Ionic mechanisms for electrical heterogeneity between rabbit Purkinje fiber and ventricular cells

Identification and characterization of two novel KCNH2 mutations contributing to long QT syndrome

We identified two different inherited mutations in KCNH2 gene, or human ether-a-go-go related gene (hERG), which are linked to Long QT Syndrome. The first mutation was in a 1-day-old infant, whereas the second was in a 14-year-old girl. The two KCNH2 mutations were transiently transfected into either human embryonic kidney (HEK) cells or human induced pluripotent stem-cell derived cardiomyocytes. We performed associated multiscale computer simulations to elucidate the arrhythmogenic potentials of the KCNH2 mutations. Genetic screening of the first and second index patients revealed a heterozygous missense mutation in KCNH2, resulting in an amino acid change (P632L) in the outer loop of the channel and substitution at position 428 from serine to proline (S428P), respectively. Heterologous expression of P632L and S428P into HEK cells produced no hERG current compared to the wild type (WT). Moreover, the co-transfection of WT and P632L yielded no hERG current; however, the co-transfection of WT and S428P yielded partial hERG current. Action potentials were prolonged in a complete or partial blockade of hERG current from computer simulations which was more severe in Purkinje than ventricular myocytes. Three dimensional simulations revealed a higher susceptibility to reentry in the presence of hERG current blockade. Our experimental findings suggest that both P632L and S428P mutations may impair the KCNH2 gene. The Purkinje cells exhibit a more severe phenotype than ventricular myocytes, and the hERG current blockade renders the ventricles an arrhythmogenic substrate from computer modeling.

ELUCIDATING THE ROLE OF THE HIS-PURKINJE SYSTEM DURING LONG QT MEDIATED ARRHYTHMIAS

Mutation in the hERG gene leading to partial or complete blockade of the rapid delayed rectifier current causes Long QT Type 2 (LQT2) phenotype, the second most common form of Long QT Syndrome. However, the exact involvement of the His-Purkinje System (HPS) remains elusive. We utilized a finite element model of the rabbit ventricles integrated with a HPS to elucidate the role of HPS during LQT2-mediated arrhythmia. Following the induction of persistent reentry from an ectopic stimulus, we isolated the HPS at different time points. Moreover, we varied the coupling resistance and the number of myocytes at the Purkinje-Myocardial Junctions (PMJs) to ascertain how the junctional parameters altered reentry dynamics. Reentry was terminated with the earliest termination time for reentry coinciding with the earliest time the HPS was isolated. This observation provides evidence of direct involvement of the HPS during LQT2-mediated ventricular arrhythmia. Increasing the coupling resistance or the number of myocytes at the PMJs reduced the percentage of successful retrograde propagation during reentry. Thus, the HPS alters reentry dynamics. Our multi-scale computer modeling outcomes offer important new understandings of probable arrhythmia mechanisms under LQT2 circumstances.

Calcium Overload or Underload? The Effects of Doxorubicin on the Calcium Dynamics in Guinea Pig Hearts

The severe doxorubicin (DOXO) side effect of cardiomyopathy limits it clinical application as an effective anticancer drug. Although Ca²⁺ overload was postulated as one of the mechanisms for this toxicity, its role was, however, disputable in terms of the contractile dysfunction. In this work, the dynamics of the intracellular Ca²⁺ signal were optically mapped in a Langendorff guinea pig heart. We found that DOXO treatment: (1) Delayed the activation of the Ca²⁺ signal. With the reference time set at the peak of the action potential (AP), the time lag between the peak of the Ca²⁺ signal and AP (Ca-AP-Lag) was significantly prolonged. (2) Slowed down the intracellular Ca²⁺ releasing and sequestering process. Both the maximum rising (MRV) and falling (MFV) velocity of the Ca²⁺ signal were decreased. (3) Shortened the duration of the Ca²⁺ signal in one cycle of Ca²⁺ oscillation. The duration of the Ca²⁺ signal at 50% amplitude (CaD50) was significantly shortened. These results suggested a reduced level of intracellular Ca²⁺ after DOXO treatment. Furthermore, we found that the effect of tachypacing was similar to that of DOXO, and, interestingly, DOXO exerted contradictory effects on the tachypaced hearts: it shortened the Ca-AP-Lag, accelerated the MRV and MFV, and prolonged the CaD50. We, therefore, concluded that DOXO had a different effect on intracellular Ca²⁺. It caused Ca²⁺ underload in hearts with sinus rhythm; this might relate to the contractile dysfunction in DOXO cardiomyopathy. It led to Ca²⁺ overload in the tachypaced hearts, which might contribute to the Ca²⁺-overload-related toxicity.

