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Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106
Submitted 15 July 2003 ; accepted in final form 12 January 2004
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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1.0-mm-diameter area around the tip of the electrode. According to computer simulations, cell uncoupling, rather than electroporation, might be the direct cause of VEP elimination and threshold increase, which was nonlinearly dependent on the size of the damaged region. Fiber rotation with depth did not substantially affect the numerical results. The study explains failure to stimulate damaged tissue within the concepts of the VEP theory.
electrophysiology; stimulation; bidomain
The defibrillation procedure also causes damage to the heart. Several clinical studies report failure of the implanted pacemaker after direct-current cardioversion of fibrillation and tachycardia (10, 14, 25, 34). In all cases, the failure was due to an acute increase in the stimulation threshold, most likely caused by current-induced tissue damage at the electrode-endomyocardial interface. This hypothesis is supported by the computer simulations of Langrill and Roth (22) demonstrating that adjacent regions of strong depolarization and hyperpolarization may be created around an implanted electrode during defibrillation.
Although chronic application of electrical stimulation leads to development of fibrosis, the cardiac tissue damage caused by acute shocks has a different nature and is mostly expressed in basophilic degeneration of the tissue (10), reflecting rupture of sarcolemmal membranes (electroporation) and, possibly, intercellular junctions (uncoupling). Several studies (2, 37) presented evidence of electroporation and ventricular pacing threshold increase during application of external shocks to rabbit hearts. Patel et al. (39) found reduction in connexin43 (Cx43) expression near the pacing site for chronic pacing of canine ventricular myocardium. We are not aware of any data on gap junction redistribution for acute strong shocks.
Recent investigation of electrical stimulation of the heart revealed an important role of cardiac tissue anisotropy in generation and propagation of excitation. In particular, it was found that, for a stimulus of any polarity, regions of depolarization and hyperpolarization are created in the vicinity of the pacing electrode tip. This phenomenon was first discovered theoretically (44) using the bidomain model (9, 30, 50), which represents cardiac tissue as two interpenetrating intracellular and interstitial domains, with different conductivities along and across the direction of the fibers, coupled via membrane resistance. For a point-size cathodal stimulus, the transmembrane potential (Vm) distribution pattern had a central depolarized virtual cathode (VC) region with a characteristic "dog-bone" shape and two elongated hyperpolarized virtual anode (VA) regions on the sides parallel to the direction of the fibers. For the opposite polarity of the stimulus, the virtual electrode polarization (VEP) pattern was symmetrically reversed.
The dog-bone VEP pattern induced by point stimulation was experimentally confirmed using electrode mapping (52) and optical imaging (16, 32, 51). The virtual electrode phenomenon resulted in formulation of a unified theory of stimulation (42, 51) and explained the mechanisms of anodal stimulation and break excitation.
Street and Plonsey (47) applied the bidomain theory and the VEP concept to investigation of the effect of fibrosis on the propagation of a planar wave front in cardiac muscle. In their simulations, they represented fibrosis as complete or partial cell uncoupling and demonstrated an important role of VEP in penetration of the wave front through the fibrous tissue.
We sought to determine how acute tissue damage created by continuous pacing with strong electric current may affect the VEP pattern and the mechanisms of electrical excitation.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Two unipolar electrodes (0.12-mm platinum-iridium Teflon-coated wires) were positioned in diagonally opposite corners of the 5 x 5-mm field of view (Fig. 1B). The reference electrode was a 9-mm-diameter Ag-AgCl disk placed in the bath away from the heart. To reach the steady state, the heart was paced with 20 preconditioning pulses with cycle length of 300 ms from a bipolar electrode placed at the apex. At a coupling interval of 350 ms from the last pulse, a test stimulus (±10 mA, 4 ms) of anodal or cathodal polarity was applied through each electrode by a current stimulus isolator (model A385, WPI, Sarasota, FL). The resulting Vm distribution was optically recorded. The pacing thresholds for 4-ms stimuli of both polarities were determined for both sites by an up-down protocol, with ECG recordings used to verify suprathreshold or subthreshold pacing. Subsequently, strong biphasic pulses (40 mA, 4 ms) were delivered at 4 Hz for 5 min through one of the electrodes. These pulses created significant tissue damage around the tip of the electrode that was noticeable by eye as a dark spot on the muscle surface. The same protocol with ±10-mA, 4-ms test stimuli was repeated to obtain Vm distributions at damaged and undamaged (control) sites. The pacing thresholds for 4-ms stimuli were determined again.
