The Magnitude of the Electromotive Force of Canine Ventricular Myocardium

Transcription

1 ELECTROMOTIVE FORCE OF CANINE VENTRICLE/Mashima et al. 757 forms. These steps may make it easier to estimate alterations in myocardial repolarization properties during drug, electrolyte, and ischemic interventions in experimental and clinical studies. Acknowledgments We gratefully acknowledge the assistance of Victoria Gohmann in preparation of the manuscript and of Melissa Vogt in preparation of the illustrations. References 1. Wilson FN, Maclcod AC Barker PS: The T-deflection of the electrocardiogram. Trans Assoc Am Phys 46: Woodbury RA: Studies on turtle hearts. End of systole, duration of refractory period, latent period of extrasystoles and influence of heart rate on aortic blood pressure. Am J Physiol 132: , Abildskov JA, Burgess MJ, Millar K, Wyatt R, Baule G: The primary T wave. A new electrocardiograph^ waveform. Am Heart J 81: , Horan LG, Hand RC, Flowers NC, Johnson JC: The multipolar content of the human electrocardiogram. Ann Biomed Eng 4: , Wilson FN, Macleod AG, Barker PS, Johnston FD: The determination and the significance of the areas of the ventricular deflections of the electrocardiogram. Am Heart J 10: 46-61, Van Dam R Th. Durrer D: The T wave and ventricular repolarization. Am J Cardiol 14: , Lepeschkin E: Modern Electrocardiography. vol I, The P-Q-R-S-T-U Complex. Baltimore. Williams & Wilkins, 1951, pp Han J, Garcia de Jalon P, Moe GK: Fibrillation threshold of premature ventricular responses. Circ Res 18: 18-25, Abildskov JA: The sequence of normal recovery of excitability in the dog heart. Circulation 52: , Harumi K. Burgess MJ, Abildskov JA: A theoretic model of the T wave. Circulation 34: , Burgess MJ, Green LS, Millar K. Wyatt R, Abildskov JA: The sequence of normal ventricular recovery. Am Heart J 84: , Autenrieth G. Surawicz B, Kuo CS: Sequence of repolarization on the ventricular surface of the dog. Am Heart J 89: Autenrieth G. Surawicz B, Kuo CS. Arita M: Primary T wave abnormalities caused by uniform and regional shortening of ventricular monophasic action potential in dog. Circulation 51: Durrer D. Van Dam RTh, Freud GE. Janse MJ. Meijler FL. and Arzbaecher RC: Total excitation of the isolated human heart. Circulation 41: Cuffin BN, Geselowitz DB: Studies of the electrocardiogram using realistic cardiac and torso models. IEEE Trans Biomed Eng 24: , Lepeschkin E: The physiological basis of the U wave. In Advances in Electrocardiography, edited by R Schlant, JW Hurst. New York. Grune & Stratton, 1972, pp Watanabe Y: Purjinje repolarization as a possible cause of the U wave in the electrocardiogram. Circulation 51: , 1975 The Magnitude of the Electromotive Force of Canine Ventricular Myocardium SABURO MASHIMA, KENICHI HARUMI, AND SATORU MURAO SUMMARY The isolated and perfused dog heart was placed in a cubic container filled with Tyrode's solution. Ventricular ectopic beats were produced by electrical stimulation of the left ventricular wall, and initial QRS vectors of these beats were determined with orthogonal leads from the surface of the container. At the same instants, the activated area on the epicardial surface was measured by means of a large number of contiguous bipolar leads from the epicardial surface. The QRS vector and the activated epicardial area were found to be nearly porportional. By use of these results and a calibration system with artificial dipoles, the double layer moment of the ventricular activation wave was calculated as 0.13 ma - cm per unit area. This value corresponds to 60% of the maximal possible strength of the tissue electromotive force. Lowering the conductivity of the surrounding solution increased the QRS voltage but not as much as the potential caused by a constant-current dipole within the solution. The relationship between the QRS voltage and the conductivity of the medium was analyzed by a simplified model of the system and was found to correspond approximately to that of a constant-current source within a spherical heart with a resistivity 2 to 3 times that of Tyrode's solution. ONE OF THE fundamental determinants in electrocardiography is the strength of the electromotive force of the heart muscle. In terms of the conventional double layer representation for myocardial activation, the electrical moment of the double layer is essential both for quantitative interpretation and simulation studies of electrocardiograms. Although the electrical activity of single cardiac fibers have been studied rather extensively, relatively few data 1 " 4 are available at present on the absolute magnitude From The Second Department of Internal Medicine, University of Tokyo, Tokyo, Japan. Address for reprints: Saburo Mashima, M.D., The Second Department of Internal Medicine, University of Tokyo, Tokyo, Japan. Received August 29, 1977; accepted for publication January 31, of the electromotive force of myocardial tissue composed of differently directed fibers and interstitial space. Although derivation of the extracellular potential from action potential configuration and electrical constants of the surrounding media theoretically may be possible, 4 ' 5 the complex structure and activation of myocardial fiber aggregates necessitate simplified models for calculation. For overall activation of tissue having larger dimensions, the double layer model has been successfully applied to the interpretation of the clinical electrocardiogram. Hence, an experimental approach to the structure and the electrical moment of the double layer could be based on the measurement of remote potential, although the model may not be adequate to explain intramural potential variations. 3

