Impact of sarcoplasmic reticulum calcium release on calcium dynamics and action potential morphology in human atrial myocytes: a computational study

Modeling specific action potentials in the human atria based on a minimal single-cell model

We present an effective method to model empirical action potentials of specific patients in the human atria based on the minimal model of Bueno-Orovio, Cherry and Fenton adapted to atrial electrophysiology. In this model, three ionic are currents introduced, where each of it is governed by a characteristic time scale. By applying a nonlinear optimization procedure, a best combination of the respective time scales is determined, which allows one to reproduce specific action potentials with a given amplitude, width and shape. Possible applications for supporting clinical diagnosis are pointed out.

Pleiotropic effects of schizophrenia-associated genetic variants in neuron firing and cardiac pacemaking revealed by computational modeling

Schizophrenia patients have an increased risk of cardiac dysfunction. A possible factor underlying this comorbidity are the common variants in the large set of genes that have recently been discovered in genome-wide association studies (GWASs) as risk genes of schizophrenia. Many of these genes control the cell electrogenesis and calcium homeostasis. We applied biophysically detailed models of layer V pyramidal cells and sinoatrial node cells to study the contribution of schizophrenia-associated genes on cellular excitability. By including data from functional genomics literature to simulate the effects of common variants of these genes, we showed that variants of voltage-gated Na⁺ channel or hyperpolarization-activated cation channel-encoding genes cause qualitatively similar effects on layer V pyramidal cell and sinoatrial node cell excitability. By contrast, variants of Ca²⁺ channel or transporter-encoding genes mostly have opposite effects on cellular excitability in the two cell types. We also show that the variants may crucially affect the propagation of the cardiac action potential in the sinus node. These results may help explain some of the cardiac comorbidity in schizophrenia, and may facilitate generation of effective antipsychotic medications without cardiac side-effects such as arrhythmia.

A computational framework for testing arrhythmia marker sensitivities to model parameters in functionally calibrated populations of atrial cells

Models of cardiac cell electrophysiology are complex non-linear systems which can be used to gain insight into mechanisms of cardiac dynamics in both healthy and pathological conditions. However, the complexity of cardiac models can make mechanistic insight difficult. Moreover, these are typically fitted to averaged experimental data which do not incorporate the variability in observations. Recently, building populations of models to incorporate inter- and intra-subject variability in simulations has been combined with sensitivity analysis (SA) to uncover novel ionic mechanisms and potentially clarify arrhythmogenic behaviors. We used the Koivumäki human atrial cell model to create two populations, representing normal Sinus Rhythm (nSR) and chronic Atrial Fibrillation (cAF), by varying 22 key model parameters. In each population, 14 biomarkers related to the action potential and dynamic restitution were extracted. Populations were calibrated based on distributions of biomarkers to obtain reasonable physiological behavior, and subjected to SA to quantify correlations between model parameters and pro-arrhythmia markers. The two populations showed distinct behaviors under steady state and dynamic pacing. The nSR population revealed greater variability, and more unstable dynamic restitution, as compared to the cAF population, suggesting that simulated cAF remodeling rendered cells more stable to parameter variation and rate adaptation. SA revealed that the biomarkers depended mainly on five ionic currents, with noted differences in sensitivities to these between nSR and cAF. Also, parameters could be selected to produce a model variant with no alternans and unaltered action potential morphology, highlighting that unstable dynamical behavior may be driven by specific cell parameter settings. These results ultimately suggest that arrhythmia maintenance in cAF may not be due to instability in cell membrane excitability, but rather due to tissue-level effects which promote initiation and maintenance of reentrant arrhythmia.

Systematic reduction of a detailed atrial myocyte model

Cardiac arrhythmias are a major health concern and often involve poorly understood mechanisms. Mathematical modeling is able to provide insights into these mechanisms which might result in better treatment options. A key element of this modeling is a description of the electrophysiological properties of cardiac cells. A number of electrophysiological models have been developed, ranging from highly detailed and complex models, containing numerous parameters and variables, to simplified models in which variables and parameters no longer directly correspond to electrophysiological quantities. In this study, we present a systematic reduction of the complexity of the detailed model of Koivumaki et al. using the recently developed manifold boundary approximation method. We reduce the original model, containing 42 variables and 37 parameters, to a model with only 11 variables and 5 parameters and show that this reduced model can accurately reproduce the action potential shape and restitution curve of the original model. The reduced model contains only five currents and all variables and parameters can be directly linked to electrophysiological quantities. Due to its reduction in complexity, simulation times of our model are decreased more than three-fold. Furthermore, fitting the reduced model to clinical data is much more efficient, a potentially important step towards patient-specific modeling.

Atrial Fibrillation Dynamics and Ionic Block Effects in Six Heterogeneous Human 3D Virtual Atria with Distinct Repolarization Dynamics

Atrial fibrillation (AF) usually manifests as reentrant circuits propagating through the whole atria creating chaotic activation patterns. Little is yet known about how differences in electrophysiological and ionic properties between patients modulate reentrant patterns in AF. The goal of this study is to quantify how variability in action potential duration (APD) at different stages of repolarization determines AF dynamics and their modulation by ionic block using a set of virtual whole-atria human models. Six human whole-atria models are constructed based on the same anatomical structure and fiber orientation, but with different electrophysiological phenotypes. Membrane kinetics for each whole-atria model are selected with distinct APD characteristics at 20, 50, and 90% repolarization, from an experimentally calibrated population of human atrial action potential models, including AF remodeling and acetylcholine parasympathetic effects. Our simulations show that in all whole-atria models, reentrant circuits tend to organize around the pulmonary veins and the right atrial appendage, thus leading to higher dominant frequency (DF) and more organized activation in the left atrium than in the right atrium. Differences in APD in all phases of repolarization (not only APD₉₀) yielded quantitative differences in fibrillation patterns with long APD associated with slower and more regular dynamics. Long APD₅₀ and APD₂₀ were associated with increased interatrial conduction block and interatrial differences in DF and organization index, creating reentry instability and self-termination in some cases. Specific inhibitions of I_K1, I_NaK, or I_Na reduce DF and organization of the arrhythmia by enlarging wave meandering, reducing the number of secondary wavelets, and promoting interatrial block in all six virtual patients, especially for the phenotypes with short APD at 20, 50, and/or 90% repolarization. This suggests that therapies aiming at prolonging the early phase of repolarization might constitute effective antiarrhythmic strategies for the pharmacological management of AF. In summary, simulations report significant differences in atrial fibrillatory dynamics resulting from differences in APD at all phases of repolarization.