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Two additional experiments were conducted to assess the extent of the tissue damage in depth by staining the hearts with propidium iodide fluorescent marker (Sigma-Aldrich, St. Louis, MO). Propidium iodide binds primarily to nucleotides in the cell nucleus and has been used previously to identify the cells with membranes that were ruptured under the influence of strong electric shocks (45). Our experimental protocol was as follows. The heart was placed in the Langendorff apparatus and perfused with the modified Tyrode solution with BDM for 30 min. Similar to the optical mapping experiments, two electrodes were placed on the left ventricular epicardial surface 5–6 mm apart. Then the perfusion was changed to Tyrode solution containing 30 µM propidium iodide. After 10 min of staining, a train of damaging (40 mA, 4 ms with 4-Hz frequency) biphasic current stimuli was applied to the left ventricular surface of the heart for 5 min through one of the electrodes. The other electrode was used to deliver two pairs of test pulses of different polarity (4 ms, ±10 mA), corresponding to the control site. After 10 min, the perfusion was switched back to the physiological solution to wash out the dye that was not trapped in the electroporated cells. After the experiment, the heart was placed in the tissue embedding medium (Fisher Chemical, Fair Lawn, NJ) and rapidly frozen by immersion into isopentane (Acros) at –65°C. The sample was sliced into 20-µm sections (with 500 µm between sections) from base to apex. The sections were mounted on poly-L-lysine-coated glass slides and stored at –65°C in the dark. The sections were examined using an epifluorescent microscope (model E600FN, Nikon) equipped with a TRITC HYQ filter cube (530- to 550-nm excitation, 565-nm dichroic mirror, >590- to 650-nm emission).
All the sections from one of the two experiments with propidium iodide staining were subjected to further immunohistochemical processing for investigation of Cx43 protein distribution. Cx43 is the main constituent of the majority of gap junction channels connecting ventricular myocytes. It can be visualized by immunolabeling, which has been described previously (6, 35). Briefly, a commercially available anti-Cx43 monoclonal antibody raised in mouse (catalog no. MAB3068, Chemicon) was used at 1:1,000 dilution. FITC-conjugated (Daco) or Cy3-conjugated (Chemicon) anti-mouse IgG secondary antibodies were used at 1:100 and 1:400 dilutions, respectively. All the antibodies were diluted in 1% bovine serum albumin in phosphate-buffered saline (PBS) before their application. The sections mounted on poly-L-lysine-coated glass slides were removed from the storage at –65°C and immersed into 90% methanol for 5 min for fixation. Then they were washed three times for 10 min in PBS. The sections were blocked for 1 h with 10% horse serum in PBS and then incubated with primary antibody overnight at 4°C. After they were washed (3 times for 10 min in PBS), the sections were incubated with the secondary antibody for 90–120 min. After the final wash (3 times for 10 min in PBS), the slides were mounted with Vectashield mounting medium (Vector Laboratories), and coverslips were applied. Cx43 immunolabeling was examined using a Nikon E600FN fluorescent microscope equipped with B2-A (450- to 490-nm excitation, 505-nm dichroic mirror, >520-nm emission) and TRITC HYQ (530- to 550-nm excitation, 565-nm dichroic mirror, >590- to 650-nm emission) filter cubes. Specificity of the labeling was confirmed by analysis of negative control slides for which the primary or the secondary antibody was omitted. In all negative control experiments, there was no signal above background fluorescence.
The immunohistochemical procedure of Cx43 labeling was applied to two more preparations that were subjected to the original protocol of stimulation with test and damaging currents but were not stained with propidium iodide or any other fluorescent marker. These Cx43 distributions were not qualitatively different from those obtained from the propidium iodide-stained heart, thus excluding any possibility of artifacts due to propidium iodide staining.
