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

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Spatial phase discontinuity at the center of moving cardiac spiral waves

BACKGROUND

Precise analysis of cardiac spiral wave (SW) dynamics is essential for effective arrhythmia treatment. Although the phase singularity (PS) point in the spatial phase map has been used to determine the cardiac SW center for decades, quantitative detection algorithms that assume PS as a point fail to trace complex and rapid PS dynamics. Through a detailed analysis of numerical simulations, we examined our hypothesis that a boundary of spatial phase discontinuity induced by a focal conduction block exists around the moving SW center in the phase map.

METHOD

In a numerical simulation model of a 2D cardiac sheet, three different types of SWs (short wavelength; long wavelength; and low excitability) were induced by regulating ion channels. Discontinuities of all boundaries among adjacent cells at each instance were evaluated by calculating the phase bipolarity (PB). The total amount of phase transition (PTA) in each cell during the study period was evaluated.

RESULTS

Pivoting, drifting, and shifting SWs were observed in the short-wavelength, low-excitability, and long-wavelength models, respectively. For both the drifting and shifting cases, long high-PB edges were observed on the SW trajectories. In all cases, the conduction block (CB) was observed at the same boundaries. These were also identical to the boundaries in the PTA maps.

CONCLUSIONS

The analysis of the simulations revealed that the conduction block at the center of a moving SW induces discontinuous boundaries in spatial phase maps that represent a more appropriate model of the SW center than the PS point.

Validating defibrillation simulation in a human-shaped phantom

BACKGROUND

We previously developed a computational model to aid clinicians in positioning implantable cardioverter-defibrillators (ICDs), especially in the case of abnormal anatomies that commonly arise in pediatric cases. We have validated the model clinically on the body surface; however, validation within the volume of the heart is required to establish complete confidence in the model and improve its use in clinical settings.

OBJECTIVE

The goal of this study was to use an animal model and thoracic phantom to record the ICD potential field within the heart and on the torso to validate our defibrillation simulation system.

METHODS

We recorded defibrillator shock potentials from an ICD suspended together with an animal heart in a human-shaped torso tank and compared them with simulated values. We also compared the scaled distribution threshold, an analog to the defibrillation threshold, calculated from the measured and simulated electric fields within the myocardium.

RESULTS

ICD potentials recorded on the tank and cardiac surface and within the myocardium agreed well with those predicted by the simulation. A quantitative comparison of the recorded and simulated potentials yielded a mean correlation of 0.94 and a relative error of 19.1%. The simulation can also predict scaled distribution thresholds similar to those calculated from the measured potential fields.

CONCLUSION

We found that our simulation could predict potential fields with high correlation with the measured values within the heart and on the torso surface. These results support the use of this model for the optimization of ICD placements.

The role of conductivity discontinuities in design of cardiac defibrillation

Fibrillation is an erratic electrical state of the heart, of rapid twitching rather than organized contractions. Ventricular fibrillation is fatal if not treated promptly. The standard treatment, defibrillation, is a strong electrical shock to reinitialize the electrical dynamics and allow a normal heart beat. Both the normal and the fibrillatory electrical dynamics of the heart are organized into moving wave fronts of changing electrical signals, especially in the transmembrane voltage, which is the potential difference between the cardiac cellular interior and the intracellular region of the heart. In a normal heart beat, the wave front motion is from bottom to top and is accompanied by the release of Ca ions to induce contractions and pump the blood. In a fibrillatory state, these wave fronts are organized into rotating scroll waves, with a centerline known as a filament. Treatment requires altering the electrical state of the heart through an externally applied electrical shock, in a manner that precludes the existence of the filaments and scroll waves. Detailed mechanisms for the success of this treatment are partially understood, and involve local shock-induced changes in the transmembrane potential, known as virtual electrode alterations. These transmembrane alterations are located at boundaries of the cardiac tissue, including blood vessels and the heart chamber wall, where discontinuities in electrical conductivity occur. The primary focus of this paper is the defibrillation shock and the subsequent electrical phenomena it induces. Six partially overlapping causal factors for defibrillation success are identified from the literature. We present evidence in favor of five of these and against one of them. A major conclusion is that a dynamically growing wave front starting at the heart surface appears to play a primary role during defibrillation by critically reducing the volume available to sustain the dynamic motion of scroll waves; in contrast, virtual electrodes occurring at the boundaries of small, isolated blood vessels only cause minor effects. As a consequence, we suggest that the size of the heart (specifically, the surface to volume ratio) is an important defibrillation variable.

