Stem cell-derived cardiomyocyte heterogeneity confounds electrophysiological insights.

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) offer potential as an in vitro model for studying drug cardiotoxicity and patient-specific cardiovascular disease. The inherent electrophysiological heterogeneity of these cells limits the depth of insights that can be drawn from well-designed experiments. In this review, we provide our perspective on some sources and the consequences of iPSC-CM heterogeneity. We demonstrate the extent of heterogeneity in the literature and explain how such heterogeneity is exacerbated by patch-clamp experimental artifacts in the manual and automated set-up. Finally, we discuss how this heterogeneity, caused by both intrinsic and extrinsic factors, limits our ability to build digital twins of patient-derived cardiomyocytes.

Single-cell ionic current phenotyping elucidates non-canonical features and predictive potential of cardiomyocytes during automated drug experiments.

All new drugs must go through preclinical screening tests to determine their proarrhythmic potential. While these assays effectively filter out dangerous drugs, they are too conservative, often misclassifying safe compounds as proarrhythmic. In this study, we attempt to address this shortcoming with a novel, medium-throughput drug-screening approach: we use an automated patch-clamp system to acquire optimized voltage clamp (VC) and action potential (AP) data from human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) at several drug concentrations (baseline, 3×, 10× and 20× the effective free plasma concentrations). With our novel method, we show correlations between INa block and upstroke slowing after treatment with flecainide or quinine. Additionally, after quinine treatment, we identify significant reductions in current during voltage steps designed to isolate If and IKs. However, we do not detect any IKr block by either drug, and upon further investigation, do not see any IKr present in the iPSC-CMs when prepared for automated patch experiments (i.e. in suspension) - this is in contrast to similar experiments we have conducted with these cells using the manual patch setup. In this study, we: (1) present a proof-of-concept demonstration of a single-cell medium-throughput drug study, and (2) characterize the non-canonical electrophysiology of iPSC-CMs when prepared for experiments in a medium-throughput setting. KEY POINTS: Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) offer potential as an in vitro model to study the proarrhythmic potential of drugs, but insights from these cells are often limited by the low throughput of manual patch-clamp. In this study, we use a medium-throughput automated patch-clamp system to acquire action potential (AP) and complex voltage clamp (VC) data from single iPSC-CMs at multiple drug concentrations. A correlation between AP upstroke and INa transients was identified and drug-induced changes in ionic currents found. We also characterize the substantially altered physiology of iPSC-CMs when patched in an automated system, suggesting the need to investigate differences between manual and automated patch experiments.

Optimization of a cardiomyocyte model illuminates role of increased INa,L in repolarization reserve.

Cardiac ion currents may compensate for each other when one is compromised by a congenital or drug-induced defect. Such redundancy contributes to a robust repolarization reserve that can prevent the development of lethal arrhythmias. Most efforts made to describe this phenomenon have quantified contributions by individual ion currents. However, it is important to understand the interplay between all major ion-channel conductances, as repolarization reserve is dependent on the balance between all ion currents in a cardiomyocyte. Here, a genetic algorithm was designed to derive profiles of nine ion-channel conductances that optimize repolarization reserve in a mathematical cardiomyocyte model. Repolarization reserve was quantified using a previously defined metric, repolarization reserve current, i.e., the minimum constant current to prevent normal action potential repolarization in a cell. The optimization improved repolarization reserve current up to 84% compared to baseline in a human adult ventricular myocyte model and increased resistance to arrhythmogenic insult. The optimized conductance profiles were not only characterized by increased repolarizing current conductances but also uncovered a previously unreported behavior by the late sodium current. Simulations demonstrated that upregulated late sodium increased action potential duration, without compromising repolarization reserve current. The finding was generalized to multiple models. Ultimately, this computational approach, in which multiple currents were studied simultaneously, illuminated mechanistic insights into how the metric's magnitude could be increased and allowed for the unexpected role of late sodium to be elucidated.NEW & NOTEWORTHY Genetic algorithms are typically used to fit models or extract desired parameters from data. Here, we use the tool to produce a ventricular cardiomyocyte model with increased repolarization reserve. Since arrhythmia mitigation is dependent on multiple cardiac ion-channel conductances, study using a comprehensive, unbiased, and systems-level approach is important. The use of this optimization strategy allowed us to find robust profiles that illuminated unexpected mechanistic determinants of key ion-channel conductances in repolarization reserve.

