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Abstract This study tested the prediction of bidomain models that unipolar stimulation of anisotropic myocardium produces transmembrane voltage changes (ΔVms) of opposite signs away from the electrode on perpendicular axes. Stimulation with a strength of 0.1 to 40 mA was applied from a point electrode on the left or right ventricle of isolated perfused rabbit hearts at 37°C to 38°C stained with the potentiometric dye di-4-ANEPPS. A laser scanner system recorded Vm-sensitive fluorescence at 63 spots in an 8×8-mm region around the electrode. Cathodal stimulation in the refractory period produced regions of −ΔVm 1 to 5 mm away from the electrode on an axis oriented parallel to the fast propagation axis to within 1.8±11° (P≥.7 for difference versus zero, n=7). Recording spots in these regions underwent +ΔVm when anodal stimulation was used. At recording spots on the slow propagation axis, cathodal stimulation produced +ΔVm and anodal stimulation produced −ΔVm. During diastolic stimulation, early excitation occurred near the electrode for cathodal stimulation or on the fast propagation axis as far as 2.8±1 mm away from the electrode for anodal stimulation. A “dog-bone” region of +ΔVm that included tissue near and away from the electrode on the slow propagation axis occurred when cathodal stimulation was given in diastole. Regions of +ΔVm occurred away from the electrode on the fast propagation axis when anodal stimulation was given in diastole. Thus, ΔVm differs in regions along and across myocardial fibers, indicating that ΔVm depends on anisotropic bidomain properties. Sites of early excitation are those where +ΔVm occurs, indicating that membrane channel excitation depends on the distribution of ΔVm.
Effects of electrical stimulation of the heart, such as the production of an action potential, reentry, defibrillation, or cardioversion, are thought to result from changes in transmembrane ion channels, whose states depend on the transmembrane voltage produced during the stimulation. In spite of its leading role in stimulation, the transmembrane voltage during stimulation of the mammalian heart has not been defined. In isolated cardiac fibers, intracellular microelectrode techniques indicated a distribution of transmembrane voltages that agrees with predictions of the classic one-dimensional cable model in which cathodally induced depolarization decreases exponentially with distance from the electrode.1 However, this distribution may not occur in the heart, but instead, a more complicated distribution that includes virtual electrode effects may occur. The virtual cathode is the region near an extracellular cathodal stimulation electrode in which the membrane is depolarized by the stimulation current. Propagation is thought to begin at the edge of the virtual cathode region, where the depolarization is just large enough to excite regenerative inwardly directed ionic current.2 The first measurements of the virtual cathode in the heart were obtained by linear back-extrapolation of activation arrival times to the time of stimulation in dog hearts. This indicated that the edge of the virtual cathode was a dog-bone shape that extended farther in the direction parallel to the slow propagation axis than in the direction parallel to the fast propagation axis. In two-dimensional rabbit or frog heart, optical techniques3 using fluorescent dye to measure transmembrane voltages during the application of stimulation current indicated a distribution of transmembrane voltage that includes reversals of polarization, ie, transmembrane voltage changes having different signs at different distances away from the stimulation electrode.4 5 Thus, regions of hyperpolarization, ie, virtual anodes, may occur during cathodal stimulation as well as a virtual cathode.
Mathematical bidomain models of stimulation in two- or three-dimensional myocardium that have incorporated resistance anisotropy representative of resistance measurements from mammalian trabecular muscles6 have predicted a reversal of polarization along the fiber axis.7 8 The reversal is consistent with measurements along fibers in rabbit epicardium.4 The models predict further that a reversal of polarization does not occur across the fiber axis; hence, polarizations of opposite sign exist away from the electrode on perpendicular axes. Optical measurements in frog ventricle indicate that reversal of polarization occurs in most directions,5 a finding that differs from the bidomain prediction of reversal on just one axis and may reflect differences in frog ventricular tissue compared with the myocardium for which the model calculations have been performed. Recent measurements in frog atrial preparations, which contain fiber structure, are consistent with the model predictions.9 Also, the extracellular measurements of activation times in canine myocardium support the bidomain predictions.2 The studies described above have indicated that polarization in the heart may be very different from that in one-dimensional fibers. Measurements of polarization in regions along and across fibers in anisotropic mammalian myocardium that could directly test the bidomain predictions have not been reported.
