© 2005 The European Society of Cardiology. Published by Elsevier Ltd. All rights reserved.
Cell and tissue responses to electric shocks
aDepartment of Biomedical Engineering, Tulane University Boggs Center, Suite 500, New Orleans, LA 70118, USA; bDepartment of Physiology and Biophysics, Kyoto University Graduate School of Medicine Kyoto, Japan
Manuscript submitted 22 December 2004. Revision received 27 July 2005. Accepted after revision 18 March 2005.
*Corresponding author. Tel.: +1 504 862 8934; fax: +1 504 862 8779. E-mail address: nataliat{at}tulane.edu (N.A. Trayanova).
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AIM: Existing models of myocardial membrane kinetics have not been able to reproduce the experimentally-observed negative bias in the asymmetry of transmembrane potential changes (
Vm) induced by strong electric shocks. The goals of this study are (1) to demonstrate that this negative bias could be reproduced by the addition, to the membrane model, of electroporation and an outward current, Ia, part of the K+ flow through the L-type Ca2+-channel, and (2) to determine how such modifications in the membrane model affect shock-induced break excitation in a 2D preparation.
METHODS AND RESULTS: We conducted simulations of shocks in bidomain fibres and sheets with membrane dynamics represented by the Luo–Rudy dynamic model (LRd'2000), to which electroporation (LRd+EP model) and the outward current, Ia, activated upon strong shock-induced depolarization (aLRd model) was added. Assuming Ia is a part of K+ flow through the L-type Ca2+-channel enabled us to reproduce both the experimentally observed rectangularly-shaped positive Vm and the value of near 2 of the negative-to-positive Vm ratio. In the sheet, Ia not only contributed to the negative bias in Vm asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive Vm. Electroporation, in its turn, was responsible for the decrease in cathode-break excitation threshold in the aLRd sheet, compared with the other two cases, as well as for the occurrence of the excitation after the shock-end rather than during the shock.
CONCLUSIONS: The incorporation of electroporation and Ia in a membrane model ensures match between simulation results and experimental data. The use of the aLRd model results in a lower threshold for shock-induced break excitation.
Key Words: L-type calcium current, virtual electrode polarization, electroporation, simulation, bidomain model, Luo–Rudy dynamic model
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Introduction |
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Electric shocks are widely used in clinical practice to terminate ventricular tachyarrhythmias. The shock electrodes deliver current into the myocardial extracellular space, resulting in the formation of regions of positive and negative membrane polarization in the tissue [1–
5]. These shock-induced changes (Vm) in transmembrane potential (Vm) lead to initiation of post-shock activations that determine shock outcome [6–9]. However, insight into the mechanisms that underlie membrane responses to electric shocks remains incomplete. Understanding the aetiology of these membrane responses, and specifically, the contribution of membrane electroporation [10–13] as well as the changes in ionic currents caused by strong shocks [14–17] to post-shock membrane behaviour is of paramount importance to the rational rather than trial-and-error improvements in defibrillation procedure.
Research has demonstrated that the delivery of a strong electric shock during the action potential plateau in cultured myocyte strands [14–16,18,19], papillary muscles [20,21], and three-dimensional myocardial preparations [2,22,23] leads to asymmetrical membrane polarization in the tissue with the negative Vm being nearly twice as large as the positive (phenomenon termed negative bias in Vm asymmetry). Furthermore, both positive and negative Vm exhibit non-linear behaviour as a function of shock strength.
Models of ventricular membrane dynamics [24–27] as well as versions of these modified for large changes in transmembrane potential [28–30] have been used to examine the relationship between shocks and the membrane responses they induce [28,30–34]. However, since they were developed to represent the normal action potential behaviour none of these membrane models has been able to reproduce the observed negative bias in the asymmetry of Vm following strong shocks, thus threatening to jeopardize the predictive value of simulations in the study of vulnerability to electric shocks and defibrillation.
