The canine virtual ventricular wall: A platform for dissecting pharmacological effects on propagation and arrhythmogenesis

Pro-Arrhythmic Effects of Discontinuous Conduction at the Purkinje Fiber-Ventricle Junction Arising From Heart Failure-Induced Ionic Remodeling - Insights From Computational Modelling

Heart failure is associated with electrical remodeling of the electrical properties and kinetics of the ion channels and transporters that are responsible for cardiac action potentials. However, it is still unclear whether heart failure-induced ionic remodeling can affect the conduction of excitation waves at the Purkinje fiber-ventricle junction contributing to pro-arrhythmic effects of heart failure, as the complexity of the heart impedes a detailed experimental analysis. The aim of this study was to employ computational models to investigate the pro-arrhythmic effects of heart failure-induced ionic remodeling on the cardiac action potentials and excitation wave conduction at the Purkinje fiber-ventricle junction. Single cell models of canine Purkinje fiber and ventricular myocytes were developed for control and heart failure. These single cell models were then incorporated into one-dimensional strand and three-dimensional wedge models to investigate the effects of heart failure-induced remodeling on propagation of action potentials in Purkinje fiber and ventricular tissue and at the Purkinje fiber-ventricle junction. This revealed that heart failure-induced ionic remodeling of Purkinje fiber and ventricular tissue reduced conduction safety and increased tissue vulnerability to the genesis of the unidirectional conduction block. This was marked at the Purkinje fiber-ventricle junction, forming a potential substrate for the genesis of conduction failure that led to re-entry. This study provides new insights into proarrhythmic consequences of heart failure-induced ionic remodeling.

Morphometric analysis of cardiac conduction fibers in horses and dogs, a comparative histological and immunohistochemical study with findings in human hearts

The principal function of the ventricular conduction system is rapid electrical activation of the ventricles. The aim of this study is to conduct a morphometric study to pinpoint the morphological parameters that define cardiac conduction cells, allowing us to distinguish them from other cells. Five male horse hearts and five male dog hearts were used in the study. The hearts were fixed in a 5% formaldehyde solution. Histological sections of 5 μm thickness were acquired and stained with hematoxylin-eosin and Masson's trichrome and cardiac conduction cells and their junctions were identified by desmin, connexin 40 and a PAS method. We found statistically significant differences in cardiac conduction fibers density and thickness, which was much higher in horses than in dogs (p = 0.000 for both values). By comparing the measured parameters of the cells in both species, we determined that cardiac conduction cells area and diameters were greater in horses than in dogs (p = 0.000 for all values). In dogs there are more junctions (30.8%) than in horses (26.1%), a statistically significant difference (p = 0.041). Our findings regarding the cardiac conduction fibers distribution in the animal species studied becomes new knowledge that contributes to the morphological study of this component of the cardiac conduction system and also makes it possible to locate exactly the site with the highest density of cardiac conduction fibers as a contribution to the cardiological study of these structures that lead to the prevention of ventricular arrhythmias and the identification of their treatment site.

Pro-arrhythmic Effects of Hydrogen Sulfide in Healthy and Ischemic Cardiac Tissues: Insight From a Simulation Study

Hydrogen sulfide (H₂S), an ambient air pollutant, has been reported to increase cardiac events in patients with cardiovascular diseases, but the underlying mechanisms remain not elucidated. This study investigated the pro-arrhythmic effects of H₂S in healthy and ischemic conditions. Experimental data of H₂S effects on ionic channels (including the L-type Ca²⁺ channel and ATP-sensitive K⁺ channel) were incorporated into a virtual heart model to evaluate their integral action on cardiac arrhythmogenesis. It was shown that H₂S depressed cellular excitability, abbreviated action potential duration, and augmented tissue’s transmural dispersion of repolarization, resulting in an increase in tissue susceptibility to initiation and maintenance of reentry. The observed effects of H₂S on cardiac excitation are more remarkable in the ischemic condition than in the healthy condition. This study provides mechanistic insights into the pro-arrhythmic effects of air pollution (H₂S), especially in the case with extant ischemic conditions.

Four Ways to Fit an Ion Channel Model

Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: method 1, fitting model equations directly to time-constant, steady-state, and I-V summary curves; method 2, fitting by comparing simulated versions of these summary curves to their experimental counterparts; method 3, fitting to the current traces themselves from a range of protocols; and method 4, fitting to a single current trace from a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are most readily available from the literature, we find it performs poorly compared to methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications.

Arrhythmia mechanisms and spontaneous calcium release: Bi-directional coupling between re-entrant and focal excitation

Spontaneous sub-cellular calcium release events (SCRE) are conjectured to promote rapid arrhythmias associated with conditions such as heart failure and atrial fibrillation: they can underlie the emergence of spontaneous action potentials in single cells which can lead to arrhythmogenic triggers in tissue. The multi-scale mechanisms of the development of SCRE into arrhythmia triggers, and their dynamic interaction with the tissue substrate, remain elusive; rigorous and simultaneous study of dynamics from the nanometre to the centimetre scale is a major challenge. The aim of this study was to develop a computational approach to overcome this challenge and study potential bi-directional coupling between sub-cellular and tissue-scale arrhythmia phenomena. A framework comprising a hierarchy of computational models was developed, which includes detailed single-cell models describing spatio-temporal calcium dynamics in 3D, efficient non-spatial cell models, and both idealised and realistic tissue models. A phenomenological approach was implemented to reproduce SCRE morphology and variability in the efficient cell models, comprising the definition of analytical Spontaneous Release Functions (SRF) whose parameters may be randomly sampled from appropriate distributions in order to match either the 3D cell models or experimental data. Pro-arrhythmogenic pacing protocols were applied to initiate re-entry and promote calcium overload, leading to the emergence of SCRE. The SRF accurately reproduced the dynamics of SCRE and its dependence on environment variables under multiple different conditions. Sustained re-entrant excitation promoted calcium overload, and led to the emergence of focal excitations after termination. A purely functional mechanism of re-entry and focal activity localisation was demonstrated, related to the unexcited spiral wave core. In conclusion, a novel approach has been developed to dynamically model SCRE at the tissue scale, which facilitates novel, detailed multi-scale mechanistic analysis. It was revealed that complex re-entrant excitation patterns and SCRE may be bi-directionally coupled, promoting novel mechanisms of arrhythmia perpetuation.

Transmural cellular heterogeneity in myocardial electromechanics

Myocardial heterogeneity is an attribute of the normal heart. We have developed integrative models of cardiomyocytes from the subendocardial (ENDO) and subepicardial (EPI) ventricular regions that take into account experimental data on specific regional features of intracellular electromechanical coupling in the guinea pig heart. The models adequately simulate experimental data on the differences in the action potential and contraction between the ENDO and EPI cells. The modeling results predict that heterogeneity in the parameters of calcium handling and myofilament mechanics in isolated ENDO and EPI cardiomyocytes are essential to produce the differences in Ca2+ transients and contraction profiles via cooperative mechanisms of mechano-calcium-electric feedback and may further slightly modulate transmural differences in the electrical properties between the cells. Simulation results predict that ENDO cells have greater sensitivity to changes in the mechanical load than EPI cells. These data are important for understanding the behavior of cardiomyocytes in the intact heart.

