Search

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Cardiac defibrillation, as accomplished nowadays by automatic, implantable devices, constitutes the most important means of combating sudden cardiac death. Advancing our understanding towards a full appreciation of the mechanisms by which a shock interacts with the heart, particularly under diseased conditions, is a promising approach to achieve an optimal therapy. The aim of this article is to assess the current state-of-the-art in whole-heart defibrillation modelling, focusing on major insights that have been obtained using defibrillation models, primarily those of realistic heart geometry and disease remodelling. The article showcases the contributions that modelling and simulation have made to our understanding of the defibrillation process. The review thus provides an example of biophysically based computational modelling of the heart (i.e. cardiac defibrillation) that has advanced the understanding of cardiac electrophysiological interaction at the organ level, and has the potential to contribute to the betterment of the clinical practice of defibrillation.

Background: Low-voltage termination of ventricular tachycardia (VT) and atrial fibrillation has shown promising results; however, the mechanisms and full range of applications remain unexplored., Objectives: To elucidate the mechanisms for low-voltage cardioversion and defibrillation and to develop an optimal low-voltage defibrillation protocol., Methods: We developed a detailed magnetic resonance imaging-based computational model of the rabbit right ventricular wall. We applied multiple low-voltage far-field stimuli of various strengths (≤1 V/cm) and stimulation rates in VT and ventricular fibrillation (VF)., Results: Of the 5 stimulation rates tested, stimuli applied at 16% or 88% of the VT cycle length (CL) were most effective in cardioverting VT, the mechanism being consecutive excitable gap decreases. Stimuli given at 88% of the VF CL defibrillated successfully, whereas a faster stimulation rate (16%) often failed because the fast stimuli did not capture enough tissue. In this model, defibrillation threshold energy for multiple low-voltage stimuli at 88% of VF CL was 0.58% of the defibrillation threshold energy for a single strong biphasic shock. Based on the simulation results, a novel 2-stage defibrillation protocol was proposed. The first stage converted VF into VT by applying low-voltage stimuli at times of maximal excitable gap, capturing large tissue volume and synchronizing depolarization; the second stage terminated VT. The energy required for successful defibrillation using this protocol was 57.42% of the energy for low-voltage defibrillation when stimulating at 88% of VF CL., Conclusions: A novel 2-stage low-voltage defibrillation protocol using the excitable gap extent to time multiple stimuli defibrillated VF with the least energy by first converting VF into VT and then terminating VT., (Copyright © 2013 Heart Rhythm Society. Published by Elsevier Inc. All rights reserved.)

Background: We recently demonstrated that high frequency alternating current (HFAC) electric fields can reversibly block propagation in the heart by inducing an oscillating, elevated transmembrane potential (Vm) that maintains myocytes in a refractory state for the field duration and can terminate arrhythmias, including ventricular fibrillation (VF)., Objectives: To quantify and characterize conduction block (CB) induced by HFAC fields and to determine whether the degree of CB can be used to predict defibrillation success., Methods: Optical mapping was performed in adult guinea pig hearts (n = 14), and simulations were performed in an anatomically accurate rabbit ventricular model. HFAC fields (50-500 Hz) were applied to the ventricles. A novel power spectrum metric of CB-the loss of spectral power in the 1-30 Hz range, termed loss of conduction power (LCP)-was assessed during the HFAC field and compared with defibrillation success and VF vulnerability., Results: LCP increased with field strength and decreased with frequency. Optical mapping experiments conducted on the epicardial surface showed that LCP and the size of CB regions were significantly correlated with VF initiation and termination. In simulations, subsurface myocardial LCP and CB sizes were more closely correlated with VF termination than surface values. Multilinear regression analysis of simulation results revealed that while CB on both the surface and the subsurface myocardium was predictive, subsurface myocardial CB was the better predictor of defibrillation success., Conclusions: HFAC fields induce a field-dependent state of CB, and defibrillation success is related to the degree and location of the CB., (Copyright © 2013. Published by Elsevier Inc.)

