An intuitive safety factor for cardiac propagation

Sinoatrial node heterogeneity and fibroblasts increase atrial driving capability in a two-dimensional human computational model

Background: Cardiac pacemaking remains an unsolved matter from many perspectives. Extensive experimental and computational studies have been performed to describe the sinoatrial physiology across different scales, from the molecular to clinical levels. Nevertheless, the mechanism by which a heartbeat is generated inside the sinoatrial node and propagated to the working myocardium is not fully understood at present. This work aims to provide quantitative information about this fascinating phenomenon, especially regarding the contributions of cellular heterogeneity and fibroblasts to sinoatrial node automaticity and atrial driving. Methods: We developed a bidimensional computational model of the human right atrial tissue, including the sinoatrial node. State-of-the-art knowledge of the anatomical and physiological aspects was adopted during the design of the baseline tissue model. The novelty of this study is the consideration of cellular heterogeneity and fibroblasts inside the sinoatrial node for investigating the manner by which they tune the robustness of stimulus formation and conduction under different conditions (baseline, ionic current blocks, autonomic modulation, and external high-frequency pacing). Results: The simulations show that both heterogeneity and fibroblasts significantly increase the safety factor for conduction by more than 10% in almost all the conditions tested and shorten the sinus node recovery time after overdrive suppression by up to 60%. In the human model, especially under challenging conditions, the fibroblasts help the heterogeneous myocytes to synchronise their rate (e.g. -82% inσ C L under 25 nM of acetylcholine administration) and capture the atrium (with 25% L-type calcium current block). However, the anatomical and gap junctional coupling aspects remain the most important model parameters that allow effective atrial excitations. Conclusion: Despite the limitations to the proposed model, this work suggests a quantitative explanation to the astonishing overall heterogeneity shown by the sinoatrial node.

Prokaryotic voltage-gated sodium channels are more effective than endogenous Nav1.5 channels in rescuing cardiac action potential conduction: an in silico study

Methods to augment Na+ current in cardiomyocytes hold potential for the treatment of various cardiac arrhythmias involving conduction slowing. Because the gene coding cardiac Na+ channel (Nav1.5) is too large to fit in a single adeno-associated virus (AAV) vector, new gene therapies are being developed to enhance endogenous Nav1.5 current (by overexpression of chaperon molecules or use of multiple AAV vectors) or to exogenously introduce prokaryotic voltage-gated Na+ channels (BacNav) whose gene size is significantly smaller than that of the Nav1.5. In this study, based on experimental measurements in heterologous expression systems, we developed an improved computational model of the BacNav channel, NavSheP D60A. We then compared in silico how NavSheP D60A expression vs. Nav1.5 augmentation affects the electrophysiology of cardiac tissue. We found that the incorporation of BacNav channels in both adult guinea pig and human cardiomyocyte models increased their excitability and reduced action potential duration. When compared with equivalent augmentation of Nav1.5 current in simulated settings of reduced tissue excitability, the addition of the BacNav current was superior in improving the safety of conduction under conditions of current source-load mismatch, reducing the vulnerability to unidirectional conduction block during premature pacing, preventing the instability and breakup of spiral waves, and normalizing the conduction and ECG in Brugada syndrome tissues with mutated Nav1.5. Overall, our studies show that compared with a potential enhancement of the endogenous Nav1.5 current, expression of the BacNav channels with their slower inactivation kinetics can provide greater anti-arrhythmic benefits in hearts with compromised action potential conduction.NEW & NOTEWORTHY Slow action potential conduction is a common cause of various cardiac arrhythmias; yet, current pharmacotherapies cannot augment cardiac conduction. This in silico study compared the efficacy of recently proposed antiarrhythmic gene therapy approaches that increase peak sodium current in cardiomyocytes. When compared with the augmentation of endogenous sodium current, expression of slower-inactivating bacterial sodium channels was superior in preventing conduction block and arrhythmia induction. These results further the promise of antiarrhythmic gene therapies targeting sodium channels.

Conduction delays across the specialized conduction system of the heart: Revisiting atrioventricular node (AVN) and Purkinje-ventricular junction (PVJ) delays

Background and significance

The specialized conduction system (SCS) of the heart was extensively studied to understand the synchronization of atrial and ventricular contractions, the large atrial to His bundle (A-H) delay through the atrioventricular node (AVN), and delays between Purkinje (P) and ventricular (V) depolarization at distinct junctions (J), PVJs. Here, we use optical mapping of perfused rabbit hearts to revisit the mechanism that explains A-H delay and the role of a passive electrotonic step-delay at the boundary between atria and the AVN. We further visualize how the P anatomy controls papillary activation and valve closure before ventricular activation.

