P and the relation between absolute "true" volume and conductance [G(t)] is written as follows: V(t) = (1/)(L²/_b)[G(t)  G^P]. Originally, Baan et al. (3) used the following equation: V(t) = (1/)(L²/_b)G(t)  V_C; other groups have used the following equation: V(t) = (1/)[(L²/_b)G(t)  V^P]. Obviously, V_C and V^P can be written in terms of G^P, but since  and _b may vary, these terms cannot be used interchangeably. To avoid confusion, we will use the nomenclature as follows: G(t) for conductance, G^P for parallel conductance, (L²/_b)G(t) for conductance volume, V^P = (L²/_b)G^P for parallel conductance volume, and V_C = (1/)(L²/_b)G^P for correction volume.

Slope factor. After correction for G^P, the signal obtained by the conductance catheter is directly proportional to absolute ventricular volume but generally underestimates true volume by a fixed percentage. To correct the underestimation,  was introduced. In practice,  is determined by comparing the conductance-derived volume [or stroke volume (SV)] with an independent measurement such as angiography or thermodilution. In animals such as dogs or sheep,  is typically 0.8 (3, 24). A key point in the present study is that the approaches that are used to determine G^P, i.e., the saline dilution method and the angiographic method (see below), do not require that  be assessed and are independent of the actual value of . Both methods analyze the raw conductance signals, rather than the calibrated conductance volume signals, to determine G^P. The only implicit assumption is that  can be regarded as constant during the cardiac cycle, but it does not necessarily need to be 1.0. This assumption is validated by testing the linearity of the relation between conductance and angiographic volume.

G^P Obtained by Hypertonic Saline Injection

In the present study, G^P obtained by hypertonic saline injection (G) was determined as the mean of three repeat hypertonic saline injections analyzed by custom-made software.

Angiography

Angiographic dimensions were calibrated on the diameter of the angiographic catheter using QCA-CMS View software (Medis, Leiden, The Netherlands). Angiographic LV volumes (V_Angio) were calculated using the area-length method (9, 36) as follows: V_Angio = (8/3)(A_RAOA_LAO)/L_RAO, where A_RAO and A_LAO are the areas enclosed by the LV contours in the RAO and LAO projections, respectively, and L_RAO and L_LAO are the lengths of the LV long axis in the RAO and LAO projections, respectively. The contours were drawn manually in all frames from two consecutive, well-opacified cardiac cycles using custom-made software.

Protocol

1

1

Comparison of Angiographic and Conductance Signals

Angiographically derived parallel conductance and . Contrast medium changes the conductivity of blood; therefore, we compared the angiographically derived volume signals with the conductance signals obtained just before contrast injection. To smooth the conductance signal and to avoid selection bias, four consecutive cardiac cycles were selected and temporally averaged. The conductance and angiographic signals were synchronized by matching the peaks (end-diastolic volume) of the two signals. The temporal resolution of the angiographic signal was 40 ms and that of the conductance signal was 4 ms; consequently, comparisons were made using data points at 40-ms intervals only. The data points from both signals were plotted vs. each other, and a linear regression was performed. The y-intercept represents the hypothetical conductance when angiographic volume equals zero and thus represents an estimate of G^P based on direct comparison with instantaneous angiographic volume. Statistical analysis of the comparative data [G vs. G^P obtained by angiography (G)] was performed by standard linear regression and Bland-Altman analysis (4).

Time-varying G^P. The analysis described above determines G^P averaged over the full cardiac cycle. To investigate whether G^P varies during the cardiac cycle, the conductance signal was calibrated using the coefficients (slope and intercept) obtained from the linear regression, and subsequently the angiographic signal was subtracted from this calibrated conductance-volume signal. The resulting difference signal represents the errors remaining after correction for mean G^P and can be interpreted as variations in G^P during the cardiac cycle. Mathematically, G^P can be written as follows: G^P(t) = G^P + dG^P(t), were G^P is the average (constant) parallel conductance and dG^P(t) the time-varying component. V_Angio is taken as the gold standard; thus it is assumed that V_Angio(t) = (1/)(L²/_b){G(t)  [G^P + dG^P(t)]}.  and G^P are obtained as the slope and intercept, respectively, of the relation between angiographic and uncalibrated conductance volume, as described above. Thus dG^P(t) = [V_Cath(t)  V_Angio(t)]/[(1/)(L²/_b)], where the calibrated conductance volume [V_Cath(t)] = (1/)(L²/_b)[G(t)  G^P]. To enable comparisons between animals and between conditions despite changes in heart rate, the conductance and angiographic signals were fitted with a cubic spline, resampled at 500 time points, and plotted on a normalized time scale.