After analysis and documentation of the data from all the sections labeled for Cx43, the sections were stained using the standard hematoxylin-eosin (Sigma) technique for conventional histology.
Numerical model.
We compared our experimental data with the results obtained from three-dimensional bidomain simulations. Figure 1A shows the geometry of the problem. Electrical behavior of a rectangular 10 x 5 x 1.5-mm slab of cardiac tissue and the adjacent 10 x 5 x 0.5-mm layer of conductive bath above it is described by the following set of partial differential equations (11, 23, 49)
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 | (2) |
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e, and b are the transmembrane, interstitial, and bath potentials, respectively, 
i and e are the intra- and interstitial conductivity tensors, respectively, 
b is the conductivity of the bath, Im is the volume density of the transmembrane current, and I0 is the volume density of the stimulation current. The 0.1 x 0.1 x 0.1-mm tip of the stimulus electrode is located in the bath 0.1 mm above the center of the upper surface of the slab. The constant parameters of the model, such as intracellular and interstitial conductivities along and across the direction of the fibers and transmembrane capacitance, were the same as those used by Latimer and Roth (23). These parameters yield the length constant transverse to the direction of the fibers (0.174 mm) and the length constant parallel to the direction of the fibers (0.434 mm). Im in Eq. 2 is a sum of the capacitive and ionic currents
 | (4) |
is the surface-to-volume ratio and Cm is the specific membrane capacitance. The ionic current Iion(Vm, t) was represented by Ohm's law for those simulations when the tissue was assumed to be equivalent to a simple resistor-capacitor network (passive model) (23) or by the modified BRDR (Beeler-Reuter ventricular action potential computer model with Drouhard-Roberge modification) ion channel kinetics (46) for the cases when the cells were assumed to be able to generate normal action potentials (active model).
To study the effect of electroporation in some of our simulations, we modified Eq. 4 by adding another ohmic term, GVm, inside the brackets, similar to the works of Krassowska (19) and Aguel et al. (1). The electroporation conductance (G) is governed by the following phenomenologically derived equation (19)
 | (5) |
The values of 
, , and 
are published in the literature (19). According to this simple model, the electroporation current increases dramatically as Vm exceeds 600 mV and, therefore, counteracts further polarization. Resealing of the pores is not accounted for in this model and does not seem to be a significant limitation if one is interested in short-term dynamics.
The interstitial space inside and the bath outside the slab are electrically coupled and, therefore, constitute a single continuous extracellular space with spatially variable conductivities. Mathematically, therefore, Eqs. 1 and 3 can be combined into a single equation with a spatially inhomogeneous conductivity tensor () and a right-hand-side source term. The joint extracellular space is limited by the six boundaries of the simulation domain. We assume that the upper boundary is held at zero potential (i.e., grounded), thus providing a sink for the current injected through the electrode. The other five boundaries are considered sealed, with the assumption that any current flow normal to the planes of those boundaries is absent. In contrast to the interstitial domain, the intracellular domain of the slab does not have direct resistive connections with the bath and, therefore, is considered sealed at the tissue-bath interface. The same types of boundary conditions were used previously in the simulations of Latimer and Roth (23). The limitations of different boundary conditions were investigated by Krassowska and Neu (20).
Although for our standard calculation we assumed straight geometry of the fibers, in some of the numerical experiments we introduced equal fiber rotation with depth from 0 to 90° and examined its effect on the results.
On the basis of our data obtained from the propidium iodide staining of the damaged area as well as immunolabeling for Cx43, we considered acute tissue damage by strong current to be cell uncoupling accompanied by electroporation of the cell membranes. We considered the effects of uncoupling and electroporation separately, because in the extreme case of complete cell uncoupling, electroporation would not markedly affect generation and propagation of the excitation because of reduction of electrical communication between the uncoupled cells. Therefore, in the first part of the numerical experiments, we assumed that a strong current stimulus leads to complete uncoupling of the cells within a sphere of certain diameter with its center under the electrode tip. The uncoupling was mathematically implemented by setting the intracellular conductances to zero while the interstitial conductances were left unaltered. Thus, in other words, the damaged tissue was imagined to be a passive, dense, anisotropic resistive network of dead cells.