Single-cell ionic current phenotyping explains stem cell-derived cardiomyocyte action potential morphology.

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) are a promising tool to study arrhythmia-related factors, but the variability of action potential (AP) recordings from these cells limits their use as an in vitro model. In this study, we use recently published brief (10 s), dynamic voltage-clamp (VC) data to provide mechanistic insights into the ionic currents contributing to AP heterogeneity; we call this approach rapid ionic current phenotyping (RICP). Features of this VC data were correlated to AP recordings from the same cells, and we used computational models to generate mechanistic insights into cellular heterogeneity. This analysis uncovered several interesting links between AP morphology and ionic current density: both L-type calcium and sodium currents contribute to upstroke velocity, rapid delayed rectifier K+ current is the main determinant of the maximal diastolic potential, and an outward current in the activation range of slow delayed rectifier K+ is the main determinant of AP duration. Our analysis also identified an outward current in several cells at 6 mV that is not reproduced by iPSC-CM mathematical models but contributes to determining AP duration. RICP can be used to explain how cell-to-cell variability in ionic currents gives rise to AP heterogeneity. Because of its brief duration (10 s) and ease of data interpretation, we recommend the use of RICP for single-cell patch-clamp experiments that include the acquisition of APs.NEW & NOTEWORTHY We present rapid ionic current phenotyping (RICP), a current quantification approach based on an optimized voltage-clamp protocol. The method captures a rich snapshot of the ionic current dynamics, providing quantitative information about multiple currents (e.g., ICa,L, IKr) in the same cell. The protocol helped to identify key ionic determinants of cellular action potential heterogeneity in iPSC-CMs. This included unexpected results, such as the critical role of IKr in establishing the maximum diastolic potential.

Diversity of cells and signals in the cardiovascular system.

This white paper is the outcome of the seventh UC Davis Cardiovascular Research Symposium on Systems Approach to Understanding Cardiovascular Disease and Arrhythmia. This biannual meeting aims to bring together leading experts in subfields of cardiovascular biomedicine to focus on topics of importance to the field. The theme of the 2022 Symposium was 'Cell Diversity in the Cardiovascular System, cell-autonomous and cell-cell signalling'. Experts in the field contributed their experimental and mathematical modelling perspectives and discussed emerging questions, controversies, and challenges in examining cell and signal diversity, co-ordination and interrelationships involved in cardiovascular function. This paper originates from the topics of formal presentations and informal discussions from the Symposium, which aimed to develop a holistic view of how the multiple cell types in the cardiovascular system integrate to influence cardiovascular function, disease progression and therapeutic strategies. The first section describes the major cell types (e.g. cardiomyocytes, vascular smooth muscle and endothelial cells, fibroblasts, neurons, immune cells, etc.) and the signals involved in cardiovascular function. The second section emphasizes the complexity at the subcellular, cellular and system levels in the context of cardiovascular development, ageing and disease. Finally, the third section surveys the technological innovations that allow the interrogation of this diversity and advancing our understanding of the integrated cardiovascular function and dysfunction.

Leak current, even with gigaohm seals, can cause misinterpretation of stem cell-derived cardiomyocyte action potential recordings.

AIMS: Human-induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have become an essential tool to study arrhythmia mechanisms. Much of the foundational work on these cells, as well as the computational models built from the resultant data, has overlooked the contribution of seal-leak current on the immature and heterogeneous phenotype that has come to define these cells. The aim of this study is to understand the effect of seal-leak current on recordings of action potential (AP) morphology. METHODS AND RESULTS: Action potentials were recorded in human iPSC-CMs using patch clamp and simulated using previously published mathematical models. Our in silico and in vitro studies demonstrate how seal-leak current depolarizes APs, substantially affecting their morphology, even with seal resistances (Rseal) above 1 GΩ. We show that compensation of this leak current is difficult due to challenges with obtaining accurate measures of Rseal during an experiment. Using simulation, we show that Rseal measures (i) change during an experiment, invalidating the use of pre-rupture values, and (ii) are polluted by the presence of transmembrane currents at every voltage. Finally, we posit that the background sodium current in baseline iPSC-CM models imitates the effects of seal-leak current and is increased to a level that masks the effects of seal-leak current on iPSC-CMs. CONCLUSION: Based on these findings, we make recommendations to improve iPSC-CM AP data acquisition, interpretation, and model-building. Taking these recommendations into account will improve our understanding of iPSC-CM physiology and the descriptive ability of models built from such data.

