INTRODUCTION

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CONDUCTANCE MEASUREMENT offers a method to generate an instantaneous left ventricular volume signal in the mouse (13). It uses an electric field generated from electrodes at the apex and immediately above the left ventricle to sense the instantaneous conductance change as the left ventricle fills and ejects blood. A signal proportional to the left ventricular blood volume is required for use in physiological studies. Unfortunately, the presently available instantaneous conductance output is a combination of blood and left ventricular muscle (2-4, 17, 27). We hypothesized that by developing a mouse conductance system that operates at several simultaneous frequencies, we could identify and possibly correct for the myocardial contribution to the instantaneous volume signal.

This hypothesis is based on the assumption that mouse myocardial conductivity will vary with frequency, whereas mouse blood conductivity will not. Prior work has shown that blood has constant electrical resistivity over a wide range of frequencies (2-100 kHz) (22). In contrast, the resistivity of myocardium is known to change with frequency: specifically, the resistivity of myocardium is lower at increased excitation frequency (8, 23-25, 33). We propose (see Fig. 1) that at lower frequencies, there is a maximal gradient between the resistivity of blood and myocardium such that the electric field generated will be primarily confined to the left ventricular cavity and, to a lesser degree, the myocardium. At higher frequencies, there will be a minimal gradient between the resistivity of blood and myocardium, and the electric field generated will not be confined to the left ventricular cavity but will extend into the myocardium. Accordingly, we hypothesized that the higher the excitation frequency, the greater the apparent end-diastolic and end-systolic conductance detected by the miniaturized conductance catheter. In addition, if this construct is correct, there should be a slight reduction in the difference between end-diastolic and end-systolic conductance at higher frequencies because the relative proportion of the signal changing from systole to diastole is smaller.

View larger version (44K): [in this window] [in a new window]   Fig. 1.   A depiction of the concept being tested. Prior work has shown that blood has constant electrical resistivity over a wide range of frequencies. In contrast, the resistivity of myocardium is known to change with frequency: specifically, the resistivity of myocardium is lower at increased input frequency. We propose that at lower frequencies, there is a maximal gradient between the resistivity of blood and myocardium such that the electrical field generated will be confined to the left ventricular cavity and, to a lesser degree, the myocardium. At higher frequencies, there would be a minimal gradient between the resistivity of blood and myocardium, and the electrical field generated would not be confined to the left ventricular cavity but extend into the myocardium. Accordingly, we hypothesized that the higher the excitation frequency, the greater the end-diastolic and end-systolic volume detected by the miniaturized conductance catheter. In addition, if this construct is correct, there should be a slight reduction in stroke volume at higher frequencies, because the field density contained within the left ventricular blood is reduced.

This approach could have an important advantage over the traditional conductance method for determining measures of ventricular function such as end-systolic elastance. Because elastance is generated during beat-by-beat changes in loading conditions, a method to determine and correct for instantaneous parallel conductance is critical and does not exist. The use of multiple simultaneous frequencies has the potential to solve this problem. The application of this approach would be in transgenic mice. There is a need to relate specific gene products to phenotype. Unfortunately, the ability to rigorously assess the cardiovascular phenotype in very small animals has lagged (6, 15). Such analysis has been available in larger animals by measurement of simultaneous left ventricular pressure and volume to examine cardiac performance in the pressure-volume plane (1, 16). The application of this approach to mice has been difficult because of the small size of the mouse heart and the rapid heart rate. Creating the technology to generate an accurate instantaneous volume signal in the transgenic mouse to generate pressure-volume relationships during occlusion of the inferior vena cava was a goal of this study.

In an effort to exploit this differential frequency response, we sought to determine whether we could empirically solve for left ventricular blood volume using a multifrequency input signal. By combining experimental data with an analytic approach consisting of a series of equations, we were able to extract an accurate estimate of left ventricular blood and myocardial components.