Modelling the effects of chloroquine on KCNJ2-linked short QT syndrome

A gain-of-function KCNJ2 D172N mutation in KCNJ2-encoded Kir2.1 channels underlies one form of short QT syndrome (SQT3), which is associated with increased susceptibility to arrhythmias and sudden death. Anti-malarial drug chloroquine was reported as an effective inhibitor of Kir2.1 channels. Using biophysically-detailed human ventricle computer models, this study assessed the effects of chloroquine on SQT3. The ten Tusscher et al. model of human ventricular cell action potential was modified to recapitulate functional changes in the inward rectifier K⁺ current (I_K1) due to heterozygous and homozygous forms of the D172N mutation. Mutant formulations were incorporated into multi-scale models. The blocking effects of chloroquine on ionic currents were modelled using IC₅₀ and Hill coefficient values from literatures. Effects of chloroquine on action potential duration (APD), effective refractory period (ERP) and pseudo-ECGs were quantified. It was shown that chloroquine caused a dose-dependent reduction in I_K1, prolonged APD, and decreased the maximum voltage heterogeneity. Chloroquine prolonged QT interval and declined the T-wave amplitude. Although chloroquine reduced tissue’s temporal vulnerability, it increased the minimum substrate size necessary for sustaining re-entry. The actions of chloroquine decreased arrhythmia risk, due to the reduced tissue vulnerability, prolonged ERP and wavelength of re-entrant excitation waves, which in combination prevented and terminated re-entry in the tissue models. In conclusion, the results of this study provide new evidence that the anti-arrhythmic effects of chloroquine on SQT3 and, by extension, to the possibility that chloroquine may be a potential therapeutic agent for SQT3 treatment.

Trigger vs. Substrate: Multi-Dimensional Modulation of QT-Prolongation Associated Arrhythmic Dynamics by a hERG Channel Activator

Background: Prolongation of the QT interval of the electrocardiogram (ECG), underlain by prolongation of the action potential duration (APD) at the cellular level, is linked to increased vulnerability to cardiac arrhythmia. Pharmacological management of arrhythmia associated with QT prolongation is typically achieved through attempting to restore APD to control ranges, reversing the enhanced vulnerability to Ca²⁺-dependent afterdepolarisations (arrhythmia triggers) and increased transmural dispersion of repolarisation (arrhythmia substrate) associated with APD prolongation. However, such pharmacological modulation has been demonstrated to have limited effectiveness. Understanding the integrative functional impact of pharmacological modulation requires simultaneous investigation of both the trigger and substrate. Methods: We implemented a multi-scale (cell and tissue) in silico approach using a model of the human ventricular action potential, integrated with a model of stochastic 3D spatiotemporal Ca²⁺ dynamics, and parameter modification to mimic prolonged QT conditions. We used these models to examine the efficacy of the hERG activator MC-II-157c in restoring APD to control ranges, examined its effects on arrhythmia triggers and substrates, and the interaction of these arrhythmia triggers and substrates. Results: QT prolongation conditions promoted the development of spontaneous release events underlying afterdepolarisations during rapid pacing. MC-II-157c applied to prolonged QT conditions shortened the APD, inhibited the development of afterdepolarisations and reduced the probability of afterdepolarisations manifesting as triggered activity in single cells. In tissue, QT prolongation resulted in an increased transmural dispersion of repolarisation, which manifested as an increased vulnerable window for uni-directional conduction block. In some cases, MC-II-157c further increased the vulnerable window through its effects on I_Na. The combination of stochastic release event modulation and transmural dispersion of repolarisation modulation by MC-II-157c resulted in an integrative behavior wherein the arrhythmia trigger is reduced but the arrhythmia substrate is increased, leading to variable and non-linear overall vulnerability to arrhythmia. Conclusion: The relative balance of reduced trigger and increased substrate underlies a multi-dimensional role of MC-II-157c in modulation of cardiac arrhythmia vulnerability associated with prolonged QT interval.

Pro-arrhythmogenic Effects of the V141M KCNQ1 Mutation in Short QT Syndrome and Its Potential Therapeutic Targets: Insights from Modeling

Gain-of-function mutations in the pore-forming subunit of I_Ks channels, KCNQ1, lead to short QT syndrome (SQTS) and lethal arrhythmias. However, how mutant I_Ks channels cause SQTS and the possibility of I_Ks-specific pharmacological treatment remain unclear. V141M KCNQ1 is a SQTS associated mutation. We studied its effect on I_Ks gating properties and changes in the action potentials (AP) of human ventricular myocytes. Xenopus oocytes were used to study the gating mechanisms of expressed V141M KCNQ1/KCNE1 channels. Computational models were used to simulate human APs in endocardial, mid-myocardial, and epicardial ventricular myocytes with and without β-adrenergic stimulation. V141M KCNQ1 caused a gain-of-function in I_Ks characterized by increased current density, faster activation, and slower deactivation leading to I_Ks accumulation. V141M KCNQ1 also caused a leftward shift of the conductance-voltage curve compared to wild type (WT) I_Ks (V_1/2 = 33.6 ± 4.0 mV for WT, and 24.0 ± 1.3 mV for heterozygous V141M). A Markov model of heterozygous V141M mutant I_Ks was developed and incorporated into the O’Hara–Rudy model. Compared to the WT, AP simulations demonstrated marked rate-dependent shortening of AP duration (APD) for V141M, predicting a SQTS phenotype. Transmural electrical heterogeneity was enhanced in heterozygous V141M AP simulations, especially under β-adrenergic stimulation. Computational simulations identified specific I_K1 blockade as a beneficial pharmacologic target for reducing the transmural APD heterogeneity associated with V141M KCNQ1 mutation. V141M KCNQ1 mutation shortens ventricular APs and enhances transmural APD heterogeneity under β-adrenergic stimulation. Computational simulations identified I_K1 blockers as a potential antiarrhythmic drug of choice for SQTS.

In silico assessment of the effects of quinidine, disopyramide and E-4031 on short QT syndrome variant 1 in the human ventricles

Aims

Short QT syndrome (SQTS) is an inherited disorder associated with abnormally abbreviated QT intervals and an increased incidence of atrial and ventricular arrhythmias. SQT1 variant (linked to the rapid delayed rectifier potassium channel current, I_Kr) of SQTS, results from an inactivation-attenuated, gain-of-function mutation (N588K) in the KCNH2-encoded potassium channels. Pro-arrhythmogenic effects of SQT1 have been well characterized, but less is known about the possible pharmacological antiarrhythmic treatment of SQT1. Therefore, this study aimed to assess the potential effects of E-4031, disopyramide and quinidine on SQT1 using a mathematical model of human ventricular electrophysiology.

Methods

The ten Tusscher et al. biophysically detailed model of the human ventricular action potential (AP) was modified to incorporate I_Kr Markov chain (MC) formulations based on experimental data of the kinetics of the N588K mutation of the KCNH2-encoded subunit of the I_Kr channels. The modified ventricular cell model was then integrated into one-dimensional (1D) strand, 2D regular and realistic tissues with transmural heterogeneities. The channel-blocking effect of the drugs on ion currents in healthy and SQT1 cells was modeled using half-maximal inhibitory concentration (IC₅₀) and Hill coefficient (nH) values from literatures. Effects of drugs on cell AP duration (APD), effective refractory period (ERP) and pseudo-ECG traces were calculated. Effects of drugs on the ventricular temporal and spatial vulnerability to re-entrant excitation waves were measured. Re-entry was simulated in both 2D regular and realistic ventricular tissue.