A recent study from our group, by Ashihara and Trayanova [35] examined which membrane model modifications could bridge the existing gap between simulation and experiment. In this study, we hypothesized that the experimentally-observed negative bias in Vm asymmetry could be reproduced by the addition, to a recent version of the Luo–Rudy dynamic (LRd) model [36], of electroporation and an outward current Ia activated upon strong shock-induced depolarization, the latter suggested by the results of a single-myocyte experimental study by Cheng et al. [37]. We further hypothesized that Ia is part of the K+ flow through the L-type Ca2+-channel. We presented initial simulation results demonstrating that in multicellular cardiac tissue preparations, Ia and electroporation underlie the negative bias in Vm asymmetry. We achieved this by comparing the behaviour of three models, the original LRd model, the LRd model to which electroporation was added (LRd+EP), and the new augmented LRd (aLRd) model that includes both electroporation and the outward current Ia.
This article extends the findings of the original contribution by Ashihara and Trayanova; it presents evidence that the modifications embodied in the aLRd model, but not LRd or LRd+EP models, indeed bridge the gap between simulation and experiment in multicellular preparations, and that these modifications, in turn, affect the threshold and timing of break excitation following the shock. Correct representation of break excitation is particularly important in understanding the mechanisms of defibrillation because its delayed onset and also the propagation pattern that ensues from it are major determinants of post-shock propagation in the heart.
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Membrane models
A recent version [36]
of the Luo–Rudy dynamic model [26,27,38,39], referred to here as ‘LRd’ was used. To the LRd model, we then added the electroporation current Iep, where the expression developed by DeBruin and Krassowska [40] was used; this membrane model was referred to as ‘LRd+EP’. Finally, to the original ICa,K in the LRd model, we added Ia as formulated by Cheng et al. [37], which, together with the addition of Iep, constituted the ‘augmented’ LRd model, or ‘aLRd’.
Protocol for simulating the behaviour of multicellular preparations in response to the shock
We simulated a one-dimensional bidomain myocardial fibre of length 800 µm (Fig. 1A). Cathodal and anodal shock electrodes (denoted as C and A) were located at fibre ends. The fibre length was equivalent to cultured myocyte strand widths [14–16,18,19]; delivery of shocks through electrodes at fibre ends corresponded to uniform-field shocks applied via line electrodes across the strand width (Fig. 1A).
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A bidomain myocardial sheet of size 3.0 cm by 2.25 cm (Fig. 1B) was also simulated. Fibres in the sheet were oriented horizontally. Two grounding electrodes (shaded bars) were positioned at the vertical borders of the sheet, while a shock electrode of size 0.75 mm by 0.75 mm was located at the sheet centre.
Eight transmembrane stimuli of 300-ms basic cycle length were applied simultaneously to all units in the fibre or sheet followed by a 10-ms square-wave monophasic shock; the shock was of varying strength and was given at various coupling intervals. Shock-induced Vm was measured as the difference between the shock-induced Vm at a given time and Vm at the corresponding time in the preceding seventh stimulus-induced action potential, and normalized to the action potential amplitude (APA). The asymmetry ratio, defined as Vm–/Vm + , was calculated from the absolute values of positive and negative change in Vm, Vm– and Vm + , measured at the fibre ends 3 ms after shock onset. For the sheet, values of Vm– and Vm + were obtained by either using opposite shock polarities or from Vm– and Vm + at the site of peak polarization in the adjacent virtual electrode following shocks of opposite polarities.
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Membrane responses to shocks in the fibre
Fig. 2A shows shock-induced polarization transients at seven recording sites along a fibre for the three membrane models following a 20-V/cm shock delivered at a coupling interval of 10 ms. The positive
Vm transients at the cathodal fibre end differ for the three models: until the time the shock is turned off, they have a monotonic shape in the case of the LRd model; the shape is non-monotonic for the LRd+EP model; and finally, the shape of the Vm transient becomes rectangular for the aLRd model. These positive transients gradually change into negative Vm transients of non-monotonic behaviour as the recording site draws closer to the anode.