	METHODS

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Conductance catheter. A 1.4-Fr miniaturized pressure-volume catheter (SPR-719; Millar Instruments, Houston, Texas) was used in these studies. The catheter has four platinum electrodes, each 0.25 mm in length, with an interelectrode spacing of 0.5, 4.5, and 0.5 mm between electrodes 1 and 2, 2 and 3, and 3 and 4, respectively. A constant excitation current (17 µA root mean square) was applied to the two outermost electrodes by using a custom signal generator/processor and bridge amplifiers developed by us and subsequently modified (MCS-100; Millar Instruments), and the two intermediate electrodes were used to measure the instantaneous voltage signal. A high-fidelity pressure transducer (frequency response flat to 10 kHz) was mounted between electrodes 2 and 3 to measure ventricular pressure.

(1)

(2)

Calculation of mouse blood volume from single-frequency data. The signal processor provides an analog voltage output. A calibration procedure was developed to convert this voltage output into conductance (µS). Known resistors were used to calibrate our instrumentation. Because conductance is the inverse of resistance, these resistors were connected to our system as the input, and a corresponding voltage was derived. The relationship of the input conductance to the output voltage was then known. This relationship was added to our data acquisition software and allowed us to obtain instantaneous conductance from the beating mouse heart. This generated G_i, which was converted to volume using Baan's simplified Eq. 2 and not Eq. 1, because we did not know G_pi. We then subtracted steady-state parallel conductance (V_p), derived by the hypertonic saline method (described in detail below) from the raw volume signal, and then multiplied by  to generate a corrected volume signal.

(3)

(4)

Calculation of mouse blood volume from multifrequency data. The conductance signal output generated from the mouse varies with time and is a combination of signals arising from both the blood and myocardium. Derivation of left ventricular chamber volume requires the assumption that, whereas resistivity of myocardium varies as a definable function of frequency, resistivity of blood is independent of frequency. As such

(5)

and

(6)

where G_ed is total measured conductance at end diastole, G_m is conductance from muscle, G_b is conductance from left ventricular blood, and f₁ and f₂ are the test frequencies used empirically. Because

(7)

subtraction of Eq. 5 from Eq. 6 yields

(8)

The resistivity of muscle is defined experimentally (see Fig. 4) and relates to conductance by an end-diastolic constant (k_ed) such that

(9)

By substitution

(10)

allowing solution for k_ed. Applying this constant to Eq. 5 provides a value for G_b,ed f1 (in µS). The same approach can be applied to end-systole, where a different k_es would be determined because k depends on shape, or to any other time throughout the cardiac cycle.

System calibration. We wanted to demonstrate that the miniaturized mouse conductance catheter would generate a constant conductance output at different frequencies. Saline with resistivities of 62, 78, 93, 109, and 125  · cm, which span the reported resistivities of blood (28), were used. The saline was placed in 6-mm-diameter test tubes in a H₂O bath at 37°C, and the conductance catheter was centered in the saline. Voltage output was determined at frequencies ranging from 500 Hz to 100 kHz.

Studies in mice. The protocol was approved by the Institutional Animal Care and Use Committee at the University of Texas Health Science Center at San Antonio and conformed with Guidelines for the Care and Use of Laboratory Animals (NIH Publication No. 86-23, Revised 1985) and Principles of Laboratory Animal Care (published by the National Society for Medical Research). CD-1 mice (n = 19) weighing 20-30 g were anesthetized by administration of methoxyflurane (Metofane; Pitman-Moore, Mundelein, IL) in a closed chamber, followed by urethan (1,000 mg/kg ip) and etomidate (25 mg/kg ip). Respiration was controlled through a tracheostomy cannula, and the animals were mechanically ventilated with room air at 60 breaths/min using a rodent ventilator (model 680; Harvard Apparatus, South Natick, MA). The chest was entered via an anterior thoracotomy. A small animal blood flow meter (T 106; Transonic Systems, Ithaca, NY) was placed around the aorta. The flowmeter was placed on the descending thoracic aorta immediately above the level of the diaphragm. For technical reasons, it could not be placed on the ascending thoracic aorta. In five additional CD-1 mice examined by echocardiography (10), 72.5 ± 4.8% of the SV ejected into the ascending thoracic aorta was determined to be present in the descending thoracic aorta. Because the flow probe was placed around the descending thoracic aorta, flow probe SV (as presented in Table 1) was normalized to correct for SV lost to the vessels of the aortic arch.