Methods

Rabbit hearts were perfused with a bolus (100-200 µl) of a voltage-sensitive dye (di4ANEPPS), blebbistatin (10-20 µM for 20 min) then the right atrial appendage and ventricular free-wall were cut to expose the AVN, P fibers (PFs), the septum, papillary muscles, and the endocardium. Fluorescence images were focused on a CMOS camera (SciMedia) captured at 1K-5 K frames/s from 100 × 100 pixels.

Results

AP propagation across the AVN-His (A-H) exhibits distinct patterns of delay and conduction blocks during S1-S2 stimulation. Refractory periods were 81 ± 9, 90 ± 21, 185 ± 15 ms for Atrial, AVN, and His, respectively. A large delay (>40 ms) occurs between atrial and AVN activation that increased during rapid atrial pacing contributing to the development of Wenckebach periodicity followed by delays within the AVN through slow or blocked conduction. The temporal resolution of the camera allowed us to identify PVJs by detecting doublets of AP upstrokes. PVJ delays were heterogeneous, fastest in PVJ that immediately trigger ventricular APs (3.4 ± 0.8 ms) and slow in regions where PF appear insulated from the neighboring ventricular myocytes (7.8 ± 2.4 ms). Insulated PF along papillary muscles conducted APs (>2 m/s), then triggered papillary muscle APs (<1 m/s), followed by APs firing of septum and endocardium. The anatomy of PFs and PVJs produced activation patterns that control the sequence of contractions ensuring that papillary contractions close the tricuspid valve 2-5 ms before right ventricular contractions.

Conclusions

The specialized conduction system can be accessed optically to investigate the electrical properties of the AVN, PVJ and activation patterns in physiological and pathological conditions.

Targeted Treatment of Inappropriate Sinoatrial Node Tachycardia Based on Electrophysiological and Structural Mechanisms

The purpose of this review is to determine the causal mechanisms and treatment of inappropriate sinoatrial tachycardia (IST), defined as a non-physiological elevation in resting heart rate. IST is defined as a resting daytime sinus rate >100 beats/minute and an average 24-hour heart rate >90 beats/minute. Potential causal mechanisms include sympathetic receptor hypersensitivity, blunted parasympathetic tone, or enhanced intrinsic automaticity within the sinoatrial node (SAN) pacemaker-conduction complex. These anomalies may coexist in the same patient. Recent ex-vivo near-infrared transmural optical imaging of the SAN in human and animal hearts provides important insights into the functional and molecular features of this complex structure. In particular, it reveals the existence of preferential sinoatrial conduction pathways that ensure robust SAN activation with electrical conduction. The mechanism of IST is debated because even high-resolution electroanatomical mapping approaches cannot reveal intramural conduction in the 3-dimensional SAN complex. It may be secondary to enhanced automaticity, intranodal re-entry, or sinoatrial conduction pathway re-entry. Different pharmacological approaches can target these mechanisms. Long-acting β blockers in IST can act on both primarily increased automaticity and dysregulated autonomic system. Ivabradine targets sources of increased SAN automaticity. Conventional or hybrid ablation may target all the described abnormalities. This review provides a state-of-the-art overview of putative IST mechanisms. In conclusion, based on current knowledge, pharmacological and ablation approaches for IST, including the novel hybrid SAN sparing ablation, are discussed.

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

The Purkinje-myocardial junction is the anatomic origin of ventricular arrhythmia in CPVT

Catecholaminergic polymorphic ventricular tachycardia (CPVT) is an arrhythmia syndrome caused by gene mutations that render RYR2 Ca release channels hyperactive, provoking spontaneous Ca release and delayed afterdepolarizations (DADs). What remains unknown is the cellular source of ventricular arrhythmia triggered by DADs: Purkinje cells in the conduction system or ventricular cardiomyocytes in the working myocardium. To answer this question, we used a genetic approach in mice to knock out cardiac calsequestrin either in Purkinje cells or in ventricular cardiomyocytes. Total loss of calsequestrin in the heart causes a severe CPVT phenotype in mice and humans. We found that loss of calsequestrin only in ventricular myocytes produced a full-blown CPVT phenotype, whereas mice with loss of calsequestrin only in Purkinje cells were comparable to WT mice. Subendocardial chemical ablation or restoration of calsequestrin expression in subendocardial cardiomyocytes neighboring Purkinje cells was sufficient to protect against catecholamine-induced arrhythmias. In silico modeling demonstrated that DADs in ventricular myocardium can trigger full action potentials in the Purkinje fiber, but not vice versa. Hence, ectopic beats in CPVT are likely generated at the Purkinje-myocardial junction via a heretofore unrecognized tissue mechanism, whereby DADs in the ventricular myocardium trigger full action potentials in adjacent Purkinje cells.