Results

At the single cell level, the drugs E-4031 and disopyramide had hardly noticeable effects on the ventricular cell APD at 90% repolarization (APD₉₀), whereas quinidine caused a significant prolongation of APD₉₀. Quinidine prolonged and decreased the maximal transmural AP heterogeneity (δV); this led to the decreased transmural heterogeneity of APD across the 1D strand. Quinidine caused QT prolongation and a decrease in the T-wave amplitude, and increased ERP and decreased temporal susceptibility of the tissue to the initiation of re-entry and increased the minimum substrate size necessary to prevent re-entry in the 2D regular model, and further terminated re-entrant waves in the 2D realistic model. Quinidine exhibited significantly better therapeutic effects on SQT1 than E-4031 and disopyramide.

Conclusions

The simulated pharmacological actions of quinidine exhibited antiarrhythmic effects on SQT1. This study substantiates a causal link between quinidine and QT interval prolongation in SQT1 and suggests that quinidine may be a potential pharmacological agent for treating SQT1 patients.

A quantitative structural and morphometric analysis of the Purkinje network and the Purkinje-myocardial junctions in pig hearts

The morpho-functional properties of the distal section of the cardiac Purkinje network (PN) and the Purkinje-myocardial junctions (PMJs) are fundamental to understanding the sequence of electrical activation in the heart. The overall structure of the system has already been described, and several computational models have been developed to gain insight into its involvement in cardiac arrhythmias or its interaction with implantable devices, such as pacemakers. However, anatomical descriptions of the PN in the literature have not enabled enough improvements in the accuracy of anatomical-based electrophysiological simulations of the PN in 3D hearts models. In this work, we study the global distribution and morphological properties of the PN, with special emphasis on the cellular and architectural characterization of its intramural branching structure, mesh-like sub-endocardial network, and the PMJs in adult pig hearts by both histopathological and morphometric evaluation. We have defined three main patterns of PMJ: contact through cell bodies, contact through cell prolongations either thick or piliform, and contact through transitional cells. Moreover, from hundreds of micrographs, we quantified the density of PMJs and provided data for the basal/medial/apical regions, anterior/posterior/septal/lateral regions and myocardial/sub-endocardial distribution. Morphometric variables, such as Purkinje cell density and thickness of the bundles, were also analyzed. After combining the results of these parameters, a different septoanterior distribution in the Purkinje cell density was observed towards the cardiac apex, which is associated with a progressive thinning of the conduction bundles and the posterolateral ascension of intramyocardial terminal scattered fibers. The study of the PMJs revealed a decreasing trend towards the base that may anatomically explain the early apical activation. The anterolateral region contains the greatest number of contacts, followed by the anterior and septal regions. This supports the hypothesis that thin distal Purkinje bundles create a junction-rich network that may be responsible for the quick apical depolarization. The PN then ascends laterally and spreads through the anterior and medial walls up to the base. We have established the first morphometric study of the Purkinje system, and provided quantitative and objective data that facilitate its incorporation into the development of models beyond gross and variable pathological descriptions, and which, after further studies, could be useful in the characterization of pathological processes or therapeutic procedures.

Species-Dependent Mechanisms of Cardiac Arrhythmia: A Cellular Focus

Although ventricular arrhythmia remains a leading cause of morbidity and mortality, available antiarrhythmic drugs have limited efficacy. Disappointing progress in the development of novel, clinically relevant antiarrhythmic agents may partly be attributed to discrepancies between humans and animal models used in preclinical testing. However, such differences are at present difficult to predict, requiring improved understanding of arrhythmia mechanisms across species. To this end, we presently review interspecies similarities and differences in fundamental cardiomyocyte electrophysiology and current understanding of the mechanisms underlying the generation of afterdepolarizations and reentry. We specifically highlight patent shortcomings in small rodents to reproduce cellular and tissue-level arrhythmia substrate believed to be critical in human ventricle. Despite greater ease of translation from larger animal models, discrepancies remain and interpretation can be complicated by incomplete knowledge of human ventricular physiology due to low availability of explanted tissue. We therefore point to the benefits of mathematical modeling as a translational bridge to understanding and treating human arrhythmia.

Ventricular fibrillation: triggers, mechanisms and therapies

Ventricular fibrillation (VF) is a common, life-threatening arrhythmia responsible for significant morbidity and mortality. Due to challenges in safely mapping VF, a comprehensive understanding of its mechanisms remains elusive. Recent findings have provided new insights into mechanisms that sustain early VF. Notably, the central role of electrical rotors and catheter-based ablation of VF rotor substrate have been recently reported. In this article, we will review data regarding four stages of VF: initiation, transition, maintenance and evolution. We will discuss the particular mechanisms for each stage and therapies targeting these mechanisms. We also examine inherited arrhythmia syndromes, including the mechanisms and therapies specific to each. We hope that the overview of VF outlined in this work will assist other investigators in designing future therapies to interrupt this life-threatening arrhythmia.

Tailor-made heart simulation predicts the effect of cardiac resynchronization therapy in a canine model of heart failure

Despite extensive studies on clinical indices for the selection of patient candidates for cardiac resynchronization therapy (CRT), approximately 30% of selected patients do not respond to this therapy. Herein, we examined whether CRT simulations based on individualized realistic three-dimensional heart models can predict the therapeutic effect of CRT in a canine model of heart failure with left bundle branch block. In four canine models of failing heart with dyssynchrony, individualized three-dimensional heart models reproducing the electromechanical activity of each animal were created based on the computer tomographic images. CRT simulations were performed for 25 patterns of three ventricular pacing lead positions. Lead positions producing the best and the worst therapeutic effects were selected in each model. The validity of predictions was tested in acute experiments in which hearts were paced from the sites identified by simulations. We found significant correlations between the experimentally observed improvement in ejection fraction (EF) and the predicted improvements in ejection fraction (P<0.01) or the maximum value of the derivative of left ventricular pressure (P<0.01). The optimal lead positions produced better outcomes compared with the worst positioning in all dogs studied, although there were significant variations in responses. Variations in ventricular wall thickness among the dogs may have contributed to these responses. Thus CRT simulations using the individualized three-dimensional heart models can predict acute hemodynamic improvement, and help determine the optimal positions of the pacing lead.

Recent developments in using mechanistic cardiac modelling for drug safety evaluation

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Modelling and simulation can streamline decision making in drug safety testing.

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Computational cardiac electrophysiology is a mature technology with a long heritage.

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There are many challenges and opportunities in using in silico techniques in future.

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We discuss how models can be used at different stages of drug discovery.

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CiPA will combine screening platforms, human cell assays and in silico predictions.

On the tenth anniversary of two key International Conference on Harmonisation (ICH) guidelines relating to cardiac proarrhythmic safety, an initiative aims to consider the implementation of a new paradigm that combines in vitro and in silico technologies to improve risk assessment. The Comprehensive In Vitro Proarrhythmia Assay (CiPA) initiative (co-sponsored by the Cardiac Safety Research Consortium, Health and Environmental Sciences Institute, Safety Pharmacology Society and FDA) is a bold and welcome step in using computational tools for regulatory decision making. This review compares and contrasts the state-of-the-art tools from empirical to mechanistic models of cardiac electrophysiology, and how they can and should be used in combination with experimental tests for compound decision making.

