Effects of electroporation on the transmembrane potential distribution in a two-dimensional bidomain model of cardiac tissue

How computer simulations of the human heart can improve anti-arrhythmia therapy

Over the last decade, the state-of-the-art in cardiac computational modelling has progressed rapidly. The electrophysiological function of the heart can now be simulated with a high degree of detail and accuracy, opening the doors for simulation-guided approaches to anti-arrhythmic drug development and patient-specific therapeutic interventions. In this review, we outline the basic methodology for cardiac modelling, which has been developed and validated over decades of research. In addition, we present several recent examples of how computational models of the human heart have been used to address current clinical problems in cardiac electrophysiology. We will explore the use of simulations to improve anti-arrhythmic pacing and defibrillation interventions; to predict optimal sites for clinical ablation procedures; and to aid in the understanding and selection of arrhythmia risk markers. Together, these studies illustrate how the tremendous advances in cardiac modelling are poised to revolutionize medical treatment and prevention of arrhythmia.

Electroporation induced by internal defibrillation shock with and without recovery in intact rabbit hearts

Defibrillation shocks from implantable cardioverter defibrillators can be lifesaving but can also damage cardiac tissues via electroporation. This study characterizes the spatial distribution and extent of defibrillation shock-induced electroporation with and without a 45-min postshock period for cell membranes to recover. Langendorff-perfused rabbit hearts (n = 31) with and without a chronic left ventricular (LV) myocardial infarction (MI) were studied. Mean defibrillation threshold (DFT) was determined to be 161.4 ± 17.1 V and 1.65 ± 0.44 J in MI hearts for internally delivered 8-ms monophasic truncated exponential (MTE) shocks during sustained ventricular fibrillation (>20 s, SVF). A single 300-V MTE shock (twice determined DFT voltage) was used to terminate SVF. Shock-induced electroporation was assessed by propidium iodide (PI) uptake. Ventricular PI staining was quantified by fluorescent imaging. Histological analysis was performed using Masson's Trichrome staining. Results showed PI staining concentrated near the shock electrode in all hearts. Without recovery, PI staining was similar between normal and MI groups around the shock electrode and over the whole ventricles. However, MI hearts had greater total PI uptake in anterior (P < 0.01) and posterior (P < 0.01) LV epicardial regions. Postrecovery, PI staining was reduced substantially, but residual staining remained significant with similar spacial distributions. PI staining under SVF was similar to previously studied paced hearts. In conclusion, electroporation was spatially correlated with the active region of the shock electrode. Additional electroporation occurred in the LV epicardium of MI hearts, in the infarct border zone. Recovery of membrane integrity postelectroporation is likely a prolonged process. Short periods of SVF did not affect electroporation injury.

Spatial distribution and extent of electroporation by strong internal shock in intact structurally normal and chronically infarcted rabbit hearts

INTRODUCTION

Although life-saving, a strong internal defibrillation shock may temporarily or permanently damage the heart via disruption of cell membranes (electroporation). Spatial extent of electroporation in intact, normal, or infarcted hearts has not been investigated. In this study, shock-induced electroporation in intact rabbit hearts with and without chronic (>4 weeks) left ventricular myocardial infarction (MI) was characterized.

METHODS AND RESULTS

A coil shock electrode was inserted in the right ventricle of Langendorff-perfused hearts. One truncated exponential monophasic shock (+300 V, 8 ms) was delivered by a 150 microF capacitor clinical defibrillator while the heart was perfused with membrane-impermeant dye propidium iodide (PI). The heart was sectioned transversely, and uptake of PI into ventricular myocardium through electropores was quantified. Histological evaluation was performed via Masson's trichrome staining. PI accumulation was minimal in the control (n = 3) and MI (n = 3) hearts without shock. Following shock delivery, (1) in control (n = 5) and MI (n = 5) hearts, electroporation mostly occurred near the shock electrode and was longitudinally distributed along the active region of the shock electrode; (2) in MI group, electroporation was significantly increased (P < 0.05) in the surviving anterior epicardial layers of the infarcted region; and (3) between the control and MI groups, the overall extent of electroporation was similar.