Analysis of the response of human iPSC-derived cardiomyocyte tissue to ICaL block. A combined in vitro and in silico approach

The high incidence of cardiac arrythmias underlines the need for the assessment of pharmacological therapies. In this field of drug efficacy, as in the field of drug safety highlighted by the Comprehensive in Vitro Proarrhythmia Assay initiative, new pillars for research have become crucial: firstly, the integration of in-silico experiments, and secondly the evaluation of fully integrated biological systems, such as human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). In this study, we therefore aimed to combine in-vitro experiments and in-silico simulations to evaluate the antiarrhythmic effect of L-type calcium current (I_CaL) block in hiPSC-CMs. For this, hiPSC-CM preparations were cultured and an equivalent virtual tissue was modeled. Re-entry patterns of electrical activation were induced and several biomarkers were obtained before and after I_CaL block. The virtual hiPSC-CM simulations were also reproduced using a tissue composed of adult ventricular cardiomyocytes (hAdultV-CMs). The analysis of phases, currents and safety factor for propagation showed an increased size of the re-entry core when I_CaL was blocked as a result of depressed cellular excitability. The bigger wavefront curvature yielded reductions of 12.2%, 6.9%, and 4.2% in the frequency of the re-entry for hiPSC-CM cultures, virtual hiPSC-CM, and hAdultV-CM tissues, respectively. Furthermore, I_CaL block led to a 47.8% shortening of the vulnerable window for re-entry in the virtual hiPSC-CM tissue and to re-entry vanishment in hAdultV-CM tissue. The consistent behavior between in-vitro and in-silico hiPSC-CMs and between in-silico hiPSC-CMs and hAdultV-CMs evidences that virtual hiPSC-CM tissues are suitable for assessing cardiac efficacy, as done in the present study through the analysis of I_CaL block.

Coupling between cardiac cells-An important determinant of electrical impulse propagation and arrhythmogenesis

Cardiac arrhythmias are an important cause of sudden cardiac death-a devastating manifestation of many underlying causes, such as heart failure and ischemic heart disease leading to ventricular tachyarrhythmias and ventricular fibrillation, and atrial fibrillation causing cerebral embolism. Cardiac electrical propagation is a main factor in the initiation and maintenance of cardiac arrhythmias. In the heart, gap junctions are the basic unit at the cellular level that host intercellular low-resistance channels for the diffusion of ions and small regulatory molecules. The dual voltage clamp technique enabled the direct measurement of electrical conductance between cells and recording of single gap junction channel openings. The rapid turnover of gap junction channels at the intercalated disk implicates a highly dynamic process of trafficking and internalization of gap junction connexons. Recently, non-canonical roles of gap junction proteins have been discovered in mitochondria function, cytoskeletal organization, trafficking, and cardiac rescue. At the tissue level, we explain the concepts of linear propagation and safety factor based on the model of linear cellular structure. Working myocardium is adequately represented as a discontinuous cellular network characterized by cellular anisotropy and connective tissue heterogeneity. Electrical propagation in discontinuous cellular networks reflects an interplay of three main factors: cell-to-cell electrical coupling, flow of electrical charge through the ion channels, and the microscopic tissue structure. This review provides a state-of-the-art update of the cardiac gap junction channels and their role in cardiac electrical impulse propagation and highlights a combined approach of genetics, cell biology, and physics in modern cardiac electrophysiology.

Electrophysiological Substrate in Patients with Barlow's Disease

Mitral valve prolapse (MVP) is the most common valvular heart disease, affecting 2-3% of the general population. Barlow's disease is a clinical syndrome characterised by MVP. Initially thought a benign condition, MVP is now recognised as a cause of sudden cardiac death and ventricular arrhythmias. The development of new imaging techniques has contributed recently to the identification of novel risk factors. Catheter ablation of ventricular arrhythmias in patients affected by MVP is traditionally considered challenging. In this review, the authors summarise the evidence on arrhythmogenesis in the context of MVP, along with risk stratification of sudden cardiac death and the available treatment options, including new catheter ablation techniques.