This article describes polarization measurements in anisotropic rabbit hearts. A laser scanner system10 recorded transmembrane voltage–sensitive dye fluorescence at 63 sites encompassing a stimulation electrode. The hypothesis that reversal of membrane polarization occurs along but not across fibers was tested. Also, the hypothesis that excitation during anodal or cathodal stimulation begins where the polarization is positive was tested.
Materials and Methods
Seven isolated New Zealand White rabbit hearts were Langendorff-perfused at 37°C to 38°C with solution containing (mmol/L) NaCl 129, KCl 4.5, CaCl2 1.8 , MgCl2 1.1, NaHCO3 14, Na2HPO4 1, and glucose 11, bubbled with 95% O2/5% CO2, at a pH of 7.3 to 7.4 and an aortic pressure of 80 cm H2O. Where indicated in figure legends, diacetyl monoxime was added to lessen motion effects in optical recordings.11 12 Intrinsic activation rate was slowed by cutting the right atrium to allow pacing at an interval of 300 to 315 ms. A transparent polycarbonate (Lexan) plate contacted the recording region to lessen movement, hold the region flat, and eliminate possible effects of solution on the epicardium (Fig 1a⇓). Plate pressure was lower than perfusion pressure to avoid occlusion of epicardial vessels.
Hearts were stained for 10 to 20 minutes with pyridinium 4-(2-(6-(dibutylamino)-2-naphthalenyl)ethenyl)-1-(3-sulfopropyl) hydroxide (di-4-ANEPPS, Molecular Probes, Inc) added to the perfusate as dye-saturated ethanol4 to produce a final dye concentration of 2 μmol/L. Transmembrane voltage changes were determined from fluorescence recordings with a laser scanner system.10 An argon laser beam with an intensity reaching the heart of 4.9±2.7 mW during recordings and a wavelength of 514 nm was steered with acousto-optic deflectors to scan 63 spots having diameters of 100 μm in an 8×8-mm region of the anterior epicardium. Fluorescence that followed changes in transmembrane voltage at the spots13 passed through a 590-nm long-pass filter and into a photomultiplier tube.
An evaluation of the thickness of myocardium that contributes to fluorescence was performed. A ventricular strip was removed from a rabbit heart stained with di-4-ANEPPS by arterial perfusion. A wedge of myocardium was produced by removing part of the ventricular wall of the strip so that the strip was thin at one end and became thicker away from the end. The strip was then placed on a wet microscope slide with the epicardial surface facing up. The laser beam was initially aimed just off the thin end and then was moved in 0.5-mm increments toward thicker myocardium. At each spot, the fluorescence intensity was measured with a photomultiplier tube having the same long-pass glass filter that was used during the experiments. After measurements, the tissue was placed under a dissecting microscope with a reticle, and the thickness along the strip was measured at 0.5-mm increments. The increase in fluorescence with increased thickness indicated the contribution of the deeper cell layers. A graph of fluorescence as a function of thickness is shown in Fig 1a⇑. Most of the increase in fluorescence occurred when the thickness was increased from 0 to 300 μm. This indicates that the estimated thickness of the tissue that contributed to the fluorescence was ≈300 μm.
The fluorescence signal was filtered at 80 000 Hz, which allowed the signal to settle quickly each time the laser beam moved to the next spot. The signal was digitized at a sampling rate of 64 000 Hz. Each sample was taken just before the beam moved to the next spot. Every millisecond, the beam completed a scan of all 63 spots, and one sample was taken of a voltage signal proportional to the stimulation current. The samples were then demultiplexed to obtain individual recordings with a sampling interval of 1 ms for each spot. Fluorescence changes during action potentials recorded with the system have been described previously.4 10 12
Membrane Polarization by Unipolar Stimulation
A chlorided silver unipolar test stimulation electrode with diameter 0.1 mm initially and 0.25 mm in later experiments (to allow higher stimulation current) was positioned with a micromanipulator so that the tip passed through a hole in the plate at the center of the recording region. A 2-cm2 silver coil return electrode on a flexible arm contacted the posterior epicardium. While the recording spots were viewed with a ×2.7 binocular loupe, a mirror that reflected laser light to the heart was adjusted so that the four central spots were just outside of the hole in the plate and the electrode lead did not block laser light for any spots.
