Virtual electrodes and deexcitation: new insights into fibrillation induction and defibrillation

A smoothed boundary bidomain model for cardiac simulations in anatomically detailed geometries

This manuscript presents a novel finite difference method to solve cardiac bidomain equations in anatomical models of the heart. The proposed method employs a smoothed boundary approach that represents the boundaries between the heart and the surrounding medium as a spatially diffuse interface of finite thickness. The bidomain boundary conditions are implicitly implemented in the smoothed boundary bidomain equations presented in the manuscript without the need of a structured mesh that explicitly tracks the heart-torso boundaries. We reported some significant examples assessing the method's accuracy using nontrivial test geometries and demonstrating the applicability of the method to complex anatomically detailed human cardiac geometries. In particular, we showed that our approach could be employed to simulate cardiac defibrillation in a human left ventricle comprising fiber architecture. The main advantage of the proposed method is the possibility of implementing bidomain boundary conditions directly on voxel structures, which makes it attractive for three dimensional, patient specific simulations based on medical images. Moreover, given the ease of implementation, we believe that the proposed method could provide an interesting and feasible alternative to finite element methods, and could find application in future cardiac research guiding electrotherapy with computational models.

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction-diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters' space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.

The Defibrillation Conundrum: New Insights into the Mechanisms of Shock-Related Myocardial Injury Sustained from a Life-Saving Therapy

Implantable cardiac defibrillators (ICDs) are recommended to prevent the risk of sudden cardiac death. However, shocks are associated with an increased mortality with a dose response effect, and a strategy of reducing electrical therapy burden improves the prognosis of implanted patients. We review the mechanisms of defibrillation and its consequences, including cell damage, metabolic remodeling, calcium metabolism anomalies, and inflammatory and pro-fibrotic remodeling. Electrical shocks do save lives, but also promote myocardial stunning, heart failure, and pro-arrhythmic effects as seen in electrical storms. Limiting unnecessary implantations and therapies and proposing new methods of defibrillation in the future are recommended.

Anisotropic Cardiac Conduction

Anisotropy is the property of directional dependence. In cardiac tissue, conduction velocity is anisotropic and its orientation is determined by myocyte direction. Cell shape and size, excitability, myocardial fibrosis, gap junction distribution and function are all considered to contribute to anisotropic conduction. In disease states, anisotropic conduction may be enhanced, and is implicated, in the genesis of pathological arrhythmias. The principal mechanism responsible for enhanced anisotropy in disease remains uncertain. Possible contributors include changes in cellular excitability, changes in gap junction distribution or function and cellular uncoupling through interstitial fibrosis. It has recently been demonstrated that myocyte orientation may be identified using diffusion tensor magnetic resonance imaging in explanted hearts, and multisite pacing protocols have been proposed to estimate myocyte orientation and anisotropic conduction in vivo. These tools have the potential to contribute to the understanding of the role of myocyte disarray and anisotropic conduction in arrhythmic states.

Effects of high-frequency biphasic shocks on ventricular vulnerability and defibrillation outcomes through synchronized virtual electrode responses

Electrical defibrillation is a well-established treatment for cardiac dysrhythmias. Studies have suggested that shock-induced spatial sawtooth patterns and virtual electrodes are responsible for defibrillation efficacy. We hypothesize that high-frequency shocks enhance defibrillation efficacy by generating temporal sawtooth patterns and using rapid virtual electrodes synchronized with shock frequency. High-speed optical mapping was performed on isolated rat hearts at 2000 frames/s. Two defibrillation electrodes were placed on opposite sides of the ventricles. An S1-S2 pacing protocol was used to induce ventricular tachyarrhythmia (VTA). High-frequency shocks of equal energy but varying frequencies of 125–1000 Hz were used to evaluate VTA vulnerability and defibrillation success rate. The 1000-Hz shock had the highest VTA induction rate in the shorter S1-S2 intervals (50 and 100 ms) and the highest VTA defibrillation rate (70%) among all frequencies. Temporal sawtooth patterns and synchronous shock-induced virtual electrode responses could be observed with frequencies of up to 1000 Hz. The improved defibrillation outcome with high-frequency shocks suggests a lower energy requirement than that of low-frequency shocks for successful ventricular defibrillation.

Conceptual Intra-Cardiac Electrode Configurations That Facilitate Directional Cardiac Stimulation for Optimal Electrotherapy

OBJECTIVE

Electrotherapy remains the most effective direct therapy against lethal cardiac arrhythmias. When an arrhythmic event is sensed, either strong electric shocks or controlled rapid pacing is automatically applied directly to the heart via an implanted cardioverter defibrillator (ICDs). Despite their success, ICDs remain a highly non-optimal therapy: the strong shocks required for defibrillation cause significant extra-cardiac stimulation, resulting in pain and long-term tissue damage, and can also limit battery life. When used in anti-tachycardia pacing mode, ICDs are also often ineffective, as the pacing electrode can be far away from the centre of the arrhythmia, making it hard for the paced wave to interrupt and terminate it.

