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BACKGROUND: In Brugada syndrome (BrS), phase 2 re-excitation/re-entry (P2R) induced by the transient outward potassium current (Ito) is a proposed arrhythmia mechanism; yet, the most common genetic defects are loss-of-function sodium channel mutations. OBJECTIVES: The authors used computer simulations to investigate how sodium channel dysfunction affects P2R-mediated arrhythmogenesis in the presence and absence of Ito. METHODS: Computer simulations were carried out in 1-dimensional cables and 2-dimensional tissue using guinea pig and human ventricular action potential models. RESULTS: In the presence of Ito sufficient to generate robust P2R, reducing sodium current (INa) peak amplitude alone only slightly potentiated P2R. When INa inactivation kinetics were also altered to simulate reported effects of BrS mutations and sodium channel blockers, however, P2R occurred even in the absence of Ito. These effects could be potentiated by delaying L-type calcium channel activation or increasing ATP-sensitive potassium current, consistent with experimental and clinical findings. INa-mediated P2R also accounted for sex-related, day and night-related, and fever-related differences in arrhythmia risk in BrS patients. CONCLUSIONS: Altered INa kinetics synergize powerfully with reduced INa amplitude to promote P2R-induced arrhythmias in BrS in the absence of Ito, establishing a robust mechanistic link between altered INa kinetics and the P2R-mediated arrhythmia mechanism.

After heart injury, dead heart muscle is replaced by scar tissue. Fibroblasts can electrically couple with myocytes, and changes in fibroblast membrane potential can lead to myocyte excitability, which suggests that fibroblast-myocyte coupling in scar tissue may be responsible for arrhythmogenesis. However, the physiologic relevance of electrical coupling of myocytes and fibroblasts and its impact on cardiac excitability in vivo have never been demonstrated. We genetically engineered a mouse that expresses the optogenetic cationic channel ChR2 (H134R) exclusively in cardiac fibroblasts. After myocardial infarction, optical stimulation of scar tissue elicited organ-wide cardiac excitation and induced arrhythmias in these animals. Complementing computational modeling with experimental approaches, we showed that gap junctional and ephaptic coupling, in a synergistic yet functionally redundant manner, excited myocytes coupled to fibroblasts.

It has been demonstrated experimentally that slow and fast conduction waves with distinct conduction velocities can occur in the same nerve system depending on the strength or the form of the stimulus, which give rise to two modes of nerve functions. However, the mechanisms remain to be elucidated. In this study, we use computer simulations of the cable equation with modified Hodgkin-Huxley kinetics and analytical solutions of a simplified model to show that stimulus-dependent slow and fast waves recapitulating the experimental observations can occur in the cable, which are the two stable conduction states of a bistable conduction behavior. The bistable conduction is caused by a positive feedback loop of the wavefront upstroke speed, mediated by the sodium channel inactivation properties. Although the occurrence of bistable conduction only requires the presence of the sodium current, adding a calcium current to the model further promotes bistable conduction by potentiating the slow wave. We also show that the bistable conduction is robust, occurring for sodium and calcium activation thresholds well within the experimentally determined ones of the known sodium and calcium channel families. Since bistable conduction can occur in the cable equation of Hodgkin-Huxley kinetics with a single inward current, i.e., the sodium current, it can be a generic mechanism applicable to stimulus-dependent fast and slow conduction not only in the nerve systems but also in other electrically excitable systems, such as cardiac muscles.

Initiation of reentry requires 2 factors: (1) a triggering event, most commonly focal excitations such as premature ventricular complexes (PVCs); and (2) a vulnerable substrate with regional dispersion of refractoriness and/or excitability, such as occurs during the T wave of the electrocardiogram when some areas of the ventricle have repolarized and recovered excitability but others have not. When the R wave of a PVC coincides in time with the T wave of the previous beat, this timing can lead to unidirectional block and initiation of reentry, known as the R-on-T phenomenon. Classically, the PVC triggering reentry has been viewed as arising focally from 1 region and propagating into another region whose recovery is delayed, resulting in unidirectional conduction block and reentry initiation. However, more recent evidence indicates that PVCs also can arise from the T wave itself. In the latter case, the PVC initiating reentry is not a separate event from the T wave but rather is causally generated from the repolarization gradient that manifests as the T wave. We call the former an R-to-T mechanism and the latter an R-from-T mechanism, which are initiation mechanisms distinct from each other. Both are important components of the R-on-T phenomenon and need to be taken into account when designing antiarrhythmic strategies. Strategies targeting suppression of triggers alone or vulnerable substrate alone may be appropriate in some instances but not in others. Preventing R-from-T arrhythmias requires suppressing the underlying dynamic tissue instabilities responsible for producing both triggers and substrate vulnerability simultaneously. The same principles are likely to apply to supraventricular arrhythmias.

Hypertrophic cardiomyopathy (HCM) is the most common heritable cardiovascular disease and often results in cardiac remodeling and an increased incidence of sudden cardiac arrest (SCA) and death, especially in youth and young adults. Among thousands of different variants found in HCM patients, variants of TNNT2 (cardiac troponin T-TNNT2) are linked to increased risk of ventricular arrhythmogenesis and sudden death despite causing little to no cardiac hypertrophy. Therefore, studying the effect of TNNT2 variants on cardiac propensity for arrhythmogenesis can pave the way for characterizing HCM in susceptible patients before sudden cardiac arrest occurs. In this study, a TNNT2 variant, I79N, was generated in human cardiac recombinant/reconstituted thin filaments (hcRTF) to investigate the effect of the mutation on myofilament Ca2+ sensitivity and Ca2+ dissociation rate using steady-state and stopped-flow fluorescence techniques. The results revealed that the I79N variant significantly increases myofilament Ca2+ sensitivity and decreases the Ca2+ off-rate constant (k off). To investigate further, a heterozygous I79N+/- TNNT2 variant was introduced into human-induced pluripotent stem cells using CRISPR/Cas9 and subsequently differentiated into ventricular cardiomyocytes (hiPSC-CMs). To study the arrhythmogenic properties, monolayers of I79N+/- hiPSC-CMs were studied in comparison to their isogenic controls. Arrhythmogenesis was investigated by measuring voltage (V m) and cytosolic Ca2+ transients over a range of stimulation frequencies. An increasing stimulation frequency was applied to the cells, from 55 to 75 bpm. The results of this protocol showed that the TnT-I79N cells had reduced intracellular Ca2+ transients due to the enhanced cytosolic Ca2+ buffering. These changes in Ca2+ handling resulted in beat-to-beat instability and triangulation of the cardiac action potential, which are predictors of arrhythmia risk. While wild-type (WT) hiPSC-CMs were accurately entrained to frequencies of at least 150 bpm, the I79N hiPSC-CMs demonstrated clear patterns of alternans for both V m and Ca2+ transients at frequencies >75 bpm. Lastly, a transcriptomic analysis was conducted on WT vs. I79N+/- TNNT2 hiPSC-CMs using a custom NanoString codeset. The results showed a significant upregulation of NPPA (atrial natriuretic peptide), NPPB (brain natriuretic peptide), Notch signaling pathway components, and other extracellular matrix (ECM) remodeling components in I79N+/- vs. the isogenic control. This significant shift demonstrates that this missense in the TNNT2 transcript likely causes a biophysical trigger, which initiates this significant alteration in the transcriptome. This TnT-I79N hiPSC-CM model not only reproduces key cellular features of HCM-linked mutations but also suggests that this variant causes uncharted pro-arrhythmic changes to the human action potential and gene expression.