CONCLUSION

Shock-induced electroporation was spatially dependent on the location and dimension of the active region of the shock electrode. The overall extent of electroporation in the MI heart was comparable with the control heart, but the surviving anterior epicardial layers in the infarcted region were more susceptible to electroporation.

Effect of electroporation on cardiac electrophysiology

Defibrillation shocks are commonly used to terminate life-threatening arrhythmias. According to the excitation theory of defibrillation, such shocks are aimed at depolarizing the membranes of most cardiac cells, resulting in resynchronization of electrical activity in the heart. If shock-induced transmembrane potentials are large enough, they can cause transient tissue damage due to electroporation. In this review, evidence is presented that electroporation of the heart tissue can occur during clinically relevant intensities of the external electrical field and that electroporation can affect the outcome of defibrillation therapy, being both pro- and antiarrhythmic.Here, we present experimental evidence for electroporation in cardiac tissue, which occurs above a threshold of 25 V/cm as evident from propidium iodide uptake, transient diastolic depolarization, and reductions of action potential amplitude and its derivative. These electrophysiological changes can induce tachyarrhythmia, due to conduction block and possibly triggered activity; however, our findings provide the foundation for future design of effective methods to deliver genes and drugs to cardiac tissues, while avoiding possible side effects such as arrhythmia and mechanical stunning.

Experimental evidence of improved transthoracic defibrillation with electroporation-enhancing pulses

There is considerable work on defibrillation wave form optimization. This paper determines the impedance changes during defibrillation, then uses that information to derive the optimum defibrillation wave form.

METHODS PART I

Twelve guinea pigs and six swine were used to measure the current wave form for square voltage pulses of a strength which would defibrillate about 50% of the time. In guinea pigs, electrodes were placed thoracically, abdominally and subcutaneously using two electrode materials (zinc and steel) and two electrode pastes (Core-gel and metallic paste).

RESULTS PART I

The measured current wave form indicated an exponentially increasing conductance over the first 3 ms, consistent with enhanced electroporation or another mechanism of time-dependent conductance. We fit this current with a parallel conductance composed of a time-independent component (g0 = 1.22 +/- 0.28 mS) and a time-dependent component described by g delta (1-e(-t/tau)), where g delta = 0.95 +/- 0.20 mS and tau = 0.82 +/- 0.17 ms in guinea pigs using zinc and Cor-gel. Different electrode placements and materials had no significant effect on this fit. From our fit, we determined the stimulating wave form that would theoretically charge the myocardial membrane to a given threshold using the least energy from the defibrillator. The solution was a very short, high voltage pulse followed immediately by a truncated ascending exponential tail.

METHODS PART II

The optimized wave forms and similar nonoptimized wave forms were tested for efficacy in 25 additional guinea pigs and six additional swine using methods similar to Part I.

RESULTS PART II

Optimized wave forms were significantly more efficacious than similar nonoptimized wave forms. In swine, a wave form with the short pulse was 41% effective while the same wave form without the short pulse was 8.3% effective (p < 0.03) despite there being only a small difference in energy (111 J versus 116 CONCLUSIONS: We conclude that a short pulse preceding a defibrillation pulse significantly improves efficacy, perhaps by enhancing electroporation.

Cell and tissue responses to electric shocks

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 (DeltaV(m)) 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, I(a), part of the K(+) flow through the L-type Ca(2+)-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, I(a), activated upon strong shock-induced depolarization (aLRd model) was added. Assuming I(a) is a part of K(+) flow through the L-type Ca(2+)-channel enabled us to reproduce both the experimentally observed rectangularly-shaped positive DeltaV(m) and the value of near 2 of the negative-to-positive DeltaV(m) ratio. In the sheet, I(a) not only contributed to the negative bias in DeltaV(m) asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaV(m). 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 I(a) 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.