Highly trabeculated structure of the human endocardium underlies asymmetrical response to low-energy monophasic shocks

Novel low-energy defibrillation therapies are thought to be driven by virtual-electrodes (VEs), due to the interaction of applied monophasic electric shocks with fine-scale anatomical structures within the heart. Significant inter-species differences in the cardiac (micro)-anatomy exist, however, particularly with respect to the degree of endocardial trabeculations, which may underlie important differences in response to low-energy defibrillation protocols. Understanding the interaction of monophasic electric fields with the specific human micro-anatomy is therefore imperative in facilitating the translation and optimisation of these promising experimental therapies to the clinic. In this study, we sought to investigate how electric fields from implanted devices interact with the highly trabeculated human endocardial surface to better understand shock success in order to help optimise future clinical protocols. A bi-ventricular human computational model was constructed from high resolution (350 μm) ex-vivo MR data, including anatomically accurate endocardial structures. Monophasic shocks were applied between a basal right ventricular catheter and an exterior ground. Shocks of varying strengths were applied with both anodal [positive right ventricle (RV) electrode] and cathodal (negative RV electrode) polarities at different states of tissue refractoriness and during induced arrhythmias. Anodal shocks induced isolated positive VEs at the distal side of "detached" trabeculations, which rapidly spread into hyperpolarised tissue on the surrounding endocardial surfaces following the shock. Anodal shocks thus depolarised more tissue 10 ms after the shock than cathodal shocks where the propagation of activation from VEs induced on the proximal side of "detached" trabeculations was prevented due to refractory endocardium. Anodal shocks increased arrhythmia complexity more than cathodal shocks during failed anti-arrhythmia shocks. In conclusion, multiple detached trabeculations in the human ventricle interact with anodal stimuli to induce multiple secondary sources from VEs, facilitating more rapid shock-induced ventricular excitation compared to cathodal shocks. Such a mechanism may help explain inter-species differences in response to shocks and help to develop novel defibrillation strategies.

Bidomain Predictions of Virtual Electrode-Induced Make and Break Excitations around Blood Vessels

Introduction and background

Virtual electrodes formed by field stimulation during defibrillation of cardiac tissue play an important role in eliciting activations. It has been suggested that the coronary vasculature is an important source of virtual electrodes, especially during low-energy defibrillation. This work aims to further the understanding of how virtual electrodes from the coronary vasculature influence defibrillation outcomes.

Methods

Using the bidomain model, we investigated how field stimulation elicited activations from virtual electrodes around idealized intramural blood vessels. Strength–interval curves, which quantify the stimulus strength required to elicit wavefront propagation from the vessels at different states of tissue refractoriness, were computed for each idealized geometry.

Results

Make excitations occurred at late diastolic intervals, originating from regions of depolarization around the vessel. Break excitations occurred at early diastolic intervals, whereby the vessels were able to excite surrounding refractory tissue due to the local restoration of excitability by virtual electrode-induced hyperpolarizations. Overall, strength–interval curves had similar morphologies and underlying excitation mechanisms compared with previous experimental and numerical unipolar stimulation studies of cardiac tissue. Including the presence of the vessel wall increased the field strength required for make excitations but decreased the field strength required for break excitations, and the field strength at which break excitations occurred was generally greater than 5 V/cm. Finally, in a more realistic ventricular slice geometry, the proximity of virtual electrodes around subepicardial vessels was seen to cause break excitations in the form of propagating unstable wavelets to the subepicardial layer.

Conclusion

Representing the blood vessel wall microstructure in computational bidomain models of defibrillation is recommended as it significantly alters the electrophysiological response of the vessel to field stimulation. Although vessels may facilitate excitation of relatively refractory tissue via break excitations, the field strength required for this is generally greater than those used in the literature on low-energy defibrillation. However, the high-intensity shocks used in standard defibrillation may elicit break excitation propagation from the coronary vasculature.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

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.

Mechanism of reentry induction by a 9-V battery in rabbit ventricles

Although the application of a 9-V battery to the epicardial surface is a simple method of ventricular fibrillation induction, the fundamental mechanisms underlying this process remain unstudied. We used a combined experimental and modelling approach to understand how the interaction of direct current (DC) from a battery may induce reentrant activity within rabbit ventricles and its dependence on battery application timing and duration. A rabbit ventricular computational model was used to simulate 9-V battery stimulation for different durations at varying onset times during sinus rhythm. Corresponding high-resolution optical mapping measurements were conducted on rabbit hearts with DC stimuli applied via a relay system. DC application to diastolic tissue induced anodal and cathodal make excitations in both simulations and experiments. Subsequently, similar static epicardial virtual electrode patterns were formed that interacted with sinus beats but did not induce reentry. Upon battery release during diastole, break excitations caused single ectopics, similar to application, before sinus rhythm resumed. Reentry induction was possible for short battery applications when break excitations were slowed and forced to take convoluted pathways upon interaction with refractory tissue from prior make excitations or sinus beats. Short-lived reentrant activity could be induced for battery release shortly after a sinus beat for longer battery applications. In conclusion, the application of a 9-V battery to the epicardial surface induces reentry through a complex interaction of break excitations after battery release with prior induced make excitations or sinus beats.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 10(6) simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.