New insights on the cardiac safety factor: Unraveling the relationship between conduction velocity and robustness of propagation

Cardiac conduction disturbances are linked with arrhythmia development. The concept of safety factor (SF) has been derived to describe the robustness of conduction, but the usefulness of this metric has been constrained by several limitations. For example, due to the difficulty of measuring the necessary input variables, SF calculations have only been applied to synthetic data. Moreover, quantitative validation of SF is lacking; specifically, the practical meaning of particular SF values is unclear, aside from the fact that propagation failure (i.e., conduction block) is characterized by SF < 1. This study aims to resolve these limitations for our previously published SF formulation and explore its relationship to relevant electrophysiological properties of cardiac tissue. First, HL-1 cardiomyocyte monolayers were grown on multi-electrode arrays and the robustness of propagation was estimated using extracellular potential recordings. SF values reconstructed purely from experimental data were largely between 1 and 5 (up to 89.1% of sites characterized). This range is consistent with values derived from synthetic data, proving that the formulation is sound and its applicability is not limited to analysis of computational models. Second, for simulations conducted in 1-, 2-, and 3-dimensional tissue blocks, we calculated true SF values at locations surrounding the site of current injection for sub- and supra-threshold stimuli and found that they differed from values estimated by our SF formulation by <10%. Finally, we examined SF dynamics under conditions relevant to arrhythmia development in order to provide physiological insight. Our analysis shows that reduced conduction velocity (Θ) caused by impaired intrinsic cell-scale excitability (e.g., due to sodium current a loss-of-function mutation) is associated with less robust conduction (i.e., lower SF); however, intriguingly, Θ variability resulting from modulation of tissue scale conductivity has no effect on SF. These findings are supported by analytic derivation of the relevant relationships from first principles. We conclude that our SF formulation, which can be applied to both experimental and synthetic data, produces values that vary linearly with the excess charge needed for propagation. SF calculations can provide insights helpful in understanding the initiation and perpetuation of cardiac arrhythmia.

Ventricular Endocardial Tissue Geometry Affects Stimulus Threshold and Effective Refractory Period

BACKGROUND

Understanding the biophysical processes by which electrical stimuli applied to cardiac tissue may result in local activation is important in both the experimental and clinical electrophysiology laboratory environments, as well as for gaining a more in-depth knowledge of the mechanisms of focal-trigger-induced arrhythmias. Previous computational models have predicted that local myocardial tissue architecture alone may significantly modulate tissue excitability, affecting both the local stimulus current required to excite the tissue and the local effective refractory period (ERP). In this work, we present experimental validation of this structural modulation of local tissue excitability on the endocardial tissue surface, use computational models to provide mechanistic understanding of this phenomena in relation to localized changes in electrotonic loading, and demonstrate its implications for the capture of afterdepolarizations.

METHODS AND RESULTS

Experiments on rabbit ventricular wedge preparations showed that endocardial ridges (surfaces of negative mean curvature) had a stimulus capture threshold that was 0.21 ± 0.03 V less than endocardial grooves (surfaces of positive mean curvature) for pairwise comparison (24% reduction, corresponding to 56.2 ± 6.4% of the energy). When stimulated at the minimal stimulus strength for capture, ridge locations showed a shorter ERP than grooves (n = 6, mean pairwise difference 7.4 ± 4.2 ms). When each site was stimulated with identical-strength stimuli, the difference in ERP was further increased (mean pairwise difference 15.8 ± 5.3 ms). Computational bidomain models of highly idealized cylindrical endocardial structures qualitatively agreed with these findings, showing that such changes in excitability are driven by structural modulation in electrotonic loading, quantifying this relationship as a function of surface curvature. Simulations further showed that capture of delayed afterdepolarizations was more likely in trabecular ridges than grooves, driven by this difference in loading.

CONCLUSIONS

We have demonstrated experimentally and explained mechanistically in computer simulations that the ability to capture tissue on the endocardial surface depends upon the local tissue architecture. These findings have important implications for deepening our understanding of excitability differences related to anatomical structure during stimulus application that may have important applications in the translation of novel experimental optogenetics pacing strategies. The uncovered preferential vulnerability to capture of afterdepolarizations of endocardial ridges, compared to grooves, provides important insight for understanding the mechanisms of focal-trigger-induced arrhythmias.

Microheterogeneity-induced conduction slowing and wavefront collisions govern macroscopic conduction behavior: A computational and experimental study

