Cardiac vulnerability to electric shocks during phase 1A of acute global ischemia

Blanca Rodríguez PhD¹, Brock M Tice BS¹, James C Eason PhD², Felipe Aguel PhD³, and Natalia Trayanova PhD¹

¹ Tulane University, New Orleans LA

² Washington and Lee University, Lexington VA

³ Food and Drug Administration, Rockville MD

Short title: Shock-induced arrhythmogenesis in acute ischemia

Financial support: This work was supported by AHA Established Investigator Award (N.T.), by NIH grant HL063195 (N.T.), by Pre-NPEBC NIH grant P20 EB001432 (Tulane Center for Computational Sciences), and by grants from the Whitaker and Keck Foundations (J.E.).

Correspondence:

Dr. Blanca Rodríguez

Department of Biomedical Engineering, Tulane University

New Orleans, LA 70118

Phone: (504) 865-5867

Fax: (504) 862-8779

e-mail: blanca@tulane.edu

This is an archive of an article published in the Heart Rhythm Journal. The final published version is available (if you are subscribed) here.

Abstract

Objective: The goal of this study is to characterize the changes in vulnerability to electric shocks during phase 1A of global ischemia in the rabbit ventricles and to provide understanding of the mechanisms responsible for these changes.

Background: Mechanisms responsible for the changes in cardiac vulnerability over the course of ischemia phase 1A remain poorly understood. This is due to the rapid ischemic change in cardiac electrophysiological properties, which renders experimental evaluation of vulnerability difficult.

Methods: To examine dynamic changes in vulnerability to electric shocks over the course of acute global ischemia phase 1A, this study uses a three-dimensional anatomically-accurate bidomain model of ischemic rabbit ventricles. Monophasic shocks are applied at various coupling intervals to construct vulnerability grids in normoxia and at various stages of ischemia phase 1A.

Results: Our simulations demonstrate that 2-3min after the onset of ischemia, the upper limit of vulnerability remains at its normoxic value, 12.75V/cm, however, arrhythmias are induced at shorter coupling intervals. As ischemia progresses, the upper limit of vulnerability decreases, reaching 6.4V/cm in the advanced stage of ischemia phase 1A, and the vulnerable window shifts towards longer coupling intervals.

Conclusions: Changes in the upper limit of vulnerability are due to an increase in the spatial extent of the shock-end excitation wavefronts and the slower recovery from shock-induced positive polarization. Shifts in the vulnerable window stem from decreases in local repolarization times and the occurrence of post-shock conduction failure caused by prolonged post-repolarization refractoriness.

Keywords: Acute ischemia, upper limit of vulnerability, reentry, excitation, conduction failure.

List of Abbreviations

ADP	Adenosine diphosphate
[ADP]i	Intracellular ADP concentration
APD	Action potential duration
ATP	Adenosine triphosphate
[ATP]i	Intracellular ATP concentration
CI	Coupling interval
CIULV	Shortest coupling interval at which the upper limit of vulnerability occurs
ERP	Refractory period
IK(ATP)	ATP-dependent potassium current
[K+]o	Extracellular potassium concentration
LLV	Lower limit of vulnerability
LV	Left ventricle
NASPE	North American Society for Pacing and Electrophysiology
PRRP	Post-repolarization refractoriness period
RV	Right ventricle
SFNa	Scaling factor for maximum conductance of sodium channels
SFCaL	Scaling factor for maximum conductance of L-Type calcium channels
ULV	Upper limit of vulnerability
VG	Vulnerable grid
Vrest	Resting potential
VW	Vulnerable window

Introduction

Understanding cardiac vulnerability to electric shocks has long been considered a route to understanding arrhythmogenesis by failed defibrillation shocks.^1-5 However, while the majority of patients that undergo defibrillation suffer from coronary disease, research on shock-induced arrhythmogenesis has mostly focused on normal hearts (see, for instance^1-3) and rarely on hearts with ischemic disease.^4,5 This is due to the fact that during acute ischemia, myocardial electrophysiological properties change rapidly.⁶ This renders experimental evaluation of arrhythmogenesis difficult: tissue state varies from shock to shock in the course of a single experiment.^4,5 Therefore, changes in cardiac vulnerability to electric shocks over the course of ischemia phase 1A remain poorly understood.