Computational cardiology: the heart of the matter

This paper reviews the newest developments in computational cardiology. It focuses on the contribution of cardiac modeling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modeling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

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.

Controlling activation site density by low-energy far-field stimulation in cardiac tissue

Tachycardia and fibrillation are potentially fatal arrhythmias associated with the formation of rotating spiral waves in the heart. Presently, the termination of these types of arrhythmia is achieved by use of antitachycardia pacing or cardioversion. However, these techniques have serious drawbacks, in that they either have limited application or produce undesirable side effects. Low-energy far-field stimulation has recently been proposed as a superior therapy. This proposed therapeutic method would exploit the phenomenon in which the application of low-energy far-field shocks induces a large number of activation sites ("virtual electrodes") in tissue. It has been found that the formation of such sites can lead to the termination of undesired states in the heart and the restoration of normal beating. In this study we investigate a particular aspect of this method. Here we seek to determine how the activation site density depends on the applied electric field through in vitro experiments carried out on neonatal rat cardiac tissue cultures. The results indicate that the activation site density increases exponentially as a function of the intracellular conductivity and the level of cell isotropy. Additionally, we report numerical results obtained from bidomain simulations of the Beeler-Reuter model that are quantitatively consistent with our experimental results. Also, we derive an intuitive analytical framework that describes the activation site density and provides useful information for determining the ratio of longitudinal to transverse conductivity in a cardiac tissue culture. The results obtained here should be useful in the development of an actual therapeutic method based on low-energy far-field pacing. In addition, they provide a deeper understanding of the intrinsic properties of cardiac cells.

Efficient simulation of cardiac electrical propagation using high order finite elements

We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

Reversible cardiac conduction block and defibrillation with high-frequency electric field

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.

Propagating unstable wavelets in cardiac tissue

Solitonlike propagating modes have been proposed for excitable tissue, but have never been measured in cardiac tissue. In this study, we simulate an experimental protocol to elicit these propagating unstable wavelets (PUWs) in a detailed three-dimensional ventricular wedge preparation. PUWs appear as fixed-shape wavelets that propagate only in the direction of cardiac fibers, with conduction velocity approximately 40% slower than normal action potential excitation. We investigate their properties, demonstrating that PUWs are not true solitons. The range of stimuli for which PUWs were elicited was very narrow (several orders of magnitude lower than the stimulus strength itself), but increased with reduced sodium conductance and reduced coupling in nonlongitudinal directions. We show that the phenomenon does not depend on the particular membrane representation used or the shape of the stimulating electrode.

Identification and functional characterization of KCNQ1 mutations around the exon 7-intron 7 junction affecting the splicing process

BACKGROUND

KCNQ1 gene encodes the delayed rectifier K(+) channel in cardiac muscle, and its mutations cause long QT syndrome type 1 (LQT1). Especially exercise-related cardiac events predominate in LQT1. We previously reported that a KCNQ1 splicing mutation displays LQT1 phenotypes.

METHODS AND RESULTS

We identified novel mutation at the third base of intron 7 (IVS7 +3A>G) in exercise-induced LQT1 patients. Minigene assay in COS7 cells and RT-PCR analysis of patients' lymphocytes demonstrated the presence of exon 7-deficient mRNA in IVS7 +3A>G, as well as c.1032G>A, but not in c.1022C>T. Real-time RT-PCR demonstrated that both IVS7 +3A>G and c.1032G>A carrier expressed significant amounts of exon-skipping mRNAs (18.8% and 44.8% of total KCNQ1 mRNA). Current recordings from Xenopus oocytes injected cRNA by simulating its ratios of exon skipping displayed a significant reduction in currents to 64.8 ± 4.5% for IVS7 +3A>G and to 41.4 ± 9.5% for c.1032G>A carrier, respectively, compared to the condition without splicing error. Computer simulation incorporating these quantitative results revealed the pronounced QT prolongation under beta-adrenergic stimulation in IVS7 +3A>G carrier model.

CONCLUSION

Here we report a novel splicing mutation IVS7 +3A>G, identified in a family with mild form LQT1 phenotypes, and examined functional outcome in comparison with three other variants around the exon 7-intron 7 junction. In addition to c.1032G>A mutation, IVS7 +3A>G generates exon-skipping mRNAs, and thereby causing LQT1 phenotype. The severity of clinical phenotypes appeared to differ between the two splicing-related mutations and to result from the amount of resultant mRNAs and their functional consequences.