Validation of quantitative measure of repolarization reserve as a novel marker of drug induced proarrhythmia.

Repolarization reserve, the robustness of a cell to repolarize even when one of the repolarization mechanisms is failing, has been described qualitatively in terms of ionic currents, but has not been quantified by a generic metric that is applicable to drug screening. Prolonged repolarization leading to repolarization failure is highly arrhythmogenic. It may lead to ventricular tachycardia caused by triggered activity from early afterdepolarizations (EADs), or it may promote the occurrence of unidirectional conduction block and reentry. Both types of arrhythmia may deteriorate into ventricular fibrillation (VF) and death. We define the Repolarization Reserve Current (RRC) as the minimum constant current necessary to prevent normal repolarization of a cell. After developing and testing RRC for nine computational ionic models of various species, we applied it experimentally to atrial and ventricular human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM), and isolated guinea-pig ventricular cardiomyocytes. In simulations, repolarization was all-or-none with a precise, model-dependent critical RRC, resulting in a discrete shift in the Action Potential Duration (APD) - RRC relation, in the occurrence of EADs and repolarization failure. These data were faithfully reproduced in cellular experiments. RRC allows simple, fast, unambiguous quantification of the arrhythmogenic propensity in cardiac cells of various origins and species without the need of prior knowledge of underlying currents and is suitable for high throughput applications, and personalized medicine applications.

Light-Activated Dynamic Clamp Using iPSC-Derived Cardiomyocytes.

iPSC-derived cardiomyocytes (iPSC-CMs) are a potentially advantageous platform for drug screening because they provide a renewable source of human cardiomyocytes. One obstacle to their implementation is their immature electrophysiology, which reduces relevance to adult arrhythmogenesis. To address this, dynamic clamp is used to inject current representing the insufficient potassium current, IK1, thereby producing more adult-like electrophysiology. However, dynamic clamp requires patch clamp and is therefore low throughput and ill-suited for large-scale drug screening. Here, we use optogenetics to generate such a dynamic-clamp current. The optical dynamic clamp (ODC) uses outward-current-generating opsin, ArchT, to mimic IK1, resulting in more adult-like action potential morphology, similar to IK1 injection via classic dynamic clamp. Furthermore, in the presence of an IKr blocker, ODC revealed expected action potential prolongation and reduced spontaneous excitation. The ODC presented here still requires an electrode to measure Vm but provides a first step toward contactless dynamic clamp, which will not only enable high-throughput screening but may also allow control within multicellular iPSC-CM formats to better recapitulate adult in vivo physiology.

Differential roles of two delayed rectifier potassium currents in regulation of ventricular action potential duration and arrhythmia susceptibility.

KEY POINTS: Arrhythmias result from disruptions to cardiac electrical activity, although the factors that control cellular action potentials are incompletely understood. We combined mathematical modelling with experiments in heart cells from guinea pigs to determine how cellular electrical activity is regulated. A mismatch between modelling predictions and the experimental results allowed us to construct an improved, more predictive mathematical model. The balance between two particular potassium currents dictates how heart cells respond to perturbations and their susceptibility to arrhythmias. ABSTRACT: Imbalances of ionic currents can destabilize the cardiac action potential and potentially trigger lethal cardiac arrhythmias. In the present study, we combined mathematical modelling with information-rich dynamic clamp experiments to determine the regulation of action potential morphology in guinea pig ventricular myocytes. Parameter sensitivity analysis was used to predict how changes in ionic currents alter action potential duration, and these were tested experimentally using dynamic clamp, a technique that allows for multiple perturbations to be tested in each cell. Surprisingly, we found that a leading mathematical model, developed with traditional approaches, systematically underestimated experimental responses to dynamic clamp perturbations. We then re-parameterized the model using a genetic algorithm, which allowed us to estimate ionic current levels in each of the cells studied. This unbiased model adjustment consistently predicted an increase in the rapid delayed rectifier K+ current and a drastic decrease in the slow delayed rectifier K+ current, and this prediction was validated experimentally. Subsequent simulations with the adjusted model generated the clinically relevant prediction that the slow delayed rectifier is better able to stabilize the action potential and suppress pro-arrhythmic events than the rapid delayed rectifier. In summary, iterative coupling of simulations and experiments enabled novel insight into how the balance between cardiac K+ currents influences ventricular arrhythmia susceptibility.