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Fig. 2B presents the spatial distribution of
Vm along the fibre length in the three cases for the same shock. In the LRd case, the portion of the fibre negatively polarized is shorter than the one positively polarized, with Vm–/Vm + <1. For the LRd+EP and aLRd fibres, the distribution of Vm is also asymmetric, however, negative Vm occupies a greater portion of the fibre length than positive Vm; in addition, Vm–/Vm + >1. Yet, differences between LRd+EP and aLRd cases are also observed: in the aLRd case, the spatial gradient of Vm is lower and the 0-mV location separating positive and negative Vm regions is shifted toward the cathode.
Fig. 2C portrays the relationship between asymmetry ratio and shock strength for the three types of membrane kinetics. The LRd asymmetry ratio is less than 1 for all shocks; it decreases with increasing shock strengths and reaches a value of 0.62 for high-strength shocks. Likewise, the LRd+EP asymmetry ratio is <1 for shocks <8 V/cm but becomes >1 and reaches a plateau level of 1.25 for stronger shocks. In contrast, the aLRd asymmetry ratio is >1 regardless of shock strength; as the shocks becomes stronger, the asymmetry ratio increases to 2.58 and then decreases to 1.25. The presence of a peak in the aLRd asymmetry ratio dependence on shock strength is the result of the lower rate of Vm– increase at higher shock strengths.
Membrane responses to shocks in the sheet
Panels A and B in Fig. 3 present shock-end Vm maps resulting from cathodal and anodal shocks of strength 20 mA delivered via the centrally-located electrode to the LRd, LRd+EP, and aLRd sheets at a coupling interval of 90 ms. To emphasize the Vm distribution around the shock electrode, each panel represents a quarter of the sheet; it is the region outlined by the dotted rectangle in Fig. 1B. As seen in panels A and B, a cloverleaf virtual electrode polarization is induced by the shock in all cases; however, the exact pattern of the polarization and its magnitude are different for the three models. In the LRd sheet, shown in Fig. 3A, Vm at the centre of the region directly polarized by the cathode and the maximum Vm in the virtual anode are 1081 and –69%APA, respectively. In comparison, in the LRd+EP sheet, Vm in the directly polarized region is less positive and Vm in the virtual anode is much more negative (maximum values 172 and –112%APA, respectively); while in the aLRd sheet, the corresponding values were 92 and –117%APA, respectively. Responses to anodal shocks, shown in Fig. 3B, indicate that in the LRd, LRd+EP, and aLRd sheets the maximum Vm values under the anode and in the virtual cathode were –543 and 105%APA, –214 and 134%APA, and –214 and 65%APA, respectively.
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Fig. 3C shows the asymmetry ratios at the centre of the region directly polarized by the physical electrode as well as the ratios in the virtual electrode (locations of maximum
Vm are indicated by the white circles in Fig. 3, panels A and B). In the LRd sheet, the asymmetry ratios in the physical and the virtual electrodes are significantly below 1 (0.50 and 0.66, respectively). In comparison, in the LRd+EP case both asymmetry ratios increase, but only the former was above 1 (1.24 and 0.84, respectively); while in the aLRd sheet, the asymmetry ratios were much larger, both being around 2 (2.33 and 1.80, respectively). Fig. 3D presents results regarding the thresholds for cathode-break excitation as a function of coupling interval in the sheet for the three models. A break excitation is a function of the collective behaviour of the cells in the sheet, and specifically, it depends on the interaction between adjacent regions of shock-induced strong positive and negative polarization. As the graph indicates, the cathode-break excitation threshold gradually decreases with the increase in coupling interval in all three cases. Clearly, inclusion of electroporation lowers the threshold significantly: while the cathode-break excitation thresholds are similar for the LRd+EP and aLRd cases, the aLRd is the lowest for any coupling interval tested. We also investigated the thresholds for anode-break excitation; we found that the inclusion of electroporation significantly lowered the threshold but the addition of Ia did not change it (data not shown).