Probing field-induced tissue polarization using transillumination fluorescent imaging

Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart, recent optical mapping studies have revealed two major discrepancies between theory and experiment: 1), the presence of negative bulk polarization recorded during strong shocks; and 2), the unexpectedly small surface polarization under shock electrodes. There is little consensus as to whether these differences result from deficiencies of experimental techniques, artifacts of tissue damage, or deficiencies of existing theories. Here, we take advantage of recently developed near-infrared voltage-sensitive dyes and transillumination optical imaging to perform, for the first time that we know of, noninvasive probing of field effects deep inside the intact ventricular wall. This technique removes some of the limitations encountered in previous experimental studies. We explicitly demonstrate that deep inside intact myocardial tissue preparations, strong electrical shocks do produce considerable negative bulk polarization previously inferred from surface recordings. We also demonstrate that near-threshold diastolic field stimulation produces activation of deep myocardial layers 2-6 mm away from the cathodal surface, contrary to theory. Using bidomain simulations we explore factors that may improve the agreement between theory and experiment. We show that the inclusion of negative asymmetric current can qualitatively explain negative bulk polarization in a discontinuous bidomain model.

Modeling the role of the coronary vasculature during external field stimulation

The exact mechanisms by which defibrillation shocks excite cardiac tissue far from both the electrodes and heart surfaces require elucidation. Bidomain theory explains this phenomena through the existence of intramural virtual electrodes (VEs), caused by discontinuities in myocardial tissue structure. In this study, we assess the modeling components essential in constructing a finite-element cardiac tissue model including blood vessels from high-resolution magnetic resonance data and investigate the specific role played by coronary vasculature in VE formation, which currently remains largely unknown. We use a novel method for assigning histologically based fiber architecture around intramural structures and include an experimentally derived vessel lumen wall conductance within the model. Shock-tissue interaction in the presence of vessels is assessed through comparison with a simplified model lacking intramural structures. Results indicate that VEs form around blood vessels for shocks > 8 V/cm. The magnitude of induced polarizations is attenuated by realistic representation of fiber negotiation around vessel cavities, as well as the insulating effects of the vessel lumen wall. Furthermore, VEs formed around large subepicardial vessels reduce epicardial polarization levels. In conclusion, we have found that coronary vasculature acts as an important substrate for VE formation, which may help interpretation of optical mapping data.

Shock induced electrical activation in structurally detailed models of pig left-ventricular tissue

Detailed models of sample specific structures in pig left-ventricular tissue have been constructed. These models include epicardial and endocardial surfaces, fiber and sheet orientations, vessels and cleavage planes with significant dimensions. This work shows that it is possible to extract from 3D tissue images reduced dimension descriptions of cleavage planes in the heart wall. These descriptions are used to analyze the response of tissue to electrical shocks of varying strengths. The presence of explicit discontinuities in the heart significantly reduces the time required for transmural activation and provides a basis for understanding successful defibrillation.

Development of an anatomically detailed MRI-derived rabbit ventricular model and assessment of its impact on simulations of electrophysiological function

Recent advances in magnetic resonance (MR) imaging technology have unveiled a wealth of information regarding cardiac histoanatomical complexity. However, methods to faithfully translate this level of fine-scale structural detail into computational whole ventricular models are still in their infancy, and, thus, the relevance of this additional complexity for simulations of cardiac function has yet to be elucidated. Here, we describe the development of a highly detailed finite-element computational model (resolution: approximately 125 microm) of rabbit ventricles constructed from high-resolution MR data (raw data resolution: 43 x 43 x 36 microm), including the processes of segmentation (using a combination of level-set approaches), identification of relevant anatomical features, mesh generation, and myocyte orientation representation (using a rule-based approach). Full access is provided to the completed model and MR data. Simulation results were compared with those from a simplified model built from the same images but excluding finer anatomical features (vessels/endocardial structures). Initial simulations showed that the presence of trabeculations can provide shortcut paths for excitation, causing regional differences in activation after pacing between models. Endocardial structures gave rise to small-scale virtual electrodes upon the application of external field stimulation, which appeared to protect parts of the endocardium in the complex model from strong polarizations, whereas intramural virtual electrodes caused by blood vessels and extracellular cleft spaces appeared to reduce polarization of the epicardium. Postshock, these differences resulted in the genesis of new excitation wavefronts that were not observed in more simplified models. Furthermore, global differences in the stimulus recovery rates of apex/base regions were observed, causing differences in the ensuing arrhythmogenic episodes. In conclusion, structurally simplified models are well suited for a large range of cardiac modeling applications. However, important differences are seen when behavior at microscales is relevant, particularly when examining the effects of external electrical stimulation on tissue electrophysiology and arrhythmia induction. This highlights the utility of histoanatomically detailed models for investigations of cardiac function, in particular for future patient-specific modeling.