2 758 CIRCULATION RESEARCH VOL. 42, No. 6. JUNE 1978 In addition to the strength of the double layer, information concerning the capability of the heart to supply electric current to the surrounding media also is necessary for quantitative electrocardiography. This problem is related to the internal resistance of the heart as a current source or to the extent to which the heart can be regarded as a constant current generator. In the present study, we experimentally determined the electrical moment of the ventricular activation wavefront in the isolated dog heart. Observations also were made on the effect of the conductivity of the surrounding medium on the measured potential. Certain theoretical considerations of the relationship of these observations to cellular electrophysiology were included. Methods Fourteen adult dogs were used. The dogs were anesthetized with pentobarbital sodium (25 mg/kg, iv). The heart was isolated, perfused through aorta with modified Tyrode's solution at 37 C, and immersed in the same solution in a cubic container with each edge 14 cm in length. Five silver electrodes were attached to each surface of the container, one at the center and others at the midpoint between the center to four edges (Fig. 1). These five electrodes were connected through 50 kfl resistors to constitute orthogonal X, Y, and Z leads. Uniformity of the lead field of each lead was checked with an artificial dipolar generator placed in the central region of the container. A shift of the dipole 2.5 cm from the center in the X, Y, and Z direction caused changes of less than 10% in the lead potential. We sutured to the lateral wall of the left ventricle a cross-shaped electrode array as shown in Figure 2. Two electrodes at the center served as stimulating electrodes to produce ventricular ectopic beats. Other electrodes, with interelectrode distance of 1 mm, were arranged in four directions from the center and used as pairs of contiguous bipolar leads to determine the local activation time of the myocardium. At a given instant, the circumference of the activation wavefront spreading from the central electrodes was assumed to be an ellipse, of which the long and short axes were obtained from the measurement of activation times. The ventricular complex in the lead from the surface of the container was amplified with high-gain DC amplifier and was observed on an oscilloscope and recorded photographically. In some of the experiments, an RC amplifier with the time constant longer than 2 seconds was used without significant distortion of the signal. Intensity of the oscilloscope beam was modulated by means of a train of pulses which produced bright spots on the beam 6 at 5- msec intervals after epicardial stimulation. Within a short period of time after the epicardial stimulation, the activation wavefront was considered to be hemispherical in shape, open only to the epicardial surface. The net effect of a double layer of this shape is equal to that of a planar layer with the same area as the epicardial opening. Up to 15 msec after epicardial stimulation, the signal was small and was sometimes not entirely free from the stimulus artifact. After 40 msec, arrival of activation at the endocardial surface might cause a discontinuity in the activation FIGURE 1 A cubic container of the perfused heart and surrounding solution. The lead X from the surface of the container is shown. Y and Z leads are constructed in a similar way. wave. Therefore, measurement was confined to the period between 20 and 40 msec after the stimulus. The spatial QRS voltage was determined from three orthogonal leads at 5-msec intervals. Since epicardial stimulation was applied to the lateral wall of the left ventricle, principal deflections appeared in the X lead. The spatial QRS voltage was divided by the area of the activation wave front at the same instant to give the voltage due to a unit area of the front. The system was calibrated with artificial dipoles. A dipole made of a thin insulated needle carrying two silver band electrodes was first placed in the X direction in the solution near the epicardial surface and a rectangular pulse of 10- to 20-msec duration was applied from a constant current generator. The resulting voltage in the X lead was measured at the plateau of the pulse. Then, the needle dipole was inserted radially in the X direction into the ventricular wall near the stimulating electrodes and the same measurement was made. Because the resistivity of muscles is higher than that of Tyrode's solution, the intramural dipole produced a larger voltage when the same amount of current was applied. The ratio of the effectiveness of intramural and outside dipoles was determined in six experiments and averaged 1.46:1. The eleclmm -21mm FIGURE 2 Schema of the electrode array which consisted of silver electrodes attached to cross-shaped flexible rubber holder. The central two electrodes serve for stimulation and the remaining for the bipolar recording.

