Published online before print December 11, 2003, doi: 10.1161/01.RES.0000111526.69133.DE
© 2004 American Heart Association, Inc.
Cellular Biology |
Nonlinear Changes of Transmembrane Potential During Electrical Shocks
Role of Membrane Electroporation
From the Department of Biomedical Engineering, University of Alabama at Birmingham, Birmingham, Ala.
Correspondence to Vladimir G. Fast, PhD, University of Alabama at Birmingham, 1670 University Blvd, VH B149, Birmingham, AL 35294. E-mail fast{at}crml.uab.edu
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Abstract |
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Defibrillation shocks induce nonlinear changes of transmembrane potential (
Vm) that determine the outcome of defibrillation. As shown earlier, strong shocks applied during action potential plateau cause nonmonotonic negative Vm, where an initial hyperpolarization is followed by Vm shift to a more positive level. The biphasic negative Vm can be attributable to (1) an inward ionic current or (2) membrane electroporation. These hypotheses were tested in cell cultures by measuring the effects of ionic channel blockers on Vm and measuring uptake of membrane-impermeable dye. Experiments were performed in cell strands (width 
0.8 mm) produced using a technique of patterned cell growth. Uniform-field shocks were applied during the action potential plateau, and Vm was measured by optical mapping. Shock-induced negative Vm exhibited a biphasic shape starting at a shock strength of 15 V/cm when estimated peak V-m was -180 mV; positive Vm remained monophasic. Application of a series of shocks with a strength of 23±1 V/cm resulted in uptake of membrane-impermeable dye propidium iodide. Dye uptake was restricted to the anodal side of strands with the largest negative Vm, indicating the occurrence of membrane electroporation at these locations. The occurrence of biphasic negative Vm was also paralleled with after-shock elevation of diastolic Vm. Inhibition of If and IK1 currents that are active at large negative potentials by CsCl and BaCl2, respectively, did not affect Vm, indicating that these currents were not responsible for biphasic Vm. These results provide evidence that the biphasic shape of Vm at sites of shock-induced hyperpolarization is caused by membrane electroporation.
Key Words: defibrillation • fluorescent imaging • membrane electroporation • virtual electrodes • secondary sources
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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The success or failure of defibrillation is determined by the magnitudes and the distribution patterns of shock-induced changes of transmembrane potential (
Vm), but the mechanisms governing the Vm dynamics are not well understood. Experiments in cardiac tissue have shown that unlike in mathematical models, shocks produce strongly nonlinear Vm responses. Shocks applied in the plateau phase of the action potential (AP) typically produce two basic types of nonlinear Vm. The first type is characterized by a monotonic Vm shape and an asymmetric distribution of Vm magnitude, with the negative Vm being much larger than positive Vm.1–7 Stronger shocks induce Vm of the second type, which is characterized by a nonmonotonic behavior of negative Vm when strong hyperpolarization is followed by a positive Vm shift.4,5 In addition, the amplitudes of both positive and negative Vm do not increase proportionally with increasing shock strength but reach saturation levels and then decrease.1,5
Several studies investigated cellular and ionic mechanisms of nonlinear Vm. It was found that the asymmetry of Vm response was reduced by the application of nifedipine, a blocker of the L-type calcium current,6 because of an increase in positive Vm and that the asymmetry was insensitive to inhibitors of outward potassium currents.5,6 This indicated that the Vm asymmetry is attributable to the outward flow of Ca current in depolarized tissue, where Vm rises above the ICa reversal potential.
Regarding the mechanism of nonmonotonic Vm, the positive Vm shift at sites of large negative Vm suggests an increase in the net inward current at these locations. There are two main hypotheses explaining the mechanism of such Vm. First, it could be attributable to an inward flow of an ionic current active at large negative potentials, such as the hyperpolarization-activated If current8–10 and the inward rectifier potassium current (IK1).11,12 Second, it could be attributable to a nonspecific leakage current caused by membrane electroporation. The goal of this study was to test these two hypotheses by studying the effects of ionic channel blockers on shock-induced Vm and by measuring cell uptake of a cell-impermeable dye. Because shock effects depend on both the geometry of cardiac tissue and the geometry of the electrical field, experiments were performed with uniform-field shocks in geometrically defined 2-dimensional cultured cell strands.