Human Purkinje in silico model enables mechanistic investigations into automaticity and pro-arrhythmic abnormalities

Cardiac Purkinje cells (PCs) are implicated in lethal arrhythmias caused by cardiac diseases, mutations, and drug action. However, the pro-arrhythmic mechanisms in PCs are not entirely understood, particularly in humans, as most investigations are conducted in animals. The aims of this study are to present a novel human PCs electrophysiology biophysically-detailed computational model, and to disentangle ionic mechanisms of human Purkinje-related electrophysiology, pacemaker activity and arrhythmogenicity. The new Trovato2020 model incorporates detailed Purkinje-specific ionic currents and Ca²⁺ handling, and was developed, calibrated and validated using human experimental data acquired at multiple frequencies, both in control conditions and following drug application. Multiscale investigations were performed in a Purkinje cell, in fibre and using an experimentally-calibrated population of PCs to evaluate biological variability. Simulations demonstrate the human Purkinje Trovato2020 model is the first one to yield: (i) all key AP features consistent with human Purkinje recordings; (ii) Automaticity with funny current up-regulation (iii) EADs at slow pacing and with 85% hERG block; (iv) DADs following fast pacing; (v) conduction velocity of 160 cm/s in a Purkinje fibre, as reported in human. The human in silico PCs population highlights that: (1) EADs are caused by I_CaL reactivation in PCs with large inward currents; (2) DADs and triggered APs occur in PCs experiencing Ca²⁺ accumulation, at fast pacing, caused by large L-type calcium current and small Na⁺/Ca²⁺ exchanger. The novel human Purkinje model unlocks further investigations into the role of cardiac Purkinje in ventricular arrhythmias through computer modeling and multiscale simulations.

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A human in silico AP model was developed to investigate arrhythmia in cardiac Purkinje.

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The new Purkinje model enables multiscale investigations from single cell to tissue.

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Populations of human Purkinje models reproduce and explain experimental variability.

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Ca²⁺-current reactivation triggers EADs in virtual Purkinje cells with weak repolarisation reserve.

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Ca²⁺ accumulation caused by increased Ca²⁺ and NCX currents triggers DADs.

A comprehensive, multiscale framework for evaluation of arrhythmias arising from cell therapy in the whole post-myocardial infarcted heart

Direct remuscularization approaches to cell-based heart repair seek to restore ventricular contractility following myocardial infarction (MI) by introducing new cardiomyocytes (CMs) to replace lost or injured ones. However, despite promising improvements in cardiac function, high incidences of ventricular arrhythmias have been observed in animal models of MI injected with pluripotent stem cell-derived cardiomyocytes (PSC-CMs). The mechanisms of arrhythmogenesis remain unclear. Here, we present a comprehensive framework for computational modeling of direct remuscularization approaches to cell therapy. Our multiscale 3D whole-heart modeling framework integrates realistic representations of cell delivery and transdifferentiation therapy modalities as well as representation of spatial distributions of engrafted cells, enabling simulation of clinical therapy and the prediction of emergent electrophysiological behavior and arrhythmogenensis. We employ this framework to explore how varying parameters of cell delivery and transdifferentiation could result in three mechanisms of arrhythmogenesis: focal ectopy, heart block, and reentry.

Mechanistic insight into spontaneous transition from cellular alternans to arrhythmia-A simulation study

Cardiac electrical alternans (CEA), manifested as T-wave alternans in ECG, is a clinical biomarker for predicting cardiac arrhythmias and sudden death. However, the mechanism underlying the spontaneous transition from CEA to arrhythmias remains incompletely elucidated. In this study, multiscale rabbit ventricular models were used to study the transition and a potential role of INa in perpetuating such a transition. It was shown CEA evolved into either concordant or discordant action potential (AP) conduction alternans in a homogeneous one-dimensional tissue model, depending on tissue AP duration and conduction velocity (CV) restitution properties. Discordant alternans was able to cause conduction failure in the model, which was promoted by impaired sodium channel with either a reduced or increased channel current. In a two-dimensional homogeneous tissue model, a combined effect of rate- and curvature-dependent CV broke-up alternating wavefronts at localised points, facilitating a spontaneous transition from CEA to re-entry. Tissue inhomogeneity or anisotropy further promoted break-up of re-entry, leading to multiple wavelets. Similar observations have also been seen in human atrial cellular and tissue models. In conclusion, our results identify a mechanism by which CEA spontaneously evolves into re-entry without a requirement for premature ventricular complexes or pre-existing tissue heterogeneities, and demonstrated the important pro-arrhythmic role of impaired sodium channel activity. These findings are model-independent and have potential human relevance.