Hearts were paced with 16 stimuli at an interval of 300 ms. The pacing stimuli were 1-mA pulses applied from a unipolar electrode on the lateral left ventricle or 9-V pulses applied from parallel 2×12-mm stainless steel mesh electrodes 1 cm apart on opposite sides of the recording region. A unipolar 10- to 20-ms test stimulation of 15 to 40 mA and either polarity was given during the refractory period of the last action potential. The test stimulation timing was chosen so that membrane polarization7 was not obscured by excitation.4 14 Tissue damage was minimized by alternating the test stimulation polarity to maintain AgCl on the electrode and minimizing the number of test stimulation pulses by recording continually during each consecutive millisecond at all laser spots. Also, no signal averaging was used, which further lessened the number of stimulation pulses. The perfusing solution contained 20 mmol/L diacetyl monoxime during recordings that were used to determine the polarization.
Excitation by Unipolar Stimulation
Fluorescence recordings were obtained of excitation produced by anodal or cathodal diastolic stimulation from the unipolar test electrode. Stimuli 20 ms in duration were given at an interstimulus interval of 315 ms and strengths of 0.1 to 10 mA. Diacetyl monoxime was not present in the perfusing solution during recordings that were used to determine excitation times and axes of fast and slow propagation.
In two rabbit hearts, regions were removed from the anterior ventricular walls, fixed with phosphate-buffered 10% formalin, embedded in paraffin, and cut into sections 5 μm thick and approximately parallel to the epicardium. Every 20th section from left ventricles was mounted on a slide and stained with hematoxylin and eosin. An Olympus Vanox AH-3 microscope equipped with a video monitor and Image I analysis software (Universal Imaging Corp) was used to determine fiber orientation.
Polarization at each spot was determined as the difference between fluorescence at the end of the test stimulation pulse and fluorescence at the same time relative to the action potential phase-zero depolarization in the previous action potential that did not receive test stimulation. Excitation time at each spot was determined at the steepest part of the depolarization just after the onset of diastolic stimulation from the test electrode. All measurements of polarizations and excitation times were obtained from unsmoothed recordings. Contours of polarization and excitation times were generated by Surfer (Golden Software, Inc), with an interpolation grid density of 0.3 mm. The regional variability theory technique of Kriging15 was used, which takes into consideration the correlation between values of the surface at short distances. Numerical results are given as mean±1 SD. Significance of the largest distance of a spot away from the electrode that underwent early excitation during anodal stimulation was determined with a two-tailed Student’s t test. Significance of differences between angles of fast propagation axes and axes of reversed polarization was determined with a paired two-tailed Student’s t test.
Membrane Polarization During Unipolar Stimulation
In seven hearts, membrane polarization during unipolar test stimulation given in the center of the recording region during an action potential was measured. Fluorescence recordings contained a pacing-induced action potential with no test stimulation and a pacing-induced action potential that received the test stimulation. Fig 2⇓ shows simultaneous recordings of action potentials that received 40-mA cathodal test stimulation. The recordings are arranged to correspond to the locations of their laser spots. The time of test stimulation is indicated above each column. The stimulation produced negative transmembrane voltage changes in regions away from the electrode on the axis from the upper left to lower right. The approximate locations of the regions are indicated by minus signs. Since cathodal stimulation is known to produce positive transmembrane voltage changes immediately adjacent to or under the electrode,4 5 the regions of negative transmembrane voltage changes were defined as reversed polarization regions. The stimulation produced positive transmembrane voltage changes in regions denoted by plus signs on a perpendicular axis, indicating that the polarization was not the reverse of that occurring under the electrode. An action potential that may have begun near the return electrode entered the lower left part of the recording region 91 ms after the stimulation.