The incidence of cardiac arrhythmias is known to be associated with tissue heterogeneities including fibrosis. However, the impact of microscopic structural heterogeneities on conduction in excitable tissues remains poorly understood. In this study, we investigated how acellular microheterogeneities affect macroscopic conduction under conditions of normal and reduced excitability by utilizing a novel platform of paired in vitro and in silico studies to examine the mechanisms of conduction. Regular patterns of nonconductive micro-obstacles were created in confluent monolayers of the previously described engineered-excitable Ex293 cell line. Increasing the relative ratio of obstacle size to intra-obstacle strand width resulted in significant conduction slowing up to 23.6% and a significant increase in wavefront curvature anisotropy, a measure of spatial variation in wavefront shape. Changes in bulk electrical conductivity and in path tortuosity were insufficient to explain these observed macroscopic changes. Rather, microscale behaviors including local conduction slowing due to microscale branching, and conduction acceleration due to wavefront merging were shown to contribute to macroscopic phenomena. Conditions of reduced excitability led to further conduction slowing and a reversal of wavefront curvature anisotropy due to spatially non-uniform effects on microscopic slowing and acceleration. This unique experimental and computation platform provided critical mechanistic insights in the impact of microscopic heterogeneities on macroscopic conduction, pertinent to settings of fibrotic heart disease.

It is well known that perturbations in the heart structure are associated with the initiation and maintenance of clinically significant cardiac arrhythmia. While previous studies have examined how single structural perturbations affect local electrical conduction, our understanding of how numerous microscopic heterogeneities act in aggregate to alter macroscopic electrical behavior is limited. In this study, we utilized simplified engineered excitable cells that contain the minimal machinery of excitability and can be directly computationally modeled. By pairing experimental and computational studies, we showed that the microscopic branching and collisions of electrical waves slow and speed conduction, respectively, resulting in macroscopic changes in the speed and pattern of electrical activation. These microscale behaviors are significantly altered under reduced excitability, resulting in exaggerated collision effects. Overall, this study helps improve our understanding of how microscopic structural heterogeneities in excitable tissue lead to abnormal action potential propagation, conducive to arrhythmias.

Termination of re-entrant atrial tachycardia via optogenetic stimulation with optimized spatial targeting: insights from computational models

KEY POINTS

Optogenetics has emerged as a potential alternative to electrotherapy for treating heart rhythm disorders, but its applicability for terminating atrial arrhythmias remains largely unexplored. We used computational models reconstructed from clinical MRI scans of fibrotic patient atria to explore the feasibility of optogenetic termination of atrial tachycardia (AT), comparing two different illumination strategies: distributed vs. targeted. We show that targeted optogenetic stimulation based on automated, non-invasive flow-network analysis of patient-specific re-entry morphology may be a reliable approach for identifying the optimal illumination target in each individual (i.e. the critical AT isthmus). The above-described approach yields very high success rates (up to 100%) and requires dramatically less input power than distributed illumination We conclude that simulations in patient-specific models show that targeted light pulses lasting longer than the AT cycle length can efficiently and reliably terminate AT if the human atria can be successfully light-sensitized via gene delivery of ChR2.

ABSTRACT

Optogenetics has emerged as a potential alternative to electrotherapy for treating arrhythmia, but feasibility studies have been limited to ventricular defibrillation via epicardial light application. Here, we assess the efficacy of optogenetic atrial tachycardia (AT) termination in human hearts using a strategy that targets for illumination specific regions identified in an automated manner. In three patient-specific models reconstructed from late gadolinium-enhanced MRI scans, we simulated channelrhodopsin-2 (ChR2) expression via gene delivery. In all three models, we attempted to terminate re-entrant AT (induced via rapid pacing) via optogenetic stimulation. We compared two strategies: (1) distributed illumination of the endocardium by multi-optrode grids (number of optrodes, N_opt  = 64, 128, 256) and (2) targeted illumination of the critical isthmus, which was identified via analysis of simulated activation patterns using an algorithm based on flow networks. The illuminated area and input power were smaller for the targeted approach (19-57.8 mm² ; 0.6-1.8 W) compared to the sparsest distributed arrays (N_opt  = 64; 124.9 ± 6.3 mm² ; 3.9 ± 0.2 W). AT termination rates for distributed illumination were low, ranging from <5% for short pulses (1/10 ms long) to ∼20% for longer stimuli (100/1000 ms). When we attempted to terminate the same AT episodes with targeted illumination, outcomes were similar for short pulses (1/10 ms long: 0% success) but improved for longer stimuli (100 ms: 54% success; 1000 ms: 90% success). We conclude that simulations in patient-specific models show that light pulses lasting longer than the AT cycle length can efficiently and reliably terminate AT in atria light-sensitized via gene delivery. We show that targeted optogenetic stimulation based on analysis of AT morphology may be a reliable approach for defibrillation and requires less power than distributed illumination.