3 ELECTROMOTIVE FORCE OF CANINE VENTRICLE/Mos/i/ma et al. trical moment of this needle-type dipole was difficult to determine, since the effective interelectrode distance could not be exactly measured because of possible electrode polarization. Hence, another dipole was constructed of a small Bakelite tube separated by an insulating barrier into two parts, each of which contained a silver electrode. The effective interpolar distance was easily determined for this dipole and the exact moment was readily calculated. The electrical moment of the needle dipole was calibrated with the tube dipole. This calibration system enabled us to express the electrical moment of the activation wave front in terms of ma cm per unit area. The second part of the experiments was concerned with evaluation of the conductivities of the solution surrounding the heart. An artificial dipole of the tube type was placed in the solution within the container, and more than 3 cm from the heart, and a rectangular pulse of constant current was applied. The extrasystolic QRS complex and the pulse artifact due to the dipole were recorded. Then, perfusion of the heart was stopped for a moment and the surrounding solution was rapidly replaced by isotonic glucose solution containing KG (2.7 mm/liter). Isotonicity and potassium concentration were maintained to protect the heart from injury. Care was taken to keep the temperature of the solution constant. Because of the higher resistivity of the new solution, the QRS voltage and pulse artifact were increased in height. After the recording was made, perfusion was reinstituted. Gradually, the surrounding solution was mixed with the perfusate and the conductivity grew higher. The perfusion was interrupted several times and the same recording procedure was repeated. The current applied to the artificial dipole was kept constant throughout the experiment, so that the amplitude of the pulse artifact was approximately porportional to the relative resistivity of the perfusing medium. Comparison of the QRS voltage with the aritificial pulse indicated the characteristics of the heart as a current source. In addition, in some of the experiments, another needle dipole was inserted into the left ventricular wall and was energized with a constant current pulse during the refractory period of the muscle. The artifact due to this intramural dipole also was recorded. The maximal QRS vector was usually used for comparison with the artificial pulse, since the configuration of the QRS complex usually was not significantly altered by the procedure. In some of the experiments, two additional vectors, early and late QRS, also 30m Sw FIGURE 3 The QRS complex in lead X of the ectopic beat originating from an epicardial site. Bright spots are spaced at 5msec intervals starting from the stimulus artifact. were examined. The early QRS vector was defined as the vector at the midpoint between the initiating stimulus and the maximum QRS voltage, in order to avoid errors from slight changes in the QRS duration caused by small changes in the environmental temperature on interruption of the perfusion. The late QRS vector was measured at an interval after the maximum vector which corresponded to that between the early and the maximum QRS vectors. Results Oscilloscope records with intensity modulation at 5msec intervals were obtained for the X, Y, and Z leads (Fig. 3), and the spatial QRS voltage was determined at each instant indicated by the bright spots. Measurements of the QRS voltage and the epicardial activation area were performed at 5-msec intervals between 20 and 40 msec after epicardial stimulation, and the result was plotted in Figure 