Simulations of post-shock electrical events in a realistic model of the normal ventricles have afforded significant insights into the mechanisms of shock-induced arrhythmogenesis^2,7 by providing information, with a high spatiotemporal resolution, regarding shock-induced electrical behavior within the myocardial depth not currently accessible by experimental techniques. The present study extends this approach to arrhythmogenesis in the acutely ischemic ventricles. The goal is to characterize the changes in vulnerability to electric shocks during phase 1A of global ischemia, and to provide understanding of the mechanisms responsible for these changes. This study focuses on global ischemia as an important step^4,5 in understanding the mechanisms that underlie vulnerability to electric shocks following an ischemic event associated with coronary heart disease.

Since break-excitations secondary to shock-induced virtual electrode polarization underlie post-shock activity in the myocardium,^1-3,8-10 we hypothesize that dynamical changes in ionic currents and concentrations over the course of ischemia phase 1A will affect the characteristics of the break-excitation wavefronts as well as their propagation, thus altering both the vulnerable window (VW) and the upper limit of vulnerability (ULV) to electric shocks. The present research tests this hypothesis.

Methods

Computational model

We used the anatomically accurate finite-element bidomain rabbit ventricular model (Fig.1) described previously.^2,7 Numerical aspects regarding ventricular discretization and finite-element solver can be found in previous publications by our group.^11,12

Global ischemia was implemented by assigning to every cell in the rabbit ventricles, the same (ischemic) membrane dynamics. Ionic currents were represented by an ischemic version8 of the Luo-Rudy dynamic model^13,14 modified for defibrillation.⁷ Specifically, to represent changes in membrane dynamics over the course of the first 10min following coronary occlusion, the extracellular potassium concentration ([K⁺]_o) was increased,^6,15,16 while the maximum conductances of Na⁺ and L-Type Ca²⁺ channels were decreased (by scaling factors SF_Na and SF_CaL), representing inhibition by acidosis.^6,17,18 Additionally, the ATP-dependent K⁺_K(ATP),¹⁹ was incorporated; its activation was regulated by hypoxia-induced changes in intracellular ATP and ADP concentrations ([ATP]_i and [ADP]_i).^6,16 current, I

Progression of ischemia phase 1A was represented by linear changes in [K⁺]_o, SF_Na and SF_CaL, and [ATP]_i and [ADP]_i.^6,15-18 To study vulnerability to shocks, three representative ischemic levels of increasing severity within this 10min-interval were singled out. These levels are referred to as initial (2-3min of occlusion), intermediate (5-7min), and advanced (8-10min of occlusion). Values of [K⁺]_o, SF_Na and SF_CaL, and [ATP]_i and [ADP]_i in normoxia and for each ischemic state are presented in Table 1. Simulations were conducted in normoxia and for each state of ischemia to construct vulnerability grids (VGs).

Table 1: Model parameters.

	Normoxia	Initial Ischemia	Intermediate Ischemia	Advanced Ischemia
[K+]o*	5.4mmol/L	7.0mmol/L	8.7mmol/L	10.4mmol/L
SFNa†	100%	93.75%	87.5%	81.25%
SFCaL‡	100%	93.75%	87.5%	81.25%
[ATP]i§	6.8mmol/L	6.25mmol/L	5.7mmol/L	5.15mmol/L
[ADP]i&	15µmol/L	36µmol/L	57µmol/L	78µmol/L

^*Extracellular K⁺ concentration.

^§ Intracellular ATP concentration.

^& Intracellular ADP concentration.

^† Scaling factor for maximum conductance of Na⁺ channels.

^‡ Scaling factor for maximum conductance of L-Type Ca²⁺ channels.

Vulnerability grids

The ventricles were paced at the apex at 250ms basic cycle length. Following the 7^th pacing stimulus, truncated-exponential 8ms-long monophasic shocks of 65% tilt were applied via two planar electrodes in the perfusing chamber (Fig.1). Electrode next to the right ventricle (RV) was a cathode.