The protocol of the current stimulus application in this case was as follows. For a given diameter of the damaged area around the electrode, a –1-mA infinitely long cathodal pulse was delivered to the slab described by the passive bidomain model. Steady-state Vm data were obtained 25 ms after the pulse application, which roughly corresponded to four time constants (6.1 ms) of the resistor-capacitor network. The three-dimensional Vm distributions were visualized using MATLAB's (Mathworks) isosurface function. Maximum and minimum transmembrane polarizations (at VC and VA) throughout the time course of the VEP development were recorded for the given diameter of the damaged region. In addition, peak VC and VA polarizations and their location were monitored for every time frame. Then the model was changed to active, and the pacing thresholds for anodal and cathodal 4-ms stimuli were obtained by repeatedly running the simulations with various stimulus strengths. Success or failure of a pulse was determined from the analysis of the resulting time series of the Vm distributions. Such an empirical approach allows calculation of the thresholds with limited accuracy (error bars in Figs. 6 and 7).
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For the same geometry of the model, infinitely long cathodal pulses were delivered to the slab described by the passive bidomain model. The current strengths varied from –0.01 mA, at which no electroporation was observed, to –10 mA, at which a significant volume of the tissue at VC and VA was electroporated. As in the case of tissue damage represented by cell uncoupling, three-dimensional Vm distributions and maximum polarizations 25 ms after the pulse application were analyzed.
We used a finite difference approach to solve Eqs. 1–3 numerically. Vm from Eq. 2 was calculated by the explicit forward Euler algorithm, and the biconjugate gradient method (41) with relative tolerance <0.001 was employed to iteratively find the extracellular potential from Eqs. 1 and 3. To reduce the expense of the simulations, the equation for the extracellular potential was solved at every fifth step during the propagation of the wave and at every step during application of the stimulus. For all simulations, we used a space step of 0.1 mm in the direction parallel to the fibers and 0.05 mm in the perpendicular direction. The space step for the bath domain was 0.1 mm. The time step was 2 µs, except for the simulations with the electroporation model, when reduction to 0.1 µs was necessary to maintain the stability of the numerical scheme. Repeating some of the simulations for the twice-smaller space and time steps yielded an error <2% for the threshold data in the active model and <6% for maximum Vm in the passive model. The calculations were performed on a Dell personal computer with a Pentium IV 2-GHz processor. The time required for 25 ms of active bidomain simulation varied from 0.5 to 2 h depending on the size of the domain and the type of the model.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Figure 3 shows the results of staining the muscle with propidium iodide for the control and damaged sites. In Fig. 3A, a photograph of the rabbit heart, the electrode through which a strong current was delivered was removed to expose the dark spot marking the damaged site. The other electrode corresponding to the control site was left untouched. The preparation was sliced as indicated by the dashed blue arrows, which mark the two planes traversing the heart through the two sites of interest. Fluorescent images of the sections corresponding to the control and damaged sites are demonstrated in Fig. 3, B and D, respectively. Even for the two pairs of ±10-mA test pulses, there is a noticeable area of electroporation around the electrode tip (Fig. 3B). For the damaged site (Fig. 3D), this area is considerably larger, reaching 1-mm diameter. In Fig. 3, C and E, the staining pattern is shown at 10x higher magnification. Red-stained cell nuclei confirm the specificity of propidium iodide staining.
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0.3-mm-diameter region near the control site, where Cx43 is absent. Figure 4B, which shows magnified images 1) at the border of the Cx43-free region and 2) inside and 3) outside that region (from left to right, respectively), provides convincing evidence for the specificity of the labeling. Figure 4C shows no substantial structural damage to the muscle under the electrode, although a barely noticeable dip on the surface indicates the location of the electrode tip.