METHODS

In this paper, we present two conceptual intra-cardiac directional electrode configurations in silico based on novel arrangements of pairs of positive-negative electrodes. Both configurations have the potential to cause preferential excitation on specific regions of the heart.

RESULTS

We demonstrate how the properties of the induced field varies spatially around the electrodes and how it depends upon the specific arrangements of dipole electrode pairs. The results show that when tested within anatomically-realistic rabbit ventricular models, both electrode configurations produce strong virtual electrodes on the targeted endocardial surfaces, with weaker virtual electrodes produced elsewhere.

CONCLUSIONS

The proposed electrode configurations may facilitate targeted far-field anti-tachycardia pacing and/or defibrillation, which may be useful in cases where conventional anti-tachycardia pacing fails. In addition, the conceptual electrode designs intrinsically confine the electric field to the immediate vicinity of the electrodes, and may, thus, minimize pain due to unnecessary extra-cardiac stimulation.

Numerical sensitivity analysis of a variational data assimilation procedure for cardiac conductivities

An accurate estimation of cardiac conductivities is critical in computational electro-cardiology, yet experimental results in the literature significantly disagree on the values and ratios between longitudinal and tangential coefficients. These are known to have a strong impact on the propagation of potential particularly during defibrillation shocks. Data assimilation is a procedure for merging experimental data and numerical simulations in a rigorous way. In particular, variational data assimilation relies on the least-square minimization of the misfit between simulations and experiments, constrained by the underlying mathematical model, which in this study is represented by the classical Bidomain system, or its common simplification given by the Monodomain problem. Operating on the conductivity tensors as control variables of the minimization, we obtain a parameter estimation procedure. As the theory of this approach currently provides only an existence proof and it is not informative for practical experiments, we present here an extensive numerical simulation campaign to assess practical critical issues such as the size and the location of the measurement sites needed for in silico test cases of potential experimental and realistic settings. This will be finalized with a real validation of the variational data assimilation procedure. Results indicate the presence of lower and upper bounds for the number of sites which guarantee an accurate and minimally redundant parameter estimation, the location of sites being generally non critical for properly designed experiments. An effective combination of parameter estimation based on the Monodomain and Bidomain models is tested for the sake of computational efficiency. Parameter estimation based on the Monodomain equation potentially leads to the accurate computation of the transmembrane potential in real settings.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

The roles of pacing interval and pacing strength in ventricular fibrillation induced by rapid pacing with 1 : 1 capture

INTRODUCTION

The roles of pacing interval (PI) and pacing strength (PS) in ventricular fibrillation (VF) induced by rapid pacing with 1 : 1 capture remain unclear.

MATERIAL AND METHODS

Epicardial unipolar electrograms (UEs) were simultaneously recorded using contact mapping in 11 swine. Activation-recovery interval (ARI) restitution was constructed at 4 sites, i.e. the apex and base of the left and right ventricles, respectively. A steady state pacing (SSP) protocol was performed to induce VF. The longest PI and the lowest PS for inducing VF were recorded. Statistical correlation analysis was performed to determine the relationship between local ARI restitution properties and PI and PS for VF induction.

RESULTS

Forty restitution curves were constructed from 11 SSP procedures. The maximal slope (Smax) of the ARI restitution curve of the right ventricular apex was positively correlated with the PI for VF induction (r = 0.761, p < 0.05). Spatial dispersions of ARI and Smax were negatively correlated with the PS for VF induction (r = -0.626 and r = -0.722, respectively, both p < 0.05).

CONCLUSIONS

Ventricular fibrillation can be induced by rapid ventricular pacing with 1 : 1 capture. The PI for VF induction was related to the Smax of the ARI restitution curve of the right ventricular apex, while PS for VF induction was associated with the spatial dispersions of ARI and its restitution property.

Local Gradients in Electrotonic Loading Modulate the Local Effective Refractory Period: Implications for Arrhythmogenesis in the Infarct Border Zone

Ectopic electrical activity that originates in the peri-infarct region can give rise to potentially lethal re-entrant arrhythmias. The spatial variation in electrotonic loading that results from structural remodelling in the infarct border zone may increase the probability that focal activity will trigger electrical capture, but this has not previously been investigated systematically. This study uses in-silico experiments to examine the structural modulation of effective refractory period on ectopic beat capture. Informed by 3-D reconstructions of myocyte organization in the infarct border zone, a region of rapid tissue expansion is abstracted to an idealized representation. A novel metric is introduced that defines the local electrotonic loading as a function of passive tissue properties and boundary conditions. The effective refractory period correlates closely with local electrotonic loading, while the action potential duration, conduction, and upstroke velocity reduce in regions of increasing electrotonic load. In the presence of focal ectopic stimuli, spatial variation in effective refractory period can cause unidirectional conduction block providing a substrate for reentrant arrhythmias. Consequently, based on the observed results, a possible novel mechanism for arrhythmogenesis in the infarct border zone is proposed.