Electroporation of the heart

Defibrillation shocks are commonly used to terminate life-threatening arrhythmias. According to the excitation theory of defibrillation, such shocks are aimed at depolarizing the membranes of most cardiac cells resulting in resynchronization of electrical activity in the heart. If shock-induced changes in transmembrane potential are large enough, they can cause transient tissue damage due to electroporation. In this review evidence is presented that (a) electroporation of the heart tissue can occur during clinically relevant intensities of the external electrical field, and (b) electroporation can affect the outcome of defibrillation therapy; being both pro- and anti-arrhythmic.

Asymmetry in membrane responses to electric shocks: insights from bidomain simulations

Models of myocardial membrane dynamics have not been able to reproduce the experimentally observed negative bias in the asymmetry of transmembrane potential changes (DeltaVm) induced by strong electric shocks delivered during the action potential plateau. The goal of this study is to determine what membrane model modifications can bridge this gap between simulation and experiment. We conducted simulations of shocks in bidomain fibers and sheets with membrane dynamics represented by the LRd'2000 model. We found that in the fiber, the negative bias in DeltaVm asymmetry could not be reproduced by addition of electroporation only, but by further addition of hypothetical outward current, Ia, activated upon strong shock-induced depolarization. Furthermore, the experimentally observed rectangularly shaped positive DeltaVm, negative-to-positive DeltaVm ratio (asymmetry ratio) = approximately 2, electroporation occurring at the anode only, and the increase in positive DeltaVm caused by L-type Ca2+-channel blockade were reproduced in the strand only if Ia was assumed to be a part of K+ flow through the L-type Ca2+-channel. In the sheet, Ia not only contributed to the negative bias in DeltaVm asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaVm. Inclusion of Ia and electroporation is thus the bridge between experiment and simulation.

Defibrillation Depends on Conductivity Fluctuations and the Degree of Disorganization in Reentry Patterns

Defibrillation depends on conductivity and disorganization.

INTRODUCTION

Cardiac fibrillation is the deterioration of the heart's normally well-organized activity into one or more meandering spiral waves, which subsequently break up into many meandering wave fronts. Delivery of an electric shock (defibrillation) is the only effective way of restoring the normal rhythm. This study focuses on examining whether higher degrees of disorganization requires higher shock strengths to defibrillate and whether microscopic conductivity fluctuations favor shock success.

METHODS AND RESULTS

We developed a three-dimensional computer bidomain model of a block of cardiac tissue with straight fibers immersed in a conductive bath. The membrane behavior was described by the Courtemanche human atrial action potential model incorporating electroporation and an acetylcholine- (ACh) dependent potassium current. Intracellular conductivities were varied stochastically around nominal values with variations of up to 50%. A single rotor reentry was initiated and, by adjusting the spatial ACh variation, the level of organization could be controlled. The single rotor could be stabilized or spiral wave breakup could be provoked leading to fibrillatory-like activity. For each level of organization, multiple shock timings and strengths were applied to compute the probability of shock success as a function of shock strength.

CONCLUSIONS

Our results suggest that the level of the small-scale conductivity fluctuations is a very important factor in defibrillation. A higher variation significantly lowers the required shock strength. Further, we demonstrated that success also heavily depends on the level of organization of the fibrillatory episode. In general, higher levels of disorganization require higher shock strengths to defibrillate.

Computer simulations of successful defibrillation in decoupled and non-uniform cardiac tissue

Aim

The aim of the present study is to investigate the origin and effect of virtual electrode polarization in uniform, decoupled and non-uniform cardiac tissue during field stimulation.

Methods

A discrete bidomain model with active membrane behaviour was used to simulate normal cardiac tissue as well as cardiac tissue that is decoupled due to fibrosis and gap junction remodelling. Various uniform and non-uniform electric fields were applied to the external domain of uniform, decoupled and non-uniform resting cardiac tissue as well as cardiac tissue in which spiral waves were induced.

Results

Field stimulation applied on non-uniform tissue results in more virtual electrodes compared with uniform tissue. The spiral waves were terminated in decoupled tissue, but not in uniform, homogeneous tissue. By gradually increasing local differences in intracellular conductivities, the amount and spread of virtual electrodes increased and the spiral waves were terminated.