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1-mm-diameter region around the point of stimulation exhibits little staining, except for a small area near the vessel, which shows some signal. However, closer examination with higher magnification (Fig. 4E, left) indicates that this signal is not specific and may possibly result from residual degraded and scattered connexin proteins, which are absent elsewhere in the region of interest (Fig. 4E, middle). At the periphery, where the damage did not occur, the staining pattern is regular, as expected: connexins are seen in bright clusters corresponding to intercalated disks between the myocytes (Fig. 4E, right). Histology (Fig. 4F) demonstrates that although the general structure of the myocardium is preserved, there are more ruptures in the area of interest and the cells are more loosely packed, probably as a result of weaker connections between them. Uncoupling of the cells within a damaged region leads to disappearance of VEP and an increase in pacing threshold. In the previous section, we presented evidence of electroporation and destruction of gap junction channels due to pacing with high-intensity electric current. Are these two cellular-level phenomena consistent with the findings of the electrophysiological study? To answer this question, we turned to mathematical modeling based on the bidomain approach. We consider the effects of cell uncoupling and electroporation separately. Assuming that intercellular conductance becomes zero everywhere within the damaged region, we focus on cell uncoupling. As demonstrated above, the size of that region depends on the strength and duration of pacing, although the exact relation remains unknown. Figure 5 shows steady-state three-dimensional VEP patterns resulting from application of a –1-mA cathodal pulse to a passive tissue slab with different-sized damaged regions. As the diameter of the damaged area grows, the central VC part of the VEP becomes larger and more circular while the side VA parts of the VEP shrink and disappear. This behavior is consistent with the experimental observations of the electrophysiological study described above. Figure 6 shows that maximum depolarization at the VC and maximum hyperpolarization at the VA calculated for the total time course of the VEP development quickly fall in absolute amplitude with an increase in the damaged area. The maximum depolarization at the VC is much greater than the maximum hyperpolarization at the VA and decreases more rapidly, because the central area is more affected by the damage.
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Figure 6C demonstrates the distance from the points of peak absolute depolarization and hyperpolarization to the center of the spherical damaged region as a function of time. Peak depolarization always remains at the boundary between the normal and damaged tissue, while the point of peak hyperpolarization diffuses away from that boundary and stops 1.0 mm from it, which roughly corresponds to two length constants along the direction of the fibers.
Passive bidomain simulations permit fair comparison between slabs with different areas of damage and eliminate the influence of the active ion channel response. Apparently, all the results obtained from the passive model can be simply reversed upon a change in the stimulus polarity. However, to calculate pacing thresholds, one needs to employ an active bidomain model. In Fig. 6D, the anodal and cathodal pacing thresholds are plotted as functions of the diameter of the damaged region. The cathodal and anodal thresholds for the normal myocardium are –0.1 ± 0.01 and +0.85 ± 0.05 mA, respectively, and they increase to –1.7 ± 0.1 and +9.5 ± 0.5 mA, respectively, when the diameter of the damaged area reaches 1.6 mm. Both thresholds increase synchronously and nonlinearly, with the anodal threshold having a slightly slower rate of rise, which qualitatively agrees with the depolarization-hyperpolarization discrepancy in Fig. 6A.
For the three- to fourfold rise in the threshold values observed in our experiments, the model predicts the damaged tissue diameter to be 0.6–0.8 mm. These parameters generally correspond to the findings from the fluorescent staining of the heart muscle with propidium iodide and Cx43 antibodies in Figs. 3 and 4.
For the simulations described above, we assumed straight geometry of the cardiac fibers in the slab. However, in reality, the fibers are curved, and their direction rotates with depth. Because the curvature effects may be neglected for tissue samples of relatively small sizes (such as ours), we investigated how rotation of the cardiac fibers might affect our results with regard to the effect of tissue damage on the VEP and pacing thresholds. We considered 90° fiber rotation throughout the depth of the slab. Figure 7, A and B, demonstrates that, as a result, the steady-state dog-bone VEP is twisted following the fiber rotation direction (counterclockwise). This twist, however, does not cause any significant changes in maximum absolute polarizations for the whole range of the diameters of the damaged area (Fig. 7C). It also does not significantly alter the curves for the anodal and cathodal thresholds (Fig. 7D). The slight discrepancies between the data for the models with and without fiber rotation for large diameters might be due to boundary condition effects.