The evolution of the cathode-break excitation patterns in the LRd (A), LRd+EP (B), and aLRd (C) sheets is portrayed in Fig. 4 (displayed area of the sheet corresponds to the rectangle outlined with dashed lines in Fig. 1). The cathodal stimulus, delivered through the centrally-located small electrode, is of duration 10 ms and strength 20 mA. It is administered at a coupling interval of 90 ms; the region around the shock electrode is still fairly refractory then (see pre-shock panels). The figure indicates that electroporation again has the largest effect on cathode-break excitation and the pattern of propagation following the strong stimulus: there is a significant difference between the transmembrane potential maps in the LRd sheet and the other two cases. The patterns are quite similar in the latter, with the main difference being the faster post-shock recovery of the shock-induced depolarization around the central electrode (see 104-ms panel in Fig. 4C). Interestingly, propagation due to cathode-break excitation commences during the shock in the LRd sheet (see short black arrows in Fig. 4A), and after the shock in the other two cases, where electroporation results, effectively, in a delay of the excitation. The reason for this difference in behaviour is the much stronger negative polarization in the virtual anode in the LRd+EP and aLRd sheets (see Fig. 3A). It holds the potential of the cells there to a very low value, preventing excitation; once the stimulus is released, these cells are able to develop an action potential. In addition, the excitation in the aLRd sheet shows a small delay compared with the LRd+EP sheet (see position of cathode-break excitation wavefront in 104-ms panels of Fig. 4) due to the weaker positive polarization under the cathode (see Fig. 3A).
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Models of myocardial membrane dynamics have not been able to reproduce the experimentally observed negative bias in the asymmetry of (strong) shock-induced
Vm during the plateau of the action potential. Here we demonstrate that with the use of the new aLRd model, a better agreement between simulations and experiments can be achieved. Furthermore, current discrepancies between simulation and experiment such as activation thresholds for cathodal and anodal stimuli [28,41,42] and the mechanisms of postshock activation initiation [6–9] can be resolved with the use of the new model. Adequate representation of Vm asymmetry might prove important in the study of the effect of shock polarity reversal on the upper limit of vulnerability and defibrillation threshold, and in the investigation of the mechanisms by which optimal biphasic shocks fail. It is our hope that the faithful reproduction of experimentally observed Vm in bidomain model studies will render computer simulations a powerful tool for the study of electrical fibrillation induction and defibrillation.
Arguments for the inclusion of electroporation and outward current Ia in the ionic model
Electroporation is known to occur following strong shocks to the heart [43–45]. Its contribution to Vm has been clarified in numerous studies [13,16,19,30,37,46–48]. It has been also demonstrated that the inclusion of electroporation in a membrane model diminishes the high value of the transmembrane potential in the vicinity of a small electrode, placing it into the physiological range [49]. Thus, inclusion of electroporation was a natural choice for an ionic model that is intended to bridge the gap between defibrillation simulations and experiments.
The study by Cheng et al. [37], analysing experiments on the responses of single myocytes to defibrillation-strength shocks, suggested that an outward current Ia activated upon strong shock-induced depolarization could explain the observed responses. However, the ionic composition of Ia, as well as its role in Vm asymmetry in multicellular cardiac preparations remains unknown. Studies have demonstrated that the inward rectifier potassium current blocker BaCl2 [14,16], the rapid delayed rectifier blocker dofetilide [14], and the hyperpolarization-activated inward current inhibitor CsCl [16] do not significantly change the degree of Vm asymmetry. On the other hand, a study by Cheek et al. [15] found an increase in positive Vm and a decrease in the negative-to-positive Vm ratio by the L-type Ca2+ current (ICa(L)) blocker nifedipine. These studies provide evidence that the depolarization-activated outward current Ia might flow through the L-type Ca2+ channel.