Determination of mouse muscle and blood resistivity. To determine the conductance of in vivo myocardium, a customized suction tetrapolar electrode device was developed using silver-coated copper wire. The four electrodes ended as blunt probes separated by 0.25 mm that were contained within a 1-mm plastic tube that could be attached to a vacuum, similar to the device developed for the canine by Steendijk et al. (24). This enabled the device to be applied directly to the epicardium of the beating mouse myocardium to determine frequency-resistivity relationships at the same time that the miniaturized mouse conductance catheter was inserted into the left ventricle to determine frequency-conductance relationships (n = 8).

Evidence that the electric field is extending into the mouse myocardium. To demonstrate the limitations of the hypertonic saline technique and the importance of an alternative technique such as multifrequency measurement, we sought to demonstrate the load dependence of V_p. Six additional CD-1 mice underwent the in vivo protocol outlined above. After the baseline conductance and flow probe data were acquired at 10 kHz, sustained aortic occlusion was performed by placing tension on a suture around the descending thoracic aorta until a new steady-state systolic pressure was achieved with increased intraventricular pressure. Hypertonic saline determination of V_p was performed at baseline and at increased load.

Mouse heart morphological measurements. To determine the wall thickness-to-chamber ratio (11, 20), three mouse hearts were cut longitudinally in 4-µm sections with a microtome and mounted on microscope slides. Staining was performed with hematoxylin and eosin. Measurements of anterior and posterior wall thickness and chamber diameter were made at the midpapillary muscle level with planimetry.

Calculations. Conductance-derived pressure-volume data were analyzed with software developed by us (PVAN) and modified by Millar Instruments. Heart rate was determined as 1/R-R interval, end-systolic pressure was pressure at the point of maximal pressure-to-volume ratio, end-diastolic pressure was the pressure at the R wave, end-systolic volume (ESV) was the minimal left ventricular volume, end-diastolic volume (EDV) was the maximal left ventricular volume, and SV was the difference (EDV  ESV).

Statistics. Within each mouse, relationships between frequency (logarithmic scale) and resistivity and between frequency and conductance were examined by scatter plots and by computing Spearman's nonparametric rank correlation coefficients. Nonparametric analyses were used because most relationships were monotone but not necessarily linear. Cochran-Mantel-Haenszel statistics based on ranks were computed to obtain global measures of correlation controlling for individual mouse effects. The average Spearman's correlation coefficients, averaged over all pairs of mice, were then computed from the resulting Friedman's test statistics (7). All computations were performed using SAS (version 6.11; SAS Institute, Cary, NC).

	RESULTS

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Figure 2 shows an example of data from an individual mouse during calculation of single-frequency V_p with bolus injection of hypertonic saline. Figure 2A shows the conductance-derived left ventricular pressure-conductance relationships during hypertonic saline washin that were used to calculate G_es and G_ed on a beat-to-beat basis, shown in Fig. 2B. The beat-to-beat changes were greater in G_ed than in G_es. Figure 2B demonstrates the calculation of V_p using Eqs. 3 and 4 in METHODS. V_p was 554.24 µS.

View larger version (22K): [in this window] [in a new window]   Fig. 2.   Data from an individual mouse during calculation of single-frequency steady-state parallel conductance (Vp) with bolus injection of hypertonic saline. A: conductance-derived left ventricular pressure-conductance relationships during hypertonic saline washin used to calculate end-systolic (Ges) and end-diastolic conductance (Ged) on a beat-by-beat basis (shown in B). B: calculation of Vp from Eqs. 3 and 4 in METHODS. Vp is 554.24 µS.

Figure 3 shows the regression lines of frequency (kHz) versus conductance (µS) of the signal processor (MCS, Houston, TX). These studies demonstrate that the conductance output of the signal processor is constant over the frequencies examined. This is critical because voltage was converted to conductance, and a varying source current would confound interpretation (because G = I/V, where G is conductance, V is voltage, and I is current; I must be constant over the frequencies examined for V to be converted to G). Moreover, the constant current output persisted despite a doubling of resistivity of saline from 62 to 125  · cm.