A shocking past: a walk through generations of defibrillation development

Defibrillation is one of the most successful and widely recognized applications of electrotherapy. Yet the historical road to its first successful application in a patient and the innovative adaptation to an implantable device is marred with unexpected turns, political and personal setbacks, and public and scientific condemnation at each new idea. Driven by dedicated scientists and ever-advancing creative applications of new technologies, from electrocardiography to high density mapping and computational simulations, the field of defibrillation persevered and continued to evolve to the life-saving tool it is today. In addition to critical technological advances, the history of defibrillation is also marked by the plasticity of the theory of defibrillation. The advancing theories of success have propelled the campaign for reducing the defibrillation energy requirement, instilling hope in the development of a painless and harmless electrical defibrillation strategy.

Imaging of Ventricular Fibrillation and Defibrillation: The Virtual Electrode Hypothesis

Ventricular fibrillation is the major underlying cause of sudden cardiac death. Understanding the complex activation patterns that give rise to ventricular fibrillation requires high resolution mapping of localized activation. The use of multi-electrode mapping unraveled re-entrant activation patterns that underlie ventricular fibrillation. However, optical mapping contributed critically to understanding the mechanism of defibrillation, where multi-electrode recordings could not measure activation patterns during and immediately after a shock. In addition, optical mapping visualizes the virtual electrodes that are generated during stimulation and defibrillation pulses, which contributed to the formulation of the virtual electrode hypothesis. The generation of virtual electrode induced phase singularities during defibrillation is arrhythmogenic and may lead to the induction of fibrillation subsequent to defibrillation. Defibrillating with low energy may circumvent this problem. Therefore, the current challenge is to use the knowledge provided by optical mapping to develop a low energy approach of defibrillation, which may lead to more successful defibrillation.

Effects of premature anodal stimulations on cardiac transmembrane potential and intracellular calcium distributions computed by anisotropic Bidomain models

AIMS

Cardiac unipolar electrode stimulations induce a particular structure of the transmembrane potential distribution (Vm), called virtual electrode polarization (VEP), which plays an important role in the mechanisms of cardiac excitation, reentry induction, and ventricular defibrillation. Recent experimental studies, based on the optical mapping techniques, have shown that premature stimulations also induce significant changes in the intracellular calcium (Cai) spatial distribution. The aim of this work is to investigate and compare by means of numerical simulations the morphology of the Vm and Cai patterns, generated by applying an S1-S2 stimulation protocol with a premature S2 anodal pulse.

METHODS AND RESULTS

We perform parallel finite element simulations of a three-dimensional orthotropic Bidomain model on a block of ventricular tissue by using four membrane models of two species (guinea pig and rabbit), that incorporate the phenomenological or more detailed mechanistic descriptions of the calcium dynamics. During the S2 anodal stimulus, the Cai spatial distribution, computed with all the considered models, presents a configuration similar to the typical VEP pattern of Vm, with a minimum inside the virtual anode and two maxima in the virtual cathodes. After the S2 stimulus turns off, the anode break excitation mechanism yields a Vm pattern exhibiting a clearly propagating wavefront. Differently, the Cai patterns do not show a clear separation between the resting and the activated regions, with the exception of one of the phenomenological models considered, but they show warped dog-bone shaped equi-level lines around an elevation in the virtual anode region.

CONCLUSION

The VEP pattern of the Cai spatial distribution during the S2 stimulus is in agreement with the previous experimental studies. Moreover, the Cai minimum in the virtual anode can be mainly attributable to the outflow of calcium ions produced by the sodium-calcium (NCX) exchanger, without a significant contribution of the ICaL current.

New insights into defibrillation of the heart from realistic simulation studies

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.

The strength-interval curve in cardiac tissue

The bidomain model describes the electrical properties of cardiac tissue and is often used to simulate the response of the heart to an electric shock. The strength-interval curve summarizes how refractory tissue is excited. This paper analyzes calculations of the strength-interval curve when a stimulus is applied through a unipolar electrode. In particular, the bidomain model is used to clarify why the cathodal and anodal strength-interval curves are different, and what the mechanism of the “dip” in the anodal strength-interval curve is.

The Mechanical Bidomain Model: A Review

The mechanical bidomain model is a new mathematical description of the elastic behavior of cardiac tissue. Its primary advantage over previous models is that it accounts for forces acting across the cell membrane arising form differences in the displacement of the intracellular and extracellular spaces. In this review, I describe the development of the mechanical bidomain model. I emphasize new predictions of the model, such as the existence of boundary layers at the tissue surface where the membrane forces are large, and pressure differences between the intracellular and extracellular spaces. Although the theoretical analysis is quite mathematical, I highlight the types of experiments that could be used to test the model predictions. Finally, I present open questions about the mechanical bidomain model that may be productive future directions for research.