The ICa(L) current has three individual components [50], namely Ca2+, K+, and Na+ currents (ICa,Ca, ICa,K, and ICa,Na, respectively), with the permeability ratio Ca2+:K+:Na+ in the voltage range of the normal action potential being 2800:3.5:1. Therefore, it is reasonable to expect that if the large outward current Ia is a part of ICa,Ca, the intracellular Ca2+ concentration ([Ca2+]i) should experience, as a consequence of Ia activation, a sudden decrease in the regions of strong shock-induced depolarization. However, in an isolated ventricular myocyte [51], in the region of large positive Vm the change in [Ca2+]i during a shock delivered at the plateau of an action potential was relatively small (
20% of the magnitude of last pacing-induced change in [Ca2+]i) [52]. This result is also supported by the argument that since the Ca2+ Nernst potential (ECa,N) is 127.5 mV and the peak of ICa,Ca occurs around 0 mV [26], ICa,Ca is expected only to be a small contribution to ICa(L) as Vm approaches ECa,N. In contrast, when Vm surpasses the reversal potential of ICa(L) (ECa=56 mV) [53,54], ICa,K becomes a major outward component of ICa(L) [26]. However, in the ventricular membrane models used in previous simulation studies of stimulation/defibrillation, ICa,K was either not included [24,25], or if included, its characteristics for Vm> ECa were not based on experimental data [26,27].
Based on the above arguments, we assert that Ia is part of ICa,K. We demonstrate below that with the proposed ICa,K modification and with the addition of electroporation to the membrane currents, an agreement between experiments and simulations regarding the tissue responses to electric shocks can be achieved.
Membrane responses to shocks in the fibre model
Experiments [14,16,19] with cultured myocyte strands of widths 500 to 2000 µm (the widths are also the distances between shock electrodes) have shown that, for shocks delivered during action potential plateau, the negative Vm transient shape (i.e., the shape of the negative Vm transient until the pulse was disconnected) changed from non-monotonic to monotonic as shock strength increased, whereas the positive Vm transient remained nearly rectangular regardless of shock strength. As shown in Fig. 2A, the negative and positive Vm transients, recorded at opposite ends of the 800-µm long aLRd fibre, are in all respects identical to the experimentally observed (compare with Figs. 5 and 6 of [14]; Figs. 3–5 of [19]; and Fig. 1 of [16]). In contrast, both LRd and LRd+EP fibres could not reproduce the rectangular positive Vm transient. This indicates that the outward current Ia was responsible for the rectangular shape of the positive Vm transient.
In addition, for high shock strengths, the negative Vm transient in the LRd+EP and aLRd fibres no longer changed with the further increase in shock strength; while in the LRd fibre, it continued to increase. This indicates that electroporation contributed to the saturation in the magnitude of the negative Vm transients, which is consistent with experimental findings [16,19,37,48,51].
Fast et al. [14] reported that shock application during action potential plateau in strands produced two types of Vm behaviour. The first type was characterized by a monotonically rising negative Vm transient and a negative bias in Vm asymmetry, with an asymmetry ratio that increased with increasing shock strength (type II behaviour as per Fast et al. [14]). Such behaviour was observed in various cardiac preparations when relatively low shock strengths were used [14–16,18–21]. The other type of behaviour (type III) was observed for strong shocks [14,16,19] and was characterized by the non-monotonic behaviour of the negative Vm transient and the negative bias in Vm asymmetry, with an asymmetry ratio that decreased with increasing shock strength. In the present study, only the aLRd fibre reproduced these two types of Vm behaviour. Furthermore, the dependence of the aLRd asymmetry ratio on shock strength (Fig. 2C, bottom) is in agreement with experimental data in terms of both peak value and shock strength at peak value. Indeed, for a 12-V/cm shock delivered to strands wider than 500 µm, the asymmetry ratio curve was found to have a maximum around 2.5 [14]. Consistent with experimental results [2,14–16,18–22], the aLRd asymmetry ratio was around 2 for shocks in the range of 8 to 20 V/cm given during the action potential plateau. In contrast, the asymmetry ratio curve for the LRd+EP fibre exhibited a non-physiologically small peak value (<1.3). The fact that the asymmetry ratio in the aLRd fibre was higher than the one in the LRd+EP fibre (Fig. 2C) for all shock strengths was due to the smaller magnitude of the positive Vm in the aLRd case, which, in turn, was due to the contribution of Ia as a large outward current in the strongly depolarized region of the fibre. Further, the asymmetric Vm distribution with the negative Vm fibre region being larger than the positive Vm region in the aLRd case (Fig. 3B) is also consistent with experimental results [14–16,18,19].