4. Each of the lines in Figure 4 corresponds to the time course in one heart. It can be seen that the initial portion of the QRS vector roughly parallels the area of the activation front. The average value of the voltage per unit area of the activation front is listed in Table 1. At 20 msec after stimulation, the QRS voltage is still small and the standard deviation is rather large. In some of the experiments, the activation time of several endocardia! sites underneath the epicardial site of stimulation was measured and was found to be between 30 and 50 msec TABLE 1 The QRS Voltage per Unit Area of Epicardial Excitation Determined at 5-msec Intervals in Six Hearts Time after the stimulus (msec) Average SD (0.072)* ORS voltage divided by epicardial activated area (mv/cm 2 ) (0.017)* * Figures in parentheses are the results of 12 experiments

4 CIRCULATION RESEARCH 760 > VOL. 42, No. 6, JUNE a. X 100 FIGURE 4 The relation between the QRS voltage and epicardial activation spread. Measurements were made at 5-msec intervals starting at 20 msec after the stimulation epicardial activated area (mm 1 ) after the stimulus on most occasions. With larger epicardial areas of activation, curving of the electrode holder arms along the epicardial surface may cause overestimation of the activation area. The 30-msec value was considered as most reliable and an additional six hearts were examined only at this instant in time. From the average of all 12 experiments, the QRS voltage per unit area of the epicardial excited area was found to be mv. The system was then calibrated with artificial dipoles. The needle-type dipole inserted into the ventricular wall produced a voltage 1.46 times as large as that due to the same dipole in the solution. Then, the tube dipole was placed in the solution and energized by current adjusted to make the dipole moment 100 fxacm. The resulting voltage in the orthogonal leads amounted to 38 (JLV. Therefore, the electrical moment of the activation front at 30-msec instant was calculated as x ^ x 38 dipole in the solution but was comparable with the increase of P2 due to the dipole within the muscle. Figure 6 shows the relation of the increase in the maximal QRS voltage to the increase in the height of the pulse P, caused by the dipole in the solution. Results of eight experiments are shown in which the height of P, was increased more than eight times compared to the control. Both the QRS and pulse voltages are indicated as the ratio Control (Tvrock-I -r= 0.13 (ma-cm) 1.46 per unit area. Fourteen experiments were performed on 12 hearts with replacement of the surrounding solution by glucose solution. This procedure increased the QRS voltage, as shown in Figure 5. A rectangular pulse (Pi) preceding the QRS in Figure 5 is the potential created by an artificial dipole immersed in the solution away from the heart. The current to this dipole was kept constant throughout the experiment, so that the pulse P, on the record was approximately proportional to the resistivity of the surrounding solution. Another pulse (P2) near the end of the QRS in Figure 5 is due to a needle dipole inserted into the left ventricular wall. In Figure 5. the upper panel is the control record and lower panel is that obtained after the replacement of the solution. The increase in the QRS voltage was not as great as that of the pulse P, due to the Glucose + Tyrode sensit ivity.f FIGURE 5 The QRS complex and the two pulse artifacts due to dipolar generators placed in the solution away from the heart (PJ and inserted into the ventricular wall (Pi). Upper panel: control with Tyrode's solution. Lower panel: effect of the solution with lower conductivity.