A novel mechanism of tandem activation of ryanodine receptors by cytosolic and SR luminal Ca2+ during excitation-contraction coupling in atrial myocytes

KEY POINTS

In atrial myocytes excitation-contraction coupling is strikingly different from ventricle because atrial myocytes lack a transverse tubule membrane system: Ca²⁺ release starts in the cell periphery and propagates towards the cell centre by Ca²⁺ -induced Ca²⁺ release from the sarcoplasmic reticulum (SR) Ca²⁺ store. The cytosolic Ca²⁺ sensitivity of the ryanodine receptor (RyRs) Ca²⁺ release channel is low and it is unclear how Ca²⁺ release can be activated in the interior of atrial cells. Simultaneous confocal imaging of cytosolic and intra-SR calcium revealed a transient elevation of store Ca²⁺ that we termed 'Ca²⁺ sensitization signal'. We propose a novel paradigm of atrial ECC that is based on tandem activation of the RyRs by cytosolic and luminal Ca²⁺ through a 'fire-diffuse-uptake-fire' (or FDUF) mechanism: Ca²⁺ uptake by SR Ca²⁺ pumps at the propagation front elevates Ca²⁺ inside the SR locally, leading to luminal RyR sensitization and lowering of the cytosolic Ca²⁺ activation threshold.

ABSTRACT

In atrial myocytes Ca²⁺ release during excitation-contraction coupling (ECC) is strikingly different from ventricular myocytes. In many species atrial myocytes lack a transverse tubule system, dividing the sarcoplasmic reticulum (SR) Ca²⁺ store into the peripheral subsarcolemmnal junctional (j-SR) and the much more abundant central non-junctional (nj-SR) SR. Action potential (AP)-induced Ca²⁺ entry activates Ca²⁺ -induced Ca²⁺ release (CICR) from j-SR ryanodine receptor (RyR) Ca²⁺ release channels. Peripheral elevation of [Ca²⁺ ]_i initiates CICR from nj-SR and sustains propagation of CICR to the cell centre. Simultaneous confocal measurements of cytosolic ([Ca²⁺ ]_i ; with the fluorescent Ca²⁺ indicator rhod-2) and intra-SR ([Ca²⁺ ]_SR ; fluo-5N) Ca²⁺ in rabbit atrial myocytes revealed that Ca²⁺ release from j-SR resulted in a cytosolic Ca²⁺ transient of higher amplitude compared to release from nj-SR; however, the degree of depletion of j-SR [Ca²⁺ ]_SR was smaller than nj-SR [Ca²⁺ ]_SR . Similarly, Ca²⁺ signals from individual release sites of the j-SR showed a larger cytosolic amplitude (Ca²⁺ sparks) but smaller depletion (Ca²⁺ blinks) than release from nj-SR. During AP-induced Ca²⁺ release the rise of [Ca²⁺ ]_i detected at individual release sites of the nj-SR preceded the depletion of [Ca²⁺ ]_SR , and during this latency period a transient elevation of [Ca²⁺ ]_SR occurred. We propose that Ca²⁺ release from nj-SR is activated by cytosolic and luminal Ca²⁺ (tandem RyR activation) via a novel 'fire-diffuse-uptake-fire' (FDUF) mechanism. This novel paradigm of atrial ECC predicts that Ca²⁺ uptake by sarco-endoplasmic reticulum Ca²⁺ -ATPase (SERCA) at the propagation front elevates local [Ca²⁺ ]_SR , leading to luminal RyR sensitization and lowering of the activation threshold for cytosolic CICR.

Refractoriness in human atria: Time and voltage dependence of sodium channel availability

BACKGROUND

Refractoriness of cardiac cells limits maximum frequency of electrical activity and protects the heart from tonic contractions. Short refractory periods support major arrhythmogenic substrates and augmentation of refractoriness is therefore seen as a main mechanism of antiarrhythmic drugs. Cardiomyocyte excitability depends on availability of sodium channels, which involves both time- and voltage-dependent recovery from inactivation. This study therefore aims to characterise how sodium channel inactivation affects refractoriness in human atria.

METHODS AND RESULTS

Steady-state activation and inactivation parameters of sodium channels measured in vitro in isolated human atrial cardiomyocytes were used to parameterise a mathematical human atrial cell model. Action potential data were acquired from human atrial trabeculae of patients in either sinus rhythm or chronic atrial fibrillation. The ex vivo measurements of action potential duration, effective refractory period and resting membrane potential were well-replicated in simulations using this new in silico model. Notably, the voltage threshold potential at which refractoriness was observed was not different between sinus rhythm and chronic atrial fibrillation tissues and was neither affected by changes in frequency (1 vs. 3Hz).

CONCLUSIONS

Our results suggest a preferentially voltage-dependent, rather than time-dependent, effect with respect to refractoriness at physiologically relevant rates in human atria. However, as the resting membrane potential is hyperpolarized in chronic atrial fibrillation, the voltage-dependence of excitability dominates, profoundly increasing the risk for arrhythmia re-initiation and maintenance in fibrillating atria. Our results thereby highlight resting membrane potential as a potential target in pharmacological management of chronic atrial fibrillation.