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Materials and Methods |
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Cell Cultures
Dissociated ventricular myocytes were obtained from neonatal Wistar rats (1 to 2 days old) and grown into cell strands with a width of 0.8 mm using the technique of patterned cell growth.5,13 Cell monolayers were incubated in UltraCulture medium (BioWhittaker) supplemented with 20 µg/mL of vitamin B12 and antibiotics at 37°C in 4% CO2. To suppress fibroblast proliferation, culture medium was supplemented with 0.1 mmol/L of bromodeoxyuridine (Sigma). To promote cell beating, 0.5 µmol/L of epinephrine was added to the medium. Culture medium was exchanged on the next day after preparation and every second day thereafter. Experiments were performed after 4 to 7 days in culture.
Optical Measurements of Vm
Cell monolayers were placed in a perfusion chamber and superfused with Hanks’ solution (Life Technologies) having a pH of 7.4 and temperature of 36°C. Cells were stained with 2.5 µmol/L solution of the Vm-sensitive dye RH-237 (Molecular Probes) for 5 to 8 minutes. The linearity of optical response over a wide range of Vm changes (±750 mV) was demonstrated for dye RH-292, which is a close analog of RH-237, in sea urchin eggs.14 Dye fluorescence was excited using a 100-W Hg lamp at 530 to 585 nm, and emitted fluorescence was measured at >650 nm using a 16x16-photodiode array (Hamamatsu) and a microscopic mapping system described previously.5,7 The system bandwidth was 0.02 to 1 kHz. Recordings were made at a sampling rate of 2 to 10 kHz per channel and a spatial resolution (center-to-center interdiode distance) of 110 and 55 µm using microscope objective lenses with x10 and x20 magnification (Fluar, Zeiss).
Cells were paced at a cycle length of 500 ms using a bipolar electrode. Rectangular uniform-field shocks with a duration of 10 ms were delivered from a custom-made generator via two platinum plate electrodes located on opposite sides of the bath. Delivery of shocks was synchronized with stimulation pulses. The delay between shocks and pacing stimuli was 30 ms, resulting in the delay between AP upstrokes and shocks of 10 to 20 ms. The field strength (E) was measured using a bipolar silver electrode (wire diameter, 0.1 mm; interelectrode distance, 1.1 mm) placed near the recording site.
A shock-induced Vm was measured as the difference between a linear fit of the plateau phase and the magnitude of the shock response.6 The fit was determined using a linear regression of the signal during the 5-ms interval before the shock. In the quantitative analysis of Vm magnitude, only those signals were included that had a constant slope before shock application. The Vm was normalized by the AP amplitude and expressed as the percentage of APA (% APA).
To elucidate the role of the If and IK1 currents in nonlinear Vm, two channel blockers were applied: the If inhibitor CsCl at a concentration of 5 mmol/L and the IK1 blocker BaCl2 at a concentration of 0.2 or 0.4 mmol/L. Three Vm measurements were made in each preparation: before drug application (control), 5 minutes after the start of drug application, and 10 to 15 minutes after drug washout.
All data were expressed as mean±SD. Differences were compared using the 2-tailed paired or unpaired Student’s t test where appropriate. The one-sample Student’s t test was used to test for significant difference of measurements from zero. Results were considered statistically significant if P<0.05.
Measurements of Dye Uptake
To determine whether shocks produced cell electroporation, shock-induced uptake of a cell-impermeable dye propidium iodide (PI, Molecular Probes) was measured. Propidium iodide was dissolved in Hanks’ solution at a concentration of 50 µmol/L and applied to cell monolayers using two methods. In the first, the PI-containing solution was continuously superfused for 6 minutes at 36°C when cells were paced at 500-ms intervals. In the second, dye solution was applied for 4 to 5 minutes at room temperature when cells were not paced. In each case, dye solution was applied twice. During first dye application, which served as a control, no shocks were given. During second dye application, a series of shocks was applied. In the case of regular cell pacing, each shock was delivered with a delay of 30 ms after a pacing stimulus. After both dye applications, the dye solution was washed out and images of dye fluorescence (excitation at 560/55 nm, emission at >615 nm) were taken at x10 magnification using a CCD videocamera.