QT prolongation, due to lengthening of the action potential duration in the ventricles, is a major risk factor of lethal ventricular arrhythmias. A widely known consequence of QT prolongation is the genesis of early afterdepolarizations (EADs), which are associated with arrhythmias through the generation of premature ventricular complexes (PVCs). However, the vast majority of the EADs observed experimentally in isolated ventricular myocytes are phase-2 EADs, and whether phase-2 EADs are mechanistically linked to PVCs in cardiac tissue remains an unanswered question. In this study, we investigate the genesis of PVCs using computer simulations with eight different ventricular action potential models of various species. Based on our results, we classify PVCs as arising from two distinct mechanisms: repolarization gradient (RG)-induced PVCs and phase-2 EAD-induced PVCs. The RG-induced PVCs are promoted by increasing RG and L-type calcium current and are insensitive to gap junction coupling. EADs are not required for this PVC mechanism. In a paced beat, a single or multiple PVCs can occur depending on the properties of the RG. In contrast, phase-2 EAD-induced PVCs occur only when the RG is small and are suppressed by increasing RG and more sensitive to gap junction coupling. Unlike with RG-induced PVCs, in each paced beat, only a single EAD-induced PVC can occur no matter how many EADs in an action potential. In the wide parameter ranges we explore, RG-induced PVCs can be observed in all models, but the EAD-induced PVCs can only be observed in five of the eight models. The links between these two distinct PVC mechanisms and arrhythmogenesis in animal experiments and clinical settings are discussed.

BackgroundSmall-conductance Ca2+-activated potassium (SK) channels play complex roles in cardiac arrhythmogenesis. SK channels colocalize with L-type Ca2+ channels, yet how this colocalization affects cardiac arrhythmogenesis is unknown.ObjectiveThe purpose of this study was to investigate the role of colocalization of SK channels with L-type Ca2+ channels in promoting J-wave syndrome and ventricular arrhythmias.MethodsWe carried out computer simulations of single-cell and tissue models. SK channels in the model were assigned to preferentially sense Ca2+ in the bulk cytosol, subsarcolemmal space, or junctional cleft.ResultsWhen SK channels sense Ca2+ in the bulk cytosol, the SK current (ISK) rises and decays slowly during an action potential, the action potential duration (APD) decreases as the maximum conductance increases, no complex APD dynamics and phase 2 reentry can be induced by ISK. When SK channels sense Ca2+ in the subsarcolemmal space or junctional cleft, ISK can rise and decay rapidly during an action potential in a spike-like pattern because of spiky Ca2+ transients in these compartments, which can cause spike-and-dome action potential morphology, APD alternans, J-wave elevation, and phase 2 reentry. Our results can account for the experimental finding that activation of ISK induced J-wave syndrome and phase 2 reentry in rabbit hearts.ConclusionColocalization of SK channels with L-type Ca2+ channels so that they preferentially sense Ca2+ in the subsarcolemmal or junctional space may result in a spiky ISK, which can functionally play a similar role of the transient outward K+ current in promoting J-wave syndrome and ventricular arrhythmias.

Spatially discordant alternans (SDA) of action potential duration (APD) has been widely observed in cardiac tissue and is linked to cardiac arrhythmogenesis. Theoretical studies have shown that conduction velocity restitution (CVR) is required for the formation of SDA. However, this theory is not completely supported by experiments, indicating that other mechanisms may exist. In this study, we carried out computer simulations using mathematical models of action potentials to investigate the mechanisms of SDA in cardiac tissue. We show that when CVR is present and engaged, such as fast pacing from one side of the tissue, the spatial pattern of APD in the tissue undergoes either spatially concordant alternans or SDA, independent of initial conditions or tissue heterogeneities. When CVR is not engaged, such as simultaneous pacing of the whole tissue or under normal/slow heart rates, the spatial pattern of APD in the tissue can have multiple solutions, including spatially concordant alternans and different SDA patterns, depending on heterogeneous initial conditions or pre-existing repolarization heterogeneities. In homogeneous tissue, curved nodal lines are not stable, which either evolve into straight lines or disappear. However, in heterogeneous itssue, curved nodal lines can be stable, depending on their initial locations and shapes relative to the structure of the heterogeneity. Therefore, CVR-induced SDA and non-CVR-induced SDA exhibit different dynamical properties, which may be responsible for the different SDA properties observed in experimental studies and arrhythmogenesis in different clinical settings.

This white paper presents principles for validating proarrhythmia risk prediction models for regulatory use as discussed at the In Silico Breakout Session of a Cardiac Safety Research Consortium/Health and Environmental Sciences Institute/US Food and Drug Administration-sponsored Think Tank Meeting on May 22, 2018. The meeting was convened to evaluate the progress in the development of a new cardiac safety paradigm, the Comprehensive in Vitro Proarrhythmia Assay (CiPA). The opinions regarding these principles reflect the collective views of those who participated in the discussion of this topic both at and after the breakout session. Although primarily discussed in the context of in silico models, these principles describe the interface between experimental input and model-based interpretation and are intended to be general enough to be applied to other types of nonclinical models for proarrhythmia assessment. This document was developed with the intention of providing a foundation for more consistency and harmonization in developing and validating different models for proarrhythmia risk prediction using the example of the CiPA paradigm.