Anti-arrhythmic strategies for atrial fibrillation: The role of computational modeling in discovery, development, and optimization

Atrial fibrillation (AF), the most common cardiac arrhythmia, is associated with increased risk of cerebrovascular stroke, and with several other pathologies, including heart failure. Current therapies for AF are targeted at reducing risk of stroke (anticoagulation) and tachycardia-induced cardiomyopathy (rate or rhythm control). Rate control, typically achieved by atrioventricular nodal blocking drugs, is often insufficient to alleviate symptoms. Rhythm control approaches include antiarrhythmic drugs, electrical cardioversion, and ablation strategies. Here, we offer several examples of how computational modeling can provide a quantitative framework for integrating multiscale data to: (a) gain insight into multiscale mechanisms of AF; (b) identify and test pharmacological and electrical therapy and interventions; and (c) support clinical decisions. We review how modeling approaches have evolved and contributed to the research pipeline and preclinical development and discuss future directions and challenges in the field.

Comparison of Detailed and Simplified Models of Human Atrial Myocytes to Recapitulate Patient Specific Properties

Computer studies are often used to study mechanisms of cardiac arrhythmias, including atrial fibrillation (AF). A crucial component in these studies is the electrophysiological model that describes the membrane potential of myocytes. The models vary from detailed, describing numerous ion channels, to simplified, grouping ionic channels into a minimal set of variables. The parameters of these models, however, are determined across different experiments in varied species. Furthermore, a single set of parameters may not describe variations across patients, and models have rarely been shown to recapitulate critical features of AF in a given patient. In this study we develop physiologically accurate computational human atrial models by fitting parameters of a detailed and of a simplified model to clinical data for five patients undergoing ablation therapy. Parameters were simultaneously fitted to action potential (AP) morphology, action potential duration (APD) restitution and conduction velocity (CV) restitution curves in these patients. For both models, our fitting procedure generated parameter sets that accurately reproduced clinical data, but differed markedly from published sets and between patients, emphasizing the need for patient-specific adjustment. Both models produced two-dimensional spiral wave dynamics for that were similar for each patient. These results show that simplified, computationally efficient models are an attractive choice for simulations of human atrial electrophysiology in spatially extended domains. This study motivates the development and validation of patient-specific model-based mechanistic studies to target therapy.

Oxidized Low-density Lipoprotein (ox-LDL) Cholesterol Induces the Expression of miRNA-223 and L-type Calcium Channel Protein in Atrial Fibrillation

Atrial fibrillation (AF) is the most common sustained arrhythmia causing high morbidity and mortality. While changing of the cellular calcium homeostasis plays a critical role in AF, the L-type calcium channel α1c protein has suggested as an important regulator of reentrant spiral dynamics and is a major component of AF-related electrical remodeling. Our computational modeling predicted that miRNA-223 may regulate the CACNA1C gene which encodes the cardiac L-type calcium channel α1c subunit. We found that oxidized low-density lipoprotein (ox-LDL) cholesterol significantly up-regulates both the expression of miRNA-223 and L-type calcium channel protein. In contrast, knockdown of miRNA-223 reduced L-type calcium channel protein expression, while genetic knockdown of endogenous miRNA-223 dampened AF vulnerability. Transfection of miRNA-223 by adenovirus-mediated expression enhanced L-type calcium currents and promoted AF in mice while co-injection of a CACNA1C-specific miR-mimic counteracted the effect. Taken together, ox-LDL, as a known factor in AF-associated remodeling, positively regulates miRNA-223 transcription and L-type calcium channel protein expression. Our results implicate a new molecular mechanism for AF in which miRNA-223 can be used as an biomarker of AF rheumatic heart disease.

Computational models of atrial cellular electrophysiology and calcium handling, and their role in atrial fibrillation

The complexity of the heart makes an intuitive understanding of the relative contribution of ion channels, transporters and signalling pathways to cardiac electrophysiology challenging. Computational modelling of cardiac cellular electrophysiology has proven useful to integrate experimental findings, extrapolate results obtained in expression systems or animal models to other systems, test quantitatively ideas based on experimental data and provide novel hypotheses that are experimentally testable. While the bulk of computational modelling has traditionally been directed towards ventricular bioelectricity, increasing recognition of the clinical importance of atrial arrhythmias, particularly atrial fibrillation, has led to widespread efforts to apply computational approaches to understanding atrial electrical function. The increasing availability of detailed, atrial-specific experimental data has stimulated the development of novel computational models of atrial-cellular electrophysiology and Ca(2+) handling. To date, more than 300 studies have employed mathematical simulations to enhance our understanding of atrial electrophysiology, arrhythmogenesis and therapeutic responses. Future modelling studies are likely to move beyond current whole-cell models by incorporating new data on subcellular architecture, macromolecular protein complexes, and localized ion-channel regulation by signalling pathways. At the same time, more integrative multicellular models that take into account regional electrophysiological and Ca(2+) handling properties, mechano-electrical feedback and/or autonomic regulation will be needed to investigate the mechanisms governing atrial arrhythmias. A combined experimental and computational approach is expected to provide the more comprehensive understanding of atrial arrhythmogenesis that is required to develop improved diagnostic and therapeutic options. Here, we review this rapidly expanding area, with a particular focus on Ca(2+) handling, and provide ideas about potential future directions.