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Data for frequency vs. conductance output of the signal generator/processor demonstrate that the conductance, and therefore current output, of the signal generator/processor is constant over the frequencies examined. This is critical because voltage is converted to conductance, and a varying source current would confound interpretation (because G = I/V, where G is conductance, V is voltage, and I is current, then I must be constant over the frequencies examined for V to be converted to G). Moreover, the constant current output persisted despite a doubling of resistivity of saline from 62 to 125  · cm.

Figure 4 is a plot of the resistivity versus frequency of mouse blood, determined by placing the miniaturized mouse conductance catheter in a tube containing blood, and of mouse left ventricular myocardium, derived from the epicardial suction tetrapolar electrodes. The mean and standard deviations from eight mice are shown. The resistivity of mouse blood is constant despite frequencies ranging from 500 Hz to 100 kHz (r² = 0.183, where r² is the correlation coefficient; P = 0.015). In contrast, the myocardial resistivity falls as frequency increases over the same frequency range (r² = 0.441, P = 0.001).

View larger version (9K): [in this window] [in a new window]   Fig. 4.   A plot of the resistivity vs. frequency of mouse blood, determined by placing the miniaturized mouse conductance catheter in a tube containing blood, superimposed on the same plot for mouse left ventricular myocardium, derived from the epicardial tetrapolar suction electrodes. Values are means ± SD from 8 mice. The resistivity of mouse blood is constant despite frequencies ranging from 500 Hz to 100 kHz (r2 = 0.183, P = 0.015). In contrast, the myocardial resistivity falls as frequency increases over the same frequency range (r2 = 0.441, P = 0.001).

Figure 5 is a plot of measured conductance, as a function of frequency, measured in vivo by the conductance catheter placed in the same eight mice shown in Fig. 4. The conductance is not corrected for parallel conductance (V_p) or electrical field inhomogeneity (). As frequency increases, both end-diastolic conductance (r² = 0.987, P = 0.001) and end-systolic conductance (r² = 0.985, P = 0.001) increase. In contrast, as frequency increases, there is a decrease in the difference between end-diastolic and end-systolic conductance (G; r² = 0.200, P = 0.008), although the correlation coefficient is low.

View larger version (14K): [in this window] [in a new window]   Fig. 5.   A plot of conductance as a function of frequency, measured in vivo by the conductance catheter placed in the same 8 mice used in the experiment shown in Fig. 4. The conductance was not corrected for Vp or electrical field in-homogeneity (). As frequency increases, both Ged (r2 = 0.987, P = 0.001) and Ges (r2 = 0.985, P = 0.001) increase. In contrast, as frequency increases, there is a decrease in the difference between Ged and Ges (G; r2 = 0.200, P = .008), although the correlation coefficient is low.

Table 1 is a comparison of the EDV, ESV, and SV values calculated by using the two methods. The first method uses multiple frequencies as proposed in this manuscript, according to Eqs. 5-10. The second method uses that proposed by Baan and co-workers (1) where the raw conductance signal is corrected for V_p and . For this analysis, two frequencies were used (10 and 100 kHz), and these frequencies were delivered simultaneously. These frequencies correspond to maximal differences in myocardial resistivity (Fig. 4) and a flat current output of the signal processor (Fig. 3).

The baseline hemodynamics of these six mice included an end-systolic pressure of 57 ± 6 mmHg, heart rate of 439 ± 19 beats/min, and flow probe SV of 16.19 ± 3.29 µl/beat. The use of two simultaneous frequencies (10 and 100 kHz) to calculate volumes according to the new method proposed in this manuscript yielded a raw SV of 6.0 ± 1.3 µl/beat (not corrected by V_p or ), EDV of 40 ± 8 µl, and ESV of 24 ± 7 µl.  was 2.75. The shape constants k_ed and k_es were 6.1 ± 0.6 and 5.3 ± 0.4 mm, respectively (P < 0.001). The standard method (single frequency  saline) yielded a raw SV of 4.3 ± 0.8 µl/beat (not corrected by V_p or ), EDV of 23 ± 4 µl, and ESV of 8 ± 2 µl.  was 3.63 ± 1.04. As the multifrequency-derived SV, ESV, and EDV increased, so did the same parameters derived with the standard method of calculation (SV, r² = 0.916; ESV, r² = 0.713; and EDV, r² = 0.933). The raw dual-frequency SV was larger than the raw single-frequency SV (P < 0.001, not corrected by V_p or ).