Variability of G^P

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Typical examples of uncalibrated conductance volume signals, (L²/_b)G(t), and angiographic volume signals in the four hemodynamic conditions are shown in Fig. 1. Linear extrapolation of all data points during the cardiac cycle, G(t) vs. V_Angio(t), yielded G, as shown in Fig. 2. These values were compared with G. All pooled data are shown in Fig. 3 (linear regression) and Fig. 4 (Bland-Altman plot). These findings indicate an excellent linear relation between the two methods. Bland-Altman analysis reveals a bias (±2 SD) of 0.002 ± 0.112 ¹, indicating an essentially zero bias with a standard deviation of 8.4% of mean G^P.

View larger version (13K): [in this window] [in a new window]   Fig. 1.   Typical example (sheep 1) of left ventricular (LV) volume signals in all 4 conditions by biplane angiography and by uncalibrated conductance volume. Rather than raw conductance [G(t)], uncalibrated (i.e., before subtraction of parallel conductance) conductance volume signals, i.e., (L2/b)G(t), are shown.

View larger version (35K): [in this window] [in a new window]   Fig. 2.   Uncalibrated conductance [G(t)] plotted vs. angiographic LV volume [VAngio(t)] for all data points from 1 cardiac cycle (see Fig. 1). Offsets of the linear regression lines (y-intercepts) define angiographically determined parallel conductances (G) for each condition. Base, baseline; Dobu, dobutamine; Gelo, gelofusine; Prop, propranolol.

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Relation between parallel conductances obtained by hypertonic saline (G) and by angiography (G). Pooled data from all animals at all conditions are shown. Solid line, linear fit; dashed line, line of identity.

View larger version (21K): [in this window] [in a new window]   Fig. 4.   Bland-Altman plot showing the mean [(G + G)/2] vs. the difference (G  G) of the 2 methods. Solid horizontal line, mean difference (bias); dashed lines, bias ± 2 SD.

Statistical analysis of the variabilities of G and G between animals and between hemodynamic conditions is given in Table 1. The results show a mean G of 0.661 ± 0.015 ¹ at baseline. This standard deviation does not include the interanimal variability. The variability between animals was 0.17 ¹, or 26% of baseline G. Variation between conditions was substantially less, but G was significantly smaller during dobutamine (0.065 ¹, or 9.8% of baseline) and significantly larger during propranolol (+0.058 ¹, or +8.7% of baseline). Results for G were essentially the same (Table 1), as also illustrated by Fig. 5, which shows mean G and G at the various conditions. _b varied significantly between animals (8.4%), although much less than G^P. The condition variabilities of _b, however, were very similar to those of G^P, suggesting that these changes in G^P were largely due to underlying changes in _b. This suggestion is substantiated by the fact that parallel conductance volume (V^P), which is equal to (L²/_b)G^P, did not differ significantly between conditions.

View larger version (19K): [in this window] [in a new window]   Fig. 5.   Mean G and G in all 4 conditions. Error bars include interanimal variability. See RESULTS and Table 1 for details and statistics.

Figure 6 shows the variations of G^P during the cardiac cycle as a percentage of its mean value. The average variation was small and not significantly different from zero; it ranged from +1.8 ± 2.4% in the midejection phase to 1.3 ± 2.6% during early filling.

View larger version (22K): [in this window] [in a new window]   Fig. 6.   Relative changes in parallel conductance (GP) during the cardiac cycle. Data from all animals were resampled, plotted on normalized time scale, and averaged. Thick line, average over all animals; thin lines, average ± SD.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Conversion of raw conductance catheter data to calibrated absolute volumes requires the assessment of G^P. G^P can be determined by direct comparison of the conductance signals with an independent measurement of absolute LV volume, such as by angiography (20), dimension crystals (2), or balloon volume (6). In addition, several methods have been proposed that enable assessment of G^P without the need for independent volumetric measurements. Baan et al. (3) used a suction method in which cavity volume was reduced to zero by means of a multihole catheter in the LV or by manual compression. The results indicate reasonable correspondence with the saline method, but the nature of this intervention clearly limits its practical application. Recently, White et al. (31) introduced a novel approach that relies on the analysis of the transient reduction of volume induced, e.g., by balloon occlusion of the inferior vena cava. By extrapolating the relation between end-diastolic volume and end-systolic volume during the intervention to a point where these volumes are equal, an estimate of the offset volume corresponding to G^P is obtained. The key assumption in this approach is that ejection fraction is constant during the volume reduction. This hemodynamic requirement may explain why the results show good correlation with the saline method in some study groups but poor agreement in several other groups. Gawne et al. (12) introduced the so-called dual-frequency method, which exploits the fact that, in the 2- to 100-kHz frequency range, blood conductivity is essentially constant whereas muscle conductivity varies. By comparing measured conductance catheter signals at two frequencies (3.3 and 33 kHz), an estimate of G^P was obtained. An inherent disadvantage of this method is that changes in frequency-independent components of G^P (i.e., the blood in the RV) will not be picked up. Although the results by Gawne et al. were promising, more recent studies in neonatal and adult pigs (32) have been disappointing. However, the method appears be applicable in mice, presumably because G^P in these hearts resides almost exclusively in the relatively thick myocardial wall (13). However, the method most widely used to determine G^P is the hypertonic saline method (3). The present study addressed the following three issues with regard to this method: the absolute accuracy of the hypertonic saline method for assessment of G^P, the variability of G^P between animals and between hemodynamic conditions, and the variability of G^P during the cardiac cycle.