Stochastic spontaneous calcium release events and sodium channelopathies promote ventricular arrhythmias

Premature ventricular complexes (PVCs), the first initiating beats of a variety of cardiac arrhythmias, have been associated with spontaneous calcium release (SCR) events at the cell level. However, the mechanisms underlying the degeneration of such PVCs into arrhythmias are not fully understood. The objective of this study was to investigate the conditions under which SCR-mediated PVCs can lead to ventricular arrhythmias. In particular, we sought to determine whether sodium (Na⁺) current loss-of-function in the structurally normal ventricles provides a substrate for unidirectional conduction block and reentry initiated by SCR-mediated PVCs. To achieve this goal, a stochastic model of SCR was incorporated into an anatomically accurate compute model of the rabbit ventricles with the His-Purkinje system (HPS). Simulations with reduced Na⁺ current due to a negative-shift in the steady-state channel inactivation showed that SCR-mediated delayed afterdepolarizations led to PVC formation in the HPS, where the electrotonic load was lower, conduction block, and reentry in the 3D myocardium. Moreover, arrhythmia initiation was only possible when intrinsic electrophysiological heterogeneity in action potential within the ventricles was present. In conclusion, while benign in healthy individuals SCR-mediated PVCs can lead to life-threatening ventricular arrhythmias when combined with Na⁺ channelopathies.

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.

Modeling the different sections of the cardiac conduction system to obtain realistic electrocardiograms

The cardiac conduction system is divided in different sections that play an important role in the cardiac depolarization sequence and define the morphology of the electrocardiogram. In this study we have built several configurations for each section based on anatomical descriptions. The effect of the morphology of the bundle branches, and the density of both Purkinje branches and Purkinje-myocardial junctions (PMJ) has been studied by comparing the pseudo-ECGs obtained with the standard precordial leads of the electrocardiogram. A functional model for the PMJs based on the existence of a conduction adaptation layer is also presented. Simulation results showed a large influence of the His bundle and bundle branches in the pseudo-ECG and helped to elucidate the most appropriate morphology. The functional PMJ model allowed bidirectional communication between the conduction system and the myocardium with realistic transmission delays between both mediums. These results can help to improve current conduction system models and improve depolarization sequences of activation in the ventricles.

Structural defects lead to dynamic entrapment in cardiac electrophysiology

Biological networks are typically comprised of many parts whose interactions are governed by nonlinear dynamics. This potentially imbues them with the ability to support multiple attractors, and therefore to exhibit correspondingly distinct patterns of behavior. In particular, multiple attractors have been demonstrated for the electrical activity of the diseased heart in situations where cardioversion is able to convert a reentrant arrhythmia to a stable normal rhythm. Healthy hearts, however, are typically resilient to abnormal rhythms. This raises the question as to how a healthy cardiac cell network must be altered so that it can support multiple distinct behaviors. Here we demonstrate how anatomic defects can give rise to multi-stability in the heart as a function of the electrophysiological properties of the cardiac tissue and the timing of activation of ectopic foci. This leads to a form of hysteretic behavior, which we call dynamic entrapment, whereby the heart can become trapped in aberrant attractor as a result of a transient change in tissue properties. We show that this can lead to a highly inconsistent relationship between clinical symptoms and underlying pathophysiology, which raises the possibility that dynamic entrapment may underlie other forms of chronic idiopathic illness.

Role of sinoatrial node architecture in maintaining a balanced source-sink relationship and synchronous cardiac pacemaking

Normal heart rhythm (sinus rhythm) depends on regular activity of the sinoatrial node (SAN), a heterogeneous collection of specialized myocytes in the right atrium. SAN cells, in general, possess a unique electrophysiological profile that promotes spontaneous electrical activity (automaticity). However, while automaticity is required for normal pacemaking, it is not necessarily sufficient. Less appreciated is the importance of the elaborate structure of the SAN complex for proper pacemaker function. Here, we review the important structural features of the SAN with a focus on how these elements help manage a precarious balance between electrical charge generated by the SAN (“source”) and the charge needed to excite the surrounding atrial tissue (“sink”). We also discuss how compromised “source-sink” balance due, for example to fibrosis, may promote SAN dysfunction, characterized by slow and/or asynchronous pacemaker activity and even failure, in the setting of cardiovascular disease (e.g., heart failure, atrial fibrillation). Finally, we discuss implications of the “source-sink” balance in the SAN complex for cell and gene therapies aimed at creating a biological pacemaker as replacement or bridge to conventional electronic pacemakers.

In silico ischaemia-induced reentry at the Purkinje-ventricle interface

AIMS

This computational modelling work illustrates the influence of hyperkalaemia and electrical uncoupling induced by defined ischaemia on action potential (AP) propagation and the incidence of reentry at the Purkinje-ventricle interface in mammalian hearts.