Variability in cardiac electrophysiology: Using experimentally-calibrated populations of models to move beyond the single virtual physiological human paradigm

Physiological variability manifests itself via differences in physiological function between individuals of the same species, and has crucial implications in disease progression and treatment. Despite its importance, physiological variability has traditionally been ignored in experimental and computational investigations due to averaging over samples from multiple individuals. Recently, modelling frameworks have been devised for studying mechanisms underlying physiological variability in cardiac electrophysiology and pro-arrhythmic risk under a variety of conditions and for several animal species as well as human. One such methodology exploits populations of cardiac cell models constrained with experimental data, or experimentally-calibrated populations of models. In this review, we outline the considerations behind constructing an experimentally-calibrated population of models and review the studies that have employed this approach to investigate variability in cardiac electrophysiology in physiological and pathological conditions, as well as under drug action. We also describe the methodology and compare it with alternative approaches for studying variability in cardiac electrophysiology, including cell-specific modelling approaches, sensitivity-analysis based methods, and populations-of-models frameworks that do not consider the experimental calibration step. We conclude with an outlook for the future, predicting the potential of new methodologies for patient-specific modelling extending beyond the single virtual physiological human paradigm.

Human atrial cell models to analyse haemodialysis-related effects on cardiac electrophysiology: work in progress

During haemodialysis (HD) sessions, patients undergo alterations in the extracellular environment, mostly concerning plasma electrolyte concentrations, pH, and volume, together with a modification of sympathovagal balance. All these changes affect cardiac electrophysiology, possibly leading to an increased arrhythmic risk. Computational modeling may help to investigate the impact of HD-related changes on atrial electrophysiology. However, many different human atrial action potential (AP) models are currently available, all validated only with the standard electrolyte concentrations used in experiments. Therefore, they may respond in different ways to the same environmental changes. After an overview on how the computational approach has been used in the past to investigate the effect of HD therapy on cardiac electrophysiology, the aim of this work has been to assess the current state of the art in human atrial AP models, with respect to the HD context. All the published human atrial AP models have been considered and tested for electrolytes, volume changes, and different acetylcholine concentrations. Most of them proved to be reliable for single modifications, but all of them showed some drawbacks. Therefore, there is room for a new human atrial AP model, hopefully able to physiologically reproduce all the HD-related effects. At the moment, work is still in progress in this specific field.

Disrupted calcium release as a mechanism for atrial alternans associated with human atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (ki_Ca) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca²⁺-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca²⁺ release slope. Iterated map analysis revealed that because SR Ca²⁺ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in ki_Ca were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca²⁺ homeostasis which drives proarrhythmic APD alternans in patients with AF.

Atrial fibrillation is an irregular heart rhythm affecting millions of people worldwide. Effective treatment of this cardiac disorder relies upon our detailed knowledge and understanding of the mechanisms that lead to arrhythmia. Recent clinical observations have suggested that alternans, a phenomenon where the shape of the electrical signal in the heart alternates from beat to beat, may play an important role in this process, but the underlying mechanisms remain unknown. In this study, we use computational models to conduct a detailed examination of the causes and contributors to alternans associated with human atrial fibrillation. We find that in atria remodeled by atrial fibrillation, alternans appears near resting heart rates because several aspects of calcium cycling are disrupted in the atrial cells. In particular, the release and uptake of calcium from the cellular storage compartment, the sarcoplasmic reticulum, becomes imbalanced, leading to alternation in calcium signals from beat to beat. These findings provide important insights into the mechanisms of proarrhythmic alternans in human atrial fibrillation which may be used to develop novel therapeutic targets and treatment strategies in the future.

Virtual ablation for atrial fibrillation in personalized in-silico three-dimensional left atrial modeling: comparison with clinical catheter ablation

BACKGROUND

Although catheter ablation is an effective rhythm control strategy for atrial fibrillation (AF), empirically-based ablation has a substantial recurrence rate. The purposes of this study were to develop a computational platform for patient-specific virtual AF ablation and to compare the anti-fibrillatory effects of 5 different virtual ablation protocols with empirically chosen clinical ablations.

METHODS

We included 20 patients with AF (65% male, 60.1 ± 10.5 years old, 80% persistent AF [PeAF]) who had undergone empirically-based catheter ablation: circumferential pulmonary vein isolation (CPVI) for paroxysmal AF (PAF) and additional posterior box lesion (L1) and anterior line (L2) for PeAF. Using patient-specific three-dimensional left atrial (LA) geometry, we generated a finite element model and tested the AF termination rate after 5 different virtual ablations: CPVI alone, CPVI + L1, CPVI + L1,2, CPVI with complex fractionated atrial electrogram (CFAE) ablation, and CFAE ablation alone.

RESULTS

1. Virtual CPVI + L1,2 ablation showed the highest AF termination rate in overall patients (55%) and PeAF patients (n = 16, 62.5%). 2. The virtual AF maintenance duration was shortest in the case of virtual CPVI + L1,2 ablation in overall patients (2.19 ± 1.28 vs. 2.91 ± 1.04 s, p = 0.009) and in patients with PeAF (2.05 ± 1.23 vs. 2.93 ± 10.2 s, p = 0.004) compared with other protocols.

CONCLUSION

Virtual AF ablation using personalized in-silico model of LA is feasible. Virtual ablation with CPVI + L1,2 shows the highest antifibrillatory effect, concordant with the empirical ablation protocol in patients with PeAF.