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.

Larger rate dependence of late sodium current in cardiac Purkinje cells: A potential link to arrhythmogenesis

BACKGROUND

Purkinje cells (PCs) have a steeper rate dependence of repolarization and are more susceptible to arrhythmic activity than do ventricular myocytes (VMs). Late sodium current (I_NaL) is rate dependent and contributes to rate dependence of repolarization.

OBJECTIVE

This study sought to test our hypothesis that PCs have a larger rate dependence of I_NaL, contributing to their steeper rate dependence of repolarization and higher susceptibility to arrhythmic activity, than do VMs.

METHODS

I_NaL was recorded in isolated rabbit PCs and VMs with the whole-cell patch clamp technique. Action potential was examined using the microelectrode technique.

RESULTS

Compared with VMs, PCs exhibited a significantly larger rate dependence of I_NaL with a larger I_NaL to basic cycle length (BCL) slope. Moreover, PCs had a larger rate dependence of I_NaL decay and slower recovery kinetics. Interestingly, the larger rate dependence of I_NaL matched to a steeper rate dependence of action potential duration (APD) in PCs. The I_NaL blocker tetrodotoxin significantly blunted, while the I_NaL enhancer anemone toxin (ATX-II) significantly increased, the rate dependence of I_NaL and APD in PCs and VMs. In the presence of ATX-II, the rate dependence of I_NaL in PCs was markedly larger than that in VMs, causing a much steeper rate dependence of APD in PCs. Accordingly, PCs exhibited greater rate-dependent electrical instability and were more prone to ATX-II-induced early afterdepolarizations, which were completely inhibited by the I_NaL inhibitor ranolazine.

CONCLUSION

PCs have a significantly larger rate dependence of I_NaL than do VMs because of distinctive I_NaL decay and recovery kinetics, which contributes to their larger rate adaptation, and simultaneously predisposes them to a higher risk of arrhythmogenesis.

From the Purkinje fibres to the ventricle: One dimensional computer simulation for the healthy and failing heart

This study used one-dimensional computer simulation to investigate the influence of heart failure on action potential conduction through the left Purkinje fibres to the left ventricle. The study was based on a rabbit model of left ventricular heart failure caused by volume and pressure overload. To simulate the effect of heart failure, we began with models of the healthy rabbit Purkinje fibre action potential and healthy left ventricular (endocardial) action potential. In the absence of ionic current measurements from failing rabbit Purkinje fibres, we assumed that changes in ionic currents mirrored changes in ion channel expression (measured at the messenger RNA level): ionic conductances were adjusted based on changes in expression of the relevant ion channels. Ionic currents in the left ventricle were adjusted in the same way, but in addition, changes in ionic currents measured in the failing rabbit left ventricle by Ruijter et al. and Powizd et al. were used in simulations. The simulations predict a gradient in action potential duration from the Purkinje fibres to the ventricle and this gradient is exacerbated in heart failure. The predicted changes in the Purkinje fibre and left ventricular action potential were compared to actual changes measured using sharp microelectrodes.

A Parsimonious Model of the Rabbit Action Potential Elucidates the Minimal Physiological Requirements for Alternans and Spiral Wave Breakup