VGs were constructed by examining the outcome of shocks of various strengths applied at several coupling intervals (CIs) (measured from the onset of the last pacing stimulus). If the shock induced arrhythmia, it was then classified. Arrhythmia was considered unsustained if one or two beats followed the immediate post-shock activation and self-terminated within 250ms of shock end. However, if a third beat was observed, arrhythmia was classified as sustained. While this choice differs from previous criteria,⁴ it was dictated by the stable arrhythmia pattern as well as by the large size of the model; longer times of simulation would be prohibitive computationally. For normoxia and each level of ischemia, ULV was determined as the lowest shock strength above which sustained reentry was no longer induced. The lower limit of vulnerability (LLV) was defined as the highest shock strength below which no sustained arrhythmia was induced. VW was determined as the interval between the shortest and the longest CIs for which sustained arrhythmia was induced. Increments in shock strength and CI used here were 1.5V/cm and 10ms, respectively. Finally, shock strengths referred to leading-edge values.

Data analysis

To analyze ischemia-induced changes in ventricular electrical behavior, activation and repolarization times were quantified at each ventricular node. At each node, local activation time was calculated following the 7^thth stimulus and the time at which the node was 70% repolarized. Action potential duration (APD) was the difference between activation and repolarization times. Refractory period (ERP) was measured using a pacing stimulus of twice diastolic threshold (S2) that followed the 7^th paced beat; ERP was determined as the maximum S2 CI that did not result in propagation. Finally, post-repolarization refractoriness period (PRRP) was defined as the difference between ERP and APD. pacing stimulus as the interval between the stimulus onset and the time of maximum action potential upstroke velocity. Local repolarization time was calculated as the interval between the onset of the 7

Results

Electrical activity in acute global ischemia

Fig.2 illustrates the effect of increasing ischemia severity on action potential morphology (panel A), APD and V_rest (panel B), ERP and PRRP (panel C), and on the maps of activation and repolarization times (panel D). Note that since action potential morphology and ERP are the same for each cell (per our implementation of global ischemia), changes in the parameters shown in panels A, B, and C over the course of acute ischemia refer to any ventricular node. In contrast, activation time is different at each node due to fiber orientation. Therefore, local repolarization time (which includes, by definition, local activation time) is different from node to node.

Figs.2A and 2B show that, as acute ischemia 1A progresses, action potential amplitude decreases, APD shortens, and V_rest becomes elevated. Furthermore, PRRP increases, while ERP exhibits a non-monotonic behavior (Fig.2C). The shape of the activation isochrones in Fig.2D is determined by fiber orientation and thus, is the same in normoxia and ischemia. However, local activation times change over the course of ischemia due to altered propagation velocity. Shortly after ischemia onset, propagation velocity increases slightly; this is due to a decrease in the difference between V_rest and the threshold for activation.⁶ Accordingly, our simulations demonstrate that the longest local activation time in the ventricles in initial and intermediate ischemia decreases to 87 and 82ms, respectively, from its normoxic value of 93ms; this corresponds to 7 and 13% increase in average conduction velocity, respectively. However, as ischemia progresses, conduction velocity decreases due to reduction in Na⁺ current by both acidosis and V_rest elevation,⁶ thereby increasing local activation times. As shown in Fig.2D, the longest local activation time in advanced ischemia increases to 111ms, which corresponds to a 16% decrease in average velocity.

In ischemia, local repolarization times decrease (Fig.2D), predominantly due to APD shortening. However, since local repolarization times also depend on local activation times, at each stage of ischemia this decrease is not homogeneous throughout the ventricles. Specifically, while in initial ischemia faster-than-normal propagation contributes to the decrease in local repolarization times, at the late stages of ischemia slow conduction slightly increases repolarization times, particularly at the base. The longest local repolarization time decreases from 222ms in normoxia to 190 and 168ms in initial and intermediate ischemia, but then increases to 184ms in advanced ischemia.