Na(+) current expression in human atrial myofibroblasts: identity and functional roles

In the mammalian heart fibroblasts have important functional roles in both healthy conditions and diseased states. During pathophysiological challenges, a closely related myofibroblast cell population emerges, and can have distinct, significant roles. Recently, it has been reported that human atrial myofibroblasts can express a Na⁺ current, I_Na. Some of the biophysical properties and molecular features suggest that this I_Na is due to expression of Na_v 1.5, the same Na⁺ channel α subunit that generates the predominant I_Na in myocytes from adult mammalian heart. In principle, expression of Na_v 1.5 could give rise to regenerative action potentials in the fibroblasts/myofibroblasts. This would suggest an active as opposed to passive role for fibroblasts/myofibroblasts in both the “trigger” and the “substrate” components of cardiac rhythm disturbances. Our goals in this preliminary study were: (i) to confirm and extend the electrophysiological characterization of I_Na in a human atrial fibroblast/myofibroblast cell population maintained in conventional 2-D tissue culture; (ii) to identify key molecular properties of the α and β subunits of these Na⁺ channel(s); (iii) to define the biophysical and pharmacological properties of this I_Na; (iv) to integrate the available multi-disciplinary data, and attempt to illustrate its functional consequences, using a mathematical model in which the human atrial myocyte is coupled via connexins to fixed numbers of fibroblasts/myofibroblasts in a syncytial arrangement. Our experimental findings confirm that a significant fraction (approximately 40–50%) of these human atrial myofibroblasts can express I_Na. However, our data suggest that I_Na may be generated by a combination of Na_v 1.9, Na_v 1.2, and Na_v 1.5. Our results, when complemented with mathematical modeling, provide a background for re-evaluating pharmacological management of supraventricular rhythm disorders, e.g., persistent atrial fibrillation.

Effects of human atrial ionic remodelling by β-blocker therapy on mechanisms of atrial fibrillation: a computer simulation

AIMS

Atrial anti-arrhythmic effects of β-adrenoceptor antagonists (β-blockers) may involve both a suppression of pro-arrhythmic effects of catecholamines, and an adaptational electrophysiological response to chronic β-blocker use; so-called 'pharmacological remodelling'. In human atrium, such remodelling decreases the transient outward (Ito) and inward rectifier (IK1) K(+) currents, and increases the cellular action potential duration (APD) and effective refractory period (ERP). However, the consequences of these changes on mechanisms of genesis and maintenance of atrial fibrillation (AF) are unknown. Using mathematical modelling, we tested the hypothesis that the long-term adaptational decrease in human atrial Ito and IK1 caused by chronic β-blocker therapy, i.e. independent of acute electrophysiological effects of β-blockers, in an otherwise un-remodelled atrium, could suppress AF.

METHODS AND RESULTS

Contemporarily, biophysically detailed human atrial cell and tissue models were used to investigate effects of the β-blocker-based pharmacological remodelling. Chronic β-blockade remodelling prolonged atrial cell APD and ERP. The incidence of small amplitude APD alternans in the CRN model was reduced. At the 1D tissue level, β-blocker remodelling decreased the maximum pacing rate at which APs could be conducted. At the three-dimensional organ level, β-blocker remodelling reduced the life span of re-entry scroll waves.

CONCLUSION

This study improves our understanding of the electrophysiological mechanisms of AF suppression by chronic β-blocker therapy. Atrial fibrillation suppression may involve a reduced propensity for maintenance of re-entrant excitation waves, as a consequence of increased APD and ERP.

Arrhythmias, elicited by catecholamines and serotonin, vanish in human chronic atrial fibrillation

Atrial fibrillation (AF) is the most common heart rhythm disorder. Transient postoperative AF can be elicited by high sympathetic nervous system activity. Catecholamines and serotonin cause arrhythmias in atrial trabeculae from patients with sinus rhythm (SR), but whether these arrhythmias occur in patients with chronic AF is unknown. We compared the incidence of arrhythmic contractions caused by norepinephrine, epinephrine, serotonin, and forskolin in atrial trabeculae from patients with SR and patients with AF. In the patients with AF, arrhythmias were markedly reduced for the agonists and abolished for forskolin, whereas maximum inotropic responses were markedly blunted only for serotonin. Serotonin and forskolin produced spontaneous diastolic Ca(2+) releases in atrial myocytes from the patients with SR that were abolished or reduced in myocytes from the patients with AF. For matching L-type Ca(2+)-current (ICa,L) responses, serotonin required and produced ∼ 100-fold less cAMP/PKA at the Ca(2+) channel domain compared with the catecholamines and forskolin. Norepinephrine-evoked ICa,L responses were decreased by inhibition of Ca(2+)/calmodulin-dependent kinase II (CaMKII) in myocytes from patients with SR, but not in those from patients with AF. Agonist-evoked phosphorylation by CaMKII at phospholamban (Thr-17), but not of ryanodine2 (Ser-2814), was reduced in trabeculae from patients with AF. The decreased CaMKII activity may contribute to the blunting of agonist-evoked arrhythmias in the atrial myocardium of patients with AF.

Mathematical approaches to understanding and imaging atrial fibrillation: significance for mechanisms and management

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This article aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention.

Are SR Ca content fluctuations or SR refractoriness the key to atrial cardiac alternans?: insights from a human atrial model

Despite the important role of electromechanical alternans in cardiac arrhythmogenesis, its molecular origin is not well understood. The appearance of calcium alternans has often been associated to fluctuations in the sarcoplasmic reticulum (SR) Ca loading. However, cytosolic calcium alternans observed without concurrent oscillations in the SR Ca content suggests an alternative mechanism related to a dysfunction in the dynamics of the ryanodine receptor (RyR2). We have investigated the effect of SR release refractoriness in the appearance of alternans, using a mathematical model of a single human atrial cell, based on the model by Nygren et al. ( 30 ), where we modified the dynamics of the RyR2 and of SR Ca release. The genesis of calcium alternans was studied stimulating the cell for different periods and values of the RyR2 recovery time from inactivation. At fast rates cytosolic calcium alternans were obtained without concurrent SR Ca content fluctuations. A transition from regular response to alternans was also observed, changing the recovery time from inactivation of the RyR2. This transition was found to be hysteretic, so for a given set of parameters different responses were observed. We then studied the relevance of RyR2 refractoriness for the generation of alternans, reproducing the same protocols as in recent experiments. In particular, restitution of Ca release during alternans was studied with a S1S2 protocol, obtaining a different response if the S2 stimulation was given after a long or a short release. We show that the experimental results can be explained by RyR2 refractoriness, arising from a slow RyR2 recovery from inactivation, stressing the role of the RyR2 in the genesis of alternans.