Intracellular calcium (Ca2+) cycling dynamics in cardiac myocytes are spatiotemporally generated by stochastic events arising from a spatially distributed network of coupled Ca2+ release units that interact with an intertwined mitochondrial network. In this study, we developed a spatiotemporal ventricular myocyte model that integrates mitochondria-related Ca2+ cycling components into our previously developed ventricular myocyte model consisting of a three-dimensional Ca2+ release unit network. Mathematical formulations of mitochondrial membrane potential, mitochondrial Ca2+ cycling, mitochondrial permeability transition pore stochastic opening and closing, intracellular reactive oxygen species signaling, and oxidized Ca2+/calmodulin-dependent protein kinase II signaling were incorporated into the model. We then used the model to simulate the effects of mitochondrial depolarization on mitochondrial Ca2+ cycling, Ca2+ spark frequency, and Ca2+ amplitude, which agree well with experimental data. We also simulated the effects of the strength of mitochondrial Ca2+ uniporters and their spatial localization on intracellular Ca2+ cycling properties, which substantially affected diastolic and systolic Ca2+ levels in the mitochondria but exhibited only a small effect on sarcoplasmic reticulum and cytosolic Ca2+ levels under normal conditions. We show that mitochondrial depolarization can cause Ca2+ waves and Ca2+ alternans, which agrees with previous experimental observations. We propose that this new, to our knowledge, spatiotemporal ventricular myocyte model, incorporating properties of mitochondrial Ca2+ cycling and reactive-oxygen-species-dependent signaling, will be useful for investigating the effects of mitochondria on intracellular Ca2+ cycling and action potential dynamics in ventricular myocytes.

BackgroundThe apamin-sensitive small-conductance calcium-activated K (SK) current IKAS modulates automaticity of the sinus node. IKAS blockade by apamin causes sinus bradycardia.ObjectiveThe purpose of this study was to test the hypothesis that IKAS modulates ventricular automaticity.MethodsWe tested the effects of apamin (100 nM) on ventricular escape rhythms in Langendorff-perfused rabbit ventricles with atrioventricular block (protocol 1) and on recorded transmembrane action potential of pseudotendons of superfused right ventricular endocardial preparations (protocol 2).ResultsAll preparations exhibited spontaneous ventricular escape rhythms. In protocol 1, apamin decreased the atrial rate from 186.2 ± 18.0 bpm to 163.8 ± 18.7 bpm (N = 6; P = .006) but accelerated the ventricular escape rate from 51.5 ± 10.7 bpm to 98.2 ± 25.4 bpm (P = .031). Three preparations exhibited bursts of nonsustained ventricular tachycardia and pauses, resulting in repeated burst termination pattern. In protocol 2, apamin increased the ventricular escape rate from 70.2 ± 13.1 bpm to 110.1 ± 2.2 bpm (P = .035). Spontaneous phase 4 depolarization was recorded from the pseudotendons in 6 of 10 preparations at baseline and in 3 in the presence of apamin. There were no changes of phase 4 slope (18.37 ± 3.55 mV/s vs 18.93 ± 3.26 mV/s, N = 3; P = .231, ), but the threshold of phase 0 activation (mV) reduced from -67.97 ± 1.53 to -75.26 ± 0.28 (P = .034). Addition of JTV-519, a ryanodine receptor 2 stabilizer, in 5 preparations reduced escape rate back to baseline.ConclusionContrary to its bradycardic effect in the sinus node, IKAS blockade by apamin accelerates ventricular automaticity and causes repeated nonsustained ventricular tachycardia in normal ventricles. ryanodine receptor 2 blockade reversed the apamin effects on ventricular automaticity.

Early afterdepolarizations (EADs) are spontaneous depolarizations during the repolarization phase of an action potential in cardiac myocytes. It is widely known that EADs are promoted by increasing inward currents and/or decreasing outward currents, a condition called reduced repolarization reserve. Recent studies based on bifurcation theories show that EADs are caused by a dual Hopf-homoclinic bifurcation, bringing in further mechanistic insights into the genesis and dynamics of EADs. In this study, we investigated the EAD properties, such as the EAD amplitude, the inter-EAD interval, and the latency of the first EAD, and their major determinants. We first made predictions based on the bifurcation theory and then validated them in physiologically more detailed action potential models. These properties were investigated by varying one parameter at a time or using parameter sets randomly drawn from assigned intervals. The theoretical and simulation results were compared with experimental data from the literature. Our major findings are that the EAD amplitude and takeoff potential exhibit a negative linear correlation; the inter-EAD interval is insensitive to the maximum ionic current conductance but mainly determined by the kinetics of ICa,L and the dual Hopf-homoclinic bifurcation; and both inter-EAD interval and latency vary largely from model to model. Most of the model results generally agree with experimental observations in isolated ventricular myocytes. However, a major discrepancy between modeling results and experimental observations is that the inter-EAD intervals observed in experiments are mainly between 200 and 500 ms, irrespective of species, while those of the mathematical models exhibit a much wider range with some models exhibiting inter-EAD intervals less than 100 ms. Our simulations show that the cause of this discrepancy is likely due to the difference in ICa,L recovery properties in different mathematical models, which needs to be addressed in future action potential model development.

The mechanisms of J wave syndrome (JWS) are incompletely understood. Here, we showed that the concomitant activation of small-conductance calcium-activated potassium (SK) current (IKAS) and inhibition of sodium current by cyclohexyl-[2-(3,5-dimethyl-pyrazol-1-yl)-6-methyl-pyrimidin-4-yl]-amine (CyPPA) recapitulate the phenotypes of JWS in Langendorff-perfused rabbit hearts. CyPPA induced significant J wave elevation and frequent spontaneous ventricular fibrillation (SVF), as well as sinus bradycardia, atrioventricular block, and intraventricular conduction delay. IKAS activation by CyPPA resulted in heterogeneous shortening of action potential (AP) duration (APD) and repolarization alternans. CyPPA inhibited cardiac sodium current (INa) and decelerated AP upstroke and intracellular calcium transient. SVFs were typically triggered by short-coupled premature ventricular contractions, initiated with phase 2 reentry and originated more frequently from the right than the left ventricles. Subsequent IKAS blockade by apamin reduced J wave elevation and eliminated SVF. β-Adrenergic stimulation was antiarrhythmic in CyPPA-induced electrical storm. Like CyPPA, hypothermia (32.0°C) also induced J wave elevation and SVF. It facilitated negative calcium-voltage coupling and phase 2 repolarization alternans with spatial and electromechanical discordance, which were ameliorated by apamin. These findings suggest that IKAS activation contributes to the development of JWS in rabbit ventricles.

