2044 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 8, AUGUST 2009 Electrical Conductivity and Permittivity of Murine Myocardium Karthik Raghavan, John E. Porterfield, Anil T. G. Kottam, Marc D. Feldman, Daniel Escobedo, Jonathan W. Valvano, Member, IEEE, and John A. Pearce ∗ , Senior Member, IEEE Abstract—A classic problem in traditional conductance mea- surement 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 sub- stantial improvement by eliminating the need for hypertonic saline injection. We present in vivo epicardial surface probe measure- ments 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 con- tribution 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 ad- ministering albumin (0.941 S/m with albumin, 0.478 S/m without albumin). Index Terms—Admittance, blood conductivity, conductance, myocardial conductivity, myocardial permittivity. I. INTRODUCTION D ETERMINATION of left ventricular (LV) pressure– volume (P –V ) relations has provided a framework for understanding cardiac mechanics in larger experimental ani- mals and humans [1]. Extension of this technique to the mouse model has proven valuable [2]. Determination of instantaneous volume in the murine LV is difficult due to the small heart size Manuscript received April 23, 2008; revised September 12, 2008. Current version published July 15, 2009. This work was supported in part by the Na- tional Institutes of Health under Grant R21 HL079926 and a U.S. Department of Veterans Affairs (VA) Merit Grant (MDF). Asterisk indicates corresponding author. K. Raghavan, J. E. Porterfield, and J. W. Valvano are with the Depart- ment of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712 USA (e-mail: karthikraghavan@mail.utexas.edu; john.porterfield@mail.utexas.edu; valvano@mail.utexas.edu). A. T. G. Kottam was with the Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712 USA. He is now with Scisense, Inc., London, ON N6E 3A1, Canada (e-mail: akottam@scisense.com). M. D. Feldman and D. Escobedo are with the Department of Medicine, The University of Texas Health Sciences Center at San Antonio, San Antonio, TX 78229 USA (e-mail: feldmanm@uthscsa.edu; escobedod@uthscsa.edu). ∗ J. A. Pearce is with the Department of Electrical and Computer Engi- neering, The University of Texas at Austin, Austin, TX 78712 USA (e-mail: jpearce@mail.utexas.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2009.2012401 (5 mm length, 160 mg mass, and 40 μL LV volume) and its rapid heart rate (500–700 beats/min). Approaches such as ul- trasonic crystals [2], MRI [3], [4], and echocardiography [4] have been used to measure instantaneous LV volume with some degree of success. Unfortunately, all these technologies have severe limitations, particularly during dynamic maneuvers, such as transient occlusion of the inferior vena cava or aorta, which are required to generate load-independent indexes of contractility. Conductance catheter technology, as introduced by Baan et al. in 1981 [6], offers a more robust alternative to gener- ate instantaneous LV P –V relations in the intact murine heart. Single-frequency conductance has been used in mice to gener- ate measures of ventricular function [5], [7], [8]. However, the traditional conductance method is limited in the mouse because the instantaneous LV conductance signal includes both blood conductance and parallel admittance in the myocardium and, unless corrected, yields an overestimate of the true LV blood volume [6]. Investigators have applied the hypertonic saline technique developed for larger mammals to determine a sin- gle value of steady-state parallel (cardiac muscle) conductance and used it for the derivation of absolute LV volume [9]. The saline technique, however, is problematic in small animals such as mice and rats since administration of even small volumes of hypertonic saline significantly alters both blood resistivity and hemodynamics (i.e., blood volume) [5], violating the framework of the governing assumptions [6]. Simultaneous measurement at two frequencies combined with the hypertonic saline technique has been proposed by other investigators [10]–[12]. However, in all cases, these methods determine only a single value of steady-state parallel conductance. Thus, conductance measure- ment in its present reduction to practice, in both small and large subjects, cannot calculate the instantaneous change in paral- lel conductance occurring throughout the cardiac cycle as the LV cavity shrinks around the intracardiac electric field during occlusion of the inferior vena cava or at end systole. Measurements of the permittivity of muscle by Gabriel et al. [13], [14] suggest that the relative permittivity of car- diac muscle exceeds 15 000 at 20 kHz. We hypothesize that the electric permittivity of muscle in vivo is so high that the admittance in the LV at frequencies in this range can be used to identify and separate the cardiac muscle component from the combined admittance measurement. The fundamental observa- tion is that blood is semiconducting, over the same frequency range, so all frequency-dependent admittance is due to the mus- cle component only, i.e., for a tetrapolar catheter in the LV, the admittance consists of two parallel components from blood and 0018-9294/$25.00 © 2009 IEEE Authorized licensed use limited to: Qualcomm. Downloaded on July 27, 2009 at 12:33 from IEEE Xplore. Restrictions apply.