Conclusion

Fast depolarization of the tissue after field stimulation may be explained by intracellular decoupling and spatial heterogeneity present in normal and pathological cardiac tissue. We demonstrated that termination of spiral waves by means of field stimulation can be achieved when the tissue is modelled as a non-uniform, anisotropic bidomain with active membrane behaviour.

Virtual electrode theory explains pacing threshold increase caused by cardiac tissue damage

The virtual electrode polarization (VEP) effect is believed to play a key role in electrical stimulation of heart muscle. However, under certain conditions, including clinically, its existence and importance remain unknown. We investigated the influence of acute tissue damage produced by continuous pacing with strong current (40-mA, 4-ms biphasic pulses with 4-Hz frequency for 5 min) on stimulus-generated VEPs and pacing thresholds. A fluorescent optical mapping technique was used to obtain stimulus-induced transmembrane potential distribution around a pacing electrode applied to the ventricular surface of a Langendorff-perfused rabbit heart ( n = 5). Maps and pacing thresholds were recorded before and after tissue damage. Spatial extents of electroporation and cell uncoupling were assessed by propidium iodide ( n = 2) and connexin43 ( n = 3) antibody staining, respectively. On the basis of these data, passive and active three-dimensional bidomain models were built to determine VEP patterns and thresholds for different-sized areas of the damaged region. Electrophysiological results showed that acute tissue damage led to disappearance of the VEP with an associated significant increase in pacing thresholds. Damage was expressed in electroporation and cell uncoupling within a ∼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.

Model of creation and evolution of stable electropores for DNA delivery

Electroporation, in which electric pulses create transient pores in the cell membrane, is becoming an important technique for gene therapy. To enable entry of supercoiled DNA into cells, the pores should have sufficiently large radii (>10 nm), remain open long enough for the DNA chain to enter the cell (milliseconds), and should not cause membrane rupture. This study presents a model that can predict such macropores. The distinctive features of this model are the coupling of individual pores through membrane tension and the electrical force on the pores, which is applicable to pores of any size. The model is used to explore the process of pore creation and evolution and to determine the number and size of pores as a function of the pulse magnitude and duration. Next, our electroporation model is combined with a heuristic model of DNA uptake and used to predict the dependence of DNA uptake on pulsing parameters. Finally, the model is used to examine the mechanism of a two-pulse protocol, which was proposed specifically for gene delivery. The comparison between experimental results and the model suggests that this model is well-suited for the investigation of electroporation-mediated DNA delivery.

Self-similar processes and flicker noise from a fluctuating nanopore in a lipid membrane

Stochastic properties of a fluctuating nanopore generated and sustained by an electric field in a lipid bilayer membrane are studied. It is shown that the process of voltage fluctuations, in the current clamp experiment, is a stochastic fractal with long memory, which is the main reason for its nonstationarity. The aging process contributes to the nonstationarity if molecular interactions in the membrane are weak. An attempt to classify the process reveals a non-Gaussian distribution with long tails, which contradicts the hypothesis of fractional Brownian motion, showing that stable motion may be possible. The self-similarity index, estimated by three different methods, depends on current value and membrane sensitivity to electric field in a well defined and explicable manner. The stochastic analysis provided for calculated conductance of nanopore revealed the process close to 1/f noise, the result observed only for the pores not exceeding 1 nm in diameter, induced in membranes with strong molecular interactions. Our results show that such a pore is the simplest biological system needed for flicker noise to occur, and the complexity of highly regulated protein channel is not a necessary factor. A case of noise 1/f(2), observed for a pore with impeded dynamics, suggests a process without memory in such a situation. A physical interpretation is presented for some of the results.