RATIONALE:The major role of a transverse-tubular (TT) network in a cardiac cell is to facilitate effective excitation-contraction coupling and signaling. The TT network structures are heterogeneous within a single cell, and vary between different types of cells and species. They are also remodeled in cardiac diseases. However, how different TT network structures predispose cardiac cells to arrhythmogenesis remains to be revealed. OBJECTIVE:To systematically investigate the roles of TT network structure and the underlying mechanisms in the genesis of intracellular calcium (Ca2+) alternans and triggered activity (TA). METHODS AND RESULTS:Based on recent experimental observations, different TT network structures, including uniformly and non-uniformly random TT distributions, were modeled in a cardiac cell model consisting of a three-dimensional network of Ca2+ release units (CRUs). Our simulations showed that both Ca2+ alternans and Ca2+ wave-mediated TA were promoted when the fraction of orphaned CRUs was in an intermediate range, but suppressed in cells exhibiting either well-organized TT networks or low TT densities. Ca2+ alternans and TA could be promoted by low TT densities when the cells were small or the CRU coupling was strong. Both alternans and TA occurred more easily in uniformly random TT networks than in non-uniformly random TT networks. Subcellular spatially discordant Ca2+ alternans was promoted by non-uniformly random TT networks but suppressed by increasing CRU coupling strength. These mechanistic insights provide a holistic understanding of the effects of TT network structure on the susceptibility to arrhythmogenesis. CONCLUSIONS:The TT network plays important roles in promoting Ca2+ alternans and TA, and different TT network structures may predispose cardiac cells differently to arrhythmogenesis.

Spontaneous calcium (Ca) waves in cardiac myocytes underlie delayed afterdepolarizations (DADs) that trigger cardiac arrhythmias. How these subcellular/cellular events overcome source-sink factors in cardiac tissue to generate DADs of sufficient amplitude to trigger action potentials is not fully understood. Here, we evaluate quantitatively how factors at the subcellular scale (number of Ca wave initiation sites), cellular scale (sarcoplasmic reticulum (SR) Ca load), and tissue scale (synchrony of Ca release in populations of myocytes) determine DAD features in cardiac tissue using a combined experimental and computational modeling approach. Isolated patch-clamped rabbit ventricular myocytes loaded with Fluo-4 to image intracellular Ca were rapidly paced during exposure to elevated extracellular Ca (2.7 mmol/L) and isoproterenol (0.25 μmol/L) to induce diastolic Ca waves and subthreshold DADs. As the number of paced beats increased from 1 to 5, SR Ca content (assessed with caffeine pulses) increased, the number of Ca wave initiation sites increased, integrated Ca transients and DADs became larger and shorter in duration, and the latency period to the onset of Ca waves shortened with reduced variance. In silico analysis using a computer model of ventricular tissue incorporating these experimental measurements revealed that whereas all of these factors promoted larger DADs with higher probability of generating triggered activity, the latency period variance and SR Ca load had the greatest influences. Therefore, incorporating quantitative experimental data into tissue level simulations reveals that increased intracellular Ca promotes DAD-mediated triggered activity in tissue predominantly by increasing both the synchrony (decreasing latency variance) of Ca waves in nearby myocytes and SR Ca load, whereas the number of Ca wave initiation sites per myocyte is less important.

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K+ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K+ channel in health and disease, as well as K+ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K+ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

Excitable systems display memory, but how memory affects the excitation dynamics of such systems remains to be elucidated. Here we use computer simulation of cardiac action potential models to demonstrate that memory can cause dynamical instabilities that result in complex excitation dynamics and chaos. We develop an iterated map model that correctly describes these dynamics and show that memory converts a monotonic first return map of action potential duration into a nonmonotonic one, resulting in a period-doubling bifurcation route to chaos.

Cardiac myocytes normally initiate action potentials in response to a current stimulus that depolarizes the membrane above an excitation threshold. Aberrant excitation can also occur due to spontaneous calcium (Ca2+) release (SCR) from intracellular stores after the end of a preceding action potential. SCR drives the Na+/Ca2+ exchange current inducing a "delayed afterdepolarization" that can in turn trigger an action potential if the excitation threshold is reached. This "triggered activity" is known to cause arrhythmias, but how it is initiated and terminated is not understood. Using computer simulations of a ventricular myocyte model, we show that initiation and termination are inherently random events. We determine the probability of those events from statistical measurements of the number of beats before initiation and before termination, respectively, which follow geometric distributions. Moreover, we elucidate the origin of randomness by a statistical analysis of SCR events, which do not follow a Poisson process observed in other eukaryotic cells. Due to synchronization of Ca2+ releases during the action potential upstroke, waiting times of SCR events after the upstroke are narrowly distributed, whereas SCR amplitudes follow a broad normal distribution with a width determined by fluctuations in the number of independent Ca2+ wave foci. This distribution enables us to compute the probabilities of initiation and termination of bursts of triggered activity that are maintained by a positive feedback between the action potential upstroke and SCR. Our results establish a theoretical framework for interpreting complex and varied manifestations of triggered activity relevant to cardiac arrhythmias.

Ventricular myocytes are excitable cells whose voltage threshold for action potential (AP) excitation is ∼-60 mV at which INa is activated to give rise to a fast upstroke. Therefore, for a short stimulus pulse to elicit an AP, a stronger stimulus is needed if the resting potential lies further away from the INa threshold, such as in hypokalemia. However, for an AP elicited by a long duration stimulus or a diastolic spontaneous calcium release, we observed that the stimulus needed was lower in hypokalemia than in normokalemia in both computer simulations and experiments of rabbit ventricular myocytes. This observation provides insight into why hypokalemia promotes calcium-mediated triggered activity, despite the resting potential lying further away from the INa threshold. To understand the underlying mechanisms, we performed bifurcation analyses and demonstrated that there is a dynamical threshold, resulting from a saddle-node bifurcation mainly determined by IK1 and INCX. This threshold is close to the voltage at which IK1 is maximum, and lower than the INa threshold. After exceeding this dynamical threshold, the membrane voltage will automatically depolarize above the INa threshold due to the large negative slope of the IK1-V curve. This dynamical threshold becomes much lower in hypokalemia, especially with respect to calcium, as predicted by our theory. Because of the saddle-node bifurcation, the system can automatically depolarize even in the absence of INa to voltages higher than the ICa,L threshold, allowing for triggered APs in single myocytes with complete INa block. However, because INa is important for AP propagation in tissue, blocking INa can still suppress premature ventricular excitations in cardiac tissue caused by calcium-mediated triggered activity. This suppression is more effective in normokalemia than in hypokalemia due to the difference in dynamical thresholds.