Elucidating the underlying mechanisms of fatal cardiac arrhythmias requires a tight integration of electrophysiological experiments, models, and theory. Existing models of transmembrane action potential (AP) are complex (resulting in over parameterization) and varied (leading to dissimilar predictions). Thus, simpler models are needed to elucidate the "minimal physiological requirements" to reproduce significant observable phenomena using as few parameters as possible. Moreover, models have been derived from experimental studies from a variety of species under a range of environmental conditions (for example, all existing rabbit AP models incorporate a formulation of the rapid sodium current, INa, based on 30 year old data from chick embryo cell aggregates). Here we develop a simple "parsimonious" rabbit AP model that is mathematically identifiable (i.e., not over parameterized) by combining a novel Hodgkin-Huxley formulation of INa with a phenomenological model of repolarization similar to the voltage dependent, time-independent rectifying outward potassium current (IK). The model was calibrated using the following experimental data sets measured from the same species (rabbit) under physiological conditions: dynamic current-voltage (I-V) relationships during the AP upstroke; rapid recovery of AP excitability during the relative refractory period; and steady-state INa inactivation via voltage clamp. Simulations reproduced several important "emergent" phenomena including cellular alternans at rates > 250 bpm as observed in rabbit myocytes, reentrant spiral waves as observed on the surface of the rabbit heart, and spiral wave breakup. Model variants were studied which elucidated the minimal requirements for alternans and spiral wave break up, namely the kinetics of INa inactivation and the non-linear rectification of IK.The simplicity of the model, and the fact that its parameters have physiological meaning, make it ideal for engendering generalizable mechanistic insight and should provide a solid "building-block" to generate more detailed ionic models to represent complex rabbit electrophysiology.

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 our understanding of the His-Purkinje system

The His-Purkinje System (HPS) is responsible for the rapid electric conduction in the ventricles. It relays electrical impulses from the atrioventricular node to the muscle cells and, thus, coordinates the contraction of ventricles in order to ensure proper cardiac pump function. The HPS has been implicated in the genesis of ventricular tachycardia and fibrillation as a source of ectopic beats, as well as forming distinct portions of reentry circuitry. Despite its importance, it remains much less well characterized, structurally and functionally, than the myocardium. Notably, important differences exist with regard to cell structure and electrophysiology, including ion channels, intracellular calcium handling, and gap junctions. Very few computational models address the HPS, and the majority of organ level modeling studies omit it. This review will provide an overview of our current knowledge of structure and function (including electrophysiology) of the HPS. We will review the most recent advances in modeling of the system from the single cell to the organ level, with considerations for relevant interspecies distinctions.

Ion Channels in the Heart

Optimal cardiac function depends on proper timing of excitation and contraction in various regions of the heart, as well as on appropriate heart rate. This is accomplished via specialized electrical properties of various components of the system, including the sinoatrial node, atria, atrioventricular node, His-Purkinje system, and ventricles. Here we review the major regionally determined electrical properties of these cardiac regions and present the available data regarding the molecular and ionic bases of regional cardiac function and dysfunction. Understanding these differences is of fundamental importance for the investigation of arrhythmia mechanisms and pharmacotherapy.

In Silico Organ Modelling in Predicting Efficacy and Safety of New Medicines

The development of new medicines faces important challenges due to difficulties in the assessment of their efficacy and their safety in the targeted human population. In silico approaches through the use of mathematical modelling and computer simulations are increasingly being used to overcome some of the limitations of current experimental methods used in the development of new medicines. This chapter describes state-of-the-art in silico approaches for the evaluation of the safety and efficacy of medicines targeting important causes of mortality such as cardiovascular disease. Firstly, we describe the in silico multi-scale mathematical models and simulation techniques required to describe drug-induced effects on physiological systems such as the heart from the subcellular to the whole organ level. Then we illustrate the power of in silico approaches used to augment experimental and clinical investigations, by providing the framework to unravel multi-scale mechanisms underlying variability in the response to medicines and to focus on effects in human rather than animal models. We devote the last part of the chapter to discussing the process of validation of in silico models and simulations, which is key in building up their credibility.

Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach

Under diseased conditions, remodeling of the cardiac tissue properties (“passive properties”) takes place; these are aspects of electrophysiological behavior that are not associated with active ion transport across cell membranes. Remodeling of the passive electrophysiological properties most often results from structural remodeling, such as gap junction down-regulation and lateralization, fibrotic growth infiltrating the myocardium, or the development of an infarct scar. Such structural remodeling renders atrial or ventricular tissue as a major substrate for arrhythmias. The current review focuses on these aspects of cardiac arrhythmogenesis. Due to the inherent complexity of cardiac arrhythmias, computer simulations have provided means to elucidate interactions pertinent to this spatial scale. Here we review the current state-of-the-art in modeling atrial and ventricular arrhythmogenesis as arising from the disease-induced changes in the passive tissue properties, as well as the contributions these modeling studies have made to our understanding of the mechanisms of arrhythmias in the heart. Because of the rapid advance of structural imaging methodologies in cardiac electrophysiology, we chose to present studies that have used such imaging methodologies to construct geometrically realistic models of cardiac tissue, or the organ itself, where the regional remodeling properties of the myocardium can be represented in a realistic way. We emphasize how the acquired knowledge can be used to pave the way for clinical applications of cardiac organ modeling under the conditions of structural remodeling.