Artifacts, assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart

Insidious experimental artifacts and invalid theoretical assumptions complicate the comparison of numerical predictions and observed data. Such difficulties are particularly troublesome when studying electrical stimulation of the heart. During unipolar stimulation of cardiac tissue, the artifacts include nonlinearity of membrane dyes, optical signals blocked by the stimulating electrode, averaging of optical signals with depth, lateral averaging of optical signals, limitations of the current source, and the use of excitation-contraction uncouplers. The assumptions involve electroporation, membrane models, electrode size, the perfusing bath, incorrect model parameters, the applicability of a continuum model, and tissue damage. Comparisons of theory and experiment during far-field stimulation are limited by many of these same factors, plus artifacts from plunge and epicardial recording electrodes and assumptions about the fiber angle at an insulating boundary. These pitfalls must be overcome in order to understand quantitatively how the heart responds to an electrical stimulus. (c) 2002 American Institute of Physics.

Entrainment by an extracellular AC stimulus in a computational model of cardiac tissue

INTRODUCTION

Cardiac tissue can be entrained when subjected to sinusoidal stimuli, often responding with action potentials sustained for the duration of the stimulus. To investigate mechanisms responsible for both entrainment and extended action potential duration, computer simulations of a two-dimensional grid of cardiac cells subjected to sinusoidal extracellular stimulation were performed.

METHODS AND RESULTS

The tissue is represented as a bidomain with unequal anisotropy ratios. Cardiac membrane dynamics are governed by a modified Beeler-Reuter model. The stimulus, delivered by a bipolar electrode, has a duration of 750 to 1,000 msec, an amplitude range of 800 to 3,200 microA/cm, and a frequency range of 10 to 60 Hz. The applied stimuli create virtual electrode polarization (VEP) throughout the sheet. The simulations demonstrate that periodic extracellular stimulation results in entrainment of the tissue. This phase-locking of the membrane potential to the stimulus is dependent on the location in the sheet and the magnitude of the stimulus. Near the electrodes, the oscillations are 1:1 or 1:2 phase-locked; at the middle of the sheet, the oscillations are 1:2 or 1:4 phase-locked and occur on the extended plateau of an action potential. The 1:2 behavior near the electrodes is due to periodic change in the voltage gradient between VEP of opposite polarity; at the middle of the sheet, it is due to spread of electrotonic current following the collision of a propagating wave with refractory tissue.

CONCLUSION

The simulations suggest that formation of VEP in cardiac tissue subjected to periodic extracellular stimulation is of paramount importance to tissue entrainment and formation of an extended oscillatory action potential plateau.

How electrode size affects the electric potential distribution in cardiac tissue

We investigate the effect of electrode size on the transmembrane potential distribution in the heart during electrical stimulation. The bidomain model is used to calculate the transmembrane potential in a three-dimensional slab of cardiac tissue. Depolarization is strongest under the electrode edge. Regions of depolarization are adjacent to regions of hyperpolarization. The average ratio of peak depolarization to peak hyperpolarization is a function of electrode radius, but over a broad range is close to three.

Theoretical modeling of the effects of shock duration, frequency, and strength on the degree of electroporation

Electroporation is becoming an increasingly important tool for introducing biologically active compounds into living cells, yet the effectiveness of this technique can be low, particularly in vivo. One way to improve the success rate is to optimize the shock protocols, but experimental studies are costly, time consuming, and yield only an indirect measurement of pore creation. Alternatively, this study models electroporation in two geometries, a space-clamped membrane and a single cell, and investigates the effects of pulse duration, frequency, shape, and strength. The creation of pores is described by a first order differential equation derived from the Smoluchowski equation. Both the membrane and the cell are exposed to monophasic and biphasic shocks of varying duration (membrane, 10 micros-100 s; cell, 0.1 micros-200 ms) and to trains of monophasic and biphasic pulses of varying frequency (membrane, 50 Hz-4 kHz; cell, 200 kHz-6 MHz). The effectiveness of each shock is measured by the fractional pore area (FPA). The results indicate that FPA is sensitive to shock duration only in a very narrow range (membrane, approximately 1 ms; cell, approximately 0.25 micros). In contrast, FPA is sensitive to shock strength and frequency of the pulse train, increasing linearly with shock strength and decreasing slowly with frequency. In all cases, monophasic shocks were at least as effective as biphasic shocks, implying that varying the strength and frequency of a monophasic pulse train is the most effective way to control the creation of pores.