Modeling defibrillation of the heart: approaches and insights

Cardiac defibrillation, as accomplished nowadays by automatic, implantable devices (ICDs), constitutes the most important means of combating sudden cardiac death. While ICD therapy has proved to be efficient and reliable, defibrillation is a traumatic experience. Thus, research on defibrillation mechanisms, particularly aimed at lowering defibrillation voltage, remains an important topic. Advancing our understanding towards a full appreciation of the mechanisms by which a shock interacts with the heart is the most promising approach to achieve this goal. The aim of this paper is to assess the current state-of-the-art in ventricular defibrillation modeling, focusing on both numerical modeling approaches and major insights that have been obtained using defibrillation models, primarily those of realistic ventricular geometry. The paper showcases the contributions that modeling and simulation have made to our understanding of the defibrillation process. The review thus provides an example of biophysically based computational modeling 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.

Mathematical modeling and simulation of ventricular activation sequences: implications for cardiac resynchronization therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy.

How hyperpolarization and the recovery of excitability affect propagation through a virtual anode in the heart

Researchers have suggested that the fate of a shock-induced wave front at the edge of a "virtual anode" (a region hyperpolarized by the shock) is a key factor determining success or failure during defibrillation of the heart. In this paper, we use a simple one-dimensional computer model to examine propagation speed through a hyperpolarized region. Our goal is to test the hypothesis that rapid propagation through a virtual anode can cause failure of propagation at the edge of the virtual anode. The calculations support this hypothesis and suggest that the time constant of the sodium inactivation gate is an important parameter. These results may be significant in understanding the mechanism of the upper limit of vulnerability.

Mechanisms of defibrillation

Electrical shock has been the one effective treatment for ventricular fibrillation for several decades. With the advancement of electrical and optical mapping techniques, histology, and computer modeling, the mechanisms responsible for defibrillation are now coming to light. In this review, we discuss recent work that demonstrates the various mechanisms responsible for defibrillation. On the cellular level, membrane depolarization and electroporation affect defibrillation outcome. Cell bundles and collagenous septae are secondary sources and cause virtual electrodes at sites far from shocking electrodes. On the whole-heart level, shock field gradient and critical points determine whether a shock is successful or whether reentry causes initiation and continuation of fibrillation.

Multiple monophasic shocks improve electrotherapy of ventricular tachycardia in a rabbit model of chronic infarction

BACKGROUND

We previously showed that the cardioversion threshold (CVT) for ventricular tachycardia (VT) is phase dependent when a single monophasic shock (1MP) is used.

OBJECTIVE

The purpose of this study was to extend these findings to a biphasic shock (1BP) and to compare the efficacy of phase-independent multiple monophasic (5MP) and biphasic shocks (5BP).

METHODS

Panoramic optical mapping with blebbistatin (5 microM) was performed in postmyocardial infarction rabbit hearts (n = 8). Flecainide (1.64 +/- 0.68 microM) was administered to promote sustained arrhythmias. 5MP and 5BP were applied within one VT cycle length (CL). Results were compared to 1BP and antitachycardia pacing.

RESULTS

We observed monomorphic VT with CL = 149.6 +/- 18.0 ms. Similar to 1MP, CVTs of 1BP were found to be phase dependent, and the maximum versus minimum CVT was 8.6 +/- 1.7 V/cm versus 3.7 +/- 1.9 V/cm, respectively (P = .0013). Efficacy of 5MP was higher than that of 1BP and 5BP. CVT was 3.2 +/- 1.4 V/cm for 5MP versus 5.3 +/- 1.9 V/cm for 5BP (P = .00027). 5MP versus averaged 1BP CVT was 3.6 +/- 2.1 V/cm versus. 6.8 +/- 1.5 V/cm, respectively (P = .00024). Antitachycardia pacing was found to be completely ineffective in this model.

CONCLUSION

Maintenance of shock-induced virtual electrode polarization by multiple monophasic shocks over a VT cycle is responsible for unpinning of reentry leading to self-termination. Elimination of virtual electrode polarization by shock polarity reversal during multiple biphasic shocks proved ineffective. A significant reduction in CVT can be achieved by applying multiple monophasic shocks within one VT CL or one single shock at the proper coupling interval.

Membrane time constant during internal defibrillation strength shocks in intact heart: effects of Na+ and Ca2+ channel blockers

INTRODUCTION

We assessed defibrillation strength shock-induced changes of the membrane time constant (tau) and membrane potential (DeltaVm) in intact rabbit hearts after administration of lidocaine, a sodium (Na(+)) channel blocker, or nifedipine, a L-type calcium (Ca(2+)) channel blocker.

METHODS AND RESULTS

We optically mapped anterior, epicardial, electrical activity during monophasic shocks (+/-100, +/-130, +/-160, +/-190, and +/-220 V; 150 microF; 8 ms) applied at 25%, 50%, and 75% of the action potential duration via a shock lead system in Langendorff-perfused hearts. The protocol was run twice for each heart under control and after lidocaine (15 microM, n = 6) or nifedipine (2 microM, n = 6) addition. tau in the virtual electrode area away from the shock lead was approximated with single-exponential fits from a total of 121,125 recordings. The same data set was used to calculate DeltaVm. We found (1) Under all conditions, there is inverse relationship between tau and DeltaVm with respect to changes of shock strength, regardless of shock polarity and phase of application: a stronger shock resulted in a larger DeltaVm, which corresponded to a smaller tau (faster cellular response); (2) Lidocaine did not cause appreciable changes in either tau or DeltaVm versus control, and (3) Nifedipine significantly increased both tau and DeltaVm in the virtual cathode area; in contrast, in the virtual anode area, this effect depended on the phase of shock application.