Table 2 is a comparison of V_p at steady-state conditions and when afterload was increased by sustained aortic occlusion. Studies were performed on six additional mice at a single frequency (10 kHz). The baseline V_p of 14.6 ± 7.0 µl increased to 19.2 ± 7.9 µl with sustained afterload (P < 0.01). The heart rate did not change (446 ± 74 to 439 ± 43 beats/min, P = not significant), but end-systolic pressure (52 ± 8 to 80 ± 11 mmHg, P < 0.01) and end-diastolic pressure both increased (3 ± 1 to 4 ± 2 mmHg, P < 0.01).

A plot of left ventricular pressure-volume relationships during the identical caval occlusion are shown in Fig. 6. The dual-frequency data were determined at 10 and 100 kHz and the single-frequency data at 10 kHz, and the latter were corrected with the hypertonic saline technique. It was anticipated that the slope of end-systolic elastance would differ if determined with single- versus dual-frequency conductance. Figure 6 demonstrates that a 20.9% difference in elastance was found (23.68 vs. 19.59 mmHg/µl, single vs. dual frequency, respectively) in this single example.

View larger version (42K): [in this window] [in a new window]   Fig. 6.   A plot of left ventricular pressure-volume relationships during the identical caval occlusion is shown for data derived from the simultaneous dual-frequency method (10 and 100 kHz, solid lines) and single-frequency method (10 kHz, dotted lines) corrected with the saline technique. As is visually evident, the 2 methods gave different end-systolic elastance [the volume intercept if the pressure is zero (extrapolated from the line defining end-systolic elastance)] = 1.53 or 2.05 µl and volumes (Ves). The left ventricular weight of this mouse was 115 mg, compared with 133 ± 8 mg for the mouse data displayed in Table 1, which may explain the smaller volumes shown here. Pes, end-systolic pressure; Vp, parallel conductance.

	DISCUSSION

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This study has demonstrated a new concept concerning the impact of excitation frequency from a miniaturized mouse conductance catheter on electric field generation. We proposed that at lower frequencies, the field would be confined to the left ventricular cavity and, to a lesser degree, the myocardium. Likewise, at higher frequencies, the electric field generated would not be confined to the left ventricular cavity but extend into the myocardium. The basis for this proposal, which we confirmed in the in vivo mouse heart, is that myocardial resistivity decreases with increasing frequency (8, 23-25, 33), whereas blood resistivity is constant at different frequencies (22). The resulting hypothesis, stating that at higher excitation frequency greater end-diastolic and end-systolic conductance and smaller G would be generated, has been confirmed in this study. Finally, we were able to empirically estimate left ventricular blood volume using two frequencies simultaneously. We combined measured resistivity of mouse myocardium with an analytic approach and were able to extract an estimate of left ventricular blood volume from the raw conductance signal.

One advantage of dual-frequency conductance documented in the present study was the detection of a larger amount of SV. The flow probe measured 16.19 ± 3.29 µl/beat compared with 4.3 ± 0.8 µl/beat for the single-field conductance technique. The dual-field technology detected 6.0 ± 1.3 µl/beat. As a result, the correction factor for electrical field inhomogeneity () as the ratio of flow probe SV to raw conductance SV would be smaller with dual frequency. Because the final step in converting the instantaneous voltage output generated by the conductance catheter to volume is multiplication by , there would be less magnification of any error. A second advantage is that the dual-field technique eliminates the need to administer hypertonic saline to determine steady-state parallel conductance. The conductance technique and Eq. 1 require knowledge of the resistivity of blood, which is always changing in a given mouse as more hypertonic saline is injected. Given the very small blood volume of mice, it is not practical to measure this changing resistivity for every condition during each experiment.