5 ELECTROMOTIVE FORCE OF CANINE VENTRICLE/M<w/»ma et al. 761 QRS 7 - _ 4 FIGURE 6 Comparison of the increase in the QRS voltage and that in the pulse artifact due to an artificial constant-current dipole produced by lowering the conductivity of the surrounding solution. Voltages are indicated as the ratio to the control value with regular Tyrode's solution. Each of the solid lines represents results of one experiment. Broken lines show the theoretical relation between the remote voltage and the conductivity of the medium for several values of the resistivity of the heart. See text. pulse of the test to the control condition. It can be seen that the increase in the QRS voltage was approximately 4 times with the medium of about 10 times higher resistivity. The broken lines in Figure 6 show the theoretical relation derived from the simplification of the system. The heart was considered as a spherical mass with conductivity different from that of the surrounding medium. The voltage due to a constant current source within the heart was calculated as (see Appendix) V = I +2r m + 2 r m /r o where r m and r () are the resistivity of the heart muscle and the surrounding solution with respect to the Tyrode's solution. Since r o is indicated by the height of the pulse P, in Figure 5, broken lines in Figure 6 were drawn according to the relation of V and r o, for several values of r m (1, 2, 4, 8, and infinity). As indicated in Figure 6, the observed relation of maximal QRS to the external resistivity follows the analytical curves fairly well in most cases, with r m values between 2 and 4. Fitting the experimental values to the equation above, the r m value was calculated on the least squares basis for each experiment. The average value of r m for all the experiments was 2.6 ± 0.6. Changes in the QRS configuration were not marked in most of the experiments with lowering of the conductivity of the medium. Nevertheless, the voltage at two additional instants, early and late QRS, was measured and the same analysis was made. The results are shown in Table 2. Sometimes slight changes in the temperature and temporary interruption of perfusion caused minor changes in the QRS duration and the distortion of the QRS configuration. Early and late QRS measurement was discarded in such cases. Table 2 also shows the same analysis of the pulse artifact due to the intramural dipole (P 2 in Fig. 5). It can be seen that early and maximal QRS, as well as the pulse of intramural dipole, were increased in voltage in a similar way. The increase of the late QRS was somewhat smaller, and sometimes deviated from the theoretical relation. These results are in accord with at least the earliest half of the QRS complex being produced by a constant current source within the ventricular wall. The r m value in Table 2 is the ratio of the resistivity of the heart and Tyrode's solution. Since Tyrode's solution used in this study had a resistivity of 62 fl cm, an r m value of 2.6 corresponds to 160 fl cm for the heart muscle. However, this does not mean the actual myocardial resistivity, but the effective resistivity of the equivalent spherical model of the heart (see Discussion and Appendix). Discussion To calculate the double layer moment, the spatial QRS voltage and the area of the epicardial activation spread 30 TABLE 2 Relative Resistivity (r m ) of the Equivalent Spherical Heart Early QRS Maximal QRS Late QRS Artificial pulse Results are expressed as mean ± SD. 2.6 ± ± ±

6 762 CIRCULATION RESEARCH VOL. 42, No. 6, JUNE 1978 msec after the stimulus were considered as most reliable. The earlier QRS vector is smaller in voltage and is susceptible to measurement errors, while, at later instants, accurate determination of the area of the activation front is difficult because of the endocardial breakthrough of the activation. Between 20 and 40 msec after the stimulation, roughly parallel increases in the QRS voltage and the excited area were observed. Moreover, at 25 and 30 msec, on the average, the QRS voltage per unit area of activation front was similar. These results seemed to justify the use of 30-msec data for the calculation. Generally, the strength of the double layer depends on the structure of the tissue and the pattern of impulse propagation in that region. The existence of the Purkinje network in the subendocardial layer may cause irregularities in the activation process and a reduction of the electrical moment of the double layer. Uniformity of the electrical moment of the layer is a simplifying assumption but is supported by Reynolds and Weller's experiments' on ectopic beats of the dog heart. Moreover, the resultant vector up to 40 msec after the epicardial stimulation was observed in this study to be approximately proportional to the epicardial activated area. Hence, the value obtained here seems to represent the uniform strength or, at least, the averaged effective electrical moment of the double layer of ventricular activation. A maximal possible value of the tissue electromotive force can be estimated from available cellular electrophysiologic data as follows: Figure 7 shows a schematic drawing of a single