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Results |
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Shock-Induced Nonlinear
VmFigure 1 demonstrates two types of nonlinear
Vm that were measured in a 0.8-mm-wide strand in response to two shocks with a strength of 10 and 28 V/cm. Both shocks were applied 11 ms after AP upstrokes. The spatial distributions of Vm were uniform, with negative Vm on the anodal side of the strand and positive Vm on the cathodal side. The weaker 10-V/cm shock (A) produced an asymmetric distribution of Vm across the strand, with V-m being greater than V+m (-154 and 55% APA, respectively). At most locations across the strand, both positive and negative Vm exhibited a simple monophasic shape. Only in the middle of the strand (site 5), Vm had a complex multiphasic shape reflecting electrotonic interaction between the nearly adjacent areas of positive and negative polarizations.
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The stronger 28-V/cm shock also produced asymmetric Vm, with peak V-m>V+m (-201% APA and 54% APA, respectively). Contrary to the weaker shock, however, the negative polarizations (traces 1 through 3) exhibited nonmonotonic behavior, where an initial large hyperpolarization was followed by a shift of Vm toward a more positive level. The maximal positive shift at the anodal edge of the strand was 103% APA, drastically reducing the degree of Vm asymmetry toward the end of the shock. The shape and the magnitude of the positive Vm at the cathodal edge (trace 7) did not change in comparison to the weaker shock.
Figure 2 presents statistical data on the magnitudes of shock-induced negative Vm changes from a total of 11 cell strands for shock strength, which varied in the range of 0 to 51 V/cm. Three parameters of negative polarizations were quantified, as shown in panel A: the peak value of V-m attained during a shock (V-m,p), V-m at the shock end (V-m,e), and the magnitude of Vm shift from the peak to the end value (V-m,ps=V-m,e-V-m,p). As shown in panel B, for shocks with a strength in the range between 0 and 10 V/cm, the peak and end values of V-m were equal. At stronger shocks, the growth of the V-m,e slowed, and it reached its maximum of 180%APA at a shock strength of 15 V/cm, when peak Vm was 200% APA. After that, the end V-m decreased, whereas the peak V-m continued to increase, reaching a maximum of 225% APA at a shock strength of 22 V/cm, and slightly decreased thereafter.
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The magnitude of V-m,ps was negligible for shocks with a strength of <10 V/cm, reflecting the simple monophasic Vm shape, and it started to increase for stronger shocks. To determine the statistically significant shock strength at which the V-m,ps magnitude exceeded zero, the V-m,ps data were grouped into 5-V/cm-wide bins centered on shock strengths of 5, 10, and 15 V/cm and so on. As shown in panel C, statistically significant V-m,ps (30±20% APA, n=12, P<0.01) was detected at a shock strength of 15 V/cm. With increasing the shock strength, the V-m,ps magnitude rapidly increased, reaching 64% APA at shock strength of 20 V/cm. Above that, V-m,ps increased more slowly, reaching a saturation level of 100% APA at 40 V/cm.
It has been reported previously that strong shocks can cause elevation of diastolic potential.15–18 To examine how the threshold for diastolic Vm elevation corresponds to the threshold of biphasic Vm, postshock Vm changes were measured in 11 cell strands. Because optical signals contained an upward drift caused by dye photobleaching, the magnitude of diastolic Vm change was measured by taking a difference between diastolic Vm levels (Vm,d) measured after shock application and those measured in control (Figure 3A). To minimize errors associated with motion artifact, optical signals were spatially averaged19 over a 5x5 area. The Vm,d values were measured 300 ms after an action potential upstroke. Shocks stronger than 20 V/cm could induce extra beats with short coupling intervals,18 preventing measurements of diastolic Vm. Therefore, these measurements were performed for shocks with a strength of up to 20 V/cm. Panel B shows the results of Vm,d measurements in all 11 strands and grouped into 5-V/cm bins. Statistically significant Vm,d (>12%APA) was observed at shock strength of 15 V/cm and higher.
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Effects of Ionic Channel Blockers on Nonlinear Vm
To examine the roles of If and IK1 ionic currents in biphasic shock responses, the effects of ionic channel blockers CsCl and BaCl2 on Vm shape and magnitude were measured. Figure 4A shows the effect of 5 mmol/L of CsCl on maximal positive and negative Vm measured at strand edges in response to an 18-V/cm shock. The shapes and the magnitudes of shock-induced Vm (black traces) were not changed from control (gray traces). Similar results were obtained in a total of 7 strands. Panel B displays the magnitudes of peak positive Vm (V+m,p), peak negative Vm (V-m,p), and positive Vm shift (V-m,ps) produced by shocks with a strength of 20±1 V/cm in comparison with control and washout values. The magnitudes of peak V-m and V-m,ps were not changed. There was a small decrease in the peak positive Vm from control, but V+m did not return to control levels after washout.