The mean ejection fraction (EF) for the dual-frequency method calculated for the six mice presented in Table 1 is 42 ± 7%. The mean EF for these same mice calculated with the single-frequency method is 68 ± 9%. Given the open-chest preparation, the heart rate, and the instrumentation used in the present study, 42% is likely a more realistic value. Why does single-frequency conductance overestimate EF in the mouse? The SV determined by the dual- and single-frequency methods will be equal because both are corrected by the flow probe SV. The single-frequency EDV is smaller than the dual-frequency EDV. Therefore, the calculated EF will always be larger with the single-frequency method.

The smaller EDV determined with single frequency compared with dual frequency is due to overestimation of parallel conductance (V_p). The hypertonic saline method as originally described by Baan et al. (1) assumes no significant effect on left ventricular volume or performance. That finding has been confirmed in larger animals where ~2% of the left ventricular blood volume is injected. In the mouse, the injection of 20 µl of hypertonic saline in the right ventricle represents a large portion of left ventricular blood volume. This causes significantly greater beat-by-beat changes in end-diastolic than in end-systolic conductance, as demonstrated in Fig. 2A. This is anticipated because the bolus of hypertonic saline produces a sudden increase in preload without a change in contractility. To determine V_p, G_es is plotted on the ordinate and G_ed on the abscissa as shown in Fig. 2B, and V_p is determined as the intercept of the extrapolated data with the line of identity. Because G_ed is changing faster than G_es, violating the assumptions of Baan et al. (1), the intersection with the line of identity will be artificially increased. The result will be an overestimation of V_p, a smaller EDV, and an overestimated EF with the single-frequency technique.

The derivation of left ventricular blood volume from multifrequency data requires two assumptions. The first is that mouse myocardial resistivity determined in vivo on the epicardial surface by the suction tetrapolar electrode is similar to the myocardial resistivity component of the miniaturized mouse conductance signal generated from within the left ventricular chamber. The traditional method used to determine myocardial resistivity is to place in vitro epicardial pins or electrode holders onto the myocardium (8, 18, 21, 30). This method is limited by injury from the electrodes and ischemia to the myocardium as an in vitro preparation. Ischemia has previously been shown to significantly increase myocardial resistivity (9, 29). The use of the blunt tetrapolar suction electrodes in the current study solves both of these problems and is similar in concept to that employed by Steendijk and co-workers (24).

The second assumption is that mouse myocardial resistivity varies with frequency, whereas mouse blood resistivity does not vary with excitation frequency. The observation that muscle resistivity decreases as the frequency of the input signal increases was established in the 19th century (14) and has been reconfirmed by several groups (8, 23-25, 33). This construct holds that at high frequency, the cell membranes should be effectively short-circuited, with tissue conductance equal to the conductivity of cytoplasm. As a result, resistivity falls. In contrast, at low frequency, the field also travels through the cell membrane that has higher resistivity. We specifically designed the tetrapolar suction electrodes with electrode spacing of 0.25 mm to be significantly less than the 1.2 ± 0.1-mm (n = 3) average anterior myocardium thickness determined morphologically. A ratio of myocardial thickness to electrode separation >1 ensures that the electrical field is confined to the myocardium and does not extend into the left ventricular blood (24). Moreover, because the intramyocardial conductance signal will pass through a substantial depth of myocardium, the fiber orientation through which it passes will vary. Because myocardial blood volume varies with the phase of the cardiac cycle and resistivity of cardiac muscle differs with fiber direction (8, 21, 24, 25), these could all be sources of variation in determining in vivo myocardial resistivity. We therefore choose to present a lumped value for resistivity, independent of fiber orientation or phase of the cardiac cycle.

There was a previous study attempting to estimate left ventricular offset volume using two stimulation frequencies. Gawne and co-workers (12) also took advantage of the fact that myocardial resistivity is dependent on input frequency, whereas blood resistivity is independent of input frequency. They hypothesized that SV would be independent of input frequency, whereas minimal volume (ESV) would vary with input frequency. Therefore, the change in ESV with frequency would be due to quantifiable V_p. However, their approach could only be applied during steady-state conditions and therefore could not be applied with changing loading conditions to generate end-systolic elastance. Furthermore, as shown in Fig. 1, our hypothesis predicts that apparent SV should not be constant but should fall at increasing frequency due to a less dense electric field in the left ventricular chamber. We confirmed that apparent SV fell with increasing input frequency, whereas Gawne et al. (12) did not. The frequencies examined by Gawne et al. did not exceed 33 kHz, a frequency maximum in the mouse that did not change myocardial resistivity. Finally, Gawne et al. wrote that an analytic solution to this problem of using multifrequency signals to solve for instantaneous parallel conductance was not possible due to the complex, changing geometry of the heart. We have solved this problem with the introduction of a shape constant, k. By determining the instantaneously changing shape constant during the cardiac cycle and during changing loading conditions, we have a more robust approach that can now be applied not just during steady state but also during the generation of load-independent measures of contractility.