Recordings of action potentials that received 40-mA unipolar anodal test stimulation are shown in Fig 3⇓. Test stimulation and recording locations were the same as in Fig 2⇑. Perpendicular axes contained regions of transmembrane voltage changes having opposite signs. Orientations of the axes were the same as those during the cathodal stimulation. Directions of transmembrane voltage changes at most recording spots were reversed compared with the cathodal stimulation. Since anodal stimulation produces negative transmembrane voltage changes immediately adjacent to or under the electrode,4 5 regions containing positive transmembrane voltage changes on the axis from the upper left to lower right were defined as reversed polarization regions. The polarization away from the electrode on the perpendicular axis was not the reverse of that occurring under the electrode.
Fig 4⇓ shows examples of measurements and contour maps of the transmembrane voltage changes produced by 15-mA unipolar test stimulation in another heart. Stimulation and recording locations were the same for both maps. Test stimulation was given 24 ms after the phase-zero depolarizations in the center of the recording region. The transmembrane voltage changes at each laser spot are indicated. Regions of reversed polarization occurred that were consistent with the results in Figs 2⇑ and 3⇑. Reversed polarization existed in the upper left and lower right of each map in which cathodal stimulation produced negative transmembrane voltage changes and anodal stimulation produced positive transmembrane voltage changes. Centers of reversed polarization regions were ≈2.5 mm away from the stimulation electrode. On the axis perpendicular to the axis containing reversed polarization regions, stimulation either had no effect, or cathodal stimulation produced positive transmembrane voltage changes and anodal stimulation produced negative transmembrane voltage changes.
In all of the seven left ventricles and the two right ventricles, which were studied after trials were completed on left ventricles, regions of reversed polarization 1 to 5 mm away from the electrode were found on one axis, and regions where polarization was not reversed 1 to 5 mm away from the electrode were found on a perpendicular axis. Thus, opposite polarizations occurred away from the electrode on perpendicular axes. These findings were not due to the method of pacing to produce the action potentials that received the test stimulation, since the pacing was performed on the lateral left ventricle away from the recording region in five of the hearts or with electric field stimulation at the recording region in two of the hearts.
Excitation by Unipolar Stimulation
Excitation after the onset of anodal or cathodal diastolic stimulation from the test electrode was studied. Examples of excitation times and isochrone contour maps of excitation produced by cathodal stimulation are shown in Fig 5a⇓. Stimulation near threshold strength (upper map) produced excitation at the four spots nearest to and surrounding the electrode 5 to 7 ms after the onset of the stimulation pulse and an approximately elliptical activation front in which the long axis was the fast propagation axis and the short axis was the slow propagation axis. When cathodal stimulation strength was increased to 8 mA (lower map), excitation at the four spots nearest to and surrounding the electrode occurred simultaneously with the onset of the stimulation pulse to within 1 ms. Propagation still occurred; however, the eccentricity of the activation front decreased near the electrode. In the four left ventricles and one right ventricle in which cathodal stimulation was studied with strengths from below the threshold strength to a maximum of 10 mA, early excitation during cathodal stimulation consistently occurred at the spots closest to the stimulation electrode.
Excitation times at the six spots >1.5 mm above or below the stimulation site that were closest to the fast propagation axis were plotted versus the distance from the stimulation site (Fig 5b⇑). The slopes of linear regressions, which indicated propagation velocities along the fast axis, were 46 cm/s for the 0.2-mA stimulation and 36 cm/s for the 8-mA stimulation. Similar analyses for spots near the slow propagation axis indicated that the propagation velocity was 16 cm/s for both stimulation strengths.
Fig 6⇓ shows measurements and contours of polarization at different times during the 8-mA cathodal diastolic stimulation. A dog-bone pattern of positive polarization oriented on the slow propagation axis occurred after the onset of stimulation. By the 8th millisecond after the onset, the dog-bone pattern had enlarged and changed significantly because of excitation at many spots. Slight negative polarization occurred at spots away from the electrode on the fast propagation axis during the 2nd and 4th ms after the onset. These spots then underwent depolarization that propagated along the fast axis (Fig 5b⇑). After the propagation, these spots remained relatively hyperpolarized for the duration of the stimulation pulse and approached their action potential plateau after the end of the pulse.