Purkinje-mediated effects in the response of quiescent ventricles to defibrillation shocks

In normal cardiac function, orderly activation of the heart is facilitated by the Purkinje system (PS), a specialized network of fast-conducting fibers that lines the ventricles. Its role during ventricular defibrillation remains unelucidated. Physical characteristics of the PS make it a poor candidate for direct electrical observation using contemporary experimental techniques. This study uses a computer modeling approach to assess contributions by the PS to the response to electrical stimulation. Normal sinus rhythm was simulated and epicardial breakthrough sites were distributed in a manner consistent with experimental results. Defibrillation shocks of several strengths and orientations were applied to quiescent ventricles, with and without PS, and electrical activation was analyzed. All shocks induced local polarizations in PS branches parallel to the field, which led to the rapid spread of excitation through the network. This produced early activations at myocardial sites where tissue was unexcited by the shock and coupled to the PS. Shocks along the apico-basal axis of the heart resulted in a significant abbreviation of activation time when the PS was present; these shocks are of particular interest because the fields generated by internal cardioverter defibrillators tend to have a strong component in the same direction. The extent of PS-induced changes, both temporal and spatial, was constrained by the amount of shock-activated myocardium. Increasing field strength decreased the transmission delay between PS and ventricular tissue at Purkinje-myocardial junctions (PMJs), but this did not have a major effect on the organ-level response. Weaker shocks directly affect a smaller volume of myocardial tissue but easily excite the PS, which makes the PS contribution to far field excitation more substantial than for stronger shocks.

Arrhythmogenic mechanisms of the Purkinje system during electric shocks: a modeling study

BACKGROUND

The function of the Purkinje system (PS) is to ensure fast and uniform activation of the heart. Although this vital role during sinus rhythm is well understood, this is not the case when shocks are applied to the heart, especially in the case of failed defibrillation. The PS activates differently from the myocardium, has different electrophysiological properties, and provides alternate propagation pathways; thus, there are many ways in which it can contribute to postshock behavior.

OBJECTIVE

The purpose of this study was to elucidate the role of the PS in the initiation and maintenance of postshock arrhythmias.

METHODS

A computer model of the ventricles including the PS was subjected to different reentry induction protocols.

RESULTS

The PS facilitated reentry induction at relatively weaker shocks. Disconnecting the PS from the ventricles during the postshock interval revealed that the PS helps stabilize early-stage reentry by providing focal breakthroughs. During later stages, the PS contributed to reentry by leading to higher frequency rotors. The PS also promoted wave front splitting during reentry due to electrotonic coupling, which prolongs action potential durations at PS-myocyte junctions. The presence of a PS results in the anchoring of reentrant activations that propagate through the pathways provided by the PS.

CONCLUSIONS

The PS is proarrhythmic in that it provides pathways that prolong activity, and it plays a supplementary role in maintaining the later stages of reentry (>800 ms).

Towards predictive modelling of the electrophysiology of the heart

The simulation of cardiac electrical function is an example of a successful integrative multiscale modelling approach that is directly relevant to human disease. Today we stand at the threshold of a new era, in which anatomically detailed, tomographically reconstructed models are being developed that integrate from the ion channel to the electromechanical interactions in the intact heart. Such models hold high promise for interpretation of clinical and physiological measurements, for improving the basic understanding of the mechanisms of dysfunction in disease, such as arrhythmias, myocardial ischaemia and heart failure, and for the development and performance optimization of medical devices. The goal of this article is to present an overview of current state-of-art advances towards predictive computational modelling of the heart as developed recently by the authors of this article. We first outline the methodology for constructing electrophysiological models of the heart. We then provide three examples that demonstrate the use of these models, focusing specifically on the mechanisms for arrhythmogenesis and defibrillation in the heart. These include: (1) uncovering the role of ventricular structure in defibrillation; (2) examining the contribution of Purkinje fibres to the failure of the shock; and (3) using magnetic resonance imaging reconstructed heart models to investigate the re-entrant circuits formed in the presence of an infarct scar.

Polarity reversal lowers activation time during diastolic field stimulation of the rabbit ventricles: insights into mechanisms

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.

Effects of unipolar stimulation on voltage and calcium distributions in the isolated rabbit heart

BACKGROUND

The effect of electric stimulation on the polarization of cardiac tissue (virtual electrode effect) is well known; the corresponding response of intracellular calcium concentration ([Ca(2+)](i)) and its dependence on coupling interval between conditioning stimulus (S1) and test stimulus (S2) has yet to be elucidated.