In silico screening of the key cellular remodeling targets in chronic atrial fibrillation

Chronic atrial fibrillation (AF) is a complex disease with underlying changes in electrophysiology, calcium signaling and the structure of atrial myocytes. How these individual remodeling targets and their emergent interactions contribute to cell physiology in chronic AF is not well understood. To approach this problem, we performed in silico experiments in a computational model of the human atrial myocyte. The remodeled function of cellular components was based on a broad literature review of in vitro findings in chronic AF, and these were integrated into the model to define a cohort of virtual cells. Simulation results indicate that while the altered function of calcium and potassium ion channels alone causes a pronounced decrease in action potential duration, remodeling of intracellular calcium handling also has a substantial impact on the chronic AF phenotype. We additionally found that the reduction in amplitude of the calcium transient in chronic AF as compared to normal sinus rhythm is primarily due to the remodeling of calcium channel function, calcium handling and cellular geometry. Finally, we found that decreased electrical resistance of the membrane together with remodeled calcium handling synergistically decreased cellular excitability and the subsequent inducibility of repolarization abnormalities in the human atrial myocyte in chronic AF. We conclude that the presented results highlight the complexity of both intrinsic cellular interactions and emergent properties of human atrial myocytes in chronic AF. Therefore, reversing remodeling for a single remodeled component does little to restore the normal sinus rhythm phenotype. These findings may have important implications for developing novel therapeutic approaches for chronic AF.

Translating intracellular calcium signaling into models

The rich experimental data on intracellular calcium has put theoreticians in an ideal position to derive models of intracellular calcium signaling. Over the last 25 years, a large number of modeling frameworks have been suggested. Here, I will review some of the milestones of intracellular calcium modeling with a special emphasis on calcium-induced calcium release (CICR) through inositol-1,4,5-trisphosphate and ryanodine receptors. I will highlight key features of CICR and how they are represented in models as well as the challenges that theoreticians face when translating our current understanding of calcium signals into equations. The selected examples demonstrate that a successful model provides mechanistic insights into the molecular machinery of the Ca²⁺ signaling toolbox and determines the contribution of local Ca²⁺ release to global Ca²⁺ patterns, which at the moment cannot be resolved experimentally.

Calcium and IP3 dynamics in cardiac myocytes: experimental and computational perspectives and approaches

Calcium plays a crucial role in excitation-contraction coupling (ECC), but it is also a pivotal second messenger activating Ca²⁺-dependent transcription factors in a process termed excitation-transcription coupling (ETC). Evidence accumulated over the past decade indicates a pivotal role of inositol 1,4,5-trisphosphate receptor (IP₃R)-mediated Ca²⁺ release in the regulation of cytosolic and nuclear Ca²⁺ signals. IP₃ is generated by stimulation of plasma membrane receptors that couple to phospholipase C (PLC), liberating IP₃ from phosphatidylinositol 4,5-bisphosphate (PIP₂). An intriguing aspect of IP₃ signaling is the presence of the entire PIP₂-PLC-IP₃ signaling cascade as well as the presence of IP₃Rs at the inner and outer membranes of the nuclear envelope (NE) which functions as a Ca²⁺ store. The observation that the nucleus is surrounded by its own putative Ca²⁺ store raises the possibility that nuclear IP₃-dependent Ca²⁺ release plays a critical role in ETC. This provides a potential mechanism of regulation that acts locally and autonomously from the global cytosolic Ca²⁺ signal underlying ECC. Moreover, there is evidence that: (i) the sarcoplasmic reticulum (SR) and NE are a single contiguous Ca²⁺ store; (ii) the nuclear pore complex is the major gateway for Ca²⁺ and macromolecules to pass between the cytosol and the nucleoplasm; (iii) the inner membrane of the NE hosts key Ca²⁺ handling proteins including the Na⁺/Ca²⁺ exchanger (NCX)/GM1 complex, ryanodine receptors (RyRs), nicotinic acid adenine dinucleotide phosphate receptors (NAADPRs), Na⁺/K⁺ ATPase, and Na⁺/H⁺ exchanger. Thus, it appears that the nucleus represents a Ca²⁺ signaling domain equipped with its own ion channels and transporters that allow for complex local Ca²⁺ signals. Many experimental and modeling approaches have been used for the study of intracellular Ca²⁺ signaling but the key to the understanding of the dual role of Ca²⁺ mediating ECC and ECT lays in quantitative differences of local [Ca²⁺] in the nuclear and cytosolic compartment. In this review, we discuss the state of knowledge regarding the origin and the physiological implications of nuclear Ca²⁺ transients in different cardiac cell types (adult atrial and ventricular myocytes) as well as experimental and mathematical approaches to study Ca²⁺ and IP₃ signaling in the cytosol and nucleus. In particular, we focus on the concept that highly localized Ca²⁺ signals are required to translocate and activate Ca²⁺-dependent transcription factors (e.g., nuclear factor of activated T-cells, NFAT; histone deacetylase, HDAC) through phosphorylation/dephosphorylation processes.