Intracellular calcium (Ca2+) alternans is a dynamical phenomenon in ventricular myocytes, which is linked to the genesis of lethal arrhythmias. Iterated map models of intracellular Ca2+ cycling dynamics in ventricular myocytes under periodic pacing have been developed to study the mechanisms of Ca2+ alternans. Two mechanisms of Ca2+ alternans have been demonstrated in these models: one relies mainly on fractional sarcoplasmic reticulum Ca2+ release and uptake, and the other on refractoriness and other properties of Ca2+ sparks. Each of the two mechanisms can partially explain the experimental observations, but both have their inconsistencies with the experimental results. Here we developed an iterated map model that is composed of two coupled iterated maps, which unifies the two mechanisms into a single cohesive mathematical framework. The unified theory can consistently explain the seemingly contradictory experimental observations and shows that the two mechanisms work synergistically to promote Ca2+ alternans. Predictions of the theory were examined in a physiologically-detailed spatial Ca2+ cycling model of ventricular myocytes.

Although considerable progress has been made in developing ablation approaches to cure atrial fibrillation (AF), outcomes are still suboptimal, especially for persistent and long-lasting persistent AF. In this topical review, we review the arrhythmia mechanisms, both reentrant and nonreentrant, that are potentially relevant to human AF at various stages/settings. We describe arrhythmia mapping techniques used to distinguish between the different mechanisms, with a particular focus on the detection of rotors. We discuss which arrhythmia mechanisms are likely to respond to ablation, and the challenges and prospects for improving upon current ablation strategies to achieve better outcomes.

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart's susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism.

Calcium (Ca) sparks are elementary events of biological Ca signaling. A normal Ca spark has a brief duration in the range of 10 to 100 ms, but long-lasting sparks with durations of several hundred milliseconds to seconds are also widely observed. Experiments have shown that the transition from normal to long-lasting sparks can occur when ryanodine receptor (RyR) open probability is either increased or decreased. Here, we demonstrate theoretically and computationally that long-lasting sparks emerge as a collective dynamical behavior of the network of diffusively coupled Ca release units (CRUs). We show that normal sparks occur when the CRU network is monostable and excitable, while long-lasting sparks occur when the network dynamics possesses multiple metastable attractors, each attractor corresponding to a different spatial firing pattern of sparks. We further highlight the mechanisms and conditions that produce long-lasting sparks, demonstrating the existence of an optimal range of RyR open probability favoring long-lasting sparks. We find that when CRU firings are sparse and sarcoplasmic reticulum (SR) Ca load is high, increasing RyR open probability promotes long-lasting sparks by potentiating Ca-induced Ca release (CICR). In contrast, when CICR is already strong enough to produce frequent firings, decreasing RyR open probability counter-intuitively promotes long-lasting sparks by decreasing spark frequency. The decrease in spark frequency promotes intra-SR Ca diffusion from neighboring non-firing CRUs to the firing CRUs, which helps to maintain the local SR Ca concentration of the firing CRUs above a critical level to sustain firing. In this setting, decreasing RyR open probability further suppresses long-lasting sparks by weakening CICR. Since a long-lasting spark terminates via the Kramers' escape process over a potential barrier, its duration exhibits an exponential distribution determined by the barrier height and noise strength, which is modulated differently by different ways of altering the Ca release flux strength.

BackgroundDelayed afterdepolarizations (DADs) have been well characterized as arrhythmia triggers, but their role in generating a tissue substrate vulnerable to reentry is not well understood.ObjectiveThe purpose of this study was to test the hypothesis that random DADs can self-organize to generate both an arrhythmia trigger and a vulnerable substrate simultaneously in cardiac tissue as a result of gap junction coupling.MethodsComputer simulations in 1-dimensional cable and 2-dimensional tissue models were performed. The cellular DAD amplitude was varied by changing the strength of sarcoplasmic reticulum calcium release. Random DAD latency and amplitude in different cells were simulated using gaussian distributions.ResultsDepending on the strength of spontaneous sarcoplasmic reticulum calcium release and other conditions, random DADs in cardiac tissue resulted in the following behaviors: (1) triggered activity (TA); (2) a vulnerable tissue substrate causing unidirectional conduction block and reentry by inactivating sodium channels; (3) both triggers and a vulnerable substrate simultaneously by generating TA in regions next to regions with subthreshold DADs susceptible to unidirectional conduction block and reentry. The probability of the latter 2 behaviors was enhanced by reduced sodium channel availability, reduced gap junction coupling, increased tissue heterogeneity, and less synchronous DAD latency.ConclusionDADs can self-organize in tissue to generate arrhythmia triggers, a vulnerable tissue substrate, and both simultaneously. Reduced sodium channel availability and gap junction coupling potentiate this mechanism of arrhythmias, which are relevant to a variety of heart disease conditions.

BackgroundHypokalemia is known to promote ventricular arrhythmias, especially in combination with class III antiarrhythmic drugs like dofetilide. Here, we evaluated the underlying molecular mechanisms.Methods and resultsArrhythmias were recorded in isolated rabbit and rat hearts or patch-clamped ventricular myocytes exposed to hypokalemia (1.0-3.5 mmol/L) in the absence or presence of dofetilide (1 μmol/L). Spontaneous early afterdepolarizations (EADs) and ventricular tachycardia/fibrillation occurred in 50% of hearts at 2.7 mmol/L [K] in the absence of dofetilide and 3.3 mmol/L [K] in its presence. Pretreatment with the Ca-calmodulin kinase II (CaMKII) inhibitor KN-93, but not its inactive analogue KN-92, abolished EADs and hypokalemia-induced ventricular tachycardia/fibrillation, as did the selective late Na current (INa) blocker GS-967. In intact hearts, moderate hypokalemia (2.7 mmol/L) significantly increased tissue CaMKII activity. Computer modeling revealed that EAD generation by hypokalemia (with or without dofetilide) required Na-K pump inhibition to induce intracellular Na and Ca overload with consequent CaMKII activation enhancing late INa and the L-type Ca current. K current suppression by hypokalemia and dofetilide alone in the absence of CaMKII activation were ineffective at causing EADs.ConclusionsWe conclude that Na-K pump inhibition by even moderate hypokalemia plays a critical role in promoting EAD-mediated arrhythmias by inducing a positive feedback cycle activating CaMKII and enhancing late INa. Class III antiarrhythmic drugs like dofetilide sensitize the heart to this positive feedback loop.