CONCLUSION

tau and DeltaVm are inversely related. Na(+) channel blocker has minimal impact on either tau or DeltaVm. Ca(2+) blocker caused polarity and phase-dependent significant changes in tau and DeltaVm.

A comparison of chronaxies for ventricular fibrillation induction, defibrillation, and cardiac stimulation: unexpected findings and their implications

INTRODUCTION

A low-energy (<or= 4 J) cardioversion shock (LEC) either terminates reentrant ventricular tachycardia (VT) or accelerates it to ventricular fibrillation (VF). Optimization of the duration and amplitude of LEC shocks could improve the success rate of VT termination without VF induction.

METHODS AND RESULTS

In order to learn how LEC shocks may be optimized, we used an animal model to compare the strength-duration curve for VF induction and the strength-duration curve for cardiac stimulation via the shock coil. Conventional implantable cardioverter-defibrillator (ICD) leads were implanted in 12 narcotized pigs from 20 kg to 25 kg in weight. Stimulation, VF induction, and defibrillation pulses were delivered by custom-designed stimulators at preset pulse durations and amplitudes. The corresponding hyperbolic strength-duration curves were constructed using the least-squares fit method and averaged for all the animals. The mean chronaxie for stimulation via the shock coil of 0.23 ms was significantly shorter than both defibrillation (4.8 ms) and VF induction (3.1 ms) chronaxie values. At a shock duration of 0.3 ms or less, the mean VF-induction threshold amplitude exceeded 300 V.

CONCLUSION

It may be reasonable to study whether LEC pulses from 0.25 ms to 0.30 ms in duration and up to 250 V in amplitude would increase therapeutic yield in VT termination without VF induction in humans. Contrary to the current belief, the discrepancy between defibrillation and stimulation chronaxie is not caused by different electrode size. We postulate that the time constant of the fast sodium channel reactivation may be the underlying reason.

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.

Modulation of shock-end virtual electrode polarisation as a direct result of 3D fluorescent photon scattering

Due to the large transmural variation in transmembrane potential following the application of strong electric shocks, it is thought that fluorescent photon scattering from depth plays a significant role in optical signal modulation at shock-end. For the first time, a model of photon scattering is used to accurately synthesize fluorescent signals over the irregular geometry of the rabbit ventricles following the application of such strong shocks. A bidomain representation of electrical activity is combined with finite element solutions to the photon diffusion equation, simulating both the excitation and emission processes, over an anatomically-based model of rabbit ventricular geometry and fiber orientation. Photon scattering from within a 3D volume beneath the epicardial optical recording site is shown to transduce differences in transmembrane potential within this volume through the myocardial wall. This leads directly to a significantly modulated optical signal response with respect to that predicted by the bidomain simulations, distorting epicardial virtual electrode polarization produced at shock-end. Furthermore, we show that this degree of distortion is very sensitive to the optical properties of the tissue, an important variable to consider during experimental mapping set-ups. These findings provide an essential first-step in aiding the interpretation of experimental optical mapping recordings following strong defibrillation shocks.

The role of mechanoelectric feedback in vulnerability to electric shock

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.

Laminar Arrangement of Ventricular Myocytes Influences Electrical Behavior of the Heart

The response of the heart to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. A long-held view of cardiac electrical anisotropy is that electrical conductivity is greatest along the myocyte axis allowing most rapid propagation of electrical activation in this direction, and that conductivity is isotropic transverse to the myocyte axis supporting a slower uniform spread of activation in this plane. In this context, knowledge of conductivity in two directions, parallel and transverse to the myofiber axis, is sufficient to characterize the electrical action of the heart. Here we present new experimental data that challenge this view. We have used a novel combination of intramural electrical mapping, and experiment-specific computer modeling, to demonstrate that left ventricular myocardium has unique bulk conductivities associated with three microstructurally-defined axes. We show that voltage fields induced by intramural current injection are influenced by not only myofiber direction, but also the transmural arrangement of muscle layers or myolaminae. Computer models of these experiments, in which measured 3D tissue structure was reconstructed in-silico, best matched recorded voltages with conductivities in the myofiber direction, and parallel and normal to myolaminae, set in the ratio 4:2:1, respectively. These findings redefine cardiac tissue as an electrically orthotropic substrate and enhance our understanding of how external shocks may act to successfully reset the fibrillating heart into a uniform electrical state. More generally, the mechanisms governing the destabilization of coordinated electrical propagation into ventricular arrhythmia need to be evaluated in the light of this discovery.