Defibrillation efficacy is decreased in infarcted hearts, but the mechanisms by which infarcted hearts are more vulnerable to electric shocks than healthy hearts remain poorly understood. The goal of this study was to provide insight into the 3D mechanisms for the increased vulnerability to electric shocks in infarcted hearts. We hypothesized that changes in virtual electrode polarizations (VEPs) and propagation delay through the peri-infarct zone (PZ) were responsible. We developed a micro anatomically detailed rabbit ventricular model with chronic myocardial infarction from magnetic resonance imaging and enriched the model with data from optical mapping experiments. We further developed a control model without the infarct. The simulation protocol involved apical pacing followed by biphasic shocks. Simulation results from both models were compared.The upper limit of vulnerability(ULV) was 8 V cm(-1) in the infarction model and 4 V cm(-1) in the control model. VEPs were less pronounced in the infarction model, providing a larger excitable area for postshock propagation but smaller transmembrane potential gradients to initiate new wavefronts. Initial post-shock transmural activation occurred at a later time in the infarction model, and the PZ served to delay propagation in subsequent beats. The presence of the PZ was found to be responsible for the increased vulnerability.

Electrical impulse propagation is an essential function in cardiac, skeletal muscle, and nervous tissue. Abnormalities in cardiac impulse propagation underlie lethal reentrant arrhythmias, including ventricular fibrillation. Temporary propagation block throughout the ventricular myocardium could possibly terminate these arrhythmias. Electrical stimulation has been applied to nervous tissue to cause reversible conduction block, but has not been explored sufficiently in cardiac tissue. We show that reversible propagation block can be achieved in cardiac tissue by holding myocardial cells in a refractory state for a designated period of time by applying a sustained sinusoidal high-frequency alternating current (HFAC); in doing so, reentrant arrhythmias are terminated. We demonstrate proof of concept using several models, including optically mapped monolayers of neonatal rat ventricular cardiomyocytes, Langendorff-perfused guinea pig and rabbit hearts, intact anesthetized adult rabbits, and computer simulations of whole-heart impulse propagation. HFAC may be an effective and potentially safer alternative to direct current application, currently used to treat ventricular fibrillation.

Background: After near-defibrillation threshold (DFT) shocks from an implantable cardioverter-defibrillator (ICD), the first postshock activation that leads to defibrillation failure arises focally after an isoelectric window (IW). The mechanisms underlying the IW remain incompletely understood., Objective: The goal of this study was to provide mechanistic insight into the origins of postshock activations and IW after ICD shocks, and to link shock outcome to the preshock state of the ventricles. We hypothesized that the nonuniform ICD field results in the formation of an intramural excitable area (tunnel) only in the left ventricular (LV) free wall, through which both pre-existing and new shock-induced wavefronts propagate during the IW., Methods: Simulations were conducted using a realistic three dimensional (3D) model of defibrillation in the rabbit ventricles. Biphasic ICD shocks of varying strengths were delivered to 27 different fibrillatory states., Results: After near-DFT shocks, regardless of preshock state, the main postshock excitable area was always located within LV free wall, creating an intramural tunnel. Either pre-existing fibrillatory or shock-induced wavefronts propagated during the IW (duration of up to 74 ms) in this tunnel and emerged as breakthroughs on LV epicardium. Preshock activity within the LV played a significant role in shock outcome: a large number of preshock filaments resulted in an IW associated with tunnel propagation of pre-existing rather than shock-induced wavefronts. Furthermore, shocks were more likely to succeed if the LV excitable area was smaller., Conclusion: The LV intramural excitable area is the primary reason for near-DFT failure. Any intervention that decreases the extent of this area will improve the likelihood of defibrillation success., (Copyright 2010 Heart Rhythm Society. Published by Elsevier Inc. All rights reserved.)

To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV-, reverse polarity is LV-) were applied to the ventricles in diastole. Experiments and simulations revealed that RV- shocks resulted in longer activation times compared with LV- shocks of the same strength. 3D simulations demonstrated that RV- shocks induced a greater volume of hyperpolarization at shock end compared with LV- shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.