fiber as a current source. Suppose the activation proceeds from left to right in the figure in the direction of X. The shaded area in the figure represents the width of the activation wavefront. The intracellular potential difference between the depolarized portion, a, and the resting portion, b, is then indicated by the height of action potential, V. Let the resistivity of the intracellular space be en, the axial current ii from a to b is then A calculated as a t V, where A is the cross-sectional area d of the fiber and d is the width of the activation wave. The total amount of the extracellular current must be equal to the intracellular current but in the opposite direction. The numerical value of <r t has been reported by Weidmann 7 as 470 fl cm for the trabecular muscle of the right ventricle. The height of the action potential is approximately 100 mv. From these values, the moment of a hypothetical thick fiber with the cross-sectional area of 1 cm 2 can be calculated as 100 =0.21(mAcm) where d is cancelled out because the moment is defined as the current multiplied by the distance. The dipole moment value corresponds to the excitation of the tissue with parallel fibers devoid of interstitial space, so that it may be regarded as the maximal possible moment of myocardial tissue. More strictly, the axial current i t within the fiber is not uniform along the fiber. The contribution of a small fiber length, dx, to the dipole moment is i,dx, and the integral of i dx = dv/cr, leads to the same results. Actual tissues are composed of randomly directed fibers and interstitial space. The direction of propagation of FIGURE 7 Schematic drawing of a hypothetical muscle fiber with cross-sectional area A in the direction X. The shaded area is the activation wave width, d. The axial current, ; ( flows in the intracellular medium of the conductivity a t. Portions a and b of the fiber are in excited and resting state, respectively, with the voltage difference V between a and b. activation is not necessarily the same as the direction of conduction in individual fibers. The value obtained experimentally in this study amounted to 60% of the maximal value estimated above and seems to be reasonable. The calculation above is clearly an oversimplification. Nevertheless, it gives an insight into the relationship between the cellular events and the extracellular potential. The intracellular conductivity <T X has a direct influence on the extracellular current flow. Recent work by demello 8 suggested the possibility that en could increase with a higher intracellular Ca 2+ concentration, which might have a profound effect on the extracellular potential. There have been several reports'" 5 on the relationship between the direct intramural potential and the electrogenesis of the heart muscle. Analyses of the relations of the action potential and the moment of the double layer have been given by Plonsey, 4 with respect to the intramural potential. The latter is, however, influenced by many factors including the size of the recording electrodes, the local activation pathway, and the conductivity of the tissue, which make interpretation difficult. Solomon and Selvester 3 found the waveform of intramural leads not readily explained by a simple double layer model. For the interpretation of the extracardiac potential, however, the double layer has a more authentic basis. Hence, from the practical standpoint, in this study, the moment of the double layer was determined from remote leads in terms of ma-cm. The dipole moment of the whole dog heart has been measured by Nelson et al. 9 as 1.27 ma-cm for the maximal QRS vector. Although the configuration of the activation wave at that instant is not known, the FIGURE 8 Simplified model of the system. The leads are assumed to have parallel flow lines and the heart is considered as a spherical inhomogeneity in the conductivity. E, and E 2 are the electric field inside and outside the sphere; cr, and <r 1 are the conductivity inside and outside the sphere, respectively.

7 ELECTROMOTIVE FORCE OF CANINE VENTRICLE/Masfoma et al. 763 effective area of the activation front was 10 cm 2 on the basis of the results of this study. To express the strength of the electromotive force as a current dipole implies constancy of the current supply by the myocardium. It is well known that the action potential of a single cardiac fiber is not readily affected by ordinary changes in extracellular conditions, which suggests a constant amount of axial current ii. However, the heart as a whole cannot be regarded as a constant current generator, as indicated by the present study with media of different conductivities. Regarding the whole heart as an electric generator, the internal resistance will be determined by the resistivity of the cardiac tissue. The experimental results indicated that the resistivity of the equivalent spherical heart was about 160 fl cm. This figure is smaller than the reported value of myocardial resistivity. 