The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

In normal heart, ventricular fibrillation can be induced by a single properly timed strong electrical or mechanical stimulus. A mechanism first proposed by Winfree and coined the “pinwheel experiment” emphasizes the timing and strength of the stimulus in inducing figure-of-eight reentry. However, the effects of cellular electrophysiological properties on vulnerability to reentry in the pinwheel scenario have not been investigated. In this study, we extend Winfree's pinwheel experiment to show how the vulnerability to reentry is affected by the graded action potential responses induced by a strong premature stimulus, action potential duration (APD), and APD restitution in simulated monodomain homogeneous two-dimensional tissue. We find that a larger graded response, longer APD, or steeper APD restitution slope reduces the vulnerable window of reentry. Strong graded responses and long APD promote tip-tip interactions at long coupling intervals, causing the two initiated spiral wave tips to annihilate. Steep APD restitution promotes wave front-wave back interaction, causing conduction block in the central common pathway of figure-of-eight reentry. We derive an analytical treatment that shows good agreement with numerical simulation results.

Quantification of shock-induced microscopic virtual electrodes assessed by subcellular resolution optical potential mapping in guinea pig papillary muscle

INTRODUCTION

The primary objective of this study was the quantitative description of shock-induced, locally occurring virtual electrodes in natural cardiac tissue.

METHODS AND RESULTS

Multiscale optical potential mapping using 10x, 20x, and 40x magnifying objectives, achieving resolutions of 0.13, 0.065, and 0.033 mm, was performed when applying uniform shocks (+/-10 V/cm, 5 ms) during diastole and action potential plateau. A procedure was developed to identify local potential deviations as depolarizing or hyperpolarizing peaks and to quantify their occurrence and characteristic amplitudes, lateral extents, and dynamics. At shock onset, peaks of either polarity developed significantly faster (tau = 0.92 +/- 0.65 ms, N = 64) than the average bulk polarization (tau = 2.25 +/- 0.96 ms, P < 0.001) and appeared locally fixed, changing their polarity at shock reversal. The mean peak magnitude (21.2 +/- 12 mV) and the amplitude distribution were essentially independent from the magnification. The peak density continuously increased with decreasing peak extent (taken at 70% of the amplitude), reaching a maximum of approximately 3 peaks/mm2 in the range of approximately 30-65 microm. There was no correlation between peak amplitude and size throughout. Potentially exciting peaks were found with a density of 0.04-0.2 peaks/mm2 corresponding to estimated 1-5 peaks/mm3.

CONCLUSIONS

Our results suggest that microscopic inhomogeneities form a substantial substrate for far-field excitation in natural cardiac tissue. Here, we effectively bridged the gap between the extensively studied myocyte cultures and larger heart preparations.

Three distinct phases of VF during global ischemia in the isolated blood-perfused pig heart

Changes in ventricular fibrillation (VF) organization occurring after the onset of global ischemia are relevant to defibrillation and survival but remain poorly understood. We hypothesized that ischemia-specific dynamic instability of the action potential (AP) causes a loss of spatiotemporal periodicity of propagation and broadening of the electrocardiogram (ECG) frequency spectrum during VF in the ischemic myocardium. We recorded voltage-sensitive fluorescence of di-4-ANEPPS (anterior left ventricle, 35 x 35 mm, 64 x 64 pixels) and the volume-conducted ECG in six blood-perfused hearts during 10 min of VF and global ischemia. We used coefficient of variation (CV) to estimate variability of AP amplitude, AP duration, and diastolic interval (CV-APA, CV-APD, and CV-DI, respectively). We computed excitation median frequency (Median_F), spectral width of the AP and ECG (SpW-AP and SpW-ECG, respectively), wavebreak incidence (WBI), and recurrence of propagation direction (RPD). We found three distinct phases of local VF dynamics: "relatively periodic" (<or=1 min, high Median_F, moderate AP variability, high WBI, low RPD), "highly periodic" (1-2 min, reduced Median_F, low AP variability, low WBI, high RPD), and "aperiodic" (3-10 min, low Median_F, high AP variability, high WBI, low RPD). In one experiment, spontaneous conversion from the aperiodic to the highly periodic phase occurred after 5 min of ischemia. The SpW-ECG was correlated with SpW-AP, CV-APD, and CV-APA. We conclude that 1) at least three distinct phases of VF dynamics are present in our model, and 2) the newly described aperiodic phase is related to ischemia-specific dynamic instability of the AP shape, which underlies broadening of the ECG spectrum during VF evolution.

Using the Upper Limit of Vulnerability to Assess Defibrillation Efficacy at Implantation of ICDs

The upper limit of vulnerability (ULV) is the weakest shock strength at or above which ventricular fibrillation (VF) is not induced when the shock is delivered during the vulnerable period. The ULV, a measurement made in regular rhythm, provides an estimate of the minimum shock strength required for reliable defibrillation that is as accurate or more accurate than the defibrillation threshold (DFT). The ULV hypothesis of defibrillation postulates a mechanistic relationship between the ULV-measured during regular rhythm-and the minimum shock strength that defibrillates reliably. Vulnerability testing can be applied at implantable cardioverter defibrillator (ICD) implant to confirm a clinically adequate defibrillation safety margin without inducing VF in 75%-95% of ICD recipients. Alternatively, the ULV provides an accurate patient-specific safety margin with a single fibrillation-defibrillation episode. Programming first ICD shocks based on patient-specific measurements of ULV rather than programming routinely to maximum output shortens charge time and may reduce the probability of syncope as ICDs age and charge times increase. Because the ULV is more reproducible than the DFT, it provides greater statistical power for clinical research with fewer episodes of VF. Limited evidence suggests that vulnerability testing is safer than conventional defibrillation testing.