Membrane responses to shocks in the sheet
Optical mapping studies [2,3] have demonstrated that for shocks delivered during the action potential plateau, the asymmetry ratios in the regions directly polarized by the physical electrode and in the virtual electrodes were around 2. In the present study we show that only the aLRd model (black bars in Fig. 3C) accurately reproduced the asymmetry ratios found in the experiment.
Further, optical mapping experiments [3,4,55] have typically recorded much smaller values of Vm than the ones predicted numerically [1,3,28], especially in the vicinity of the unipolar shock electrode. A possible reason for this discrepancy is the depth-averaging in the optically recorded signal [56]. Another reason could be the lack of both an Ia-like current and electroporation in these bidomain simulations; indeed, in the aLRd sheet (Fig. 3, panels A and B), both positive and negative Vm values near the shock electrode were considerably diminished by the inclusion of these two factors.
Faithful reproduction of virtual electrode polarization around a small unipolar electrode is important not only in understanding the basic mechanisms of stimulation with strong shocks; cathode-break excitation ensuing from this polarization has also been implicated in myocardial capture during fibrillation [57] and in fibrillation control [58].
Simulations of unipolar stimulation in the sheet revealed that the thresholds for break excitation (both cathode-break and anode-break) are different for the three membrane models. Inclusion of electroporation (LRd+EP and aLRd models) results in a significant decrease in this threshold for all coupling intervals. On the other hand, inclusion of Ia (aLRd model) results in small additional decrease in the threshold for cathode-break excitation and no change in the threshold for anode-break excitation. This is due to the fact that the Ia-mediated weaker positive polarization under the cathode in the aLRd sheet is concomitant with a stronger negative polarization in the region of the virtual anode compared with the LRd+EP case (Fig. 3, panel A), whereas weaker positive polarization in the region of the virtual cathode in the aLRd sheet compared with the LRd+EP case does not result in a different negative polarization under the anode (Fig. 3, panel B), since the membrane there already has electroporated.
Most importantly, however, cathode-break excitation in the original LRd model takes place before the end of the shock. Regardless of the early onset, this excitation is not cathode-make since the propagation that ensues from it is not characterized by a full-blown sodium channel activation or calcium transient (data not shown), both of which occur in the case of cathode-make excitation. The reason for the premature start of the cathode-break excitation is that in this case the shock-induced depolarization under the electrode is very high, providing a stimulus for the excitation of the recovered cells in the adjacent virtual anodes. Similar behaviour was observed in simulations of unipolar stimulation in sheets with other membrane dynamics. Indeed, the study of Skouibine et al. [33] compared cathode-break excitation with and without electroporation in a sheet incorporating the Beeler-Reuter-Drouhard-Roberge [59] ionic model and documented lack and presence, respectively, of break excitation before the end of the shock (Fig. 1 of [33]), regardless of the fact that a much older model of electroporation [60] was used in this study. This implicates electroporation as the major factor in determining the post-shock delay in the cathode-break excitations. The Ia current has also an additional contribution to the post-shock delay of cathode-break excitation; it is possible that this hypothetical current might contribute, to a much larger degree, to the break excitation mechanism in diseased tissue.
Conclusions
The present study provided insight into the asymmetry in positive vs. negative (strong) shock-induced Vm as well as the threshold and pattern of cathode-break excitation. While further experiments are needed to confirm the ionic composition of Ia, the new aLRd model lends itself as a useful tool in the studies of electrical fibrillation induction and defibrillation. Incorporation of aLRd membrane kinetics in bidomain models of stimulation/defibrillation allows us to resolve discrepancies between experiments and simulations, ultimately increasing the utility of computer simulations in cardiac electrophysiology.
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This study was supported by NIH Grants HL063195 and HL074283, a grant from the American Heart Association, and a Leading Project for Biosimulation from the Ministry of Education, Culture, Sports, Science and Technology in Japan.
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