Excitation times and isochrone contour maps of excitation produced by anodal diastolic stimulation are shown in Fig 7⇓. Stimulation and recording locations were the same as in Fig 5⇑. Stimulation near the anodal threshold strength (Fig 7⇓, upper map) produced early excitation away from the electrode on the fast propagation axis. When anodal stimulation strength was increased to 8 mA (lower map), excitation times decreased and early excitation still occurred at spots away from the electrode on the fast propagation axis. In all of the four left ventricles and one right ventricle that were studied with anodal stimulation strengths in the range from below the threshold strength to a maximum of 10 mA, the anodal stimulation consistently produced early excitation at spots away from the electrode on the fast propagation axis. The largest distance of a spot away from the electrode that underwent early excitation in the five ventricles was 2.8±1 mm (P=.002 for distance versus zero, n=5). The propagation velocities on the slow axis for the 1- and 8-mA anodal stimulation were 19 and 18 cm/s, respectively.
Fig 8⇓ shows measurements and contours of polarization at different times during the 8-mA anodal diastolic stimulation. During the first 4 ms after the onset of stimulation, rapid positive polarization occurred at spots away from the electrode on the fast propagation axis. Polarization at spots 2 to 3 mm from the electrode site on the fast axis was larger than polarization at the four spots closest to the electrode, consistent with early excitation away from the electrode along fibers. During the remainder of the stimulation pulse, regions away from the electrode on the slow propagation axis underwent progressively more positive polarization consistent with slow propagation across the myocardial fibers. By the 18th ms, which was after excitation had occurred at most of the recording spots, polarization at spots away from the electrode on the fast propagation axis was more positive than the action potential plateau, whereas polarization near or away from the electrode on the slow propagation axis was less positive than the plateau. Polarization at these spots then approached the action potential plateau during the 8 ms after the pulse ended.
Comparison of Reversed Polarization Axis With Fast Propagation Axis
Orientations of the axis passing through centers of regions of reversed polarization during 15- to 40-mA stimulation in the refractory period and the axis of fast propagation during ≈0.2- to 1-mA cathodal diastolic stimulation from the test electrode were determined in five left ventricles and two right ventricles. Angles of axes relative to a common side of the array of laser spots were determined. Differences between angles of the fast propagation axes and the axes that contained reversed polarization were 1.3±11° for anodal stimulation in the refractory period (P=.78 for difference versus zero, n=7) and 1.8±11° for cathodal stimulation in the refractory period (P=.7 for difference versus zero, n=7).
Orientation of Fibers
Fig 9⇓ shows photomicrographs of sections near the anterior epicardial surface of rabbit ventricles. The myocardium in both the left and right ventricles contained fibers. In two hearts, sections from the anterior left ventricular epicardial surface indicated fiber orientation from the left lateroapical region to the right laterobasal region at an approximate angle of 30±14° relative to the equatorial plane of the heart. This angle was similar to the angle of the fast propagation axis for cathodal diastolic stimulation on the anterior left ventricle in six hearts, which was 28±12° relative to the equatorial plane. Serial sections from different depths in the left ventricular wall of two hearts indicated that fiber orientation rotated counterclockwise with increasing depth relative to the epicardial surface. The rotation at a depth of 0.3 mm was 6±8°. Rotation as large as 75±29° relative to the epicardium was found near the endocardium.
This is the first report of membrane polarization in the region surrounding the electrode during unipolar stimulation in anisotropic mammalian myocardium. The polarization is different from that in one-dimensional myocardial preparations. In isolated trabecular muscles or Purkinje fibers, polarization decreases approximately exponentially in accordance with the fiber space constant and becomes zero at a sufficient distance from an electrode. The polarization does not change sign except near an electrode of the opposite polarity.1 16 17 18 In rabbit hearts, polarization just a few millimeters away from the electrode in the fiber direction was found to be negative for cathodal stimulation and positive for anodal stimulation, which is the opposite of polarization immediately adjacent to or under the electrode.4 5 Thus, a sign change occurred in the direction of fibers, which is shown in Figs 3⇑ and 4⇑. In the direction perpendicular to fibers, polarization was found to be positive for cathodal stimulation and negative for anodal stimulation, which is the same as polarization under the electrode. Thus, no sign change occurred in the direction perpendicular to fibers. Contour maps and measurements at laser spots in Figs 4⇑, 6⇑, and 8⇑ show the regions away from the electrode in the direction parallel to fibers in which polarization changed sign and the dog-bone–shaped region perpendicular to fibers in which hyperpolarization occurred during anodal stimulation or depolarization occurred during cathodal stimulation.