A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart

A bidomain reaction-diffusion model of the human heart was developed, and potentials resulting from normal depolarization and repolarization were compared with results from a compatible monodomain model. Comparisons were made for an empty isolated heart and for a heart with fluid-filled ventricles. Both sinus rhythm and ectopic activation were simulated. The bidomain model took 2 days on 32 processors to simulate a complete cardiac cycle. Differences between monodomain and bidomain results were extremely small, even for the extracellular potentials, which in case of the monodomain model were computed with a high-resolution forward model. Propagation of activation was 2% faster in the bidomain model than in the monodomain model. Electrograms computed with monodomain and bidomain models were visually indistinguishable. We conclude that, in the absence of applied currents, propagating action potentials on the scale of a human heart can be studied with a monodomain model.

Role of intramural virtual electrodes in shock-induced activation of left ventricle: Optical measurements from the intact epicardial surface

BACKGROUND

According to one hypothesized mechanism of defibrillation, shocks directly excite the bulk of ventricular myocardium in the excitable state due to intramural virtual electrodes; however, this hypothesis has not been examined in intact myocardium.

OBJECTIVES

The purpose of this study was examine the role of intramural virtual electrodes in shock-induced activation of intact left ventricular (LV) tissue.

METHODS

Twelve isolated porcine LV preparations were stained with a transmembrane potential (V(m))-sensitive dye by two methods: (1) surface staining and (2) global staining via coronary perfusion. Shocks (E approximately 0.8-48 V/cm, duration = 10 ms) were applied across the wall from epicardium to endocardium during diastole via transparent electrodes. Shock-induced V(m) responses were measured optically from the intact epicardial surface after surface staining and global staining.

RESULTS

Surface-staining recordings demonstrated different V(m) responses to cathodal and anodal shocks. Whereas cathodal shocks caused depolarization and rapid activation of the epicardial surface, anodal shocks induced hyperpolarization and delayed surface activation. In contrast, global-staining V(m) responses to cathodal and anodal shocks were qualitatively similar. Both responses were characterized by activation with small latency and rapid propagation. Weak shocks of both polarities induced monotonic action potential upstrokes; stronger shocks induced nonmonotonic upstrokes with two rising phases at shock onset and end. Such features of global-staining V(m) responses as make activation of the epicardium by anodal shocks and the nonmonotonic action potential upstrokes can be explained by the presence of subepicardial intramural virtual electrodes.

CONCLUSION

These data suggest that shocks induce intramural virtual electrodes that directly excite LV tissue and account for the shape of optical V(m) responses recorded from the epicardial surface.

The effect of the fiber curvature gradient on break excitation in cardiac tissue

BACKGROUND

Break excitation has been hypothesized as a mechanism for the initiation of reentry in cardiac tissue. One way break excitation can occur is by virtual electrodes formed due to a curving fiber geometry. In this article, we are concerned with the relationship between the peak gradient of fiber curvature and the threshold for break stimulation and the initiation of reentry.

METHODS

We calculate the maximum gradient of fiber curvature for different scales of fiber geometry in a constant tissue size (20x20 mm), and also examine the mechanisms by which reentry initiation fails.

RESULTS

For small peak gradients, reentry fails because break excitation does not occur. For larger peak gradients, reentry fails because break excitation fails to develop into full-scale reentry. For strong stimuli above the upper limit of vulnerability, reentry fails because the break excitation propagates through the hyperpolarized region and then encounters refractory tissue, causing the wave front to die.

Do Intramural Virtual Electrodes Facilitate Successful Defibrillation? Model-Based Analysis of Experimental Evidence

INTRODUCTION

Recent computer model and experimental studies have suggested that microscopic intramural collagenous planes may facilitate successful defibrillation through the generation of shock-induced virtual electrodes deep within the ventricular wall. Evidence supporting the existence of intramural virtual electrodes has been drawn from several recent studies, which map shock-induced membrane potential (Vm) over the cut transmural surface of dissected segments of porcine left ventricle (LV). The artificially created transmural boundary in these experiments is impermeable to intracellular current. It is not known how this constraint limits the interpretation of these experiments in terms of the shock response of the intact ventricle.