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Similar results were found when BaCl2 (0.2 or 0.4 mmol/L in 3 and 5 strands, respectively) was applied in a total of 8 strands subjected to 16±1 V/cm shocks. As shown in panel C, magnitudes of peak V-m, peak V+m, and V-m,ps were not changed. Thus, the biphasic shape of V-m was not affected by both drugs.
Shock-Induced Dye Uptake
To test whether shocks induced membrane electroporation, uptake of fluorescent cell-impermeable dye propidium iodide was measured in 9 cell monolayers. In 5 monolayers, PI was applied by continuous superfusion at 36°C during regular cell pacing. In 4 other monolayers, dye solution was applied at room temperature when cells were not paced. Qualitatively similar results were obtained in both series of measurements.
Figure 5 shows the result of PI application to a cell strand (A1) at room temperature. In control conditions, PI was applied for 4 minutes when no shocks were given. Fluorescent image of PI staining taken after dye washout (A2) revealed an appearance of randomly distributed fluorescent spots, which can be attributed to staining of cell debris that contains nucleic acid material. During the second PI application, a series of shocks with a strength of 31 V/cm and duration of 20 ms was given at an interval of 2 seconds. This resulted in increase of dye fluorescence at the left side of the strand (A3). To accentuate the shock-induced changes in dye fluorescence, the control image was subtracted from the image taken after shock application, and the resulting image was filtered using a median filter. The differential image (A4) clearly demonstrates dye uptake at the anodal side of the strand, where shock-induced negative Vm is expected. Panel B presents spatial profiles of fluorescence intensity taken by averaging images along the vertical dimension. The profiles show that the shock-induced dye uptake was localized within a distance of 150 µm from the anodal strand edge.
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Dye uptake at the anodal strand edge was observed in a total 4 monolayers subjected to a series of 33±3 V/cm shocks (duration, 20 ms; interval, 2 to 6 seconds) at room temperature without pacing and in 5 monolayers when shocks with a strength of 23±1 V/cm (duration, 10 ms; interval, 3 seconds) were applied during regular pacing. In different monolayers, shocks of different polarities were applied. Dye uptake always occurred at the side facing the anode.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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The knowledge of Vm changes caused by electrical shocks is important for understanding the mechanisms of defibrillation. The present study investigated the cellular mechanism of nonlinear shock-induced
Vm in cultured cell strands. The findings of this work are that (1) the threshold for occurrence of biphasic negative Vm was 15 V/cm in the 0.8-mm-wide cell strands; (2) the occurrence of biphasic negative Vm correlated with uptake of a cell-impermeable dye at the anodal side of cell strands; and (3) biphasic Vm was not affected by blockers of IK1 and If channels. These results provide evidence that biphasic Vm was caused by membrane electroporation.
Nonlinear Shock-Induced Vm
With the exception of very weak shocks,5 shock-induced Vm exhibits strongly nonlinear behavior. Studies in different tissue preparations demonstrated that shocks of moderate strength applied during the AP plateau produce monotonic Vm with an asymmetric distribution, where negative Vm is much larger than positive Vm.1–7 Experiments in cell cultures provided evidence that such polarization asymmetry is caused by the outward flow of Ca2+ current at sites of positive Vm.6 Stronger shocks induce Vm of another type, which is characterized by a biphasic shape of negative Vm, where an initial strong hyperpolarization is followed by a return of Vm to a more positive level. Vm responses of this type were observed in single cells,4,5 cultured cell monolayers,4,5 and porcine left ventricular preparations.20 In cell cultures, the occurrence of biphasic Vm was paralleled with postshock arrhythmias, indicating that they share the same ionic mechanism.18 In the present as well in the previous study,5 the biphasic shape was observed only at sites of negative Vm, whereas positive Vm remained monophasic at all shock strengths, indicating that the source of positive Vm shift is localized at sites of negative Vm rather than electrotonically mediated from the areas of positive Vm. The field threshold for the occurrence of the biphasic Vm response measured here in the 0.8-mm-wide strands is 15 V/cm. At this shock strength, the magnitude of peak negative Vm was 200% APA (Figure 2). Assuming the APA magnitude of 100 mV and the plateau AP level of 20 mV, this corresponds to the Vm threshold of -180 mV. The biphasic Vm shape became prominent at a shock strength of 20 V/cm, where the magnitude of positive Vm shift reached 64% APA, and it reached saturation at stronger shocks. The saturation of Vm,ps was likely attributable to the limited system bandwidth and underestimation of the magnitude of peak V-m during strong shocks when the V-m waveform has a shape of a narrow spike. This factor, however, did not preclude the precise determination of the threshold for the occurrence of biphasic V-m and the Vm magnitudes at shock strengths <20 V/cm, because at such shock strengths, the Vm waveforms are relatively slow and are not limited by the system bandwidth.