Electroporation alone cannot explain disappearance of VEP for damaged tissue. Besides uncoupling, electroporation is another phenomenon associated with high-intensity electric shocks. We incorporated a simple description of electroporation into the original bidomain model to determine whether electroporation could be the second cause of VEP disappearance and the corresponding pacing threshold increase.
Figure 8, A and B, shows three-dimensional VEP patterns 25 ms after an infinitely long –10-mA cathodal pulse to passive tissue slabs without and with electroporation, respectively. Because of the symmetry, only quarters of the slabs are shown. In other words, the complete picture of the Vm distribution can be imagined by reflecting the image symmetrically with respect to the front vertical planes and the origin. For the no-electroporation case in Fig. 8A, adjacent central VC and VA are shown. Electroporation (Fig. 8B) leads to shrinkage of the central part of the VC and sharp extension of the VA toward the center. Thus the smooth and oval contours of the image in Fig. 8A, which as shown previously (23) are largely due to the shunting effect of the bath, are replaced by a more dog-bone configuration. For a very strong –10-mA pulse, separate regions of electroporation are found in the VC and VA areas. The shapes of these regions resemble the miniaturized copies of the VC and VA areas, in agreement with the occurrence of electroporation when absolute Vm reaches a certain threshold. Indeed, as shown in Fig. 8C, maximum and minimum values of Vm at VC and VA in the model with electroporation do not exceed ±710 mV, as opposed to the model without electroporation, where they grow linearly with increase in I0. The first cells at the VC area electroporate at –1 mA I0, as can be inferred from the beginning of the saturation part of the VC-electroporation curve. Interestingly, electroporation at the VC leads to stronger hyperpolarization at the VA areas than without electroporation. Because of this amplifying effect, the cells at the VA reach nearly –700 mV and electroporate at about –5-mA current strength, rather than at about –10 mA, as one would expect from the linear model. The same conclusions can be drawn from the analysis of G normalized to the resting state conductance (Gm; Fig. 8D). Electroporation at VA starts at higher current strengths and grows slower than that at VC. However, the volume of the electroporated cells at VA grows faster than that at VC (Fig. 8D).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Our experimental results demonstrate a clear qualitative agreement between disappearance of the VEP pattern (Fig. 2) and increase in pacing thresholds (Table 1) as a result of tissue damage by pacing with strong current. The cathodal and anodal threshold values (Table 1) for the normal tissue are similar to those obtained by others (7, 29). Tissue damage increases both thresholds three- to fourfold. Although such an outcome might be expected, it may not be true in a broader sense. For example, lesions created by radio-frequency ablation can decrease pacing thresholds (26). The standard deviation for the data (Table 1) does not allow us to conclude whether one of the thresholds is affected more than the other.
One of the most important points that we attempted to address in our study was the molecular nature of the processes that occur in the cardiac muscle subject to localized strong electric shocks and are generally referred to as "tissue damage." There is no detailed knowledge about these processes. Electroporation can be one of the outcomes and has been observed in experiments with single cells (15) and cardiac tissue preparations (17, 33, 48). Its presence in our experiments was indirectly supported by staining with propidium iodide (Fig. 3). A significant difference in the size of the stained areas for the control and damaged sites proved that electroporation was due to electrical stimulation and was strength and/or duration dependent. On the basis of the photomicrographs, we estimate the electroporated area to be within 1 mm from the pacing electrode tip for pacing with high-intensity damaging current.
Another phenomenon underlying tissue damage could be cell uncoupling. In diseased muscle, the cardiac cells uncouple (13) and are transformed into connective tissue cells. This was used in the model of Street and Plonsey (47). Al-Khadra et al. (2) demonstrated slowing of conduction in response to defibrillating shocks. In our work, it was not possible to accurately measure and compare local conduction velocities for the tissue before and after damage immediately after application of the test pulse, because the virtual electrode configurations and activation patterns were different for these two cases. Instead, we measured average conduction velocity along the direction of the fibers, defined as the distance along that direction traveled by the developed wave front of excitation divided by the time elapsed from the start of the pulse application. These two velocities before and after the damage were 35 ± 3 and 39 ± 5 cm/s, respectively (not significantly different). The seeming controversy with the cell uncoupling hypothesis can be explained by the simple fact that the –10-mA current used for the test pulses was higher than the thresholds for intact and damaged tissues, thus providing a strong enough electric field to reach and excite all the cells simultaneously in a fairly large area around the electrode tip. In other words, for the test pulses, there was no propagation of the excitation through the region of damage.