BackgroundTransient outward K currents (Ito) have been reported both to suppress and to facilitate early afterdepolarizations (EADs) when repolarization reserve is reduced. Here, we used the dynamic clamp technique to analyze how Ito accounts for these paradoxical effects on EADs by influencing the dynamic evolution of repolarization reserve during the action potential.Methods and resultsIsolated patch-clamped rabbit ventricular myocytes were exposed to either oxidative stress (H2O2) or hypokalemia to induce bradycardia-dependent EADs at a long pacing cycle length of 6 s, when native rabbit Ito is substantial. EADs disappeared when the pacing cycle length was shortened to 1 s, when Ito becomes negligible because of incomplete recovery from inactivation. During 6-s pacing cycle length, EADs were blocked by the Ito blocker 4-aminopyridine, but reappeared when a virtual current with appropriate Ito-like properties was reintroduced using the dynamic clamp (n=141 trials). During 1-s pacing cycle length in the absence of 4-aminopyridine, adding a virtual Ito-like current (n=1113 trials) caused EADs to reappear over a wide range of Ito conductance (0.005-0.15 nS/pF), particularly when inactivation kinetics were slow (τinact≥20 ms) and the pedestal (noninactivating component) was small (

Early afterdepolarizations (EADs) associated with prolongation of the cardiac action potential (AP) can create heterogeneity of repolarization and premature extrasystoles, triggering focal and reentrant arrhythmias. Because the L-type Ca(2+) current (ICa,L) plays a key role in both AP prolongation and EAD formation, L-type Ca(2+) channels (LTCCs) represent a promising therapeutic target to normalize AP duration (APD) and suppress EADs and their arrhythmogenic consequences. We used the dynamic-clamp technique to systematically explore how the biophysical properties of LTCCs could be modified to normalize APD and suppress EADs without impairing excitation-contraction coupling. Isolated rabbit ventricular myocytes were first exposed to H2O2 or moderate hypokalemia to induce EADs, after which their endogenous ICa,L was replaced by a virtual ICa,L with tunable parameters, in dynamic-clamp mode. We probed the sensitivity of EADs to changes in the (a) amplitude of the noninactivating pedestal current; (b) slope of voltage-dependent activation; (c) slope of voltage-dependent inactivation; (d) time constant of voltage-dependent activation; and (e) time constant of voltage-dependent inactivation. We found that reducing the amplitude of the noninactivating pedestal component of ICa,L effectively suppressed both H2O2- and hypokalemia-induced EADs and restored APD. These results, together with our previous work, demonstrate the potential of this hybrid experimental-computational approach to guide drug discovery or gene therapy strategies by identifying and targeting selective properties of LTCC.

Despite key advances in the clinical management of life-threatening ventricular arrhythmias, culminating with the development of implantable cardioverter-defibrillators and catheter ablation techniques, pharmacologic/biologic therapeutics have lagged behind. The fundamental issue is that biological targets are molecular factors. Diseases, however, represent emergent properties at the scale of the organism that result from dynamic interactions between multiple constantly changing molecular factors. For a pharmacologic/biologic therapy to be effective, it must target the dynamic processes that underlie the disease. Here we propose a classification of ventricular arrhythmias that is based on our current understanding of the dynamics occurring at the subcellular, cellular, tissue and organism scales, which cause arrhythmias by simultaneously generating arrhythmia triggers and exacerbating tissue vulnerability. The goal is to create a framework that systematically links these key dynamic factors together with fixed factors (structural and electrophysiological heterogeneity) synergistically promoting electrical dispersion and increased arrhythmia risk to molecular factors that can serve as biological targets. We classify ventricular arrhythmias into three primary dynamic categories related generally to unstable Ca cycling, reduced repolarization, and excess repolarization, respectively. The clinical syndromes, arrhythmia mechanisms, dynamic factors and what is known about their molecular counterparts are discussed. Based on this framework, we propose a computational-experimental strategy for exploring the links between molecular factors, fixed factors and dynamic factors that underlie life-threatening ventricular arrhythmias. The ultimate objective is to facilitate drug development by creating an in silico platform to evaluate and predict comprehensively how molecular interventions affect not only a single targeted arrhythmia, but all primary arrhythmia dynamics categories as well as normal cardiac excitation-contraction coupling.

Early afterdepolarizations (EADs) and delayed afterdepolarizations (DADs) are voltage oscillations known to cause cardiac arrhythmias. EADs are mainly driven by voltage oscillations in the repolarizing phase of the action potential (AP), while DADs are driven by spontaneous calcium (Ca) release during diastole. Because voltage and Ca are bidirectionally coupled, they modulate each other's behaviors, and new AP and Ca cycling dynamics can emerge from this coupling. In this study, we performed computer simulations using an AP model with detailed spatiotemporal Ca cycling incorporating stochastic openings of Ca channels and ryanodine receptors to investigate the effects of Ca-voltage coupling on EAD and DAD dynamics. Simulations were complemented by experiments in mouse ventricular myocytes. We show that: 1) alteration of the Ca transient due to increased ryanodine receptor leakiness and/or sarco/endoplasmic reticulum Ca ATPase activity can either promote or suppress EADs due to the complex effects of Ca on ionic current properties; 2) spontaneous Ca waves also exhibit complex effects on EADs, but cannot induce EADs of significant amplitude without the participation of ICa,L; 3) lengthening AP duration and the occurrence of EADs promote DADs by increasing intracellular Ca loading, and two mechanisms of DADs are identified, i.e., Ca-wave-dependent and Ca-wave-independent; and 4) Ca-voltage coupling promotes complex EAD patterns such as EAD alternans that are not observed for solely voltage-driven EADs. In conclusion, Ca-voltage coupling combined with the nonlinear dynamical behaviors of voltage and Ca cycling play a key role in generating complex EAD and DAD dynamics observed experimentally in cardiac myocytes, whose mechanisms are complex but analyzable.