Figure 2: Action potentials (A), V_rest and APD (B), ERP and PRRP (C), and activation and repolarization maps (D) following the 7^th paced beat in normoxia and the three levels of ischemia phase 1A.

Ischemia-induced changes in VGs

VGs for normoxia and the three ischemia stages are shown in Fig.3. Areas colored in dark gray correspond to induction of sustained arrhythmias, while light gray regions refer to unsustained arrhythmias. Each dot represents a simulation; among these, data points marked by special symbols are episodes examined in detail later. As evident from Fig.3, the dark gray area progressively decreases with increasing ischemia severity due to changes in ULV and VW.

ULV is 12.75V/cm in normoxia and remains unchanged in initial ischemia; it decreases to 9.6 and 6.4V/cm as ischemia progresses. The shortest CI at which ULV occurs (CI_ULV) decreases in initial ischemia, but increases in the later ischemic stages. LLV remains unchanged at 1.5V/cm until it drops to 0.75V/cm in advanced ischemia.

In initial and intermediate ischemia, VW is reduced by the decrease of the longest CI at which sustained reentries occur (Fig.3, right border of dark gray areas). However, the shortest CI at which unsustained arrhythmias are induced (Fig.3, left border of light gray areas) also decreases. Therefore, the range of CIs for which arrhythmias (sustained and unsustained) are induced is of similar width in normoxia and in initial and intermediate ischemia. In advanced ischemia, VW is also reduced; it is shifted towards longer CIs with increases in both shortest and longest CI.

Altogether, the vulnerability of the rabbit ventricles to electric shocks decreases with the progression of global ischemia phase 1A. This is due to the decrease in both ULV and VW.

Post-shock activity

To elucidate the mechanisms responsible for changes in vulnerability during ischemia phase 1A, Fig.4 examines the post-shock activity for shocks below (panel A) and above (panel B) ULV. Shock strengths are shown under each 0ms panel. All shocks in Fig.4 are applied at the respective CI_ULV (shown under each pre-shock panel); the pre-shock state of the ventricles at CI_ULV is the state most vulnerable to reentry induction at high shock strengths. Episodes depicted in Fig.4A correspond to entries marked with O symbols in Fig.3 (inside dark gray regions), while episodes portrayed in Fig.4B are denoted in Fig.3 by asterisks (outside of dark gray regions). Shown in Fig.4 are maps of anterior transmembrane potential distribution and a diagram showing features of post-shock activity in each case. Green lines represent excitation wavefronts at shock end, while solid red arrows indicate direction of their propagation. In intermediate and advanced ischemia, dashed red arrows indicate direction of decremental conduction and dashed black lines mark locations at which conduction becomes decremental. In all cases, activity on the posterior side of the ventricles is nearly symmetrical to the one on the anterior (not shown).

In normoxia and ischemia, the shock induces two main areas of opposite-in-sign virtual electrode polarization on the epicardium; the positive is next to the cathode (Fig.4, 0ms panels). Following shocks below ULV, propagation of post-shock excitation proceeds from apex to base through the LV shock-induced excitable gap (Fig.4A, red arrow, 0 and 22ms panels). Shock-induced refractoriness, mainly in the RV, causes a transient block (Fig.4A). Eventually, RV recovers, and propagation returns towards the apex, completing the first reentrant cycle (80 and 117ms panels, and diagram). The same type of reentry is induced in both normoxia and ischemia: a scroll wave in the anterior of the ventricles and, symmetrically, another in the posterior (not shown), establishing a figure-of-eight with a common pathway in the apex. While in initial ischemia ventricular preshock state and post-shock activity remain similar to these in normoxia (Fig.4A), differences develop as ischemia progresses. First, the spatial extent of the activation wavefront at shock end (represented by the length of the green line in Fig.4A) increases in the late stages of ischemia as compared to normoxia. This finding is further quantified in Fig.5, where the spatial extent (size) of the shock-end wavefronts (calculated as number of nodes activated at shock end as percentage of all ventricular nodes) is presented for normoxia and the two late stages of ischemia as a function of CI for the 6.4V/cm shock. Black crosses in this figure indicate episodes corresponding to CI_ULV, and demonstrate an increase in shock-end wavefront extent in the late stages of ischemia as compared to normoxia. Second, Fig.4A shows that, at 22ms post-shock, most of the RV remains depolarized for a longer post-shock period in the late stages of ischemia than in normoxia. Indeed, the percentage of nodes depolarized above -5mV at shock end that remain depolarized above that level 22ms later is 76% in normoxia, and 94.1 and 94.5% in intermediate and advanced ischemia, respectively.