Myokit: A simple interface to cardiac cellular electrophysiology

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

A model model: a commentary on DiFrancesco and Noble (1985) 'A model of cardiac electrical activity incorporating ionic pumps and concentration changes'

This paper summarizes the advances made by the DiFrancesco and Noble (DFN) model of cardiac cellular electrophysiology, which was published in Philosophical Transactions B in 1985. This model was developed at a time when the introduction of new techniques and provision of experimental data had resulted in an explosion of knowledge about the cellular and biophysical properties of the heart. It advanced the cardiac modelling field from a period when computer models considered only the voltage-dependent channels in the surface membrane. In particular, it included a consideration of changes of both intra- and extracellular ionic concentrations. In this paper, we summarize the most important contributions of the DiFrancesco and Noble paper. We also describe how computer modelling has developed subsequently with the extension from the single cell to the whole heart as well as its use in understanding disease and predicting the effects of pharmaceutical interventions. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

EFFECTS OF ACUTE GLOBAL ISCHEMIA ON RE-ENTRANT ARRHYTHMOGENESIS: A SIMULATION STUDY

Sudden cardiac death is mainly caused by arrhythmogenesis. For a functional abnormal heart, such as an ischemic heart, the probability of arrhythmia occurring is greatly increased. During myocardial ischemia, re-entry is prone to degenerate into ventricular fibrillation (VF). Therefore it has important meaning to investigate the intricate mechanisms underlying VF under an ischemic condition in order to better facilitate therapeutic interventions. In this paper, to analyze the functional influence of acute global ischemia on cardiac electrical activity and subsequently on re-entrant arrhythmogenesis, we take into account three main pathophysiological consequences of ischemia: hyperkalaemia, acidosis, and anoxia, and develop a 3D human ventricular ischemic model that combines a detailed biophysical description of the excitation kinetics of human ventricular cells with an integrated geometry of human ventricular tissue which incorporates fiber direction anisotropy and the stimulation activation sequence. The results show that under acute global ischemia, the tissue excitability and the slope of ventricular cellular action potential duration restitution (APDR) are greatly decreased. As a result, the complexity of VF activation patterns is reduced. For the three components of ischemia, hyperkalaemia is the dominant contributor to the stability of re-entry under acute global ischemia. Increasing [K+]o acts to prolong the cell refractory period, reduce the tissue excitability and slow the conduction velocity. Our results also show that VF can be eliminated by decreasing cellular excitability, primarily by elevating the concentration value of extracellular K+.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

Cellular mechanism of cardiac alternans: an unresolved chicken or egg problem

T-wave alternans, a specific form of cardiac alternans, has been associated with the increased susceptibility to cardiac arrhythmias and sudden cardiac death (SCD). Plenty of evidence has related cardiac alternans at the tissue level to the instability of voltage kinetics or Ca(2+) handling dynamics at the cellular level. However, to date, none of the existing experiments could identify the exact cellular mechanism of cardiac alternans due to the bi-directional coupling between voltage kinetics and Ca(2+) handling dynamics. Either of these systems could be the origin of alternans and the other follows as a secondary change, therefore making the cellular mechanism of alternans a difficult chicken or egg problem. In this context, theoretical analysis combined with experimental techniques provides a possibility to explore this problem. In this review, we will summarize the experimental and theoretical advances in understanding the cellular mechanism of alternans. We focus on the roles of action potential duration (APD) restitution and Ca(2+) handling dynamics in the genesis of alternans and show how the theoretical analysis combined with experimental techniques has provided us a new insight into the cellular mechanism of alternans. We also discuss the possible reasons of increased propensity for alternans in heart failure (HF) and the new possible therapeutic targets. Finally, according to the level of electrophysiological recording techniques and theoretical strategies, we list some critical experimental or theoretical challenges which may help to determine the origin of alternans and to find more effective therapeutic targets in the future.

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.

Evolution and pharmacological modulation of the arrhythmogenic wave dynamics in canine pulmonary vein model

Aims

Atrial fibrillation (AF), the commonest cardiac arrhythmia, has been strongly linked with arrhythmogenic sources near the pulmonary veins (PVs), but underlying mechanisms are not fully understood. We aim to study the generation and sustenance of wave sources in a model of the PV tissue.

Methods and results

A previously developed biophysically detailed three-dimensional canine atrial model is applied. Effects of AF-induced electrical remodelling are introduced based on published experimental data, as changes of ion channel currents (I_CaL, I_K1, I_to, and I_Kur), the action potential (AP) and cell-to-cell coupling levels. Pharmacological effects are introduced by blocking specific ion channel currents. A combination of electrical heterogeneity (AP tissue gradients of 5–12 ms) and anisotropy (conduction velocities of 0.75–1.25 and 0.21–0.31 m/s along and transverse to atrial fibres) can results in the generation of wave breaks in the PV region. However, a long wavelength (171 mm) prevents the wave breaks from developing into re-entry. Electrical remodelling leads to decreases in the AP duration, conduction velocity and wavelength (to 49 mm), such that re-entry becomes sustained. Pharmacological effects on the tissue heterogeneity and vulnerability (to wave breaks and re-entry) are quantified to show that drugs that increase the wavelength and stop re-entry (I_K1 and I_Kur blockers) can also increase the heterogeneity (AP gradients of 26–27 ms) and the likelihood of wave breaks.

Conclusion

Biophysical modelling reveals large conduction block areas near the PVs, which are due to discontinuous fibre arrangement enhanced by electrical heterogeneity. Vulnerability to re-entry in such areas can be modulated by pharmacological interventions.

Computational modeling of inhibition of voltage-gated Ca channels: identification of different effects on uterine and cardiac action potentials

The uterus and heart share the important physiological feature whereby contractile activation of the muscle tissue is regulated by the generation of periodic, spontaneous electrical action potentials (APs). Preterm birth arising from premature uterine contractions is a major complication of pregnancy and there remains a need to pursue avenues of research that facilitate the use of drugs, tocolytics, to limit these inappropriate contractions without deleterious actions on cardiac electrical excitation. A novel approach is to make use of mathematical models of uterine and cardiac APs, which incorporate many ionic currents contributing to the AP forms, and test the cell-specific responses to interventions. We have used three such models-of uterine smooth muscle cells (USMC), cardiac sinoatrial node cells (SAN), and ventricular cells-to investigate the relative effects of reducing two important voltage-gated Ca currents-the L-type (ICaL) and T-type (ICaT) Ca currents. Reduction of ICaL (10%) alone, or ICaT (40%) alone, blunted USMC APs with little effect on ventricular APs and only mild effects on SAN activity. Larger reductions in either current further attenuated the USMC APs but with also greater effects on SAN APs. Encouragingly, a combination of ICaL and ICaT reduction did blunt USMC APs as intended with little detriment to APs of either cardiac cell type. Subsequent overlapping maps of ICaL and ICaT inhibition profiles from each model revealed a range of combined reductions of ICaL and ICaT over which an appreciable diminution of USMC APs could be achieved with no deleterious action on cardiac SAN or ventricular APs. This novel approach illustrates the potential for computational biology to inform us of possible uterine and cardiac cell-specific mechanisms. Incorporating such computational approaches in future studies directed at designing new, or repurposing existing, tocolytics will be beneficial for establishing a desired uterine specificity of action.