Three-dimensional computer model of the right atrium including the sinoatrial and atrioventricular nodes predicts classical nodal behaviours

The aim of the study was to develop a three-dimensional (3D) anatomically-detailed model of the rabbit right atrium containing the sinoatrial and atrioventricular nodes to study the electrophysiology of the nodes. A model was generated based on 3D images of a rabbit heart (atria and part of ventricles), obtained using high-resolution magnetic resonance imaging. Segmentation was carried out semi-manually. A 3D right atrium array model (∼3.16 million elements), including eighteen objects, was constructed. For description of cellular electrophysiology, the Rogers-modified FitzHugh-Nagumo model was further modified to allow control of the major characteristics of the action potential with relatively low computational resource requirements. Model parameters were chosen to simulate the action potentials in the sinoatrial node, atrial muscle, inferior nodal extension and penetrating bundle. The block zone was simulated as passive tissue. The sinoatrial node, crista terminalis, main branch and roof bundle were considered as anisotropic. We have simulated normal and abnormal electrophysiology of the two nodes. In accordance with experimental findings: (i) during sinus rhythm, conduction occurs down the interatrial septum and into the atrioventricular node via the fast pathway (conduction down the crista terminalis and into the atrioventricular node via the slow pathway is slower); (ii) during atrial fibrillation, the sinoatrial node is protected from overdrive by its long refractory period; and (iii) during atrial fibrillation, the atrioventricular node reduces the frequency of action potentials reaching the ventricles. The model is able to simulate ventricular echo beats. In summary, a 3D anatomical model of the right atrium containing the cardiac conduction system is able to simulate a wide range of classical nodal behaviours.

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.

The role of Purkinje-myocardial coupling during ventricular arrhythmia: a modeling study

The Purkinje system is the fast conduction network of the heart which couples to the myocardium at discrete sites called Purkinje-Myocyte Junctions (PMJs). However, the distribution and number of PMJs remains elusive, as does whether a particular PMJ is functional. We hypothesized that the Purkinje system plays a role during reentry and that the number of functional PMJs affect reentry dynamics. We used a computer finite element model of rabbit ventricles in which we varied the number of PMJs. Sustained, complex reentry was induced by applying an electric shock and the role of the Purkinje system in maintaining the arrhythmia was assessed by analyzing phase singularities, frequency of activation, and bidirectional propagation at PMJs. For larger junctional resistances, increasing PMJ density increased the mean firing rate in the Purkinje system, the percentage of successful retrograde conduction at PMJs, and the incidence of wave break on the epicardium. However, the mean firing of the ventricles was not affected. Furthermore, increasing PMJ density above 13/ did not alter reentry dynamics. For lower junctional resistances, the trend was not as clear. We conclude that Purkinje system topology affects reentry dynamics and conditions which alter PMJ density can alter reentry dynamics.

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.

Sensitivity of rabbit ventricular action potential and Ca²⁺ dynamics to small variations in membrane currents and ion diffusion coefficients

Little is known about how small variations in ionic currents and Ca²⁺ and Na⁺ diffusion coefficients impact action potential and Ca²⁺ dynamics in rabbit ventricular myocytes. We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys. J., 2004) to 5%-10% changes in currents conductance, channels distribution, and ion diffusion in rabbit ventricular cells. We found that action potential duration and Ca²⁺ peaks are highly sensitive to 10% increase in L-type Ca²⁺ current; moderately influenced by 10% increase in Na⁺-Ca²⁺ exchanger, Na⁺-K⁺ pump, rapid delayed and slow transient outward K⁺ currents, and Cl⁻ background current; insensitive to 10% increases in all other ionic currents and sarcoplasmic reticulum Ca²⁺ fluxes. Cell electrical activity is strongly affected by 5% shift of L-type Ca²⁺ channels and Na⁺-Ca²⁺ exchanger in between junctional and submembrane spaces while Ca²⁺-activated Cl⁻-channel redistribution has the modest effect. Small changes in submembrane and cytosolic diffusion coefficients for Ca²⁺, but not in Na⁺ transfer, may alter notably myocyte contraction. Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model. Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca²⁺ signaling.