Experimental and clinical studies have shown that ventricular dilatation is associated with increased arrhythmogenesis and elevated defibrillation threshold; however, the underlying mechanisms remain poorly understood. The goal of the present study was to test the hypothesis that (1) stretch-activated channel (SAC) recruitment and (2) geometrical deformations in organ shape and fiber architecture lead to increased arrhythmogenesis by electric shocks following acute ventricular dilatation. To elucidate the contribution of these two factors, the study employed, for the first time, a combined electro-mechanical simulation approach. Acute dilatation was simulated in a model of rabbit ventricular mechanics by raising the LV end-diastolic pressure from 0.6 (control) to 4.2 kPa (dilated). The output of the mechanics model was used in the electrophysiological model. Vulnerability to shocks was examined in the control, the dilated ventricles, and in the dilated ventricles that also incorporated currents through SAC as a function of local strain, by constructing vulnerability grids. Results showed that dilatation-induced deformation alone decreased upper limit of vulnerability (ULV) slightly and did not result in increased vulnerability. With SAC recruitment in the dilated ventricles, the number of shock-induced arrhythmia episodes increased by 37% (from 41 to 56) and the lower limit of vulnerability (LLV) decreased from 9 to 7 V/cm, while ULV did not change. The heterogeneous activation of SAC caused by the heterogeneous fiber strain in the ventricular walls was the main reason for increased vulnerability to electric shocks since it caused dispersion of electrophysiological properties in the tissue, resulting in postshock unidirectional block and establishment of reentry.

Comprehensive understanding of the ventricular response to shocks is the approach most likely to succeed in reducing defibrillation threshold. We propose a new theory of shock-induced arrhythmogenesis that unifies all known aspects of the response of the heart to monophasic (MS) and biphasic (BS) shocks. The central hypothesis is that submerged "tunnel" propagation of postshock activations through shock-induced intramural excitable areas underlies fibrillation induction and the existence of isoelectric window. We conducted simulations of fibrillation induction using a realistic bidomain model of rabbit ventricles. Following pacing, MS and BS of various strengths/timings were delivered. The results demonstrated that, during the isoelectric window, an activation originated deep within the ventricular wall, arising from virtual electrodes; it then propagated fully intramurally through an excitable tunnel induced by the shock, until it emerged onto the epicardium, becoming the earliest-propagated postshock activation. Differences in shock outcomes for MS and BS were found to stem from the narrower BS intramural postshock excitable area, often resulting in conduction block, and the difference in the mechanisms of origin of the postshock activations, namely intramural virtual electrode-induced phase singularity for MS and virtual electrode-induced propagated graded response for BS. This study provides a novel analysis of the 3D mechanisms underlying the origin of postshock activations in the process of fibrillation induction by MS and BS and the existence of isoelectric window. The tunnel propagation hypothesis could open a new avenue for interventions exploration to achieve significantly lower defibrillation threshold.

While defibrillation is the only means for prevention of sudden cardiac death, key aspects of the process, such as the intramural virtual electrodes (VEs), remain controversial. Experimental studies had attempted to assess intramural VEs by using wedge preparations and recording activity from the cut surface; however, applicability of this approach remains unclear. These studies found, surprisingly, that for strong shocks, the entire cut surface was negatively polarized, regardless of boundary conditions. The goal of this study is to examine, by means of bidomain simulations, whether VEs on the cut surface represent a good approximation to VEs in depth of the intact wall. Furthermore, we aim to explore mechanisms that could give rise to negative polarization on the cut surface. A model of wedge preparation was used, in which fiber orientation could be changed, and where the cut surface was subjected to permeable and impermeable boundary conditions. Small-scale mechanisms for polarization were also considered. To determine whether any distortions in the recorded VEs arise from averaging during optical mapping, a model of fluorescent recording was employed. The results indicate that, when an applied field is spatially uniform and impermeable boundary conditions are enforced, regardless of the fiber orientation VEs on the cut surface faithfully represent those intramurally, provided tissue properties are not altered by dissection. Results also demonstrate that VEs are sensitive to the conductive layer thickness above the cut surface. Finally, averaging during fluorescent recordings results in large negative VEs on the cut surface, but these do not arise from small-scale heterogeneities.

Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitation of the technique is signal distortion due to photon scattering. The goal of this experimental/simulation study is to investigate the role of three-dimensional photon scattering in optical signal distortion during ventricular tachycardia (VT) and defibrillation. A three-dimensional realistic bidomain rabbit ventricular model was combined with a model of photon transport. Shocks were applied via external electrodes to induce sustained VT, and transmembrane potentials (V(m)) were compared with synthesized optical signals (V(opt)). Fluorescent recordings were conducted in isolated rabbit hearts to validate simulation results. Results demonstrate that shock-induced membrane polarization magnitude is smaller in V(opt) and in experimental signals as compared to V(m). This is due to transduction of potentials from weakly polarized midmyocardium to the epicardium. During shock-induced reentry and in sustained VT, photon scattering, combined with complex wavefront dynamics, results in optical action potentials near a filament exhibiting i), elevated resting potential, ii), reduced amplitude relative to pacing, and iii), dual-humped morphologies. A shift of up to 4 mm in the phase singularity location was observed in V(opt) maps when compared to V(m). This combined experimental/simulation study provides an interpretation of optical recordings during VT and defibrillation.

Background: Studies have demonstrated that failed defibrillation shocks often are followed by an electrically quiescent period (isoelectric window); however, the underlying mechanisms remain incompletely understood. We recently suggested a new mechanism termed "virtual electrode polarization-induced propagated graded responses" (VEPiPGRs) that might play a role in the origin of the global postshock activation following the isoelectric window., Objectives: The purpose of this study to elucidate the circumstances under which VEPiPGR activations originate for shocks given to paced right ventricular preparations. Specifically, we examined the dependence of VEPiPGRs on coupling interval (CI) and shock polarity and whether VEPiPGRs emerge preferentially on the epicardium or the endocardium., Methods: Simultaneous endocardial and epicardial activity in isolated right ventricular preparations (n = 4) was imaged optically following shocks of strength +/-5A. All VEPiPGRs were analyzed, and the time T from shock end to activation onset was recorded (isoelectric window is the smallest T among activations that propagated globally)., Results: VEPiPGR activations occurred for CIs in the range from 80 to 150 ms. Average duration of T was 64.5 +/- 18.15 ms, with T decreasing as CI increased (Tmax = 82 ms, Tmin = 46 ms, linear-fit slope = -0.675). The average earliest CI at which cathodal (+5A) shocks resulted in VEPiPGRs was 87 ms compared with 116 ms for anodal (-5A) shocks. All VEPiPGR activations emerged first on the epicardium in a focal pattern, and all induced ventricular fibrillation., Conclusion: The global activation that terminates the isoelectric window could result from VEPiPGRs that find an exit pathway. VEPiPGRs originate at the sites of maximum action potential abbreviation by the shock, always on the epicardium for the preparation used here.

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.

Although effects of shock strength and waveform on cardiac vulnerability to electric shocks have been extensively documented, the contribution of ventricular anatomy to shock-induced polarization and postshock propagation and thus, to shock outcome, has never been quantified; this is caused by lack of experimental methodology capable of mapping 3-D electrical activity. The goal of this study was to use optical imaging experiments and 3-D bidomain simulations to investigate the role of structural differences between left and right ventricles in vulnerability to electric shocks in rabbit hearts. The ventricles were paced apically, and uniform-field, truncated-exponential, monophasic shocks of reversed polarity were applied over a range of coupling intervals (CIs) in experiment and model. Experiments and simulations revealed that reversing the direction of externally-applied field (RV- or LV- shocks) alters the shape of the vulnerability area (VA), the 2-D grid encompassing episodes of arrhythmia induction. For RV- shocks, VA was nearly rectangular indicating little dependence of postshock arrhythmogenesis on CI. For LV- shocks, the probability of arrhythmia induction was higher for longer than for shorter CIs. The 3-D simulations demonstrated that these effects stem from the fact that reversal of field direction results in relocation of the main postshock excitable area from LV wall (RV- shocks) to septum (LV- shocks). Furthermore, the effect of septal (but not LV) excitable area in postshock propagation was found to strongly depend on preshock state. Knowledge regarding the location of the main postshock excitable area within the 3-D ventricular volume could be important for improving defibrillation efficacy.