METHODS AND RESULTS

Unidimensional and bidimensional models of the Purkinje-ventricle subsystem, including ischaemic conditions (defined as phase 1B) in the ventricle and an ischaemic border zone, were developed by altering several important electrophysiological parameters of the Luo-Rudy AP model of the ventricular myocyte. Purkinje electrical activity was modelled using the equations of DiFrancesco and Noble. Our study suggests that an extracellular potassium concentration [K(+)]o >14 mM and a slight decrease in intercellular coupling induced by ischaemia in ventricle can cause conduction block from Purkinje to ventricle. Under these conditions, propagation from ventricle to Purkinje is possible. Thus, unidirectional block (UDB) and reentry can result. When conditions of UDB are met, retrograde propagation with a long delay (320 ms) may re-excite Purkinje cells, and give rise to a reentrant pathway. This induced reentry may be the origin of arrhythmias observed in phase 1B ischaemia.

CONCLUSION

In a defined setting of ischaemia (phase 1B), a small amount of uncoupling between ventricular cells, as well as between Purkinje and ventricular tissue, may induce UDBs and reentry. Hyperkalaemia is also confirmed to be an important factor in the genesis of reentrant rhythms, since it regulates the range of coupling in which UDBs may be induced.

Electrophysiological and structural remodeling in heart failure modulate arrhythmogenesis. 1D simulation study

Background

Heart failure is a final common pathway or descriptor for various cardiac pathologies. It is associated with sudden cardiac death, which is frequently caused by ventricular arrhythmias. Electrophysiological remodeling, intercellular uncoupling, fibrosis and autonomic imbalance have been identified as major arrhythmogenic factors in heart failure etiology and progression.

Objective

In this study we investigate in silico the role of electrophysiological and structural heart failure remodeling on the modulation of key elements of the arrhythmogenic substrate, i.e., electrophysiological gradients and abnormal impulse propagation.

Methods

Two different mathematical models of the human ventricular action potential were used to formulate models of the failing ventricular myocyte. This provided the basis for simulations of the electrical activity within a transmural ventricular strand. Our main goal was to elucidate the roles of electrophysiological and structural remodeling in setting the stage for malignant life-threatening arrhythmias.

Results

Simulation results illustrate how the presence of M cells and heterogeneous electrophysiological remodeling in the human failing ventricle modulate the dispersion of action potential duration and repolarization time. Specifically, selective heterogeneous remodeling of expression levels for the Na⁺/Ca²⁺ exchanger and SERCA pump decrease these heterogeneities. In contrast, fibroblast proliferation and cellular uncoupling both strongly increase repolarization heterogeneities. Conduction velocity and the safety factor for conduction are also reduced by the progressive structural remodeling during heart failure.

Conclusion

An extensive literature now establishes that in human ventricle, as heart failure progresses, gradients for repolarization are changed significantly by protein specific electrophysiological remodeling (either homogeneous or heterogeneous). Our simulations illustrate and provide new insights into this. Furthermore, enhanced fibrosis in failing hearts, as well as reduced intercellular coupling, combine to increase electrophysiological gradients and reduce electrical propagation. In combination these changes set the stage for arrhythmias.

A comprehensive multiscale framework for simulating optogenetics in the heart

Optogenetics has emerged as an alternative method for electrical control of the heart, where illumination is used to elicit a bioelectric response in tissue modified to express photosensitive proteins (opsins). This technology promises to enable evocation of spatiotemporally precise responses in targeted cells or tissues, thus creating new possibilities for safe and effective therapeutic approaches to ameliorate cardiac function. Here, we present a comprehensive framework for multi-scale modelling of cardiac optogenetics, allowing both mechanistic examination of optical control and exploration of potential therapeutic applications. The framework incorporates accurate representations of opsin channel kinetics and delivery modes, spatial distribution of photosensitive cells, and tissue illumination constraints, making possible the prediction of emergent behaviour resulting from interactions at sub-organ scales. We apply this framework to explore how optogenetic delivery characteristics determine energy requirements for optical stimulation and to identify cardiac structures that are potential pacemaking targets with low optical excitation threshold.

Sodium current reduction unmasks a structure-dependent substrate for arrhythmogenesis in the normal ventricles

Background

Organ-scale arrhythmogenic consequences of source-sink mismatch caused by impaired excitability remain unknown, hindering the understanding of pathophysiology in disease states like Brugada syndrome and ischemia.

Objective

We sought to determine whether sodium current (I_Na) reduction in the structurally normal heart unmasks a regionally heterogeneous substrate for the induction of sustained arrhythmia by premature ventricular contractions (PVCs).