In experiments with frog ventricle, polarization changes sign away from a point electrode.5 The sign change occurs in most directions, which differs from results in rabbit hearts and predictions of bidomain models in which the sign change occurs only in the fiber direction. Differences in the methods used in the frog and rabbit experiments, eg, superfusion of myocardium versus arterial perfusion, may affect the stimulation current pathway and polarization. Also, the different results may represent differences in ventricles of different species.19 Bidomain models predict that direction dependence of polarization requires myocardial fiber structure with distinct longitudinal and transverse axes.7 8 Such fiber structure exists in rabbit hearts, as evident from elliptical activation isochrones (Fig 5a⇑) and myocardial sections (Fig 9⇑). Fiber structure was not documented in the study of frog ventricle.5 Recent results from frog atria, which had fiber structure, are consistent with the bidomain prediction.9 Direction dependence of polarization in rabbit hearts occurred in both ventricles, consistent with the idea that anisotropic fiber structure, present in both ventricles, is important for polarization. The importance of fiber structure for polarization is further supported by the finding that the axis on which the sign changes occurred in rabbit hearts was not significantly different from the fast propagation axis.
Myocardial sections indicated that fibers rotate counterclockwise from epicardium to endocardium in rabbit left ventricle, which is the same direction that fibers rotate in the left ventricle of dog hearts.20 Membrane polarization and excitation still occurred in the manner predicted by bidomain models that have not incorporated fiber rotation. Perhaps the rotation is not a major factor in the effects that were measured. Rotation within the estimated thickness of myocardium that contributed to the fluorescence was small (mean rotation of 6°). Also, intracellular and extracellular resistances in the direction toward deeper fibers are probably high because that is a transverse direction. High resistances would lessen both the amount of stimulation current that reaches deeper fibers and the interactions among fibers having different depths.
The distribution of polarization that was predicted for two-dimensional myocardium7 is not qualitatively different from that for three-dimensional myocardium,8 which indicates that the third dimension may not greatly influence the polarization. This is consistent with the fact that the predicted polarization was found on both right and left ventricles, even though more fibers exist below the epicardium on the left ventricle. The activation pattern in Fig 7⇑ may not result from excitation of deeper layers underneath the stimulation electrode, with breakthroughs occurring at a certain distance from the electrode. Since depolarization does not occur away from the electrode transverse to fibers during anodal stimulation, depolarization is not expected away from the electrode in the direction toward deeper layers. This is consistent with calculations indicating that the polarity reversal does not occur in the direction toward deeper layers in a three-dimensional myocardial model (Fig 2⇑ of Reference 88 ). Finally, if excitation occurred in deeper layers under the electrode, the earliest breakthrough would be expected at the spots nearest the electrode, since propagation distance to those spots would be smallest. The early excitation in Fig 7⇑ was not an artifact introduced by smoothing or inadequate sampling, since time differences larger than the sampling interval of 1 ms occurred, particularly for the 1-mA stimulation, and the measurements were obtained from unsmoothed recordings.