Electrophysiological and structural determinants of electrotonic modulation of repolarization by the activation sequence

Spatial dispersion of repolarization is known to play an important role in arrhythmogenesis. Electrotonic modulation of repolarization by the activation sequence has been observed in some species and tissue preparations, but to varying extents. Our study sought to determine the mechanisms underlying species- and tissue-dependent electrotonic modulation of repolarization in ventricles. Epi-fluorescence optical imaging of whole rat hearts and pig left ventricular wedges were used to assess epicardial spatial activation and repolarization characteristics. Experiments were supported by computer simulations using realistic geometries. Tight coupling between activation times (AT) and action potential duration (APD) were observed in rat experiments but not in pig. Linear correlation analysis found slopes of −1.03 ± 0.59 and −0.26 ± 0.13 for rat and pig, respectively (p < 0.0001). In rat, maximal dispersion of APD was 11.0 ± 3.1 ms but dispersion of repolarization time (RT) was relatively homogeneous (8.2 ± 2.7, p < 0.0001). However, in pig no such difference was observed between the dispersion of APD and RT (17.8 ± 6.1 vs. 17.7 ± 6.5, respectively). Localized elevations of APD (12.9 ± 8.3%) were identified at ventricular insertion sites of rat hearts both in experiments and simulations. Tissue geometry and action potential (AP) morphology contributed significantly to determining influence of electrotonic modulation. Simulations of a rat AP in a pig geometry decreased the slope of AT and APD relationships by 70.6% whereas slopes were increased by 75.0% when implementing a pig AP in a rat geometry. A modified pig AP, shortened to match the rat APD, showed little coupling between AT and APD with greatly reduced slope compared to the rat AP. Electrotonic modulation of repolarization by the activation sequence is especially pronounced in small hearts with murine-like APs. Tissue architecture and AP morphology play an important role in electrotonic modulation of repolarization.

hERG inhibitors with similar potency but different binding kinetics do not pose the same proarrhythmic risk: implications for drug safety assessment

INTRODUCTION

Since the discovery of the link that exists between drug-induced hERG inhibition and Torsade de Pointes (TdP), extreme attention has been given to avoid new drugs inhibiting this channel. hERG inhibition is routinely screened for in new drugs and, typically, IC50 values are compared to projected plasma concentrations to define a safety margin.

METHODS AND RESULTS

We aimed to show that drugs with similar hERG potency are not uniformly pro-arrhythmic-this depends on the drug binding kinetics and mode of action (trapped or not) rather than the IC50 value only. We used a mathematical model of hERG and its related encoded current IKr to simulate drug binding in different configurations. Expression systems mimicking the screening process were first investigated. hERG model was then incorporated into a canine action potential (AP) and tissue model to study the impact of drug binding configurations on AP and pseudo-ECG (QT interval prolongation). Our data show that: (1) trapped and not trapped configurations and different binding kinetics could be identified during hERG screening; (2) slow binding, not trapped drugs, induced less AP prolongation and minimal QT interval prolongation (4.7%) at a concentration equal to the IC50 whereas maximal pro-arrhythmic risk was observed for trapped drugs at the same concentration (QT interval prolongation, 23.1%).

CONCLUSION

Our study demonstrates the need for screening for hERG binding configurations rather than potency alone. It also demonstrates the potential link between hERG, drug mode of action and TdP, and the need to question the current regulatory guidance.

A framework for myoarchitecture analysis of high resolution cardiac MRI and comparison with diffusion tensor MRI

The ventricular myocardium has a structure of branching laminae through which course regularly orientated myofibers, an architecture important in excitation and contraction. Quantifying this architecture is vital for understanding normal and disease states in the heart and for assessing their impact on electrical function. These data are also highly important in the construction of scientifically and clinically useful computer models of cardiac electrical behavior. Detailed structural information has previously been obtained from serial imaging. In this work we assess the potential for high-resolution (HR) MRI as a means to furnish useful myoarchitecture and compare and contrast this approach with the growing use of DT. Using rat hearts, we conclude that both approaches have strengths and weaknesses, however, HR-MRI may provide a consistently more robust picture of the myoarchitecture in small hearts.

Pro-arrhythmogenic effects of atrial fibrillation-induced electrical remodelling: insights from the three-dimensional virtual human atria

Chronic atrial fibrillation (AF) is associated with structural and electrical remodelling in the atria, which are associated with a high recurrence of AF. Through biophysically detailed computer modelling, this study investigated mechanisms by which AF-induced electrical remodelling promotes and perpetuates AF. A family of Courtemanche–Ramirez–Nattel variant models of human atrial cell action potentials (APs), taking into account of intrinsic atrial electrophysiological properties, was modified to incorporate various experimental data sets on AF-induced changes of major ionic channel currents (I_CaL, I_Kur, I_to, I_K1, I_Ks, I_NaCa) and on intracellular Ca²⁺ handling. The single cell models for control and AF-remodelled conditions were incorporated into multicellular three-dimensional (3D) atrial tissue models. Effects of the AF-induced electrical remodelling were quantified as the changes of AP profile, AP duration (APD) and its dispersion across the atria, and the vulnerability of atrial tissue to the initiation of re-entry. The dynamic behaviour of re-entrant excitation waves in the 3D models was characterised. In our simulations, AF-induced electrical remodelling abbreviated atrial APD non-uniformly across the atria; this resulted in relatively short APDs co-existing with marked regional differences in the APD at junctions of the crista terminalis/pectinate muscle, pulmonary veins/left atrium. As a result, the measured tissue vulnerability to re-entry initiation at these tissue junctions was increased. The AF-induced electrical remodelling also stabilized and accelerated re-entrant excitation waves, leading to rapid and sustained re-entry. Under the AF-remodelled condition, re-entrant scroll waves in the 3D model degenerated into persistent and erratic wavelets, leading to fibrillation. In conclusion, realistic 3D atrial tissue models indicate that AF-induced electrical remodelling produces regionally heterogeneous and shortened APD; these respectively facilitate initiation and maintenance of re-entrant excitation waves.

Combining wet and dry research: experience with model development for cardiac mechano-electric structure-function studies

Since the development of the first mathematical cardiac cell model 50 years ago, computational modelling has become an increasingly powerful tool for the analysis of data and for the integration of information related to complex cardiac behaviour. Current models build on decades of iteration between experiment and theory, representing a collective understanding of cardiac function. All models, whether computational, experimental, or conceptual, are simplified representations of reality and, like tools in a toolbox, suitable for specific applications. Their range of applicability can be explored (and expanded) by iterative combination of 'wet' and 'dry' investigation, where experimental or clinical data are used to first build and then validate computational models (allowing integration of previous findings, quantitative assessment of conceptual models, and projection across relevant spatial and temporal scales), while computational simulations are utilized for plausibility assessment, hypotheses-generation, and prediction (thereby defining further experimental research targets). When implemented effectively, this combined wet/dry research approach can support the development of a more complete and cohesive understanding of integrated biological function. This review illustrates the utility of such an approach, based on recent examples of multi-scale studies of cardiac structure and mechano-electric function.

High-throughput screening of drug-binding dynamics to HERG improves early drug safety assessment

The use of computational models to predict drug-induced changes in the action potential (AP) is a promising approach to reduce drug safety attrition but requires a better representation of more complex drug-target interactions to improve the quantitative prediction. The blockade of the human ether-a-go-go-related gene (HERG) channel is a major concern for QT prolongation and Torsade de Pointes risk. We aim to develop quantitative in-silico AP predictions based on a new electrophysiological protocol (suitable for high-throughput HERG screening) and mathematical modeling of ionic currents. Electrophysiological recordings using the IonWorks device were made from HERG channels stably expressed in Chinese hamster ovary cells. A new protocol that delineates inhibition over time was applied to assess dofetilide, cisapride, and almokalant effects. Dynamic effects displayed distinct profiles for these drugs compared with concentration-effects curves. Binding kinetics to specific states were identified using a new HERG Markov model. The model was then modified to represent the canine rapid delayed rectifier K+ current at 37°C and carry out AP predictions. Predictions were compared with a simpler model based on conductance reduction and were found to be much closer to experimental data. Improved sensitivity to concentration and pacing frequency variables was obtained when including binding kinetics. Our new electrophysiological protocol is suitable for high-throughput screening and is able to distinguish drug-binding kinetics. The association of this protocol with our modeling approach indicates that quantitative predictions of AP modulation can be obtained, which is a significant improvement compared with traditional conductance reduction methods.