Bifurcations, sustained oscillations and torus bursting involving ionic concentrations dynamics in a canine atrial cell model

Atrial fibrillation is a disorganization of the electrical propagation in the atria often initiated by ectopic beats. This spontaneous activity might be associated with the appearance of sustained oscillations in some portion of the tissue. Adrenergic stress and specific gene polymorphisms known to promote atrial fibrillation are notably related to calcium and potassium channel conductances. We performed codimension-one and two bifurcation analysis along these conductances in an ionic canine atrial myocyte model. Two Hopf bifurcations were found, related to two distinct mechanisms: (1) a fast calcium gating-driven oscillator, and (2) a slow concentration-driven oscillator. These two mechanisms interact through a double Hopf bifurcation (HH) in a neighborhood of which a torus (Neimark-Sacker) bifurcation leads to bursting. A complex codimension-two theoretical scenario was identified around HH, through systematic comparison with the attractors found numerically. The concentration oscillator was further decomposed to reveal the minimal oscillating subnetwork, in which the Na(+)/Ca(2+) exchanger plays a prominent role.

Cellular and molecular mechanisms of atrial arrhythmogenesis in patients with paroxysmal atrial fibrillation

BACKGROUND

Electrical, structural, and Ca2+ -handling remodeling contribute to the perpetuation/progression of atrial fibrillation (AF). Recent evidence has suggested a role for spontaneous sarcoplasmic reticulum Ca2+ -release events in long-standing persistent AF, but the occurrence and mechanisms of sarcoplasmic reticulum Ca2+ -release events in paroxysmal AF (pAF) are unknown.

METHOD AND RESULTS

Right-atrial appendages from control sinus rhythm patients or patients with pAF (last episode a median of 10-20 days preoperatively) were analyzed with simultaneous measurements of [Ca2+]i (fluo-3-acetoxymethyl ester) and membrane currents/action potentials (patch-clamp) in isolated atrial cardiomyocytes, and Western blot. Action potential duration, L-type Ca2+ current, and Na+ /Ca2+ -exchange current were unaltered in pAF, indicating the absence of AF-induced electrical remodeling. In contrast, there were increases in SR Ca2+ leak and incidence of delayed after-depolarizations in pAF. Ca2+ -transient amplitude and sarcoplasmic reticulum Ca2+ load (caffeine-induced Ca2+ -transient amplitude, integrated Na+/Ca2+ -exchange current) were larger in pAF. Ca2+ -transient decay was faster in pAF, but the decay of caffeine-induced Ca2+ transients was unaltered, suggesting increased SERCA2a function. In agreement, phosphorylation (inactivation) of the SERCA2a-inhibitor protein phospholamban was increased in pAF. Ryanodine receptor fractional phosphorylation was unaltered in pAF, whereas ryanodine receptor expression and single-channel open probability were increased. A novel computational model of the human atrial cardiomyocyte indicated that both ryanodine receptor dysregulation and enhanced SERCA2a activity promote increased sarcoplasmic reticulum Ca2+ leak and sarcoplasmic reticulum Ca2+ -release events, causing delayed after-depolarizations/triggered activity in pAF.

CONCLUSIONS

Increased diastolic sarcoplasmic reticulum Ca2+ leak and related delayed after-depolarizations/triggered activity promote cellular arrhythmogenesis in pAF patients. Biochemical, functional, and modeling studies point to a combination of increased sarcoplasmic reticulum Ca2+ load related to phospholamban hyperphosphorylation and ryanodine receptor dysregulation as underlying mechanisms.

In-silico modeling of atrial repolarization in normal and atrial fibrillation remodeled state

Atrial fibrillation (AF) is the most common cardiac arrhythmia, and the total number of AF patients is constantly increasing. The mechanisms leading to and sustaining AF are not completely understood yet. Heterogeneities in atrial electrophysiology seem to play an important role in this context. Although some heterogeneities have been used in in-silico human atrial modeling studies, they have not been thoroughly investigated. In this study, the original electrophysiological (EP) models of Courtemanche et al., Nygren et al. and Maleckar et al. were adjusted to reproduce action potentials in 13 atrial regions. The parameter sets were validated against experimental action potential duration data and ECG data from patients with AV block. The use of the heterogeneous EP model led to a more synchronized repolarization sequence in a variety of 3D atrial anatomical models. Combination of the heterogeneous EP model with a model of persistent AF-remodeled electrophysiology led to a drastic change in cell electrophysiology. Simulated Ta-waves were significantly shorter under the remodeling. The heterogeneities in cell electrophysiology explain the previously observed Ta-wave effects. The results mark an important step toward the reliable simulation of the atrial repolarization sequence, give a deeper understanding of the mechanism of atrial repolarization and enable further clinical investigations.

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

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

Extraction of sub-microscopic Ca fluxes from blurred and noisy fluorescent indicator images with a detailed model fitting approach

The release of Ca from intracellular stores is key to cardiac muscle function; however, the molecular control of intracellular Ca release remains unclear. Depletion of the intracellular Ca store (sarcoplasmic reticulum, SR) may play an important role, but the ability to measure local SR Ca with fluorescent Ca indicators is limited by the microscope optical resolution and properties of the indicator. This leads to an uncertain degree of spatio-temporal blurring, which is not easily corrected (by deconvolution methods) due to the low signal-to-noise ratio of the recorded signals. In this study, a 3D computer model was constructed to calculate local Ca fluxes and consequent dye signals, which were then blurred by a measured microscope point spread function. Parameter fitting was employed to adjust a release basis function until the model output fitted recorded (2D) Ca spark data. This ‘forward method’ allowed us to obtain estimates of the time-course of Ca release flux and depletion within the sub-microscopic local SR associated with a number of Ca sparks. While variability in focal position relative to Ca spark sites causes more out-of-focus events to have smaller calculated fluxes (and less SR depletion), the average SR depletion was to 20±10% (s.d.) of the resting level. This focus problem implies that the actual SR depletion is likely to be larger and the five largest depletions analyzed were to 8±6% of the resting level. This profound depletion limits SR release flux during a Ca spark, which peaked at 8±3 pA and declined with a half time of 7±2 ms. By comparison, RyR open probability declined more slowly, suggesting release termination is dominated by neither SR Ca depletion nor intrinsic RyR gating, but results from an interaction of these processes.