OBJECTIVE

Because uncovering the transmembrane potential (V(m))-[Ca(2+)](i) relationship during an electric shock is imperative for understanding arrhythmia induction and defibrillation, we aimed to study simultaneous V(m) and [Ca(2+)](i) responses to strong unipolar stimulation.

METHODS

We used a dual-camera optical system to image concurrently V (m) and [Ca(2+)](i) responses to unipolar stimulation (20 ms +/- 20 mA) in Langendorff-perfused rabbit hearts. RH-237 and Rhod-2 fluorescent dyes were used to measure V(m) and [Ca(2+)](i), respectively. The S1-S2 interval ranged from 10 to 170 ms to examine stimulation during the action potential.

RESULTS

The [Ca(2+)](i) deflections were less pronounced than changes in V(m) for all S1-S2 intervals. For cathodal stimulation, [Ca(2+)](i) at the central virtual cathode region increased with prolongation of S1-S2 interval. For anodal stimulation, [Ca(2+)](i) at the central virtual anode area decreased with shortening of the S1-S2 interval. At very short S1-S2 intervals (10-20 ms), when S2 polarization was superimposed on the S1 action potential upstroke, the [Ca(2+)](i) distribution did not follow V(m) and produced a more complex pattern. After S2 termination [Ca(2+)](i) exhibited three outcomes in a manner similar to V(m): non-propagating response, break stimulation, and make stimulation.

CONCLUSIONS

Changes in the [Ca(2+)](i) distribution correlate with the behavior of the V (m) distribution for S1-S2 coupling intervals longer than 20 ms; at shorter intervals S2 creates more heterogeneous [Ca(2+)](i) distribution in comparison with V(m). Stimulation in diastole and at very short coupling intervals caused V(m)-[Ca(2+)](i) uncoupling at the regions of positive polarization (virtual cathode).

Behaviour of the purkinje system during defibrillation-strength shocks

During normal sinus rhythm, orderly activation of the heart is facilitated by a specialized network of fibres lining the ventricles called the Purkinje system (PS). Characteristic features of the PS encourage coordinated depolarization of spatially disparate endocardial sites. Although the basic role of the PS is well understood, many questions regarding its behaviour, especially during the process of defibrillation, remain unanswered. Purkinje fibres react differently during large electrical shocks than the myocardium on which they run because they are oriented in different directions than the endocardial fibres, they possess distinct electrophysiology, and they are part of a system that is one-dimensional in nature. Because of the small size of Purkinje fibres and their positioning on the endocardium, in vivo observation of PS-related phenomena remains problematic. Therefore, computer modelling offers a unique opportunity to investigate the role of the PS during defibrillation. In this paper, the effects of defibrillation-strength shocks on a finite element model of the ventricles coupled to a distinct PS are ascertained. Results indicate that the presence of the PS has a profound impact on the course of activation in the ventricles. During shocks, depolarizations are elicited at bends and bifurcations in the PS. Subsequently, this activity spreads throughout the PS in all directions, creating numerous regions of myocardial depolarization and accelerating the excitation of the whole structure. These excitations are explained by the cable-like nature of Purkinje fibres, which exposes them to vastly different electrical field effects than bulk myocardium due to abrupt conductivity tensor changes.

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.

The role of photon scattering in optical signal distortion during arrhythmia and defibrillation

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.

The role of transmural ventricular heterogeneities in cardiac vulnerability to electric shocks

Transmural electrophysiological heterogeneities have been shown to contribute to arrhythmia induction in the heart; however, their role in defibrillation failure has never been examined. The goal of this study is to investigate how transmural heterogeneities in ionic currents and gap-junctional coupling contribute to arrhythmia generation following defibrillation strength shocks. This study used a 3D anatomically realistic bidomain model of the rabbit ventricles. Transmural heterogeneity in ionic currents and reduced sub-epicardial intercellular coupling were incorporated based on experimental data. The ventricles were paced apically, and truncated-exponential monophasic shocks of varying strength and timing were applied via large external electrodes. Simulations demonstrate that inclusion of transmural heterogeneity in ionic currents results in an increase in vulnerability to shocks, reflected in the increased upper limit of vulnerability, ULV, and the enlarged vulnerable window, VW. These changes in vulnerability stem from increased post-shock dispersion in repolarisation as it increases the likelihood of establishment of re-entrant circuits. In contrast, reduced sub-epicardial coupling results in decrease in both ULV and VW. This decrease is caused by altered virtual electrode polarisation around the region of sub-epicardal uncoupling, and specifically, by the increase in (1) the amount of positively polarised myocardium at shock-end and (2) the spatial extent of post-shock wavefronts.

Evaluating intramural virtual electrodes in the myocardial wedge preparation: simulations of experimental conditions

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.