Increasing shock strength above the ULV increases the size of the shock-end wavefronts in the LV free wall (Figs.4A and 4B, compare green line length in diagrams). Indeed, the wavefront size increases from 0.78 to 1.0% in normoxia, from 0.91 to 1.2% in initial ischemia, from 2.1 to 2.5% in intermediate ischemia, and from 1.39 to 1.95% in advanced ischemia. Thus, despite lower shock strengths, green lines are longer in the late stages of ischemia as compared to normoxia and initial ischemia. As a result, propagation on the epicardium in Fig.4B terminates shortly after shock end in all cases. In normoxia and initial ischemia, this is due to wavefront collision; Fig.4B, 20ms panels, shows the transmembrane potential maps following collision. However, as ischemia severity increases, activity dies out also because of decremental conduction (Fig.4B, dashed red arrows and 20ms panels). When the epicardium recovers from this immediate post-shock activation, an extrasystole is induced following a breakthrough in some cases (light gray areas above ULV in Fig.3). In the remaining cases, activity dies out everywhere and not only on the epicardium (white regions above ULV in Fig.3).

For shocks above the ULV, episodes of extrasystole occur more frequently during initial and intermediate ischemia than in normoxia. Fig.6 illustrates generation of an extrasystole by a 9.6V/cm shock applied at CI=140ms in intermediate ischemia. Shown are maps of transmembrane potential on the anterior and posterior epicardium, and on a plane through the ventricles. When the shock is turned off, propagation starts at the apex but becomes decremental when it reaches the location marked by the black dashed lines in the 12ms panels. All activity dies out on the epicardium shortly thereafter (22ms panel, arrows in anterior and posterior), but a wave propagates within the LV wall (22ms panel, arrow in transmural view). This wave has no signature on the epicardium until it breaks through the surface 60ms post-shock (arrows in 60ms panels). However, the majority of the myocardium is already recovered at that time, thus propagation proceeds in all directions (80 and 140ms panels). With no unidirectional block, reentry is not established, and activity dies out after the extrasystole (200ms panel).

Figure 6: Transmembrane potential distribution in intermediate ischemia following a shock of strength 9.6V/cm applied at CI=140ms. Times refer to shock end. Arrows refer to events discussed in the text. Color scale as in Fig.4.

Discussion

This study uses, for the first time, a sophisticated computer model of ventricular electrophysiology to provide mechanistic insight into the dynamic changes in cardiac vulnerability to electric shocks during phase 1A of acute global ischemia. Our results demonstrate that ULV diminishes as ischemia progresses, while the range of CIs that comprises the VW shifts as a function of ischemia severity. Altogether, the ventricles become less vulnerable to electric shocks as global ischemia phase 1A progresses. These changes in vulnerability stem from ischemia-related alterations in the characteristics of the post-shock activations and their propagation. The present discussion dissects the mechanisms specific to each level of acute ischemia phase 1A.

Simulation of acute global ischemia

Previous studies have shown that changes in myocardial electrophysiological behavior during ischemia phase 1A are mainly due to the impact of hyperkalemia, acidosis, and hypoxia on ionic concentrations and currents.^6,20 However, the time course of these changes depends on a variety of factors, among which are the degree of coronary flow reduction and animal species.⁶ This study focuses on rabbit arrhythmogenesis; thus, changes in [K⁺]_o, maximum conductances of Na⁺ and L-Type Ca²⁺ channels, and [ATP]_i and [ADP]_i incorporated in the model are specific to the rabbit heart during the first 10min of complete elimination of perfusion. Accordingly, alterations in action potential morphology and conduction velocity over the course of ischemia phase 1A, as obtained in our study, are consistent with experimental data.^6,15,16 In the following sections we discuss how changes in these electrophysiological properties affect post-shock activity in the ventricles, and thus, vulnerability to shocks, as presented in Fig.3.