Application of micro-computed tomography with iodine staining to cardiac imaging, segmentation, and computational model development

Micro-computed tomography (micro-CT) has been widely used to generate high-resolution 3-D tissue images from small animals nondestructively, especially for mineralized skeletal tissues. However, its application to the analysis of soft cardiovascular tissues has been limited by poor inter-tissue contrast. Recent ex vivo studies have shown that contrast between muscular and connective tissue in micro-CT images can be enhanced by staining with iodine. In the present study, we apply this novel technique for imaging of cardiovascular structures in canine hearts. We optimize the method to obtain high-resolution X-ray micro-CT images of the canine atria and its distinctive regions-including the Bachmann's bundle, atrioventricular node, pulmonary arteries and veins-with clear inter-tissue contrast. The imaging results are used to reconstruct and segment the detailed 3-D geometry of the atria. Structure tensor analysis shows that the arrangement of atrial fibers can also be characterized using the enhanced micro-CT images, as iodine preferentially accumulates within the muscular fibers rather than in connective tissues. This novel technique can be particularly useful in nondestructive imaging of 3-D cardiac architectures from large animals and humans, due to the combination of relatively high speed ( ~ 1 h/per scan of the large canine heart) and high voxel resolution (36 μm) provided. In summary, contrast micro-CT facilitates fast and nondestructive imaging and segmenting of detailed 3-D cardiovascular geometries, as well as measuring fiber orientation, which are crucial in constructing biophysically detailed computational cardiac models.

Application of cardiac electrophysiology simulations to pro-arrhythmic safety testing

Concerns over cardiac side effects are the largest single cause of compound attrition during pharmaceutical drug development. For a number of years, biophysically detailed mathematical models of cardiac electrical activity have been used to explore how a compound, interfering with specific ion-channel function, may explain effects at the cell-, tissue- and organ-scales. With the advent of high-throughput screening of multiple ion channels in the wet-lab, and improvements in computational modelling of their effects on cardiac cell activity, more reliable prediction of pro-arrhythmic risk is becoming possible at the earliest stages of drug development. In this paper, we review the current use of biophysically detailed mathematical models of cardiac myocyte electrical activity in drug safety testing, and suggest future directions to employ the full potential of this approach.

Slowed propagation across the compacta-trabeculata interface: a consequence of fiber and sheet anisotropy

Transmural myocardial activation is influenced by myocardial structure, including structural differences between the compacta (Cta) and the trabeculata (Tta), although this has not been fully explained. Hearts from rats were Langendorff perfused, stained with DI-4-ANEPPS, the apex was cut off and fluorescence acquired from the exposed short-axis surface. The hearts were stimulated at 160 ms cycle length at the anterior, lateral, posterior left ventricle (LV) and septal sub-epicardial sites. Conduction velocity perpendicular to the wave front orientation was measured in each pixel using a gradient-based approach. After optical mapping the cut surface was imaged using a light microscope and the extent of the Cta and Tta mapped and validated against 50 u, m isotropic MRI images. We used a 3D rat ventricle computational model, with architecture obtained from 200 u, m isotropic diffusion tensor MRI and kinetics from the modified Pandit model to determine the relative roles of fibers and sheets on propagation. We show in the experimental study that circumferential propagation around the LV cavity is fast in the Cta: 63.2±19.5 and is slower in the Tta: 32.7±11.0(∗) (mean ± s.d cms-1, ∗ p < 0.01 by two sample t test). In the simulation study the pattern and velocity are not replicated in an isotropic model (I), are partially replicated in a simulation study including fiber anisotropy (A) and is more fully replicated in orthotropic (O) ventricles (fiber and sheet anisotropy), where the circumferential propagation velocity is, I: Cta: 54.2±3.9; Tta:54.3±3.9; A: Cta:43.6±3.2; Tta: 40.6±6.6; O: Cta: 63.2±19.5; Tta: 32.7±11.9(∗). We show that sheet orientation is important in understanding activation differences between Cta and Tta.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

Early modelling of cardiac cells (1960-1980) was based on extensions of the Hodgkin-Huxley nerve axon equations with additional channels incorporated, but after 1980 it became clear that processes other than ion channel gating were also critical in generating electrical activity. This article reviews the development of models representing almost all cell types in the heart, many different species, and the software tools that have been created to facilitate the cardiac Physiome Project.

An in silico canine cardiac midmyocardial action potential duration model as a tool for early drug safety assessment

Cell lines expressing ion channels (IC) and the advent of plate-based electrophysiology device have enabled a molecular understanding of the action potential (AP) as a means of early QT assessment. We sought to develop an in silico AP (isAP) model that provides an assessment of the effect of a compound on the myocyte AP duration (APD) using concentration-effect curve data from a panel of five ICs (hNav1.5, hCav1.2, hKv4.3/hKChIP2.2, hKv7.1/hminK, hKv11.1). A test set of 53 compounds was selected to cover a range of selective and mixed IC modulators that were tested for their effects on optically measured APD. A threshold of >10% change in APD at 90% repolarization (APD90) was used to signify an effect at the top test concentration. To capture the variations observed in left ventricular midmyocardial myocyte APD data from 19 different dogs, the isAP model was calibrated to produce an ensemble of 19 model variants that could capture the shape and form of the APs and also quantitatively replicate dofetilide- and diltiazem-induced APD90 changes. Provided with IC panel data only, the isAP model was then used, blinded, to predict APD90 changes greater than 10%. At a simulated concentration of 30 μM and based on a criterion that six of the variants had to agree, isAP prediction was scored as showing greater than 80% predictivity of compound activity. Thus, early in drug discovery, the isAP model allows integrating separate IC data and is amenable to the throughput required for use as a virtual screen.

Altered spatial calcium regulation enhances electrical heterogeneity in the failing canine left ventricle: implications for electrical instability

Myocytes across the left ventricular (LV) wall of the mammalian heart are known to exhibit heterogeneity of electrophysiological properties; however, the transmural variation of cellular electrophysiology and Ca2+ homeostasis in the failing LV is incompletely understood. We studied action potentials (APs), the L-type calcium (Ca2+) current ( ICa,L), and intracellular Ca2+ transients ([Ca2+]i) of subendocardial (Endo), midmyocardial (Mid), and subepicardial (Epi) tissue layers in the canine normal and tachycardia pacing-induced failing left ventricles. Heart failure (HF) was associated with significant prolongation of the AP duration in Mid myocytes. There were no differences in ICa,L density in normal Endo, Mid, and Epi myocytes, whereas in the failing heart, ICa,L density was downregulated by 45% and 26% (at +10 mV) in Endo and Mid myocytes, respectively. The rates of sarcoplasmic reticulum (SR) Ca2+ release and decay of the [Ca2+]i were slowed, and the amplitude of the [Ca2+]i was depressed in Endo and Epi myocytes isolated from failing, compared with normal, hearts. Experiments in sodium (Na+)-free solutions showed that Epi and Mid myocytes of the failing ventricle exhibit a greater reliance on the Na+-Ca2+ exchanger to remove cytosolic Ca2+ than myocytes isolated from normal hearts. Simulation studies in Endo, Mid, and Epi canine myocytes demonstrate the importance of L-type current density and SR Ca2+ uptake in modulating the potentially arrhythmogenic repolarization in HF. In conclusion, these results demonstrate that spatially heterogeneous decreases in ICa,L and defective cytosolic Ca2+ removal contribute to the altered [Ca2+]i and AP profiles across the canine failing LV. These distinct electrophysiological features in myocytes from a failing heart contribute to a characteristic electrogram arising from increased dispersion of refractoriness across the LV, which may result in significant arrhythmogenic sequellae.