Cardiac defibrillation and the role of mechanoelectric feedback in postshock arrhythmogenesis

Ventricular dilatation increases the defibrillation threshold (DFT). In order to elucidate the mechanisms responsible for this increase, the present article investigates changes in the postshock behavior of the myocardium upon stretch. A two-dimensional electro-mechanical model of cardiac tissue incorporating heterogeneous fiber orientation was used to explore the effect of sustained stretch on postshock behavior via (a) recruitment of mechanosensitive channels (MSC) and (b) tissue deformation and concomitant changes in tissue conductivities. Recruitment of MSC had no influence on vulnerability to electric shocks as compared to control, but increased the complexity of postshock VF patterns. Stretch-induced deformation and changes in tissue conductivities resulted in a decrease in vulnerability to electric shocks.

Arrhythmogenesis in the heart: Multiscale modeling of the effects of defibrillation shocks and the role of electrophysiological heterogeneity

The mechanisms of initiation of ventricular arrhythmias as well as those behind the complex spatiotemporal wave dynamics and its filament organization during ventricular fibrillation (VF) are the topic of intense research and debate. Mechanistic inquiry into the various mechanisms that lead to arrhythmia initiation and VF maintenance is hampered by the inability of current experimental techniques to resolve, with sufficient accuracy, electrical behavior confined to the depth of the ventricles. The objective of this article is to demonstrate that realistic 3D simulations of electrical activity in the heart are capable of bringing a new level of understanding of the mechanisms that underlie arrhythmia initiation and subsequent organization. The article does this by presenting the results of two multiscale simulation studies of ventricular electrical behavior. The first study aims to uncover the mechanisms responsible for rendering the ventricles vulnerable to electric shocks during a specific interval of time, the vulnerable window. The second study focuses on elucidating the role of electrophysiological heterogeneity, and specifically, differences in action potential duration in various ventricular structures, in VF organization. Both studies share common multiscale modeling approaches and analysis, including characterization of scroll-wave filament dynamics.

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.

Modeling electroporation in a single cell

Electroporation uses electric pulses to promote delivery of DNA and drugs into cells. This study presents a model of electroporation in a spherical cell exposed to an electric field. The model determines transmembrane potential, number of pores, and distribution of pore radii as functions of time and position on the cell surface. For a 1-ms, 40 kV/m pulse, electroporation consists of three stages: charging of the cell membrane (0-0.51 micros), creation of pores (0.51-1.43 micros), and evolution of pore radii (1.43 micros to 1 ms). This pulse creates approximately 341,000 pores, of which 97.8% are small ( approximately 1 nm radius) and 2.2% are large. The average radius of large pores is 22.8 +/- 18.7 nm, although some pores grow to 419 nm. The highest pore density occurs on the depolarized and hyperpolarized poles but the largest pores are on the border of the electroporated regions of the cell. Despite their much smaller number, large pores comprise 95.3% of the total pore area and contribute 66% to the increased cell conductance. For stronger pulses, pore area and cell conductance increase, but these increases are due to the creation of small pores; the number and size of large pores do not increase.

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.

Synthesis of voltage-sensitive optical signals: application to panoramic optical mapping

Fluorescent photon scattering is known to distort optical recordings of cardiac transmembrane potentials; however, this process is not well quantified, hampering interpretation of experimental data. This study presents a novel model, which accurately synthesizes fluorescent recordings over the irregular geometry of the rabbit ventricles. Using the model, the study aims to provide quantification of fluorescent signal distortion for different optical characteristics of the preparation and of the surrounding medium. A bi-domain representation of electrical activity is combined with finite element solutions to the photon diffusion equation simulating both the excitation and emission processes, along with physically realistic boundary conditions at the epicardium, which allow simulation of different experimental setups. We demonstrate that distortion in the optical signal as a result of fluorescent photon scattering is truly a three-dimensional phenomenon and depends critically upon the geometry of the preparation, the scattering properties of the tissue, the direction of wavefront propagation, and the specifics of the experimental setup. Importantly, we show that in an anatomically accurate model of ventricular geometry and fiber orientation, the morphology of the optical signal does not provide reliable information regarding the intramural direction of wavefront propagation. These findings underscore the potential of the new model in interpreting experimental data.