Vulnerability during initial ischemia

During initial ischemia, reduced APD and local activation times lead to a decrease in local repolarization times with PRRP remaining similar to that in normoxia (Fig.2C). Therefore, (nearly) the same level of recovery is established earlier in initial ischemia as compared to normoxia. This explains the overall leftward shift of the light and dark gray areas in Fig.3, second panel; similar is the shift in CI_ULV. As the tissue state at CI_ULV is similar in normoxia and in initial ischemia (see also Fig.4A), ULV is not altered.

Nevertheless, the significant decrease in ERP affects post-shock activity by resulting in faster recovery from shock-induced positive polarization. Faster recovery decreases the likelihood of unidirectional block, thus reducing the probability that a post-shock wave will reenter and establish sustained arrhythmia.⁸ This explains why there are less sustained arrhythmias and more extrasystoles in initial ischemia than in normoxia (Fig.3, second panel).

Vulnerability in the late stages of acute ischemia

As acute ischemia progresses, APD shortens and V_rest becomes elevated (Fig.2B), while ERP and propagation velocity exhibit a non-monotonic behavior (Fig.2C and Fig.2D, activation maps). In addition, PRRP increases (Fig.2C). The prolongation of post-repolarization refractoriness is caused by V_rest elevation, which increases the time constants for recovery of Na⁺ inactivation gates and decreases the steady-state values of these gating variables.²⁰ However, the steady state values remain unchanged as long as V_rest is below -80mV,²⁰ but they quickly decrease with the increase in V_rest above -80mV. This explains why the increase in PRRP shown in Fig.2C becomes faster when V_rest exceeds -80mV, i.e. at the transition between initial and intermediate ischemia.

The decrease in repolarization times in intermediate and advanced ischemia (Fig.2D) results in increase in the amount of tissue repolarized at a given CI as compared to normoxia; however, some of this tissue remains in prolonged post-repolarization refractoriness, particularly around the base. Significant changes in post-shock activity during the late stages of ischemia phase 1A thus take place; these ultimately result in a diminished ULV and a rightward shift in the VW.

The fact that in intermediate/advanced ischemia tissue is more recovered in the apical portion of the ventricles at a given CI leads to an increase in the spatial extent of shock-end wavefronts (occurring close to the apex)⁹ furthermore, the likelihood of them being blocked by the prolonged refractoriness in positively-polarized regions increases, resulting in a diminished ULV. and to a longer shock-induced refractoriness in the RV, as determined here. Wavefronts of larger spatial extent traverse the post-shock excitable gap faster for the same shock strength;

Prolonged post-repolarization refractoriness causes conduction failure that results in a rightward shift in the VW for intermediate and advanced ischemia. Indeed, if it were not for the emergence of conduction failure, the leftward shift of the light and dark gray areas in Fig.3, as observed in initial ischemia, would have continued in the later stages as well, because of decrease in local repolarization times. Conduction failure occurs for short CIs and high shock strengths; as shown in Fig.4B, post-shock propagation becomes decremental as it reaches the location of the black dashed lines, manifesting low post-shock excitability. We found that diminished post-shock excitability is caused by a delay in recovery of Na⁺ inactivation gates in the late stages of ischemia. In normoxia and initial ischemia, the shock-induced negative polarization in the LV resets the Na⁺ inactivation gates there, but is insufficient to do so as ischemia progresses further. As demonstrated by the repolarization maps in Fig.2D, the apical regions are always more recovered than the rest of the ventricles. Therefore, post-shock activations manage to traverse the apical regions only to fail in the less-recovered basal portions (Fig.4B, regions above black dashed lines). Consequently, conduction failure resulting from increase in post-repolarization refractoriness is the mechanism responsible for rightward shift in the VW in the late stages of ischemia phase 1A.