Slow [Na+]i dynamics impacts arrhythmogenesis and spiral wave reentry in cardiac myocyte ionic model.

Accumulation of intracellular Na+ is gaining recognition as an important regulator of cardiac myocyte electrophysiology. The intracellular Na+ concentration can be an important determinant of the cardiac action potential duration, can modulate the tissue-level conduction of excitation waves, and can alter vulnerability to arrhythmias. Mathematical models of cardiac electrophysiology often incorporate a dynamic intracellular Na+ concentration, which changes much more slowly than the remaining variables. We investigated the dependence of several arrhythmogenesis-related factors on [Na+]i in a mathematical model of the human atrial action potential. In cell simulations, we found that [Na+]i accumulation stabilizes the action potential duration to variations in several conductances and that the slow dynamics of [Na+]i impacts bifurcations to pro-arrhythmic afterdepolarizations, causing intermittency between different rhythms. In long-lasting tissue simulations of spiral wave reentry, [Na+]i becomes spatially heterogeneous with a decreased area around the spiral wave rotation center. This heterogeneous region forms a functional anchor, resulting in diminished meandering of the spiral wave. Our findings suggest that slow, physiological, rate-dependent variations in [Na+]i may play complex roles in cellular and tissue-level cardiac dynamics.

Regularity of beating of small clusters of embryonic chick ventricular heart-cells: experiment vs. stochastic single-channel population model.

The transmembrane potential is recorded from small isopotential clusters of 2-4 embryonic chick ventricular cells spontaneously generating action potentials. We analyze the cycle-to-cycle fluctuations in the time between successive action potentials (the interbeat interval or IBI). We also convert an existing model of electrical activity in the cluster, which is formulated as a Hodgkin-Huxley-like deterministic system of nonlinear ordinary differential equations describing five individual ionic currents, into a stochastic model consisting of a population of ∼20 000 independently and randomly gating ionic channels, with the randomness being set by a real physical stochastic process (radio static). This stochastic model, implemented using the Clay-DeFelice algorithm, reproduces the fluctuations seen experimentally: e.g., the coefficient of variation (standard deviation/mean) of IBI is 4.3% in the model vs. the 3.9% average value of the 17 clusters studied. The model also replicates all but one of several other quantitative measures of the experimental results, including the power spectrum and correlation integral of the voltage, as well as the histogram, Poincaré plot, serial correlation coefficients, power spectrum, detrended fluctuation analysis, approximate entropy, and sample entropy of IBI. The channel noise from one particular ionic current (IKs), which has channel kinetics that are relatively slow compared to that of the other currents, makes the major contribution to the fluctuations in IBI. Reproduction of the experimental coefficient of variation of IBI by adding a Gaussian white noise-current into the deterministic model necessitates using an unrealistically high noise-current amplitude. Indeed, a major implication of the modelling results is that, given the wide range of time-scales over which the various species of channels open and close, only a cell-specific stochastic model that is formulated taking into consideration the widely different ranges in the frequency content of the channel-noise produced by the opening and closing of several different types of channels will be able to reproduce precisely the various effects due to membrane noise seen in a particular electrophysiological preparation.

Illuminating Myocyte-Fibroblast Homotypic and Heterotypic Gap Junction Dynamics Using Dynamic Clamp.

Fibroblasts play a significant role in the development of electrical and mechanical dysfunction of the heart; however, the underlying mechanisms are only partially understood. One widely studied mechanism suggests that fibroblasts produce excess extracellular matrix, resulting in collagenous septa that slow propagation, cause zig-zag conduction paths, and decouple cardiomyocytes, resulting in a substrate for cardiac arrhythmia. An emerging mechanism suggests that fibroblasts promote arrhythmogenesis through direct electrical interactions with cardiomyocytes via gap junction (GJ) channels. In the heart, three major connexin (Cx) isoforms, Cx40, Cx43, and Cx45, form GJ channels in cell-type-specific combinations. Because each Cx is characterized by a unique time- and transjunctional voltage-dependent profile, we investigated whether the electrophysiological contributions of fibroblasts would vary with the specific composition of the myocyte-fibroblast (M-F) GJ channel. Due to the challenges of systematically modifying Cxs in vitro, we coupled native cardiomyocytes with in silico fibroblast and GJ channel electrophysiology models using the dynamic-clamp technique. We found that there is a reduction in the early peak of the junctional current during the upstroke of the action potential (AP) due to GJ channel gating. However, effects on the cardiomyocyte AP morphology were similar regardless of the specific type of GJ channel (homotypic Cx43 and Cx45, and heterotypic Cx43/Cx45 and Cx45/Cx43). To illuminate effects at the tissue level, we performed multiscale simulations of M-F coupling. First, we developed a cell-specific model of our dynamic-clamp experiments and investigated changes in the underlying membrane currents during M-F coupling. Second, we performed two-dimensional tissue sheet simulations of cardiac fibrosis and incorporated GJ channels in a cell type-specific manner. We determined that although GJ channel gating reduces junctional current, it does not significantly alter conduction velocity during cardiac fibrosis relative to static GJ coupling. These findings shed more light on the complex electrophysiological interplay between cardiac fibroblasts and myocytes.

Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithms.

Mathematical models of cardiac electrophysiology are instrumental in determining mechanisms of cardiac arrhythmias. However, the foundation of a realistic multiscale heart model is only as strong as the underlying cell model. While there have been myriad advances in the improvement of cellular-level models, the identification of model parameters, such as ion channel conductances and rate constants, remains a challenging problem. The primary limitations to this process include: (1) such parameters are usually estimated from data recorded using standard electrophysiology voltage-clamp protocols that have not been developed with model building in mind, and (2) model parameters are typically tuned manually to subjectively match a desired output. Over the last decade, methods aimed at overcoming these disadvantages have emerged. These approaches include the use of optimization or fitting tools for parameter estimation and incorporating more extensive data for output matching. Here, we review recent advances in parameter estimation for cardiomyocyte models, focusing on the use of more complex electrophysiology protocols and global search heuristics. We also discuss future applications of such parameter identification, including development of cell-specific and patient-specific mathematical models to investigate arrhythmia mechanisms and predict therapy strategies.

Cell-specific cardiac electrophysiology models.

The traditional cardiac model-building paradigm involves constructing a composite model using data collected from many cells. Equations are derived for each relevant cellular component (e.g., ion channel, exchanger) independently. After the equations for all components are combined to form the composite model, a subset of parameters is tuned, often arbitrarily and by hand, until the model output matches a target objective, such as an action potential. Unfortunately, such models often fail to accurately simulate behavior that is dynamically dissimilar (e.g., arrhythmia) to the simple target objective to which the model was fit. In this study, we develop a new approach in which data are collected via a series of complex electrophysiology protocols from single cardiac myocytes and then used to tune model parameters via a parallel fitting method known as a genetic algorithm (GA). The dynamical complexity of the electrophysiological data, which can only be fit by an automated method such as a GA, leads to more accurately parameterized models that can simulate rich cardiac dynamics. The feasibility of the method is first validated computationally, after which it is used to develop models of isolated guinea pig ventricular myocytes that simulate the electrophysiological dynamics significantly better than does a standard guinea pig model. In addition to improving model fidelity generally, this approach can be used to generate a cell-specific model. By so doing, the approach may be useful in applications ranging from studying the implications of cell-to-cell variability to the prediction of intersubject differences in response to pharmacological treatment.

Voltage and calcium dynamics both underlie cellular alternans in cardiac myocytes.

Cardiac alternans, a putative trigger event for cardiac reentry, is a beat-to-beat alternation in membrane potential and calcium transient. Alternans was originally attributed to instabilities in transmembrane ion channel dynamics (i.e., the voltage mechanism). As of this writing, the predominant view is that instabilities in subcellular calcium handling are the main underlying mechanism. That being said, because the voltage and calcium systems are bidirectionally coupled, theoretical studies have suggested that both mechanisms can contribute. To date, to our knowledge, no experimental evidence of such a dual role within the same cell has been reported. Here, a combined electrophysiological and calcium imaging approach was developed and used to illuminate the contributions of voltage and calcium dynamics to alternans. An experimentally feasible protocol, quantification of subcellular calcium alternans and restitution slope during cycle-length ramping alternans control, was designed and validated. This approach allows simultaneous illumination of the contributions of voltage and calcium-driven instability to total cellular instability as a function of cycle-length. Application of this protocol in in vitro guinea-pig left-ventricular myocytes demonstrated that both voltage- and calcium-driven instabilities underlie alternans, and that the relative contributions of the two systems change as a function of pacing rate.

Dependence of phase-2 reentry and repolarization dispersion on epicardial and transmural ionic heterogeneity: a simulation study.