The use of dual-frequency conductance is relevant to crossing the major hurdle of applying conductance measurements to evaluate left ventricular function in the pressure-volume plane. A traditional limitation of conductance measurements has been changing parallel conductance during occlusion of the inferior vena cava to generate end-systolic elastance, effective arterial elastance, and additional measures of ventricular function generated from pressure-volume analysis (2, 5). The currently accepted technique of using small injections of hypertonic saline to correct for parallel conductance is only accurate during steady-state conditions (1, 17). Small and physically insignificant changes in parallel conductance occur throughout the cardiac cycle (17, 26, 31). However, during a change in loading conditions, parallel conductance is also changing (2, 5). This was confirmed in the current study where sustained aortic occlusion, which allowed a significant increase in aortic pressure, increased V_p from 14.6 ± 7.0 to 19.2 ± 7.9 µl (P < 0.01, Table 2) in six mice. Occlusion of the inferior vena cava results in the left ventricle shrinking around a fixed electric field generated from a conductance catheter. Therefore, the amount of field leakage into the left ventricular myocardium and surrounding structures changes instantaneously. For these reasons it has not been possible to determine the absolute slope of end-systolic elastance with conductance measurements.

There are two limitations of this study. The first is whether dual-frequency conductance will only be successfully applied to the mouse or whether it can be generalized to larger species. The mouse has a greater ratio of left ventricular wall thickness to chamber radius than larger species [mouse 1.0 ± 0.3 (n = 3) vs. human 0.45] (11, 20). Therefore, more of the mouse conductance signal will derive from the myocardium, making it an ideal species for multifrequency studies. This may not be true in larger dilated hearts. For instance, in patients with dilated cardiomyopathy, little of the electrical field generated from the conductance catheter reaches the myocardium (32). Dual-frequency measurement may not be useful to determine an accurate estimate of left ventricular volumes in this setting.

Second, it is not currently known how the shape constant k varies during inferior vena cava occlusion. The ability to generate instantaneous G_p i with multifrequency measurements is dependent on determining k not only at end diastole and end systole but also throughout the cardiac cycle and with different loading conditions. The conductance of myocardium at a given frequency is equal to the resistivity of myocardium multiplied by the shape constant. Because the shape varies with the cardiac cycle and load, and because myocardial resistivity varies with frequency and not the cardiac cycle or load, once the relationship between k and cardiac cycle/loading condition is defined, correction for parallel conductance at any time during the cardiac cycle or loading condition will be feasible. In the present study, k decreased from 6.1 ± 0.6 to 5.3 ± 0.4 mm between end diastole and end systole. An assessment of how k varies with changing loading conditions will require further studies.

In conclusion, we have been able to estimate left ventricular blood volume in the mouse with a miniaturized multifrequency mouse conductance system. Such an approach has the capability to determine instantaneous parallel conductance and determine an accurate estimate of ventricular function with left ventricular pressure-volume analysis, which has not been previously possible. The value of this approach would be increased if the conductance catheter could be placed and calibrated from the carotid artery. Attempts to add a velocity transducer to the shaft of the conductance catheter are in progress. This would eliminate the need for the flow probe. Dual frequency would allow calibration for parallel conductance, eliminating the need for bolus hypertonic saline. Resistivity of mouse myocardium may vary in different strains, especially transgenic strains. However, once these resistivities are determined and published, investigators may be able to use them without measuring them in every mouse. With such refinements, the development of the multifrequency catheter-based system to determine left ventricular function could be a tool to relate specific gene products to phenotype in the transgenic mouse.