Comparison with previous studies

We are aware of only two experimental studies that investigated the effect of acute global ischemia on cardiac vulnerability to electric shocks.^4,5 In both studies, acute global ischemia was simulated by partial reduction in coronary flow, while here we represent acute global ischemia following complete elimination of coronary flow. Previous experimental studies have reported that, if perfusion is not totally suppressed, arrhythmias are more frequent and acidosis is less severe than in zero-flow ischemia.^21,22 Thus, differences in cardiac vulnerability to electric shocks between low-flow ischemia (as in references [4,5]) and zero-flow ischemia (as in the present research) are to be expected.

Cheng et al.⁵ studied vulnerability following 30min of low-flow acute ischemia, when the action potential was temporarily stable, thus avoiding the rapid electrophysiological changes characteristic of ischemia phase 1A. At that time, cellular uncoupling had already taken place in their preparations; thus, comparison with our simulation results is not appropriate.

In a study by Behrens et al.,⁴ ULV and VW were determined by delivering biphasic shocks in the interval between 10 and 15min from the onset of partial coronary flow reduction. Tissue electrophysiology changed significantly during that period; for instance, APD₉₀ decreased from 77 to 66% of its normal value. We observed a similar change in the transition between intermediate and advanced ischemia. Clearly, the electrophysiological properties in Behrens et al. study⁴ were different from shock to shock, thus ULV and VW in a given heart represented averages over different stages of acute ischemia possibly resulting in an overestimation of the VW.

In the majority of Behrens et al. experiments (6 out of 10) ULV significantly decreased as compared to normoxia; in one case ULV remained unchanged. These findings are consistent with our results. In addition, Behrens et al. found that the left VW border shifted towards shorter CIs; they related this change to the decrease in repolarization times. In our study, similar shift of the shortest CI was observed in initial and intermediate ischemia (Fig.3); however, it pertained to unsustained arrhythmias. A possible explanation for this difference is that in our model membrane dynamics are the same in every cell, while dispersion of refractoriness in the experimental preparation increased over time. The increased dispersion of refractoriness could have increased the likelihood of reentry induction at short CIs in Behrens et al. experiments.

Limitations

The limitations of the model have been described elsewhere;⁷ here we discuss limitations specific to this study. While the increase in [K⁺]_o, I_K(ATP) activation, and decreases in Na⁺ and L-type Ca²⁺ channel conductances are responsible for the majority of alterations in action potential morphology and refractoriness during ischemia phase 1A, other changes in membrane kinetics⁶ as well as transmural heterogeneity in membrane dynamics may contribute to changes in vulnerability. Despite these limitations, the study provides, for the first time, detailed understanding of the mechanisms underlying the evolution of vulnerability over the course of global ischemia phase 1A.

Global ischemia may not, however, represent the conditions of clinical ischemia, thus it is not clear whether the mechanisms uncovered in this study could be extrapolated to the events following coronary occlusion. Furthermore, shock-induced arrhythmogenesis in the rabbit ventricles might not be directly translated to events in the much larger human heart.

Acknowledgements

For this work Dr. Rodríguez was awarded first prize in the Young Investigator Award Competition at the NASPE-Heart Rhythm Society Meeting in 2004; a portion of this work was thus published previously in abstract form.²³ The authors thank Dr. JM Ferrero Jr (Universidad Politécnica de Valencia, Spain) for helpful comments and suggestions.

References

1. Efimov IR, Cheng Y, Van Wagoner DR, et al. Virtual electrode-induced phase singularity: a basic mechanism of defibrillation failure. Circ Res. 1998;82:918-925.

2. Rodríguez B, Trayanova N. Upper limit of vulnerability in a defibrillation model of the rabbit ventricles. J Electrocardiol. 2003;36(Suppl):51-56.

3. Trayanova N. Concepts of ventricular defibrillation. Phil Trans R Soc Lond. 2001;359:1327-1337.

4. Behrens S, Li C, Franz MR. Effects of myocardial ischemia on ventricular fibrillation inducibility and defibrillation efficacy. J Am Coll Cardiol. 1997;29:817-824.