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria--the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.

Development and application of human virtual excitable tissues and organs: from premature birth to sudden cardiac death

The electrical activity of cardiac and uterine tissues has been reconstructed by detailed computer models in the form of virtual tissues. Virtual tissues are biophysically and anatomically detailed, and represent quantitatively predictive models of the physiological and pathophysiological behaviours of tissue within an isolated organ. The cell excitation properties are quantitatively reproduced by equations that describe the kinetics of a few dozen proteins. These equations are derived from experimental measurements of membrane potentials, ionic currents, fluxes, and concentrations. Some of the measurements were taken from human cells and human ion channel proteins expressed in non-human cells, but they were mostly taken from cells of other animal species. Data on tissue geometry and architecture are obtained from the diffusion tensor magnetic resonance imaging of ex vivo or post mortem tissue, and are used to compute the spread of current in the tissue. Cardiac virtual tissues are well established and reproduce normal and pathological patterns of cardiac excitation within the atria or ventricles of the human heart. They have been applied to increase the understanding of normal cardiac electrophysiology, to evaluate the candidate mechanisms for re-entrant arrhythmias that lead to sudden cardiac death, and to predict the tissue level effects of mutant or pharmacologically-modified ion channels. The human full-term virtual uterus is still in development. This virtual tissue reproduces the in vitro behaviour of uterine tissue biopsies, and provides possible mechanisms for premature labour.

Quantitative prediction of the arrhythmogenic effects of de novo hERG mutations in computational models of human ventricular tissues

Mutations to hERG which result in changes to the rapid delayed rectifier current I(Kr) can cause long and short QT syndromes and are associated with an increased risk of cardiac arrhythmias. Experimental recordings of I(Kr) reveal the effects of mutations at the channel level, but how these changes translate to the cell and tissue levels remains unclear. We used computational models of human ventricular myocytes and tissues to predict and quantify the effects that de novo hERG mutations would have on cell and tissue electrophysiology. Mutations that decreased I(Kr) maximum conductance resulted in an increased cell and tissue action potential duration (APD) and a long QT interval on the electrocardiogram (ECG), whereas those that caused a positive shift in the inactivation curve resulted in a decreased APD and a short QT. Tissue vulnerability to re-entrant arrhythmias was correlated with transmural dispersion of repolarisation, and any change to this vulnerability could be inferred from the ECG QT interval or T wave peak-to-end time. Faster I(Kr) activation kinetics caused cell APD alternans to appear over a wider range of pacing rates and with a larger magnitude, and spatial heterogeneity in these cellular alternans resulted in discordant alternans at the tissue level. Thus, from channel kinetic data, we can predict the tissue-level electrophysiological effects of any hERG mutations and identify how the mutation would manifest clinically, as either a long or short QT syndrome with or without an increased risk of alternans and re-entrant arrhythmias.

Construction and validation of anisotropic and orthotropic ventricular geometries for quantitative predictive cardiac electrophysiology

Reaction-diffusion computational models of cardiac electrophysiology require both dynamic excitation models that reconstruct the action potentials of myocytes as well as datasets of cardiac geometry and architecture that provide the electrical diffusion tensor D, which determines how excitation spreads through the tissue. We illustrate an experimental pipeline we have developed in our laboratories for constructing and validating such datasets. The tensor D changes with location in the myocardium, and is determined by tissue architecture. Diffusion tensor magnetic resonance imaging (DT-MRI) provides three eigenvectors e(i) and eigenvalues λ(i) at each voxel throughout the tissue that can be used to reconstruct this architecture. The primary eigenvector e(1) is a histologically validated measure of myocyte orientation (responsible for anisotropic propagation). The secondary and tertiary eigenvectors (e(2) and e(3)) specify the directions of any orthotropic structure if λ(2) is significantly greater than λ(3)-this orthotropy has been identified with sheets or cleavage planes. For simulations, the components of D are scaled in the fibre and cross-fibre directions for anisotropic simulations (or fibre, sheet and sheet normal directions for orthotropic tissues) so that simulated conduction velocities match values from optical imaging or plunge electrode experiments. The simulated pattern of propagation of action potentials in the models is partially validated by optical recordings of spatio-temporal activity on the surfaces of hearts. We also describe several techniques that enhance components of the pipeline, or that allow the pipeline to be applied to different areas of research: Q ball imaging provides evidence for multi-modal orientation distributions within a fraction of voxels, infarcts can be identified by changes in the anisotropic structure-irregularity in myocyte orientation and a decrease in fractional anisotropy, clinical imaging provides human ventricular geometry and can identify ischaemic and infarcted regions, and simulations in human geometries examine the roles of anisotropic and orthotropic architecture in the initiation of arrhythmias.

Computational modelling of the initiation and development of spontaneous intracellular Ca2+ waves in ventricular myocytes

Intracellular Ca(2+) dynamics provides excitation-contraction coupling in cardiac myocytes. Under pathological conditions, spontaneous Ca(2+) release events can lead to intracellular Ca(2+) travelling waves, which can break, giving transitory or persistent intracellular re-entrant Ca(2+) scroll waves. Intracellular Ca(2+) waves can trigger cellular delayed after-depolarizations of membrane potential, which if they occur in a cluster of a few hundred neighbouring myocytes may lead to cardiac arrhythmia. Quantitative prediction of the initiation and propagation of intracellular Ca(2+) waves requires the dynamics of Ca(2+)-induced Ca(2+) release, and the intracellular spatial distribution of Ca(2+) release units (CRUs). The spatial distribution of ryanodine receptor clusters within a few sarcomeres was reconstructed directly from confocal imaging measurements. It was then embedded into a three-dimensional ventricular cell model, with a resting membrane potential and simple stochastic Ca(2+)-induced Ca(2+) release dynamics. Isotropic global Ca(2+) wave propagation can be produced within the anisotropic intracellular architecture, by isotropic local Ca(2+) diffusion, and the branching Z-disc structure providing inter Z-disc pathways for Ca(2+) propagation. The branching Z-disc provides a broader spatial distribution of ryanodine receptor clusters across Z-discs, which reduces the likelihood of wave initiation by spontaneous Ca(2+) releases. Intracellular Ca(2+) dynamics during catecholaminergic polymorphic ventricular tachycardia (CPVT) was simulated phenomenologically by increasing the Ca(2+) sensitivity factor of the CRU, which results in an increased rate of Ca(2+) release events. Flecainide has been shown to prevent arrhythmias in a murine model of CPVT and in patients. The modelled actions of flecainide on the time course of Ca(2+) release events prevented the initiation of Ca(2+) waves.