Vulnerability to electric shocks in the regionally-ischemic ventricles

Although the majority of patients undergoing defibrillation suffer from coronary heart disease, little is known about defibrillation in the setting of ischemic disease. The goal of this study is to aid understanding of defibrillation failure in ischemic hearts by studying changes in cardiac vulnerability to electric shocks the first 10 min following LAD occlusion. To do so, a 3D anatomically-accurate electrophysiologically-detailed bidomain model of the regionally ischemic ventricles following LAD occlusion was developed based on experimental data. The ventricles were paced at the apex and truncated exponential monophasic shocks were applied over a range of coupling intervals to determine the upper limit of vulnerability (ULV) and the vulnerable window (VW) in normoxia and 10 min post-occlusion. Simulation results demonstrate that, despite the profound electrophysiological changes in the ischemic region, the ULV remains unchanged 10 min post-occlusion because following high shock strengths gesULV virtual electrode polarization and postshock behavior remain unaffected by ischemia. However, the range of coupling intervals comprising the VW increases from spanning 60 ms in normoxia to 90 ms at 10 min post-occlusion. The increased in vulnerability in regional ischemia stems from the fact that slow conduction and increased dispersion of refractoriness in the ischemic region increase the likelihood of the establishment of a reentrant circuit following shocks of strength<ULV.

Transmural electrophysiological heterogeneities in action potential duration increase the upper limit of vulnerability

Transmural dispersion in action potential duration (APD) has been shown to contribute to arrhythmia induction in the heart. However, its role in termination of lethal arrhythmias by defibrillation shocks has never been examined. The goal of this study is to investigate how transmural dispersion in APD affects cardiac vulnerability to electric shocks, in an attempt to better understand the mechanisms behind defibrillation failure. This study used a three- dimensional, geometrically accurate finite element bidomain rabbit ventricular model. Transmural heterogeneities in ionic currents were incorporated based on experimental data to generate the transmural APD profile recorded in adult rabbits during pacing. Results show that the incorporation of transmural APD heterogeneities in the model causes an increase in the upper limit of vulnerability from 26.7 V/cm in the homogeneous APD ventricles to 30.5 V/cm in the ventricles with heterogeneous transmural APD profile. Examination of shock-end virtual electrode polarisation and postshock electrical activity reveals that the higher ULV in the heterogeneous model is caused by increased dispersion in postshock repolarisation within the LV wall, which increases the likelihood of the establishment of intramural re-entrant circuits.

Cell and tissue responses to electric shocks

AIM

Existing models of myocardial membrane kinetics have not been able to reproduce the experimentally-observed negative bias in the asymmetry of transmembrane potential changes (DeltaV(m)) induced by strong electric shocks. The goals of this study are (1) to demonstrate that this negative bias could be reproduced by the addition, to the membrane model, of electroporation and an outward current, I(a), part of the K(+) flow through the L-type Ca(2+)-channel, and (2) to determine how such modifications in the membrane model affect shock-induced break excitation in a 2D preparation.

METHODS AND RESULTS

We conducted simulations of shocks in bidomain fibres and sheets with membrane dynamics represented by the Luo-Rudy dynamic model (LRd'2000), to which electroporation (LRd + EP model) and the outward current, I(a), activated upon strong shock-induced depolarization (aLRd model) was added. Assuming I(a) is a part of K(+) flow through the L-type Ca(2+)-channel enabled us to reproduce both the experimentally observed rectangularly-shaped positive DeltaV(m) and the value of near 2 of the negative-to-positive DeltaV(m) ratio. In the sheet, I(a) not only contributed to the negative bias in DeltaV(m) asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaV(m). Electroporation, in its turn, was responsible for the decrease in cathode-break excitation threshold in the aLRd sheet, compared with the other two cases, as well as for the occurrence of the excitation after the shock-end rather than during the shock.

CONCLUSIONS

The incorporation of electroporation and I(a) in a membrane model ensures match between simulation results and experimental data. The use of the aLRd model results in a lower threshold for shock-induced break excitation.

Refractory Gradient is Responsible for the Increase in Ventricular Vulnerability Under Sodium Channel Blockade

BACKGROUND

Previous studies have shown that sodium channel (I(Na)) blockade increases ventricular vulnerability; however, there were differences in the degree of the increase. Because the vulnerable window (VW) is altered by the type of preshock refractory gradient (RG), the hypothesis was that the differences in the arrhythmogenesis of I(Na) blockade result from the different types of preshock RG employed.

METHODS AND RESULTS

Simulations of regio(Na)l electric shock following constant pacing stimuli in 2-dimensional bidomain myocardial sheets under I(Na) blockade were conducted using 3 types of preshock RG: longitudinally tilted (LRG), transversely tilted (TRG), and non-tilted RG (NRG). The increase in the degree of I(Na) blockade almost linearly decreased the conduction velocity. The action potential duration in the LRG and TRG cases was non-linearly shortened with the increase in INa blockade because of electrotonic influences, whereas in the case of NRG it was slightly prolonged. In both LRG and TRG cases, the VW for reentry induction by electric shock was considerably widened by the INa blockade; however, this was not the case for NRG in which the VW was rather narrowed by the INa blockade.

CONCLUSION

The type of preshock RG alters the degree of the increase in ventricular vulnerability under INa blockade.