In February 2014, a group of scientists convened as part of the University of California Davis Cardiovascular Symposium to bring together experimental and mathematical modelling perspectives and discuss points of consensus and controversy on the topic of sodium in the heart. This paper summarizes the topics of presentation and discussion from the symposium, with a focus on the role of aberrant sodium channels and abnormal sodium homeostasis in cardiac arrhythmias and pharmacotherapy from the subcellular scale to the whole heart. Two following papers focus on Na(+) channel structure, function and regulation, and Na(+)/Ca(2+) exchange and Na(+)/K(+) ATPase. The UC Davis Cardiovascular Symposium is a biannual event that aims to bring together leading experts in subfields of cardiovascular biomedicine to focus on topics of importance to the field. The focus on Na(+) in the 2014 symposium stemmed from the multitude of recent studies that point to the importance of maintaining Na(+) homeostasis in the heart, as disruption of homeostatic processes are increasingly identified in cardiac disease states. Understanding how disruption in cardiac Na(+)-based processes leads to derangement in multiple cardiac components at the level of the cell and to then connect these perturbations to emergent behaviour in the heart to cause disease is a critical area of research. The ubiquity of disruption of Na(+) channels and Na(+) homeostasis in cardiac disorders of excitability and mechanics emphasizes the importance of a fundamental understanding of the associated mechanisms and disease processes to ultimately reveal new targets for human therapy.

Phospholamban (PLB) inhibits the activity of cardiac sarcoplasmic reticulum (SR) Ca(2+)-ATPase (SERCA2a). Phosphorylation of PLB during sympathetic activation reverses SERCA2a inhibition, increasing SR Ca(2+) uptake. However, sympathetic activation also modulates multiple other intracellular targets in ventricular myocytes (VMs), making it impossible to determine the specific effects of the reversal of PLB inhibition on the spontaneous SR Ca(2+) release. Therefore, it remains unclear how PLB regulates rhythmic activity in VMs. Here, we used the Fab fragment of 2D12, a monoclonal anti-PLB antibody, to test how acute reversal of PLB inhibition affects the spontaneous SR Ca(2+) release in normal VMs. Ca(2+) sparks and spontaneous Ca(2+) waves (SCWs) were recorded in the line-scan mode of confocal microscopy using the Ca(2+) fluorescent dye Fluo-4 in isolated permeabilized mouse VMs. Fab, which reverses PLB inhibition, significantly increased the frequency, amplitude, and spatial/temporal spread of Ca(2+) sparks in VMs exposed to 50 nM free [Ca(2+)]. At physiological diastolic free [Ca(2+)] (100-200 nM), Fab facilitated the formation of whole-cell propagating SCWs. At higher free [Ca(2+)], Fab increased the frequency and velocity, but decreased the decay time of the SCWs. cAMP had little additional effect on the frequency or morphology of Ca(2+) sparks or SCWs after Fab addition. These findings were complemented by computer simulations. In conclusion, acute reversal of PLB inhibition alone significantly increased the spontaneous SR Ca(2+) release, leading to the facilitation and organization of whole-cell propagating SCWs in normal VMs. PLB thus plays a key role in subcellular Ca(2+) dynamics and rhythmic activity of VMs.

In heart failure (HF), T-tubule (TT) disruption contributes to dyssynchronous calcium (Ca) release and impaired contraction, but its role in arrhythmogenesis remains unclear. In this study, we investigate the effects of TT disruption and other HF remodeling factors on Ca alternans in ventricular myocytes using computer modeling. A ventricular myocyte model with detailed spatiotemporal Ca cycling modeled by a coupled Ca release unit (CRU) network was used, in which the L-type Ca channels and the ryanodine receptor (RyR) channels were simulated by random Markov transitions. TT disruption, which removes the L-type Ca channels from the associated CRUs, results in "orphaned" RyR clusters and thus provides increased opportunity for spark-induced Ca sparks to occur. This effect combined with other HF remodeling factors promoted alternans by two distinct mechanisms: 1) for normal sarco-endoplasmic reticulum Ca ATPase (SERCA) activity, alternans was caused by both CRU refractoriness and coupling. The increased opportunity for spark-induced sparks by TT disruption combined with the enhanced CRU coupling by Ca elevation in the presence or absence of increased RyR leakiness facilitated spark synchronization on alternate beats to promote Ca alternans; 2) for down-regulated SERCA, alternans was caused by the sarcoplasmic reticulum (SR) Ca load-dependent mechanism, independent of CRU refractoriness. TT disruption and increased RyR leakiness shifted and steepened the SR Ca release-load relationship, which combines with down-regulated SERCA to promote Ca alternans. In conclusion, the mechanisms of Ca alternans for normal and down-regulated SERCA are different, and TT disruption promotes Ca alternans by both mechanisms, which may contribute to alternans at different stages of HF.

BACKGROUND: Long QT syndrome type 1 (LQT1) is a congenital disease arising from a loss of function in the slowly activating delayed potassium current IKs, which causes early afterdepolarizations (EADs) and polymorphic ventricular tachycardia (pVT). OBJECTIVE: The purpose of this study was to investigate the mechanisms underlying pVT using a transgenic rabbit model of LQT1. METHODS: Hearts were perfused retrogradely, and action potentials were recorded using a voltage-sensitive dye and CMOS cameras. RESULTS: Bolus injection of isoproterenol (140 nM) induced pVT initiated by focal excitations from the right ventricle (RV; n = 16 of 18 pVTs). After the pVT was initiated, complex focal excitations occurred in both the RV and the left ventricle, which caused oscillations of the QRS complexes on ECG, consistent with the recent proposal of multiple shifting foci caused by EAD chaos. Moreover, the action potential upstroke in pVT showed a bimodal distribution, demonstrating the coexistence of 2 types of excitation that interacted to produce complex pVT: Na(+) current (INa)-mediated fast conduction and L-type Ca(2+) current (ICa)-mediated slow conduction coexist, manifesting as pVT. Addition of 2 μM tetrodotoxin to reduce INa converted pVT into monomorphic VT. Reducing late INa in computer simulation converted pVT into a single dominant reentry, agreeing with experimental results. CONCLUSION: Our study demonstrates that pVT in LQT1 rabbits is initiated by focal excitations from the RV and is maintained by multiple shifting foci in both ventricles. Moreover, wave conduction in pVT exhibits bi-excitability, that is, fast wavefronts driven by INa and slow wavefronts driven by ICa co-exist during pVT.