Role of Ionic Currents in Biphasic Vm
Positive Vm changes during shocks reflect an increase in the net inward current. Therefore, it could be expected that the mechanism of the positive Vm shift was related to the flow of an inward ionic current operating at large negative Vm levels. Two such currents are known, inward rectifier IK1 and hyperpolarization-induced If current. The If current, which was implicated in anodal break excitation,10 can have the activation threshold in ventricular myocytes of some species as negative as -170 mV,9 which is close to the threshold for the occurrence of biphasic Vm. In rat ventricular myocytes, however, the If threshold is lower, -90 mV.10,21 Accordingly, inhibition of the If current with CsCl did not alter the shape of Vm in the present study. The other inward current, IK1, has a linear voltage dependence at Vm <-90 mV,11 making it unlikely to account for biphasic Vm occurring at more negative Vm levels. Accordingly, blocking IK1 with BaCl2 did not affect the shape of nonlinear Vm. It should be mentioned that IK1 current might become smaller with increasing cell culture age.22 This could explain the lack of the effect of BaCl2 on the magnitude of negative Vm, and it can potentially limit the extrapolation of the BaCl2 data to the intact adult myocardium. However, it does not affect the interpretation of data regarding the possible role of IK1 in biphasic Vm in cultured cell monolayers. Therefore, it can be concluded that the two ionic currents, IK1 and If, are not responsible for nonlinear Vm investigated in this study.
Role of Membrane Electroporation in Biphasic Vm
The other possible mechanism of nonmonotonic Vm is membrane electroporation. In single cells, electroporation can be readily detected by measuring changes in membrane conductance.23 In multicellular preparations, electroporation can be detected by observing uptake of a membrane-impermeable dye.24 In several studies,16,17 elevation of diastolic potential was used as a sign of membrane electroporation, but no study until now has established a causative link between the two phenomena using direct measurements of electroporation. Therefore, mechanisms other than electroporation contributing to diastolic Vm elevation after shocks could not be excluded.16
Shock-induced dye uptake demonstrating electroporation was reported previously in cell cultures24 at shock strength of >100 V/cm, which is much higher than the threshold for biphasic Vm observed here, leaving a possibility that a different mechanism was responsible for Vm of this type. A previous attempt to measure cell uptake of Lucifer Yellow dye at a lower shock strength18 failed, probably because of insufficient sensitivity of these measurements. The present study used propidium iodide dye, which is likely to be a more sensitive indicator of electroporation because it becomes fluorescent only on entering cells and binding to nucleic acids. In addition, multiple shocks were applied to increase chances for dye diffusion through short-lived pores expected at relatively weak shocks. As a result of combination of these two factors, dye uptake was observed at shock strength of 23 V/cm that was very close to the threshold for biphasic V-m. This provides evidence supporting the hypothesis that electroporation was the cause for biphasic Vm.
It should be noted that registration of a biphasic Vm signal does not necessarily indicate the occurrence of membrane electroporation at this particular location. Thus, biphasic negative Vm waveforms were observed in the strand middle (Figure 1B, traces 3 and 4), where shock-induced Vm changes were within physiological range (<100 mV) and where no electroporation was detected in the dye uptake measurements (Figure 5). Such biphasic V-m was the result of electrotonic interaction with the area of largest negative Vm at the anodal strand edge where electroporation took place.