10 However, the value of r m in this study is not identical the resistivity of the tissue, but is only an empirical index of internal resistance of the equivalent spherical heart. The late QRS sometimes deviated from the theoretical curves based on the model, probably because the geometry of the activation wave in interventricular septum and right ventricle is more complicated in shape and is distant from the stimulating electrodes. In addition, experimental errors are larger with the late QRS voltage, which is susceptible to minor conduction delay. Appendix To obtain analytical relations, certain simplification of the system will be made. The heart is assumed to be a sphere with conductivity cr, immersed in the solution with conductivity cr 2. Consider an ideal lead with parallel lead flow lines (Fig. 8). When the steady current I is impressed on the lead, the electric field inside the sphere E, and in the outside solution remote from the heart E 2 obey the following relation, according to the classical example of the potential theory" E2 3 cr 2 2o- 2 (1) The reciprocity theorem 12 states that the sensitivity of this lead to the generator inside and outside the heart is proportional to E, and E 2, respectively. If the lead X in the present experiment is reciprocally energized with current I, the induced electric field remote from the heart is proportional to I/cr 2, and the field inside the heart to 31/ O-, + 2 cr 2. Hence, the voltage due to the constant current dipole located outside is proportional to I/o- 2, and that in the heart to 3/cr, + 2 cr 2. Denoting the control conductivity of Tyrode's solution by <z 0, a change in the outside conductivity from <x 0 to cr 2 will change the QRS voltage by the factor cr, + 2 a 0 <T cr 2 Expressing the conductivity by the ratio to that of regular Tyrode's solution (a,, = 1), and introducing the resistivity of the heart muscle r m = 1/cr, and that of the outside solution r,, = l/cr 2, the relation (Equation 1) above is transformed as v = ' + 2 r "_ (2) r m /r o ' V ; where V is the ratio of the resulting voltage to the control voltage with regular Tyrode's solution. Broken lines in Figure 6 illustrate this relation between V and r o. The spherical inhomogeneity considered above is, although simple, not the only model for the interpretation of the experimental results. For instance, a spherical shell seems to simulate the heart more closely. 13 Suppose a concentric spherical shell is located in an infinite medium and a parallel field E (l is applied from the outside. Taking the x axis in the direction of impressed field, the ratio of the x component of electric field E x within the shell to E o is, according to the boundary conditions, 14 2 cr 2 3 er 2 2 cr 2 cr, cr 2 cr 3 O", cr 2 cr 2 cr 3 3 cr 2 $(>- )] where r is the distance from the center, cr,, cr 2, and cr ;! are the conductivities of outside, intramural, and cavitary media, respectively. As indicated in Equation 3, the electric field varies with location inside the shell. Reciprocally, this means the effectiveness of the dipolar generator depends on its location in the ventricular wall. However, the influence of the outside conductivity cr, on the remote potential can be shown as nearly uniform over locations of the generator under the condition corresponding to the present experiment. As the cavitary fluid was regular Tyrode's solution throughout the experiment, <r a was replaced by unity. The geometry of the shell was arbitrarily chosen as 2a = b. Then, corresponding to curves in Figure 6, the relationship between Ex and cr, was evaluted for several locations within the shell. Results indicated that this model gave curves similar to those in Figure 6 with only small variations for different locations in the shell. References 1. Reynolds EW, Weller DA: An experimental study of the electromotive forces of the heart. Am Heart J 69: 56-61, Vander Ark CR, Reynolds EW: An experimental study of propagated electrical activity in the canine heart. Circ Res 26: , Solomon HC, Selvester RH: Current dipole moment density of the heart. Am Heart J 81: , Plonsey R: An evaluation of several cardiac activation models. J Electrocardiol 7: , Spach MS, Barr RC, Serwer GA, Kootsey JM, Johnson EA: Extracellular potentials related to intracellular action potentials in the dog Purkinje system. Circ Res 30: , Sato C, Mashima S, Harumi K, Murao, S: The preset timer and its application. J Electrocardiol 3: , Weidmann S: Electrical constants of trabecular muscle from mammalian heart. J Physiol 210: , demello, WC: Effect of intracellular injection of calcium and strontium on cell communication in heart. J Physiol 250: , Nelson CV, Angelakos ET, Gastonguay PR: Dipole moments of dog. monkey and lamb hearts. Circ Res 17: , Rush S, Abildskov JA, McFee R: Resistivity of body tissues at low frequencies. Circ Res 12: Jeans JH: The Mathematical Theory of Electricity and Magnetism. Cambridge University Press, 1927, pp Plonsey R: Reciprocity applied to volume conductors and the ECG. IEEE Trans Biomed Electron 10: 9-12, McFee R, Rush S: Qualitative effects of thoracic resistivity variations on the interpretation of electrocardiograms: The "Brody effect." Am Heart J 74: , Weber E: Electromagnetic Theory. Static Field and Their Mapping. New York, Dover Publications, 1965, pp