Role of virtual electrodes in arrhythmogenesis: pinwheel experiment revisited

INTRODUCTION

Recent experimental evidence demonstrates that a point stimulus generates a nonuniform distribution of transmembrane potential (virtual electrode pattern) consisting of large adjacent areas of depolarization and hyperpolarization. This simulation study focuses on the role of virtual electrodes in reentry induction.

METHODS AND RESULTS

We simulated the electrical behavior of a sheet of myocardium using a two-dimensional bidomain model with straight fibers. Membrane kinetics were represented by the Beeler-Reuter Drouhard-Roberge model. Simulations were conducted for equal and unequal anisotropy ratios. S1 wavefront was planar and propagated parallel or perpendicular to the fibers. S2 unipolar stimulus was cathodal or anodal. With regard to unequal anisotropy, for both cathodal and anodal stimuli, the S2 stimulus negatively polarizes some portion of membrane, deexciting it and opening an excitable pathway in a region of otherwise unexcitable tissue. Reentry is generated by break excitation of this tissue and subsequent propagation through deexcited and recovered areas of myocardium. Figure-of-eight and quatrefoil reentry are observed, with figure-of-eight most common. Figure-of-eight rotation is seen in the direction predicted by the critical point hypothesis. With regard to equal anisotropy, reentry was observed for cathodal stimuli only at strengths > -95 A/m.

CONCLUSION

The key to reentry induction is the close proximity of S2-induced excited and deexcited areas, with adjacent nonexcited areas available for propagation.

Modeling electroporation in a single cell. I. Effects Of field strength and rest potential

This study develops a model for a single cell electroporated by an external electric field and uses it to investigate the effects of shock strength and rest potential on the transmembrane potential V(m) and pore density N around the cell. As compared to the induced potential predicted by resistive-capacitive theory, the model of electroporation predicts a smaller magnitude of V(m) throughout the cell. Both V(m) and N are symmetric about the equator with the same value at both poles of the cell. Larger shocks do not increase the maximum magnitude of V(m) because more pores form to shunt the excess stimulus current across the membrane. In addition, the value of the rest potential does not affect V(m) around the cell because the electroporation current is several orders of magnitude larger than the ionic current that supports the rest potential. Once the field is removed, the shock-induced V(m) discharges within 2 micros, but the pores persist in the membrane for several seconds. Complete resealing to preshock conditions requires approximately 20 s. These results agree qualitatively and quantitatively with the experimental data reported by Kinosita and coworkers for unfertilized sea urchin eggs exposed to large electric fields.

Anode/cathode make and break phenomena in a model of defibrillation

The goal of this simulation study is to examine, in a sheet of myocardium, the contribution of anode and cathode break phenomena in terminating a spiral wave reentry by the defibrillation shock. The tissue is represented as a homogeneous bidomain with unequal anisotropy ratios. Two case studies are presented in this article: tissue that can electroporate at high levels of transmembrane potential, and model tissue that does not support electroporation. In both cases, the spiral wave is initiated via cross-field stimulation of the bidomain sheet. The extracellular defibrillation shock is delivered via two small electrodes located at opposite tissue boundaries. Modifications in the active membrane kinetics enable the delivery of high-strength defibrillation shocks. Numerical solutions are obtained using an efficient semi-implicit predictor-corrector scheme that allows one to execute the simulations within reasonable time. The simulation results demonstrate that anode and/or cathode break excitations contribute significantly to the activity during and after the shock. For a successful defibrillation shock, the virtual electrodes and the break excitations restrict the spiral wave and render the tissue refractory so it cannot further maintain the reentry. The results also indicate that electroporation alters the anode/cathode break phenomena, the major impact being on the timing of the cathode-break excitations. Thus, electroporation results in different patterns of transmembrane potential distribution after the shock. This difference in patterns may or may not result in change of the outcome of the shock.