The voltage threshold for electroporation estimated from optical recordings of Vm at the anodal strand edges was 180 mV. This is significantly lower than the electroporation threshold of 300 mV reported from measurements of changes in membrane conductance in single frog myocytes in response to 5-ms-long voltage pulses.25,26 The difference in thresholds between this and the present study could be attributable to differences in the pulse duration, different experimental conditions, as well as different cell species.
Membrane electroporation is believed to play several important roles in defibrillation. It was implicated in detrimental effects of shocks, such as loss of tissue excitability, loss of mechanical function, generation of postshock arrhythmias, and defibrillation failure at very strong shocks.15,18,23,27 It was also proposed that electroporation might play an antiarrhythmic role in defibrillation.17 Typically, electroporation is associated with very strong shocks, but, according to the present study, it has a relatively low field threshold of 15 V/cm. Such field strength is only three times higher than the minimal field strength required for defibrillation,28,29 indicating that electroporation has a common occurrence during defibrillation. The finding that electroporation is correlated with biphasic Vm provides a sensitive and relatively simple method for detection of electroporation in whole hearts using short optical Vm recordings.
An important finding of this work is that membrane electroporation was restricted to the areas of negative shock-induced polarization. This corresponds to the results of two previous studies, one of them demonstrating that postshock arrhythmias in cell cultures originated from the areas of shock-induced hyperpolarization18 and the other showing that contractile injury caused by strong shocks in isolated myocytes occurred first at the cell end facing the anode.30 Together, these data indicate that the detrimental effects of shocks are associated predominantly with negative polarizations. The fact that electroporation did not occur in the positively polarized areas can be explained by the saturation of positive Vm at much lower levels (100 mV)5 than the one necessary for electroporation. The reason for such saturation is likely to be the outward flow of Ca2+ current at sites of positive Vm when Vm exceeds the ICa reversal potential.6 Thus, the ionic properties of the cell membrane reduce the likelihood of reaching very high Vm levels, protecting cardiac cells from the detrimental effects of strong electrical shocks. The fact that detrimental shock effects are restricted to negatively polarized areas suggests a strategy for designing defibrillation electrodes in such a way as to minimize the exposure of cardiac tissue to large negative polarizations.
Limitations
Application of the results of this study to the intact adult myocardium can be potentially limited by age- and species-dependent differences in ionic membrane properties between neonatal rat myocytes and cells of other types. Thus, the threshold for If current in dog and guinea pig ventricular cells was reported to be more negative than in the rat myocytes.10 This current, however, has much longer activation times than the duration of shocks used in this study. Therefore, the contribution of If current to biphasic Vm waveforms during such shocks is expected to be negligible in these cell types as well. The IK1 current was reported to be stronger in freshly isolated cells than in cultured cells.22 Therefore, it may play a more prominent role in some effects of shocks in the intact tissue in comparison to cell cultures. Regarding the mechanism of biphasic Vm, however, IK1 is unlikely to play an important role in the intact tissue, because its reversal potential is far from the threshold for the occurrence of Vm of this type.
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Acknowledgments |
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This work was supported by NIH Grant HL67748. We thank Reuben Collins for help with preparation of cell cultures.
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Footnotes |
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Original received July 18, 2003; resubmission received November 24, 2003; accepted November 25, 2003.
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References |
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N. Trayanova Defibrillation of the heart: insights into mechanisms from modelling studies Exp Physiol, March 1, 2006; 91(2): 323 - 337. [Abstract] [Full Text] [PDF]
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 V. P. Nikolski and I. R. Efimov Electroporation of the heart Europace, January 1, 2005; 7(s2): S146 - S154. [Abstract] [Full Text] [PDF]
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T. Ashihara and N. A. Trayanova Cell and tissue responses to electric shocks Europace, January 1, 2005; 7(s2): S155 - S165. [Abstract] [Full Text] [PDF]
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 V. G. Fast, E. R. Cheek, A. E. Pollard, and R. E. Ideker Effects of Electrical Shocks on Cai2+ and Vm in Myocyte Cultures Circ. Res., June 25, 2004; 94(12): 1589 - 1597. [Abstract] [Full Text] [PDF]
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 O. F. Sharifov and V. G. Fast Intramural Virtual Electrodes in Ventricular Wall: Effects on Epicardial Polarizations Circulation, May 18, 2004; 109(19): 2349 - 2356. [Abstract] [Full Text] [PDF]
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