Transmural IK(ATP) heterogeneity as a determinant of activation rate gradient during early ventricular fibrillation: mechanistic insights from rabbit ventricular models

BACKGROUND

Activation rate (AR) gradients develop during ventricular fibrillation (VF), with the highest AR on the surface near Purkinje system (PS) terminals (endocardium in humans and rabbits and epicardium in pigs). The application of glibenclamide to block adenosine triphosphate (ATP)-sensitive potassium current (IK(ATP)) before VF induction eliminates transmural AR gradients and prevents the induction of sustained arrhythmia. It remains unclear whether the PS, which is resistant to ischemia, is also a factor in AR heterogeneity.

OBJECTIVE

To dissect IK(ATP) and PS contributions to AR gradients during VF by using detailed computer simulations.

METHODS

We constructed rabbit ventricular models with either subendocardial or subepicardial PS terminals. Physiologically relevant IK(ATP) gradients were implemented, and early VF was induced and observed.

RESULTS

Prominent AR gradients were observed only in models with large IK(ATP) gradients. The critical underlying factor of AR gradient maintenance was refractoriness in low-IK(ATP) regions, which blocked the propagation of action potentials from high-IK(ATP) regions. The PS played no role in transmural AR gradient maintenance, but did cause local spatial heterogeneity of AR on the surface adjacent to terminals. Simulated glibenclamide application during VF led to spontaneous arrhythmia termination within a few seconds in most cases, which builds on previous experimental findings of anti-VF properties of glibenclamide pretreatment.

CONCLUSION

Differential IK(ATP) across the ventricular wall is an important factor underlying AR gradients during VF; thus, higher epicardial AR in pigs is most likely due to an abundance of epicardial IK(ATP). For terminating early VF, our results suggest that IK(ATP) modulation is a stronger target than Purkinje ablation.

Structure, function and clinical relevance of the cardiac conduction system, including the atrioventricular ring and outflow tract tissues

It is now over 100years since the discovery of the cardiac conduction system, consisting of three main parts, the sinus node, the atrioventricular node and the His-Purkinje system. The system is vital for the initiation and coordination of the heartbeat. Over the last decade, immense strides have been made in our understanding of the cardiac conduction system and these recent developments are reviewed here. It has been shown that the system has a unique embryological origin, distinct from that of the working myocardium, and is more extensive than originally thought with additional structures: atrioventricular rings, a third node (so called retroaortic node) and pulmonary and aortic sleeves. It has been shown that the expression of ion channels, intracellular Ca(2+)-handling proteins and gap junction channels in the system is specialised (different from that in the ordinary working myocardium), but appropriate to explain the functioning of the system, although there is continued debate concerning the ionic basis of pacemaking. We are beginning to understand the mechanisms (fibrosis and remodelling of ion channels and related proteins) responsible for dysfunction of the system (bradycardia, heart block and bundle branch block) associated with atrial fibrillation and heart failure and even athletic training. Equally, we are beginning to appreciate how naturally occurring mutations in ion channels cause congenital cardiac conduction system dysfunction. Finally, current therapies, the status of a new therapeutic strategy (use of a specific heart rate lowering drug) and a potential new therapeutic strategy (biopacemaking) are reviewed.

Fusion during entrainment of orthodromic reciprocating tachycardia is enhanced for basal pacing sites but diminished when pacing near Purkinje system end points

BACKGROUND

In the electrophysiological laboratory, orthodromic atrioventricular reciprocating tachycardia (ORT) can be distinguished from atrial tachycardia and atrioventricular node reentry tachycardia by identifying orthodromic and antidromic wavefront fusion during ventricular overdrive pacing (VOP). Previous work has shown that basal VOP near the accessory pathway (AP) increases the likelihood of observing fusion; however, in a third of cases, fusion is not appreciable regardless of VOP location.

OBJECTIVE

To explore the hypothesis that pacing near His-Purkinje system (PS) end points reduces fusion quality, which may explain patients with nonresponsive ORT.

METHODS

In a novel computer model of ORT, simulations were performed with a variety of AP locations and pacing sites; results were analyzed to assess factors influencing fusion quality in pseudo-electrocardiogram signals.