According to bidomain models of two- or three-dimensional anisotropic myocardium, the presence or absence of sign change of polarization depends on intracellular and extracellular resistances.7 8 The models predicted no sign change if the ratio of transverse to longitudinal resistance in the intracellular domain equals the ratio in the extracellular domain. Measurements indicate that the ratios of transverse to longitudinal resistance are different in the intracellular domain (9.4) compared with the extracellular domain (2.7) in superfused calf trabecular muscles.6 Also, propagation velocity is slower and ventricular extracellular voltage is smaller in the transverse direction compared with the longitudinal direction in canine myocardium,21 22 23 which suggests that resistance differences exist in the two directions. No measurements of ratios of transverse to longitudinal resistance in intracellular and extracellular domains exist for rabbit myocardium or for arterially perfused myocardium of any species. If the ratios are different in the two domains, the bidomain model predicts that sign change of polarization occurs in the direction parallel to fibers and does not occur in the direction perpendicular to fibers. The existence of this direction dependence in perfused rabbit myocardium suggests that the resistance ratios are different in the two domains.
The investigators who first predicted results such as those described in the present study7 subsequently stated that it is “hard to explain in words the geometrically complex response of the anisotropic bidomain to injected current.”24 It may be possible to anticipate regions of depolarization and hyperpolarization by considering the pattern of current flow in tissue with differing resistance anisotropy in intracellular and extracellular domains. Since the longitudinal resistances in the intracellular and extracellular domains are lower than the transverse resistances in the two domains, intracellular and extracellular currents favor the longitudinal direction. Because of the higher resistance anisotropy ratio in the intracellular domain than in the extracellular domain, intracellular current favors the longitudinal direction more than extracellular current does. Calculations of the orientations and strengths of the current densities have been illustrated in Fig 5c⇑ and 5d⇑ of Reference 77 . Because of the complex current distribution, different regions exist in different domains where the current may converge and undergo an enhancement of the normal increase in current density upon nearing the electrode. Fig 5c⇑ of Reference 77 shows that intracellular current flows approximately longitudinally until it nears the electrode, where it must begin to flow in the transverse direction in order to reach the electrode. The intracellular current converges near the transverse axis, which should enhance intracellular current density and produce an intracellular anodal effect that depolarizes the membrane (Fig 3f⇑ of Reference 77 ). Since the extracellular resistance anisotropy ratio is smaller than the intracellular ratio, extracellular current begins to flow transversely farther from the electrode than occurs for intracellular current. This was shown in the region beyond 1.5 mm from the electrode near the longitudinal axis (Fig 5d⇑ of Reference 77 ). In this region, extracellular current converges, which should enhance extracellular current density and produce an extracellular anodal effect that hyperpolarizes the membrane (Fig 3f⇑ of Reference 77 ).
Magnitudes of polarization during the refractory period may be affected by nonlinear membrane properties. It was found that magnitudes of polarization at a given spot were not the same for both stimulation polarities, and at five spots in Fig 4⇑ (spots at row 4, column 3; row 5, column 5; row 5, column 6; row 6, column 4; and row 7, column 4), polarization with a negative sign occurred for both stimulation polarities. It is possible that polarization was influenced by changes in bidomain space constants due to differences in membrane resistance where hyperpolarization occurred compared with depolarization. The membrane time constant observed with pulses during the action potential plateau of isolated papillary muscles is smaller when positive compared with negative polarization occurs during the pulse,25 suggesting that the membrane resistance is smaller when the positive polarization occurs. This would produce a smaller space constant, which may explain why the region of positive polarization near the electrode during cathodal stimulation is smaller than the region of negative polarization near the electrode during anodal stimulation (Fig 4⇑). Membrane nonlinearities did not produce the direction dependence of polarization that was found, since a bidomain model predicted the direction dependence without incorporating any membrane nonlinearities in the model.7 Also, the direction dependence occurred for stimulation in diastole (Figs 6⇑ and 8⇑) as well as stimulation during the action potential plateau (Figs 2 to 4), even though the states of nonlinear membrane ion channels are different during diastole than they are during the action potential plateau.
The absence of negative polarization at the four recording spots closest to the stimulation electrode just after the onset of anodal stimulation (eg, Fig 8⇑, 2nd or 4th ms) may be due to the electrotonic interaction with cells a short distance away in the direction of fibers that were undergoing regenerative phase-zero depolarization. The finding that polarization at the four spots during the remainder of the stimulation pulse was less positive than the action potential plateau (eg, Fig 8⇑, 18th ms) indicates that negative polarization was produced by the anodal stimulation.