Accuracy of the Hypertonic Saline Method

1

A limitation in most studies lies in the dependence of the results on . In principle, the error in the G can be determined directly by subtracting an independent volume measurement from the conductance-derived absolute volume. However, this approach requires that  is determined, which introduces an error source. Alternatively, analysis of conductance volumes corrected for G^P, but not for , is possible, but only when multiple data points are available from different animals or from different hemodynamic conditions. In that case, the error in G^P can be derived from the offset of the relation between volume by conductance and by the independent method. Although the latter approach does not require measurement of , it does implicitly assume that the variability in  (between animals or between conditions) is small. In contrast, in our study, the relation with angiography was obtained by using all data points from a full cardiac cycle. Thus the only implicit assumption is that  is constant (but not necessarily 1.0) within the cardiac cycle, and neither the absolute value of  nor variations of  between animals or between hemodynamic conditions affected our results. A previous study by Szwarc et al. (26), using single-field excitation, yielded significant, but small, changes in  during ejection. Our results (Table 2), with dual-field excitation, show an excellent linear relation between conductance and angiographic volume and indicate that, for all practical purposes,  can be regarded as constant during the cardiac cycle.

Variability of G^P Between Animals and Between Hemodynamic Conditions

Within-subject variability of G^P was investigated in the present study by repeating the assessments after interventions aimed at inducing different hemodynamic conditions. The results in Table 1 indicate that, during dobutamine infusion, G was decreased by 9.8% (G by 8.6%), whereas after propranolol infusion, G increased by +8.7% (G by +6.4%). Previous studies have shown that G^P is sensitive to changes in RV volume (5, 6, 23); thus these changes may reflect the effects of dobutamine and the effects of propranolol on the latter. However, _b was also changed: during dobutamine infusion, _b decreased by 8.5% compared with baseline, whereas after propranolol infusion, _b was +8.3% higher than control. These changes in _b reflect changes in hematocrit, which, during dobutamine infusion, may be increased because of an increased transcapillary fluid shift or red cell recruitment from the spleen (8, 11, 15, 30), whereas, conversely, gelofusine infusion leads to a decrease in hematocrit and, thus, an increase in _b. Thus, because the physical structures that contribute to G^P (i.e., myocardial wall, RV cavity, lungs) contain blood, the changes in G^P may, in fact, be largely due to changes in _b rather than geometrical changes. Interestingly, this means that the parallel conductance volume, which is calculated as V^P = (L²/_b)G^P, would be much less affected. Indeed, statistical analysis (Table 1) shows that changes in V^P were <2.4% and not statistically significant.

The dependence of G^P (or V^P) on hemodynamic conditions has been investigated in several previous studies. Szwarc et al. (27) measured V^P by the saline method in intact dogs at baseline, after volume loading, and after bleeding and did not find significant differences despite large changes in hemodynamic status. Boltwood et al. (5) estimated V^P by repeated saline injections under a variety of loading conditions: compared with control, V^P was unchanged during occlusion of the pulmonary artery or the aorta but was significantly reduced (9%) during occlusion of the inferior vena cava. This may reflect the influence of reduced RV volume during caval occlusion. The influence of RV volume was also demonstrated in a study from our group (23) where embolization of the right coronary artery, dilating the RV, caused a 20% increase in G^P. In general, these changes in G^P do not invalidate the method but indicate the need to reassess G^P after substantial changes in hemodynamic conditions.

Variability of G^P During the Cardiac Cycle

Conclusions