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

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

Optimal velocity and safety of discontinuous conduction through the heterogeneous Purkinje-ventricular junction

Slow and discontinuous wave conduction through nonuniform junctions in cardiac tissues is generally considered unsafe and proarrythmogenic. However, the relationships between tissue structure, wave conduction velocity, and safety at such junctions are unknown. We have developed a structurally and electrophysiologically detailed model of the canine Purkinje-ventricular junction (PVJ) and varied its heterogeneity parameters to determine such relationships. We show that neither very fast nor very slow conduction is safe, and there exists an optimal velocity that provides the maximum safety factor for conduction through the junction. The resultant conduction time delay across the PVJ is a natural consequence of the electrophysiological and morphological differences between the Purkinje fiber and ventricular tissue. The delay allows the PVJ to accumulate and pass sufficient charge to excite the adjacent ventricular tissue, but is not long enough for the source-to-load mismatch at the junction to be enhanced over time. The observed relationships between the conduction velocity and safety factor can provide new insights into optimal conditions for wave propagation through nonuniform junctions between various cardiac tissues.

Mechanisms of transition from normal to reentrant electrical activity in a model of rabbit atrial tissue: interaction of tissue heterogeneity and anisotropy

Experimental evidence suggests that regional differences in action potential (AP) morphology can provide a substrate for initiation and maintenance of reentrant arrhythmias in the right atrium (RA), but the relationships between the complex electrophysiological and anatomical organization of the RA and the genesis of reentry are unclear. In this study, a biophysically detailed three-dimensional computer model of the right atrial tissue was constructed to study the role of tissue heterogeneity and anisotropy in arrhythmogenesis. The model of Lindblad et al. for a rabbit atrial cell was modified to incorporate experimental data on regional differences in several ionic currents (primarily, I(Na), I(CaL), I(K1), I(to), and I(sus)) between the crista terminalis and pectinate muscle cells. The modified model was validated by its ability to reproduce the AP properties measured experimentally. The anatomical model of the rabbit RA (including tissue geometry and fiber orientation) was based on a recent histological reconstruction. Simulations with the resultant electrophysiologically and anatomically detailed three-dimensional model show that complex organization of the RA tissue causes breakdown of regular AP conduction patterns at high pacing rates (>11.75 Hz): as the AP in the crista terminalis cells is longer, and electrotonic coupling transverse to fibers of the crista terminalis is weak, high-frequency pacing at the border between the crista terminalis and pectinate muscles results in a unidirectional conduction block toward the crista terminalis and generation of reentry. Contributions of the tissue heterogeneity and anisotropy to reentry initiation mechanisms are quantified by measuring action potential duration (APD) gradients at the border between the crista terminalis and pectinate muscles: the APD gradients are high in areas where both heterogeneity and anisotropy are high, such that intrinsic APD differences are not diminished by electrotonic interactions. Thus, our detailed computer model reconstructs complex electrical activity in the RA, and provides new insights into the mechanisms of transition from focal atrial tachycardia into reentry.

Regional differences in rabbit atrial action potential properties: mechanisms, consequences and pharmacological implications

Regional differences in electrical action potential (AP) properties can provide a substrate for atrial arrhythmias. We quantify such differences by developing detailed AP models for the left (LA) and right (RA) rabbit atrial cells in order to study the underlying electrophysiological mechanisms, as well as their impacts on vulnerable properties of the atrial tissue. The transient outward current, Ito, is identified as the major factor contributing to the AP differences between the LA and RA cells, which suggests a potential pharmacological target for reducing heterogeneity and vulnerability of the atria.

Experiment-specific models of ventricular electrical activation: construction and application

Experimental intramural recordings of electrical activity at high resolution have been made in the in-vivo pig LV free wall. To analyze features of these recordings experiment-specific 3D computer models of tissue structures and electrical behavior around the recording sites were constructed. The construction of the models used novel tissue image registration, correction and feature extraction methods. Appropriate model conductivity parameters were deduced from measurements and used to replicate features of experimental recordings.

d,l-Sotalol at therapeutic concentrations facilitates the occurrence of long-lasting non-stationary reentry during ventricular fibrillation in isolated rabbit hearts

BACKGROUND

The effects of d,l-sotalol at therapeutic concentrations (

METHODS AND RESULTS

By using an optical mapping system, epicardial activation patterns of VF were studied in 6 Langendorff-perfused rabbit hearts at baseline, during 10 mg/L d,l-sotalol infusion, and after washout. In an additional 4 hearts, action potential duration (APD), conduction velocity, and wavelength (WL) restitutions were determined. During d,l-sotalol infusion, VF was terminated in 3 of the 6 hearts. Only 1 heart developed transient ventricular tachycardia (VT). d,l-Sotalol reduced the number of phase singularities (ie, wavebreak) during VF (P<0.05), and it also increased the occurrence frequency (P<0.05) and lifespan (P<0.05) of epicardial reentry during VF. These reentries were non-stationary in nature and did not anchor on anatomical structures. Restitution data showed that d,l-sotalol flattened APD restitution. Furthermore, APD dispersion and spatial heterogeneity of restitutions were not enhanced by d,l-sotalol.

CONCLUSIONS

d,l-Sotalol at therapeutic concentrations decreased wavebreak and facilitated the occurrence of long-lasting, non-stationary reentry during VF. However, VT rarely occurred. The related mechanisms include: (1) flattening of APD restitution without enhancement of spatial heterogeneity of electrophysiological properties, causing wavefront organization, and (2) WL prolongation, preventing steady anchoring of reentry.

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Key Words

• d,l-sotalol
• reentry
• ventricular fibrillation

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MESH Headings

• Action Potentials/drug effects
• Action Potentials/physiology
• Animals
• Anti-Arrhythmia Agents/pharmacology
• Disease Models, Animal
• Dose-Response Relationship, Drug
• Electrocardiography
• Electrophysiologic Techniques, Cardiac
• Heart Conduction System/drug effects
• Heart Conduction System/physiopathology
• Heart Ventricles/drug effects
• Heart Ventricles/physiopathology
• Rabbits
• Sotalol/pharmacology
• Tachycardia, Ventricular/physiopathology
• Ventricular Fibrillation/physiopathology

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Grants

• P01 HL078931 NHLBI NIH HHS
• P01 HL078931-03 NHLBI NIH HHS

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Affiliation(s)

Yu-Cheng Hsieh Cardiovascular Center, Taichung Veterans General Hospital and Department of Internal Medicine, Faculty of Medicine, Institute of Clinical Medicine, Cardiovascular Research Center, National Yang-Ming University School of Medicine, Taipei, Taiwan
Tzyy-Leng Horng Department of Applied Mathematics, Feng-Chia University, Taichung, Taiwan
Shien-Fong Lin Krannert Institute of Cardiology and the Division of Cardiology, Department of Medicine, Indiana University School of Medicine, Indianapolis, IN
Tung-Chao Lin Cardiovascular Center, Taichung Veterans General Hospital and Department of Internal Medicine, Faculty of Medicine, Institute of Clinical Medicine, Cardiovascular Research Center, National Yang-Ming University School of Medicine, Taipei, Taiwan
Chih-Tai Ting Cardiovascular Center, Taichung Veterans General Hospital and Department of Internal Medicine, Faculty of Medicine, Institute of Clinical Medicine, Cardiovascular Research Center, National Yang-Ming University School of Medicine, Taipei, Taiwan
Tsu-Juey Wu Cardiovascular Center, Taichung Veterans General Hospital and Department of Internal Medicine, Faculty of Medicine, Institute of Clinical Medicine, Cardiovascular Research Center, National Yang-Ming University School of Medicine, Taipei, Taiwan

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