To assess cell uncoupling under the influence of acute pacing with high-intensity current, we employed immunofluorescent labeling of Cx43 proteins, which has become a broadly accepted method for study of the molecular substrate of conduction in the heart. In all three hearts at the damaged site, we observed a Cx43-free region with a distinct border. On the basis of these data, we assumed that electrical stimulation resulted in closing and subsequent destruction of the gap junction channels. The idea that gap junctions were eliminated by the stimulation does not seem strange, because their distribution has been known to be very sensitive to various kinds of external interferences and conditions, including chronic pacing (39), ischemia (4), and heart failure (18). The speed with which Cx43 might have been degraded in response to the acute pacing was comparatively fast. In our experiments, the hearts were allowed to hang in the perfusion system for only 10–15 min after application of the protocol and before they were frozen. For instance, in the study of Beardslee et al. (4), 15 min of global ischemia corresponded to the onset of cell uncoupling, while full uncoupling was reached at 40 min.
While electroporation is a transient effect that lasts for several seconds (31) until the pores seal and is accompanied by spontaneous afterdepolarizations (17, 38), cell uncoupling is a more stable phenomenon. We have to acknowledge here that the short- and long-term consequences of the acute high-intensity pacing are not limited to these two phenomena, but there may be other effects, such as mechanical effects, due to direct touch by the electrode and bubble formation, and thermal, chemical (free radicals after local electrolysis), ischemia effects, due to high workload locally. Our approach includes only a couple of specific, yet important, aspects and cannot address all the mechanisms involved in tissue damage.
We based our simulations on the assumption that cell uncoupling and electroporation could be considered separately and their effects in combination would be additive. In the model with uncoupling, the damaged cells around the pacing electrode were completely uncoupled. Obviously, incorporation of electroporation in this case would not modify our results. For partially uncoupled cells, electroporation may have produced afterdepolarizations, which were not observed in the experiments. Nevertheless, our assumption represents an important limitation to the conclusions of our work.
For the model with cell uncoupling, the results are in good agreement with the data obtained in the experiment: we observed disappearance and subsequent elimination of VEP associated with an increase in the pacing threshold. Cathodal and anodal thresholds grow fairly synchronously with the diameter of the damaged region, although the rate of rise for the anodal threshold is slightly slower (Fig. 6D). This agrees with the passive model results: the maximum VA hyperpolarization is reduced to a lesser extent than the maximum VC depolarization, because the latter is located in the center under the electrode tip, and therefore its very peak is reduced by the damage (Fig. 6A).
There is substantial discrepancy in the threshold values as well as in the anodal-to-cathodal threshold ratio between the simulation and the experimental data. For instance, for normal undamaged tissue, our model yields –0.1 ± 0.1 and +0.85 ± 0.05 mA for cathodal and anodal thresholds, respectively, with a ratio of 8.5, while the experimental values are –0.30 ± 0.08 and +1.19 ± 0.37 mA, with a ratio of 4. This discrepancy was pointed out and discussed by Patel and Roth (40, 42). Although the larger thresholds in the experiments can be attributed to the contaminating effects of the excitation-contraction uncoupler BDM and the fluorescent dye, as well as some tissue damage from the test stimuli, the larger theoretical anodal-to-cathodal ratio (10 vs. 3–4 in the experiments) remains a mystery. Roth and Patel numerically investigated the effect of the size of the stimulation electrode on the VEP (40) and the pacing thresholds (42). They demonstrated that, for a cathodal stimulus applied to a passive tissue, the initial ratio of peak depolarization to peak hyperpolarization of 200 is reduced to 30 for the electrodes with larger radius (>2 mm) (40). Our simulations are somewhat similar to those of Roth, because we also studied stimulation by electric field, with different effective radius determined by the size of the damaged area. For our 0.0- to 0.8-mm radii, the ratio of maximum depolarization to maximum hyperpolarization decreased exponentially from 18.1 to 5.5 and the ratio of the anodal-to-cathodal thresholds also fell exponentially from 8.5 to 5.0. For a large area of damage, the first and the last ratios are very similar. The discrepancy for the smaller areas of damage may be due to the fact that, as mentioned by Roth, "luminal length and wave front curvature make excitation more difficult than the peak depolarization would suggest" (40). Thus, for the typical area of the pacing-induced tissue damage, the anodal and cathodal thresholds increase almost synchronously, showing a power law with an exponent of 1.5–2 (Fig. 6D). These results are in agreement with those obtained previously for different pacing electrode lengths (42).
