The conductance catheter technique could be improved by determining instantaneous parallel conductance (G(P)), which is known to be time varying, and by including a time-varying calibration factor in Baan's equation [alpha(t)]. We have recently proposed solutions to the problems of both time-varying G(P) and time-varying alpha, which we term "admittance" and "Wei's equation," respectively. We validate both our solutions in mice, compared with the currently accepted methods of hypertonic saline (HS) to determine G(P) and Baan's equation calibrated with both stroke volume (SV) and cuvette. We performed simultaneous echocardiography in closed-chest mice (n = 8) as a reference for left ventricular (LV) volume and demonstrate that an off-center position for the miniaturized pressure-volume (PV) catheter in the LV generates end-systolic and diastolic volumes calculated by admittance with less error (P < 0.03) (-2.49 +/- 15.33 microl error) compared with those same parameters calculated by SV calibrated conductance (35.89 +/- 73.22 microl error) and by cuvette calibrated conductance (-7.53 +/- 16.23 microl ES and -29.10 +/- 31.53 microl ED error). To utilize the admittance approach, myocardial permittivity (epsilon(m)) and conductivity (sigma(m)) were calculated in additional mice (n = 7), and those results are used in this calculation. In aortic banded mice (n = 6), increased myocardial permittivity was measured (11,844 +/- 2,700 control, 21,267 +/- 8,005 banded, P < 0.05), demonstrating that muscle properties vary with disease state. Volume error calculated with respect to echo did not significantly change in aortic banded mice (6.74 +/- 13.06 microl, P = not significant). Increased inotropy in response to intravenous dobutamine was detected with greater sensitivity with the admittance technique compared with traditional conductance [4.9 +/- 1.4 to 12.5 +/- 6.6 mmHg/microl Wei's equation (P < 0.05), 3.3 +/- 1.2 to 8.8 +/- 5.1 mmHg/microl using Baan's equation (P = not significant)]. New theory and method for instantaneous G(P) removal, as well as application of Wei's equation, are presented and validated in vivo in mice. We conclude that, for closed-chest mice, admittance (dynamic G(P)) and Wei's equation (dynamic alpha) provide more accurate volumes than traditional conductance, are more sensitive to inotropic changes, eliminate the need for hypertonic saline, and can be accurately extended to aortic banded mice.
A classic problem in traditional conductance measurement of left ventricular (LV) volume is the separation of the contributions of myocardium from blood. Measurement of both the magnitude and the phase of admittance allow estimation of the time-varying myocardial contribution, which provides a substantial improvement by eliminating the need for hypertonic saline injection. We present in vivo epicardial surface probe measurements of electrical properties in murine myocardium using two different techniques (a digital and an analog approach). These methods exploit the capacitive properties of the myocardium, and both methods yield similar results. The relative permittivity varies from approximately 100,000 at 2 kHz to approximately 5000 at 50 kHz. The electrical conductivity is approximately constant at 0.16 S/m over the same frequency range. These values can be used to estimate and eliminate the time-varying myocardial contribution from the combined signal obtained in LV conductance catheter measurements, thus yielding the blood contribution alone. To study the effects of albumin on the blood conductivity, we also present electrical conductivity estimates of murine blood with and without typical administrations of albumin during the experiment. The blood conductivity is significantly altered (p < 0.0001) by administering albumin (0.941 S/m with albumin, 0.478 S/m without albumin).
Real time left ventricular (LV) pressure-volume (P-V) loops have provided a framework for understanding cardiac mechanics in experimental animals and humans. Conductance measurements have been used for the past 25 years to generate an instantaneous left ventricular (LV) volume signal. The standard conductance method yields a combination of blood and ventricular muscle conductance; however, only the blood signal is used to estimate LV volume. The state of the art techniques like hypertonic saline injection and IVC occlusion, determine only a single steady-state value of the parallel conductance of the cardiac muscle. This is inaccurate, since the cardiac muscle component should vary instantaneously throughout the cardiac cycle as the LV contracts and fills, because the distance from the catheter to the muscle changes. The capacitive nature of cardiac muscle can be used to identify its contribution to the combined conductance signal. This method, in contrast to existing techniques, yields an instantaneous estimate of the parallel admittance of cardiac muscle that can be used to correct the measurement in real time. The corrected signal consists of blood conductance alone. We present the results of real time in vivo measurements of pressure-admittance and pressure-phase loops inside the murine left ventricle. We then use the magnitude and phase angle of the measured admittance to determine pressure volume loops inside the LV on a beat by beat basis. These results may be used to achieve a substantial improvement in the state of the art in this measurement method by eliminating the need for hypertonic saline injection.
Cardiac volume estimation in the Left Ventricle from impedance or admittance measurement is subject to two major sources of error: parallel current pathways in surrounding tissues and a non uniform current density field. The accuracy of volume estimation can be enhanced by incorporating the complex electrical properties of myocardium to identify the muscle component in the measurement and by including the transient nature of the field non uniformity. Cardiac muscle is unique in that the permittivity is high enough at audio frequencies to make the muscle component of the signal identifiable in the imaginary part of an admittance measurement. The muscle contribution can thus be uniquely identified and removed from the combined muscle - blood measurement. In general, both error sources are transient and are best removed in real time as data are collected. This paper reviews error correction methods and establishes that the relative magnitudes of the error concerns are different in small and large hearts.
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