The transmembrane voltages after phase-3 repolarization of the action potentials at spots surrounding the stimulation electrode in Fig 3⇑ did not return to the prestimulation resting transmembrane voltages. This may result from membrane electropermeabilization, which decreases the membrane resistance.26 Electropermeabilization produced by an electrical ablation or field stimulation pulse shifts the resting transmembrane voltage closer to 0 mV, which has been shown by intracellular microelectrode recordings in isolated tissue and optical recordings in isolated single myocytes.27 28 29 The transmembrane voltage threshold for development of electropermeabilization, while less than ≈0.5V,26 29 was probably larger than the transmembrane voltages that were measured during the stimulation pulse at the spots nearest the stimulation electrode in Fig 3⇑. Perhaps cells closer to the stimulation electrode underwent very large transmembrane voltage changes during the pulse, became electropermeabilized, and then electrotonically caused the positive shifts in the resting transmembrane voltages at the recording spots surrounding the electrode. The bidomain model that predicted the direction-dependent sign change of polarization in three-dimensional myocardium has also evaluated the effect of electropermeabilization simulated by a 100-fold increase in the membrane leak conductance.8 No qualitative changes in the results were found after the electropermeabilization was incorporated into the model. Thus, even if electropermeabilization occurred, the results in Fig 3⇑ are still consistent with the bidomain model.
The stimulation-excitation delay at the recording spots in Fig 5a⇑ decreased when the stimulation strength was changed from 0.2 to 8 mA. This effect was predicted in Fig 5⇑ of Reference 88 , in which the delay decreased abruptly when the cathodal strength was increased from a near-threshold value. The measurements showed further that the longitudinal propagation velocity decreased for the 8-mA cathodal stimulation compared with the 0.2-mA stimulation (Fig 5b⇑). Slower propagation may result from stimulation-induced hyperpolarization, which increases the difference between the transmembrane voltage and the threshold transmembrane voltage for excitation. For propagation to occur, local circuit current may need to discharge the membrane all the way from the hyperpolarized transmembrane voltage to the threshold transmembrane voltage. This would require more of the local circuit current when larger hyperpolarization exists, leaving less of the current available to excite downstream cells.
The polarization may account for excitation produced by unipolar cathodal stimulation in intact canine hearts in which the location from which the action potential propagation originated was determined from bipolar extracellular recordings by extrapolating back to the time of stimulation.2 In that study, propagation originated away from the electrode approximately perpendicular to fibers, which corresponds to the edge of a virtual cathode region of positive polarization during stimulation. The positive polarization may directly excite those cells in which the polarization is large enough to activate inward sodium current. In the present experiments, excitation determined from transmembrane voltage–sensitive recordings occurred first near the cathodal electrode, which is expected from the bidomain model prediction that positive polarization within the virtual cathode region is greatest near the electrode.7 8 24 When stimulation strength was increased, the activation front became less eccentric and more circular during the first few milliseconds of stimulation than the front produced by weaker stimuli. This indicated earlier excitation away from the electrode in the direction perpendicular to fibers, which should result from increased magnitudes of positive polarization of cells within the virtual cathode region when stimulation strength was increased. For stronger stimulation, the virtual cathode oriented perpendicular to fibers may produce a dog-bone–shaped region within which all cells are directly excited. Then the action potential may propagate from the edge of this region, producing the propagation that was measured with extracellular recordings.2 Also, early excitation and repolarization in a region oriented across fibers, which occurred in previous reports but were not explained at the time,30 31 may be produced by the polarization as discussed in Reference 22 . Finally, recent fluorescence measurements by Wikswo et al32 are in excellent agreement with the present results.
This study was supported by grant NC-91-G-14 from the American Heart Association, North Carolina Affiliate, Inc; a grant from the Whitaker Foundation; grant HL-52003 from the National Heart, Lung, and Blood Institute; and grant Al-G-950032 from the American Heart Association, Alabama Affiliate, Inc.
Previously published in part in abstract form (Circulation. 1994;90[suppl 1]:I-176).
- Received February 22, 1995.
- Accepted August 27, 1995.
- © 1995 American Heart Association, Inc.
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