RESULTS

Entrainment by basal VOP near the AP was more likely to produce fusion visible on simulated electrocardiograms compared to entrainment by apical VOP, but this advantage was dramatically diminished when the pacing site was also near PS end points. Prediction of fusion quality based on AP proximity alone was dramatically improved when corrected to penalize for PS proximity.

CONCLUSIONS

These results suggest that basal VOP near the AP and far from the PS is optimal; this could be tested in patients. A denser basal ramification of PS fibers is known to exist in a minority of human hearts; our findings indicate that this unusual PS configuration is a plausible explanation for ORT cases where fusion is never observed in spite of entrainment by basal VOP near the AP.

Modeling effects of L-type ca(2+) current and na(+)-ca(2+) exchanger on ca(2+) trigger flux in rabbit myocytes with realistic T-tubule geometries

The transverse tubular system of rabbit ventricular myocytes consists of cell membrane invaginations (t-tubules) that are essential for efficient cardiac excitation-contraction coupling. In this study, we investigate how t-tubule micro-anatomy, L-type Ca²⁺ channel (LCC) clustering, and allosteric activation of Na⁺/Ca²⁺ exchanger by L-type Ca²⁺ current affects intracellular Ca²⁺ dynamics. Our model includes a realistic 3D geometry of a single t-tubule and its surrounding half-sarcomeres for rabbit ventricular myocytes. The effects of spatially distributed membrane ion-transporters (LCC, Na⁺/Ca²⁺ exchanger, sarcolemmal Ca²⁺ pump, and sarcolemmal Ca²⁺ leak), and stationary and mobile Ca²⁺ buffers (troponin C, ATP, calmodulin, and Fluo-3) are also considered. We used a coupled reaction-diffusion system to describe the spatio-temporal concentration profiles of free and buffered intracellular Ca²⁺. We obtained parameters from voltage-clamp protocols of L-type Ca²⁺ current and line-scan recordings of Ca²⁺ concentration profiles in rabbit cells, in which the sarcoplasmic reticulum is disabled. Our model results agree with experimental measurements of global Ca²⁺ transient in myocytes loaded with 50 μM Fluo-3. We found that local Ca²⁺ concentrations within the cytosol and sub-sarcolemma, as well as the local trigger fluxes of Ca²⁺ crossing the cell membrane, are sensitive to details of t-tubule micro-structure and membrane Ca²⁺ flux distribution. The model additionally predicts that local Ca²⁺ trigger fluxes are at least threefold to eightfold higher than the whole-cell Ca²⁺ trigger flux. We found also that the activation of allosteric Ca²⁺-binding sites on the Na⁺/Ca²⁺ exchanger could provide a mechanism for regulating global and local Ca²⁺ trigger fluxes in vivo. Our studies indicate that improved structural and functional models could improve our understanding of the contributions of L-type and Na⁺/Ca²⁺ exchanger fluxes to intracellular Ca²⁺ dynamics.

Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology

Computational models in physiology often integrate functional and structural information from a large range of spatiotemporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and skepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace, and refine animal experiments. A fundamental requirement to fulfill these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations among experiments, models, and simulations in cardiac electrophysiology. We describe the processes, data, and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. We argue that validation is part of the whole MSE system and is contingent upon 1) understanding and coping with sources of biovariability; 2) testing and developing robust techniques and tools as a prerequisite to conducting physiological investigations; 3) defining and adopting standards to facilitate the interoperability of experiments, models, and simulations; 4) and understanding physiological validation as an iterative process that contributes to defining the specific aspects of cardiac electrophysiology the MSE system targets, rather than being only an external test, and that this is driven by advances in experimental and computational methods and the combination of both.

Subcellular heterogeneity of sodium current properties in adult cardiac ventricular myocytes

BACKGROUND

Sodium channel α-subunits in ventricular myocytes (VMs) segregate either to the intercalated disc or to lateral membranes, where they associate with region-specific molecules.

OBJECTIVE

To determine the functional properties of sodium channels as a function of their location in the cell.

METHODS

Local sodium currents were recorded from adult rodent VMs and Purkinje cells by using the cell-attached macropatch configuration. Electrodes were placed either in the cell midsection (M) or at the cell end (area originally occupied by the intercalated disc [ID]). Channels were identified as tetrodotoxin (TTX)-sensitive (TTX-S) or TTX-resistant (TTX-R) by application of 100 nM of TTX.