BackgroundRemodeling of cardiac repolarizing currents, such as the downregulation of slowly activating K+ channels (IKs), could underlie ventricular fibrillation (VF) in heart failure (HF). We evaluated the role of Iks remodeling in VF susceptibility using a tachypacing HF model of transgenic rabbits with Long QT Type 1 (LQT1) syndrome.Methods and resultsLQT1 and littermate control (LMC) rabbits underwent three weeks of tachypacing to induce cardiac myopathy (TICM). In vivo telemetry demonstrated steepening of the QT/RR slope in LQT1 with TICM (LQT1-TICM; pre: 0.26±0.04, post: 0.52±0.01, P

Ventricular arrhythmias have complex causes and mechanisms. Despite extensive investigation involving many clinical, experimental, and computational studies, effective biological therapeutics are still very limited. In this article, we review our current understanding of the mechanisms of ventricular arrhythmias by summarizing the state of knowledge spanning from the molecular scale to electrical wave behavior at the tissue and organ scales and how the complex nonlinear interactions integrate into the dynamics of arrhythmias in the heart. We discuss the challenges that we face in synthesizing these dynamics to develop safe and effective novel therapeutic approaches.

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

In the healthy heart, cardiac myocytes form an electrical syncytium embedded in a supportive fibroblast-rich extracellular matrix designed to optimize the electromechanical coupling for maximal contractile efficiency of the heart. In the injured heart, however, fibroblasts are activated and differentiate into myofibroblasts that proliferate and generate fibrosis as a component of the wound-healing response. This review discusses how fibroblasts and fibrosis, while essential for maintaining the structural integrity of the heart wall after injury, have undesirable electrophysiological effects by disrupting the normal electrical connectivity of cardiac tissue to increase the vulnerability to arrhythmias. We emphasize the dual contribution of fibrosis in altering source-sink relationships to create a vulnerable substrate while simultaneously facilitating the emergence of triggers such as afterdepolarization-induced premature ventricular complexes-both factors combining synergistically to promote initiation of reentry. We also discuss the potential role of fibroblasts and myofibroblasts in directly altering myocyte electrophysiology in a pro-arrhythmic fashion. Insight into these processes may open up novel therapeutic strategies for preventing and treating arrhythmias in the setting of heart disease as well as avoiding potential arrhythmogenic consequences of cell-based cardiac regeneration therapy. This article is part of a Special Issue entitled "Myocyte-Fibroblast Signaling in Myocardium."

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

Calcium (Ca(2+)) waves generating oscillatory Ca(2+) signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca(2+) waves is random in space and time, while under other conditions, waves occur repetitively from preferred locations (pacemaker sites) from which they entrain the whole cell. In this study, we use computer simulations to investigate the self-organization of Ca(2+) sparks into pacemaker sites generating Ca(2+) oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca(2+) release unit (CRU) network model, we show that Ca(2+) waves occur randomly in space and time when the Ca(2+) level is low, but as the Ca(2+) level increases, waves occur repetitively from the same sites. Our analysis indicates that this transition to entrainment can be attributed to the fact that random Ca(2+) sparks self-organize into Ca(2+) oscillations differently at low and high Ca(2+) levels. At low Ca(2+), the whole cell Ca(2+) oscillation frequency of the coupled CRU system is much slower than that of an isolated single CRU. Compared to a single CRU, the distribution of interspike intervals (ISIs) of the coupled CRU network exhibits a greater variation, and its ISI distribution is asymmetric with respect to the peak, exhibiting a fat tail. At high Ca(2+), however, the coupled CRU network has a faster frequency and lesser ISI variation compared to an individual CRU. The ISI distribution of the coupled network no longer exhibits a fat tail and is well-approximated by a Gaussian distribution. This same Ca(2+) oscillation behaviour can also be achieved by varying the number of ryanodine receptors per CRU or the distance between CRUs. Using these results, we develop a theory for the entrainment of random oscillators which provides a unified explanation for the experimental observations underlying the emergence of pacemaker sites and Ca(2+) oscillations.

Animal and clinical studies have demonstrated that oxidative stress, a common pathophysiological factor in cardiac disease, reduces repolarization reserve by enhancing the L-type calcium current, the late Na, and the Na-Ca exchanger, promoting early afterdepolarizations (EADs) that can initiate ventricular tachycardia and ventricular fibrillation (VT/VF) in structurally remodeled hearts. Increased ventricular fibrosis plays a key facilitatory role in allowing oxidative-stress induced EADs to manifest as triggered activity and VT/VF, since normal non-fibrotic hearts are resistant to arrhythmias when challenged with similar or higher levels of oxidative stress. The findings imply that antifibrotic therapy, in addition to therapies designed to suppress EAD formation at the cellular level, may be synergistic in reducing the risk of sudden cardiac death.

In normal cardiac myocytes, the action potential duration (APD) is several hundred milliseconds. However, experimental studies showed that under certain conditions, APD could be excessively long (or ultralong), up to several seconds. Unlike the normal APD, the ultralong APD increases sensitively with pacing cycle length even when the pacing rate is very slow, exhibiting a sensitive slow rate-dependence. In addition, these long action potentials may or may not exhibit early afterdepolarizations (EADs). Although these phenomena are well known, the underlying mechanisms and ionic determinants remain incompletely understood. In this study, computer simulations were performed with a simplified action potential model. Modifications to the L-type calcium current (I(Ca,L)) kinetics and the activation time constant of the delayed rectifier K current were used to investigate their effects on APD. We show that: 1) the ultralong APD and its sensitive slow rate-dependence are determined by the steady-state window and pedestal I(Ca,L) currents and the activation speed and the recovery of the delayed rectifier K current; 2) whether an ultralong action potential exhibits EADs or not depends on the kinetics of I(Ca,L); 3) increasing inward currents elevates the plateau voltage, which in general prolongs APD, however, this can also shorten APD when the APD is already ultralong under certain conditions; and 4) APD alternans occurs at slow pacing rates due to the sensitive slow rate-dependence and the ionic determinants are different from the ones causing APD alternans at fast heart rates.