Energy requirements for successful antiarrhythmia shocks are arrhythmia specific. However, it remains unclear why the probability of shock success decreases with increasing arrhythmia complexity. The goal of this research was to determine whether a diminished probability of shock success results from an increased number of functional reentrant circuits in the myocardium, and if so, to identify the responsible mechanisms. To achieve this goal, we assessed shock efficacy in a bidomain defibrillation model of a 4-mm-thick slice of canine ventricles. Shocks were applied between a right ventricular cathode and a distant anode to terminate either a single scroll wave (SSW) or multiple scroll waves (MSWs). From the 160 simulations conducted, dose-response curves were constructed for shocks given to SSWs and MSWs. The shock strength that yielded a 50% probability of success (ED(50)) for SSWs was found to be 13% less than that for MSWs, which indicates that a larger number of functional reentries results in an increased defibrillation threshold. The results also demonstrate that an isoelectric window exists after both failed and successful shocks; however, shocks of strength near the ED(50) value that were given to SSWs resulted in 16.3% longer isoelectric window durations than the same shocks delivered to MSWs. Mechanistic inquiry into these findings reveals that the two main factors underlying the observed relationships are 1) smaller virtual electrode polarizations in the tissue depth, and 2) differences in preshock tissue state. As a result of these factors, intramural excitable pathways leading to delayed breakthrough on the surface were formed earlier after shocks given to MSWs compared with SSWs and thus resulted in a lower defibrillation threshold for shocks given to SSWs.

Introduction: A heart in fibrillation can be entrained by long-lasting alternating current (AC) stimuli, leading to defibrillation. To investigate the role entrainment plays in defibrillation, computer simulations of AC cardioversion in a three-dimensional slice of the canine heart were performed., Methods and Results: A bidomain finite element model of a 1-mm thick slice across the ventricles of a canine heart was used to simulate termination of transmural reentry with AC shocks. Cardioversion defibrillation thresholds (DFTs) were determined for 200-msec (L) AC shocks at varying frequencies. At the DFT, the entire tissue is entrained by the AC shock. DFT decreases as the frequency of the long-lasting AC shock increases. We hypothesize that this decrease is due to the short period of the high-frequency AC waveform, leaving strong virtual electrode polarization (VEP) after the shock ends. To test this hypothesis, the end-shock VEP were compared for different frequencies, demonstrating stronger polarization as frequency increased. To examine whether entrainment by the long-lasting AC shock contributes to the VEP at the end of the shock, additional simulations were conducted using single-period (Z) AC waveforms. Z waveform DFTs were higher than L waveform DFTs; the Z waveform VEP was weaker than the L waveform VEP at the same frequency. This indicates that entrainment contributes to the development of stronger VEP and, thus, to lower DFT at high frequencies., Conclusion: This study offers for the first time a mechanistic insight into cardioversion with long-lasting AC shocks.

The mechanisms behind the superiority of optimal biphasic defibrillation shocks over monophasic are not fully understood. This simulation study examines how the shock polarity and second-phase magnitude of biphasic shocks influence the virtual electrode polarization (VEP) pattern, and thus the outcome of the shock in a bidomain model representation of ventricular myocardium. A single spiral wave is initiated in a two-dimensional sheet of myocardium that measures 2 x 2 cm(2). The model incorporates non-uniform fiber curvature, membrane kinetics suitable for high strength shocks, and electroporation. Line electrodes deliver a spatially uniform extracellular field. The shocks are biphasic, each phase lasting 10 ms. Two different polarities of biphasic shocks are examined as the first-phase configuration is held constant and the second-phase magnitude is varied between 1 and 10 V/cm. The results show that for each polarity, varying the second-phase magnitude reverses the VEP induced by the first phase in an asymmetric fashion. Further, the size of the post-shock excitable gap is dependent upon the second-phase magnitude and is a factor in determining the success or failure of the shock. The maximum size of a post-shock excitable gap that results in defibrillation success depends on the polarity of the shock, indicating that the refractoriness of the tissue surrounding the gap also contributes to the outcome of the shock.

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.

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.