AIMS: Phase-2 reentry (P2R) is a local arrhythmogenic phenomenon where electrotonic current propagates from a spike-and-dome action potential region to re-excite a loss-of-dome action potential region. While ionic heterogeneity has been shown to underlie P2R within the epicardium and has been hypothesized to occur transmurally, we are unaware of any study that has investigated the effects of combining these heterogeneities as they occur in the heart. Thus, we tested the hypothesis that P2R can result by either epicardial or transmural heterogeneity and that the realistic combination of the two would increase the likelihood of P2R. METHODS AND RESULTS: We used computational ionic models of cardiac myocyte dynamics to investigate initiation and development of P2R in simulated tissues with different ionic heterogeneities. In one-dimensional transmural cable simulations, P2R occurred when the conductance of the transient outward current in the epicardial region was near the range for which epicardial action potentials switched intermittently between spike-and-dome and loss-of-dome morphologies. Phase-2 reentry was more likely in two-dimensional tissue simulations by both epicardial and transmural heterogeneity and could expand beyond its local initiation site to create a macroscopic reentry. CONCLUSION: The characteristics and stability of action potential morphology in the epicardium are important determinants of the occurrence of both transmural and epicardial P2R and its associated arrhythmogenesis.

Resolving artefacts in voltage-clamp experiments with computational modelling: an application to fast sodium current recordings.

Cellular electrophysiology is the foundation of many fields, from basic science in neurology, cardiology, oncology to safety critical applications for drug safety testing, clinical phenotyping, etc. Patch-clamp voltage clamp is the gold standard technique for studying cellular electrophysiology. Yet, the quality of these experiments is not always transparent, which may lead to erroneous conclusions for studies and applications. Here, we have developed a new computational approach that allows us to explain and predict the experimental artefacts in voltage-clamp experiments. The computational model captures the experimental procedure and its inadequacies, including: voltage offset, series resistance, membrane capacitance and (imperfect) amplifier compensations, such as series resistance compensation and supercharging. The computational model was validated through a series of electrical model cell experiments. Using this computational approach, the artefacts in voltage-clamp experiments of cardiac fast sodium current, one of the most challenging currents to voltage clamp, were able to be resolved and explained through coupling the observed current and the simulated membrane voltage, including some typically observed shifts and delays in the recorded currents. We further demonstrated that the typical way of averaging data for current-voltage relationships would lead to biases in the peak current and shifts in the peak voltage, and such biases can be in the same order of magnitude as those differences reported for disease-causing mutations. Therefore, the presented new computational pipeline will provide a new standard of assessing the voltage-clamp experiments and interpreting the experimental data, which may be able to rectify and provide a better understanding of ion channel mutations and other related applications.

Nonlinear dynamics in cardiology.

The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counterintuitively, result from a gradual change in a system parameter-this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level that are focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work has suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity.

Effects of electrical and structural remodeling on atrial fibrillation maintenance: a simulation study.

Atrial fibrillation, a common cardiac arrhythmia, often progresses unfavourably: in patients with long-term atrial fibrillation, fibrillatory episodes are typically of increased duration and frequency of occurrence relative to healthy controls. This is due to electrical, structural, and contractile remodeling processes. We investigated mechanisms of how electrical and structural remodeling contribute to perpetuation of simulated atrial fibrillation, using a mathematical model of the human atrial action potential incorporated into an anatomically realistic three-dimensional structural model of the human atria. Electrical and structural remodeling both shortened the atrial wavelength--electrical remodeling primarily through a decrease in action potential duration, while structural remodeling primarily slowed conduction. The decrease in wavelength correlates with an increase in the average duration of atrial fibrillation/flutter episodes. The dependence of reentry duration on wavelength was the same for electrical vs. structural remodeling. However, the dynamics during atrial reentry varied between electrical, structural, and combined electrical and structural remodeling in several ways, including: (i) with structural remodeling there were more occurrences of fragmented wavefronts and hence more filaments than during electrical remodeling; (ii) dominant waves anchored around different anatomical obstacles in electrical vs. structural remodeling; (iii) dominant waves were often not anchored in combined electrical and structural remodeling. We conclude that, in simulated atrial fibrillation, the wavelength dependence of reentry duration is similar for electrical and structural remodeling, despite major differences in overall dynamics, including maximal number of filaments, wave fragmentation, restitution properties, and whether dominant waves are anchored to anatomical obstacles or spiralling freely.