RESULTS

Average peak current amplitude was larger in ID than in M and largest at the site of contact between attached cells. TTX-S channels were found only in the M region of VMs and not in Purkinje myocytes. TTX-R channels were found in both M and ID regions, but their biophysical properties differed depending on recording location. Sodium current in rat VMs was upregulated by tumor necrosis factor-alpha. The magnitude of current increase was largest in the M region, but this difference was abolished by application of 100 nM of TTX.

CONCLUSIONS

Our data suggest that (a) a large fraction of TTX-R (likely Na(v)1.5) channels in the M region of VMs are inactivated at normal resting potential, leaving most of the burden of excitation to TTX-R channels in the ID region; (b) cell-cell adhesion increases functional channel density at the ID; and (c) TTX-S (likely non-Na(v)1.5) channels make a minimal contribution to sodium current under control conditions, but they represent a functional reserve that can be upregulated by exogenous factors.

Systematic characterization of the ionic basis of rabbit cellular electrophysiology using two ventricular models

Several mathematical models of rabbit ventricular action potential (AP) have been proposed to investigate mechanisms of arrhythmias and excitation-contraction coupling. Our study aims at systematically characterizing how ionic current properties modulate the main cellular biomarkers of arrhythmic risk using two widely-used rabbit ventricular models, and comparing simulation results using the two models with experimental data available for rabbit. A sensitivity analysis of AP properties, Ca²⁺ and Na⁺ dynamics, and their rate dependence to variations (±15% and ±30%) in the main transmembrane current conductances and kinetics was performed using the Shannon et al. (2004) and the Mahajan et al. (2008a,b) AP rabbit models. The effects of severe transmembrane current blocks (up to 100%) on steady-state AP and calcium transients, and AP duration (APD) restitution curves were also simulated using both models. Our simulations show that, in both virtual rabbit cardiomyocytes, APD is significantly modified by most repolarization currents, AP triangulation is regulated mostly by the inward rectifier K⁺ current (I(K1)) whereas APD rate adaptation as well as [Na⁺](i) rate dependence is influenced by the Na⁺/K⁺ pump current (I(NaK)). In addition, steady-state [Ca²⁺](i) levels, APD restitution properties and [Ca²⁺](i) rate dependence are strongly dependent on I(NaK), the L-Type Ca²⁺ current (I(CaL)) and the Na⁺/Ca²⁺ exchanger current (I(NaCa)), although the relative role of these currents is markedly model dependent. Furthermore, our results show that simulations using both models agree with many experimentally-reported electrophysiological characteristics. However, our study shows that the Shannon et al. model mimics rabbit electrophysiology more accurately at normal pacing rates, whereas Mahajan et al. model behaves more appropriately at faster rates. Our results reinforce the usefulness of sensitivity analysis for further understanding of cellular electrophysiology and validation of cardiac AP models.

Ionic mechanisms of electrophysiological properties and repolarization abnormalities in rabbit Purkinje fibers

Purkinje cells play an important role in drug-induced arrhythmogenesis and are widely used in preclinical drug safety assessments. Repolarization abnormalities such as action potential (AP) prolongation and early afterdeploarizations (EAD) are often observed in vitro upon pharmacological interventions. However, because drugs do not act on only one defined target, it is often difficult to fully explain the mechanisms of action and their potential arrhythmogenicity. Computational models, when appropriately detailed and validated, can be used to gain mechanistic insights into the mechanisms of action of certain drugs. Nevertheless, no model of Purkinje electrophysiology that is able to reproduce characteristic Purkinje responses to drug-induced changes in ionic current conductances such as AP prolongation and EAD generation currently exists. In this study, a novel biophysically detailed model of rabbit Purkinje electrophysiology was developed by integration of data from voltage-clamp and AP experimental recordings. Upon validation, we demonstrate that the model reproduces many key electrophysiological properties of rabbit Purkinje cells. These include: AP morphology and duration, both input resistance and rate dependence properties as well as response to hyperkalemia. Pharmacological interventions such as inward rectifier K(+) current and rapid delayed rectifier K(+) current block as well as late Na(+) current increase result in significant AP changes. However, enhanced L-type Ca(2+) current (i(CaL)) dominates in EAD genesis in Purkinje fibers. In addition, i(CaL) inactivation dynamics and intercellular coupling in tissue strongly modulate EAD formation. We conclude that EAD generation in Purkinje cells is mediated by an increase in i(CaL) and modulated by its inactivation kinetics.