Optical mapping experimental data demonstrated a tendency for anodal stimulation to be more sensitive to the tissue damage than cathodal. Such a conclusion is based on the comparison of relative decreases in the maximum side polarizations; for anodal stimuli the maximum polarization at the VC decreased by 4 times while for cathodal stimuli the maximum absolute polarization decreased only by 1.5 times. Another argument speaking in favor of higher sensitivity of the anodal stimulation to the tissue damage comes from the comparison of the increases in cathodal and anodal thresholds (Table 1), even though the last differences were not statistically significant. Our simulations did not demonstrate a similar discrepancy with respect to the polarity of the test stimulus. We believe that one possible way to reconcile the modeling and experimental results on this issue is to consider incomplete cell uncoupling. It seems plausible that some of the cells close to the pacing electrode tip may stay coupled and functional for longer than others. This would lead to a greater positive effect on the cathodal than on the anodal threshold. In our modeling work, we did not consider various degrees of cell uncoupling. We recognize it as a limitation to our results.
The extent to which a shock-induced depolarization penetrates the heart wall was theoretically shown to be dependent on the degree of the fiber rotation with depth (12). For our geometry of the problem and the electrode configuration, the most noticeable modification of the VEP was expressed in its twist in the direction of the fiber rotation, rather than changes in the shape. Fiber rotation did not change the maximum polarizations and the thresholds.
For the electroporation model of tissue damage, our simulations reproduce the results of the computational study by Aguel et al. (1), who investigated the effects of electroporation on the Vm distribution around two opposite-polarity electrodes in a two-dimensional bidomain model. Our model is different in several respects. 1) It is three dimensional; therefore, it provides Vm distribution inside the slab and, most importantly, yields realistic current values. 2) We stimulated through one electrode using the upper boundary of the domain as the current sink, which is similar to the bipolar electrode configuration. 3) Our model contains a layer of conductive bath on top of the tissue, which was shown to play an important role on VEP (23, 24) and is the case in the majority of the experimental situations. Nevertheless, the main conclusions are similar. 1) Electroporation starts at absolute Vm approaching 700 mV. 2) Electroporation leads to a sharper and more pronounced dog-bone-shaped VEP with higher absolute values of Vm at the side VA areas. These results are in absolute contrast to those observed in our optical mapping experiments, even though electroporation, in principle, could lead to a transient increase in pacing thresholds as a result of an elevation in poststimulation resting potential. Thus electroporation, although present during and after the acute pacing with high-intensity current, cannot be responsible for disappearance of the VEP pattern and the associated increase in pacing thresholds, which then should be due to the cell uncoupling. We do not take into account and investigate all the causal relations between various processes that occur during tissue damage but, rather, search for direct and simple explanations. From this point of view, our analysis of the mechanisms of damage is rather speculative.
Our results are subject to a number of limitations. In the experiments, we used the excitation-contraction uncoupler BDM, which is known to modify the properties of the ion channels. Optical mapping collects averaged fluorescence not only from the surface of the epicaridum, but also from a thin layer below the surface. The simulations used a bidomain model, which is an approximation and does not account for a discontinuous cellular structure of the tissue and the associated sawtooth effect (21); its role and importance remain controversial (43). We also used BRDR ionic kinetics for the active model as one of the most simple and robust. Nevertheless, a number of substantially more accurate cellular models are available (27, 28).
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