METHODS AND RESULTS

This study uses a realistic 3D computer model of LV myocardium to aid experimental interpretation. The model incorporates a microstructural description of intramural cleavage plane discontinuities measured by confocal microscopy of rat LV. Electrical shocks are applied across the model tissue, with and without introduced transmural boundaries. Shocks of varying strength (4-40 V/cm) are also applied to the model and the response analyzed. Results show that shock-induced Vm changes (deltaVm) on a transmural tissue boundary are significantly different to deltaVm of the intact ventricle, and the extent of difference depends on boundary orientation. However, the presence and qualitative behavior of intramural virtual electrodes is preserved irrespective of boundary placement. The model also confirms experimental observations that most rapid transmural activation occurs for shocks of strength 5-10 V/cm. Two distinct mechanisms suppress virtual electrode propagation, and hence slow tissue activation, outside of this optimal shock strength range.

CONCLUSIONS

This study supports the hypothesis that distributed microscopic intramural virtual electrodes contribute to rapid activation of the ventricular wall during defibrillation.

Defibrillation of the heart: insights into mechanisms from modelling studies

Despite its critical role in restoring cardiac rhythm and thus in saving human life, cardiac defibrillation remains poorly understood. Further mechanistic inquiry is hampered by the inability of presently available experimental techniques to resolve, with sufficient accuracy, electrical behaviour confined to the depth of the ventricles. The objective of this review article is to demonstrate that realistic 3-D simulations of the ventricular defibrillation process in close conjunction with experimental observations are capable of bringing a new level of understanding of the electrical events that ensue from the interaction between fibrillating myocardium and applied shock. The article does this by reviewing the results of two studies, one on vulnerability to electric shocks and another on defibrillation. An overview of the modelling tools used in these studies is also provided.

How to explain why "unequal anisotropy ratios" is important using pictures but no mathematics

"Unequal anisotropy ratios" is an important property of cardiac tissue. Many of the fundamental mechanisms governing how the heart responds to an electrical shock require unequal anisotropy ratios. In this paper, I explain the role of unequal anisotropy ratios using pictures rather than mathematics. My goal is to develop physical insight, so has to understand qualitatively why the condition of unequal anisotropy ratios is so important.

Role of microscopic tissue structure in shock-induced activation assessed by optical mapping in myocyte cultures

INTRODUCTION

Termination of ventricular fibrillation by electric shocks is believed to be due to the direct activation of large tissue mass that may be caused by microscopic virtual electrodes formed at discontinuities in tissue structure. Here, microscopic shock-induced activation was measured optically in myocyte cultures; spatially averaged microscopic Vm measurements were compared with macroscopic measurements from left ventricular (LV) tissue.

METHODS AND RESULTS

Experiments were performed in linear cell strands of different width (approximately 0.1 and 0.8 mm) and isolated porcine LV preparations. Uniform field shocks were applied across strands or LV preparations during diastole and action potential (AP) plateau. Depending on shock strength, three different types of activation were observed in cell strands. Weakest shocks produced "delayed make" activation that started on the cathodal strand side after long latency and rapidly spread to the anodal side. Stronger shocks caused "make" activation with short latency and rapid spread across strands. Strongest shocks caused nonuniform "make-break" activation where the cathodal side was activated with a short latency but activation of the anodal side was delayed until after the shock end due to a large negative shock-induced polarization. Spatial averaging of Vm responses across 0.1-mm (but not 0.8-mm) strands resulted in AP upstrokes and plateau polarizations that closely resembled the Vm responses measured in LV myocardium. The shock strength for the transition between fast and delayed activation in 0.1-mm cell strands and LV myocardium was similar as well.

CONCLUSION

These data provide evidence that microscopic tissue structures with dimensions of approximately hundred microns are responsible for shock-induced activation of ventricular tissue.

Examination of stimulation mechanism and strength-interval curve in cardiac tissue

Understanding the basic mechanisms of excitability through the cardiac cycle is critical to both the development of new implantable cardiac stimulators and improvement of the pacing protocol. Although numerous works have examined excitability in different phases of the cardiac cycle, no systematic experimental research has been conducted to elucidate the correlation among the virtual electrode polarization pattern, stimulation mechanism, and excitability under unipolar cathodal and anodal stimulation. We used a high-resolution imaging system to study the spatial and temporal stimulation patterns in 20 Langendorff-perfused rabbit hearts. The potential-sensitive dye di-4-ANEPPS was utilized to record the electrical activity using epifluorescence. We delivered S1-S2 unipolar point stimuli with durations of 2-20 ms. The anodal S-I curves displayed a more complex shape in comparison with the cathodal curves. The descent from refractoriness for anodal stimulation was extremely steep, and a local minimum was clearly observed. The subsequent ascending limb had either a dome-shaped maximum or was flattened, appearing as a plateau. The cathodal S-I curves were smoother, closer to a hyperbolic shape. The transition of the stimulation mechanism from break to make always coincided with the final descending phase of both anodal and cathodal S-I curves. The transition is attributed to the bidomain properties of cardiac tissue. The effective refractory period was longer when negative stimuli were delivered than for positive stimulation. Our spatial and temporal analyses of the stimulation patterns near refractoriness show always an excitation mechanism mediated by damped wave propagation after S2 termination.