5. Cheng Y, Mowrey KA, Nikolski V, et al. Mechanisms of shock-induced arrhythmogenesis during acute global ischemia. Am J Physiol. 2002;282:H2141-H2151.

6. Carmeliet E. Cardiac Ionic Currents and Acute Ischemia: From Channels to Arrhythmias. Physiol Rev. 1999;79:917-1017.

7. Trayanova NA, Eason JC, Aguel F. Computer simulations of cardiac defibrillation: A look inside the heart. Comput Visual Sci. 2002;4:259-270.

8. Rodríguez B, Tice BM, Eason JC, Aguel F, Ferrero JM Jr, Trayanova N. Effect of acute global ischemia on the upper limit of vulnerability: a simulation study. Am J Physiol (Heart and Circ Physiol). 2004;286:H2078-H2088.

9. Evans FG, Ideker RE, Gray RA. Effect of shock-induced changes in transmembrane potential on reentrant waves and outcome during cardioversion of isolated rabbit hearts. J Cardiovasc Electrophysiol. 2002;13:1118-1127.

10. Skouibine K, Trayanova N, Moore P. Success and failure of the defibrillation shock: insights from a simulation study. J Cardiovasc Electrophysiol. 2000;11:785-796.

11. Meunier JM, Eason JC, Trayanova NA. Termination of reentry by a long-lasting AC shock in a slice of canine heart: a computational study. J Cardiovasc Electrophysiol. 2002; 13:1253-1261.

12. Eason JC and Malkin RA. A simulation study evaluating the performance of high-density electrode arrays on myocardial tissue. IEEE Transactions on Biomedical Engineering. 2000;47:893-901.

13. Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res. 1994;74:1071-1096.

14. Zeng J, Laurita KR, Rosenbaum DS, Rudy Y. Two components of the delayed rectifier K+ current in ventricular myocytes of the guinea pig type. Theoretical formulation and their role in repolarization. Circ Res. 1995;77:140-152.

15. Weiss JN, Shine KI. [K⁺]_o accumulation and electrophysiological alterations during early myocardial ischemia. Am J Physiol. 1982;243:H318-H327.

16. Weiss JN, Venkatesh N, Lamp ST. ATP-sensitive K⁺ channels and cellular K⁺ loss in hypoxic and ischemic mammalian ventricle. J Physiol(Lond). 1992;447:649-673.

17. Sato R, Noma A, Kurachi Y. Effects of intracellular acidification on membrane currents in ventricular cells of the guinea pig. Circ Res. 1985;57:553-561.

18. Kagiyama Y, Hill JL, Gettes LS. Interaction of acidosis and increased extracellular potassium on action potential characteristics and conduction. Circ Res. 1982;51:614-623.

19. Ferrero JM Jr, Sáiz J, Ferrero JM, Thakor N. Simulation of action potentials from metabolically impaired cardiac myocytes. Role of ATP-sensitive K⁺ current. Circ Res. 1996;79:208-221.

20. Shaw R, Rudy Y. Electrophysiological effects of acute myocardial ischemia: a theoretical study of altered cell excitability and action potential duration. Cardiovasc Res. 1997;35:256-272.

21. Penny WJ, Sheridan DJ. Arrhythmias and cellular electrophysiological changes during myocardial ischaemia and reperfusion. Cardiovasc Res. 1983;17(6):363-72.

22. Pike MM, Luo CS, Clark MD, Kirk KA, Kitakaze M, Madden MC, Cragoe EJ Jr, Pohost GM. NMR measurements of Na⁺ and cellular energy in ischemic rat heart: role of Na⁺-H⁺ exchange. Am J Physiol (Heart Circ Physiol). 1993;265:H2017-H2026.

23. Rodríguez B, Tice B, Eason J, Aguel F, Trayanova N. Cardiac vulnerability to electric shocks during phase 1A of acute global ischemia. Heart Rhythm. 2004;1(1):S90.