Introduction: Defibrillation shocks, when delivered through internal electrodes, establish transmembrane potentials (Vm) large enough to electroporate the membrane of cardiac cells. The effects of such shocks on the transmembrane potential distribution are investigated in a two-dimensional rectangular sheet of cardiac muscle modeled as a bidomain with unequal anisotropy ratios., Methods and Results: The membrane is represented by a capacitance Cm, a leakage conductance g(l) and a variable electroporation conductance G, whose rate of growth depends exponentially on the square of Vm. The stimulating current Io, 0.05-20 A/m, is delivered through a pair of electrodes placed 2 cm apart for stimulation along fibers and 1 cm apart for stimulation across fibers. Computer simulations reveal three categories of response to Io: (1) Weak Io, below 0.2 A/m, cause essentially no electroporation, and Vm increases proportionally to Io. (2) Strong Io, between 0.2 and 2.5 A/m, electroporate tissue under the physical electrode. Vm is no longer proportional to Io; in the electroporated region, the growth of Vm is halted and in the region of reversed polarity (virtual electrode), the growth of Vm is accelerated. (3) Very strong Io, above 2.5 A/m, electroporate tissue under the physical and the virtual electrodes. The growth of Vm in all electroporated regions is halted, and a further increase of Io increases both the extent of the electroporated regions and the electroporation conductance G., Conclusion: These results indicate that electroporation of the cardiac membrane plays an important role in the distribution of Vm induced by defibrillation strength shocks.

This paper examines the combined action of cardiac fiber curvature and transmural fiber rotation in polarizing the myocardium under the conditions of a strong electrical shock. The study utilizes a three-dimensional finite element model and the continuous bidomain representation of cardiac tissue to model steady-state polarization resulting from a defibrillation-strength uniform applied field. Fiber architecture is incorporated in the model via the shape of the heart, an ellipsoid of variable ellipticity index, and via an analytical function, linear or nonlinear, describing the transmural fiber rotation. Analytical estimates and numerical results are provided for the location and shape of the "bulk" polarization (polarization away from the tissue boundaries) as a function of the fiber field, or more specifically, of the conductivity changes in axial and radial direction with respect to the applied electrical field lines. Polarization in the tissue "bulk" is shown to exist only under the condition of unequal anisotropy ratios in the extra- and intracellular spaces. Variations in heart geometry and, thus, fiber curvature, are found to lead to change in location of the zones of significant membrane polarization. The transmural fiber rotation function modulates the transmembrane potential profile in the radial direction. A higher gradient of the transmural transmembrane potential is observed in the presence of fiber rotation as compared to the no rotation case. The analysis presented here is a step forward in understanding the interaction between tissue structure and applied electric field in establishing the pattern of membrane polarization during the initial phase of the defibrillation shock.

This simulation study presents an inquiry into the mechanisms by which a strong electric shock halts life-threatening cardiac arrhythmias. It examines the "extension of refractoriness" hypothesis for defibrillation which postulates that the shock induces an extension of the refractory period of cardiac cells thus blocking propagating waves of arrhythmia and fibrillation. The present study uses a model of the defibrillation process that represents a sheet of myocardium as a biodomain with unequal anisotropy ratios. The tissue consists of curved fibers in which spiral wave reentry is initiated. The defibrillation shock is delivered via two line electrodes that occupy opposite tissue boundaries. Simulation results demonstrate that a large-scale region of depolarization is induced throughout most of the tissue. This depolarization extends the refractoriness of the cells in the region. In addition, new wavefronts are generated from the regions of induced hyperpolarization that further restrict the spiral wave pathway and cause its termination.

Optimizing lead placement in transvenous defibrillation remains central to the clinical aspects of the defibrillation procedure. Studies involving superior vena cava (SVC) return electrodes have found that left ventricular (LV) leads or septal positioning of the right ventricular (RV) lead minimizes the voltage defibrillation threshold (VDFT) in endocardial lead-->SVC defibrillation systems. However, similar studies have not been conducted for active-can configurations. The goal of this study was to determine the optimal lead position to minimize the VDFT for systems incorporating an active can. This study used a high resolution finite element model of a human torso that includes the fiber architecture of the ventricular myocardium to find the role of lead positioning in a transvenous LEAD-->can defibrillation electrode system. It was found that, among single lead systems, posterior positioning of leads in the right ventricle lowers VDFTs appreciably. Furthermore, a septal location of leads resulted in lower VDFTs than free-wall positioning. Increasing the number of leads, and thus the effective lead surface area in the right ventricle also resulted in lower VDFTs. However, the lead configuration that resulted in the lowest VDFTs is a combination of mid-cavity right ventricle lead and a mid-cavity left ventricle lead. The addition of a left ventricular lead resulted in a reduction in the size of the low gradient regions and a change of its location from the left ventricular free wall to the septal wall.