Methods

We conducted simulations in rabbit ventricular computer models with 930 unique combinations of PVC location (10 sites) and coupling interval (250–400 ms), I_Na reduction (30 or 40% of normal levels), and post-PVC sinus rhythm (arrested or persistent). Geometric characteristics and source-sink mismatch were quantitatively analyzed by calculating ventricular wall thickness and a newly formulated 3D safety factor (SF), respectively.

Results

Reducing I_Na to 30% of its normal level created a substrate for sustained arrhythmia induction by establishing large regions of critical source-sink mismatch (SF<1) for ectopic wavefronts propagating from thin to thick tissue. In the same simulations but with 40% of normal I_Na, PVCs did not induce reentry because the volume of tissue with SF<1 was >95% smaller. Likewise, when post-PVC sinus activations were persistent instead of arrested, no ectopic excitations initiated sustained reentry because sinus activation breakthroughs engulfed the excitable gap.

Conclusion

Our new SF formulation can quantify ectopic wavefront propagation robustness in geometrically complex 3D tissue with impaired excitability. This novel methodology was applied to show that I_Na reduction precipitates source-sink mismatch, creating a potent substrate for sustained arrhythmia induction by PVCs originating near regions of ventricular wall expansion, such as the RV outflow tract.

Non-uniform dispersion of the source-sink relationship alters wavefront curvature

The distribution of cellular source-sink relationships plays an important role in cardiac propagation. It can lead to conduction slowing and block as well as wave fractionation. It is of great interest to unravel the mechanisms underlying evolution in wavefront geometry. Our goal is to investigate the role of the source-sink relationship on wavefront geometry using computer simulations. We analyzed the role of variability in the microscopic source-sink relationship in driving changes in wavefront geometry. The electrophysiological activity of a homogeneous isotropic tissue was simulated using the ten Tusscher and Panfilov 2006 action potential model and the source-sink relationship was characterized using an improved version of the Romero et al. safety factor formulation (SF_m2). Our simulations reveal that non-uniform dispersion of the cellular source-sink relationship (dispersion along the wavefront) leads to alterations in curvature. To better understand the role of the source-sink relationship in the process of wave formation, the electrophysiological activity at the initiation of excitation waves in a 1D strand was examined and the source-sink relationship was characterized using the two recently updated safety factor formulations: the SF_m2 and the Boyle-Vigmond (SF_VB) definitions. The electrophysiological activity at the initiation of excitation waves was intimately related to the SF_m2 profiles, while the SF_VB led to several counterintuitive observations. Importantly, with the SF_m2 characterization, a critical source-sink relationship for initiation of excitation waves was identified, which was independent of the size of the electrode of excitation, membrane excitability, or tissue conductivity. In conclusion, our work suggests that non-uniform dispersion of the source-sink relationship alters wavefront curvature and a critical source-sink relationship profile separates wave expansion from collapse. Our study reinforces the idea that the safety factor represents a powerful tool to study the mechanisms of cardiac propagation in silico, providing a better understanding of cardiac arrhythmias and their therapy.

Subepicardial action potential characteristics are a function of depth and activation sequence in isolated rabbit hearts

BACKGROUND

Electric excitability in the ventricular wall is influenced by cellular electrophysiology and passive electric properties of the myocardium. Action potential (AP) rise time, an indicator of myocardial excitability, is influenced by conduction pattern and distance from the epicardial surface. This study examined AP rise times and conduction velocity as the depolarizing wavefront approaches the epicardial surface.

METHODS AND RESULTS

Two-photon excitation of di-4-aminonaphthenyl-pyridinum-propylsulfonate was used to measure electric activity at discrete epicardial layers of isolated Langendorff-perfused rabbit hearts to a depth of 500 μm. Endo-to-epicardial wavefronts were studied during right atrial or ventricular endocardial pacing. Similar measurements were made with epi-to-endocardial, transverse, and longitudinal pacing protocols. Results were compared with data from a bidomain model of 3-dimensional (3D) electric propagation within ventricular myocardium. During right atrial and endocardial pacing, AP rise time (10%-90% of upstroke) decreased by ≈50% between 500 and 50 μm from the epicardial surface, whereas conduction velocity increased and AP duration was only slightly shorter (≈4%). These differences were not observed with other conduction patterns. The depth-dependent changes in rise time were larger at higher pacing rates. Modeling data qualitatively reproduced the behavior seen experimentally and demonstrated a parallel reduction in peak I(Na) and electrotonic load as the wavefront approaches the epicardial surface.

CONCLUSIONS

Decreased electrotonic load at the epicardial surface results in more rapid AP upstrokes and higher conduction velocities compared with the bulk myocardium. Combined effects of tissue depth and pacing rate on AP rise time reduce conduction safety and myocardial excitability within the ventricular wall.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

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.