Calcium levels inside myocytes regulate the heart's force of contraction. Calcium is released from the primary intracellular store called the sarcoplasmic reticulum. Calcium release was directly observed as ‘calcium sparks’ using fluorescent calcium indicators inside the cell. More recently, calcium levels inside the store have been measured as calcium ‘blinks’. These suggest that some depletion of store calcium occurs during cell excitation; however, the actual extent of depletion is made uncertain by the complex sarcoplasmic reticulum shape, dye saturation and optical properties of the microscope. While previous studies have assumed idealized microscope properties, we measured microscope blurring and applied it to a computer model of calcium movements inside the cell. In this model, calcium release was adjusted to match the simulated blurred calcium signals to experimental results. The calculations show that the depth of local sarcoplasmic reticulum calcium depletion is much greater than inferred from calcium blinks and that the time-course of calcium release is affected by this depletion. An estimate for the time-course of gating of the ion channels that regulate calcium release inside the cell was also calculated. We suggest that the time-course of SR Ca release arises from a complex interaction of Ca depletion and channel gating.

Benchmarking electrophysiological models of human atrial myocytes

Mathematical modeling of cardiac electrophysiology is an insightful method to investigate the underlying mechanisms responsible for arrhythmias such as atrial fibrillation (AF). In past years, five models of human atrial electrophysiology with different formulations of ionic currents, and consequently diverging properties, have been published. The aim of this work is to give an overview of strengths and weaknesses of these models depending on the purpose and the general requirements of simulations. Therefore, these models were systematically benchmarked with respect to general mathematical properties and their ability to reproduce certain electrophysiological phenomena, such as action potential (AP) alternans. To assess the models' ability to replicate modified properties of human myocytes and tissue in cardiac disease, electrical remodeling in chronic atrial fibrillation (cAF) was chosen as test case. The healthy and remodeled model variants were compared with experimental results in single-cell, 1D and 2D tissue simulations to investigate AP and restitution properties, as well as the initiation of reentrant circuits.

Human atrial fibrillation: insights from computational electrophysiological models

Computational electrophysiology has proven useful to investigate the mechanisms of cardiac arrhythmias at various spatial scales, from isolated myocytes to the whole heart. This article reviews how mathematical modeling has aided our understanding of human atrial myocyte electrophysiology to study the contribution of structural and electrical remodeling to human atrial fibrillation. Potential new avenues of investigation and model development are suggested.

Towards personalized clinical in-silico modeling of atrial anatomy and electrophysiology

Computational atrial models aid the understanding of pathological mechanisms and therapeutic measures in basic research. The use of biophysical models in a clinical environment requires methods to personalize the anatomy and electrophysiology (EP). Strategies for the automation of model generation and for evaluation are needed. In this manuscript, the current efforts of clinical atrial modeling in the euHeart project are summarized within the context of recent publications in this field. Model-based segmentation methods allow for the automatic generation of ready-to-simulate patient-specific anatomical models. EP models can be adapted to patient groups based on a-priori knowledge and to the individual without significant further data acquisition. ECG and intracardiac data build the basis for excitation personalization. Information from late enhancement (LE) MRI can be used to evaluate the success of radio-frequency ablation (RFA) procedures and interactive virtual atria pave the way for RFA planning. Atrial modeling is currently in a transition from the sole use in basic research to future clinical applications. The proposed methods build the framework for model-based diagnosis and therapy evaluation and planning. Complex models allow to understand biophysical mechanisms and enable the development of simplified models for clinical applications.

An image-based model of the whole human heart with detailed anatomical structure and fiber orientation

Many heart anatomy models have been developed to study the electrophysiological properties of the human heart. However, none of them includes the geometry of the whole human heart. In this study, an anatomically detailed mathematical model of the human heart was firstly reconstructed from the computed tomography images. In the reconstructed model, the atria consisted of atrial muscles, sinoatrial node, crista terminalis, pectinate muscles, Bachmann's bundle, intercaval bundles, and limbus of the fossa ovalis. The atrioventricular junction included the atrioventricular node and atrioventricular ring, and the ventricles had ventricular muscles, His bundle, bundle branches, and Purkinje network. The epicardial and endocardial myofiber orientations of the ventricles and one layer of atrial myofiber orientation were then measured. They were calculated using linear interpolation technique and minimum distance algorithm, respectively. To the best of our knowledge, this is the first anatomically-detailed human heart model with corresponding experimentally measured fibers orientation. In addition, the whole heart excitation propagation was simulated using a monodomain model. The simulated normal activation sequence agreed well with the published experimental findings.

Computational modeling of the human atrial anatomy and electrophysiology

This review article gives a comprehensive survey of the progress made in computational modeling of the human atria during the last 10 years. Modeling the anatomy has emerged from simple "peanut"-like structures to very detailed models including atrial wall and fiber direction. Electrophysiological models started with just two cellular models in 1998. Today, five models exist considering e.g. details of intracellular compartments and atrial heterogeneity. On the pathological side, modeling atrial remodeling and fibrotic tissue are the other important aspects. The bridge to data that are measured in the catheter laboratory and on the body surface (ECG) is under construction. Every measurement can be used either for model personalization or for validation. Potential clinical applications are briefly outlined and future research perspectives are suggested.

Phospholamban and cardiac function: a comparative perspective in vertebrates

Phospholamban (PLN) is a small phosphoprotein closely associated with the cardiac sarcoplasmic reticulum (SR). Dephosphorylated PLN tonically inhibits the SR Ca-ATPase (SERCA2a), while phosphorylation at Ser16 by PKA and Thr17 by Ca(2+) /calmodulin-dependent protein kinase (CaMKII) relieves the inhibition, and this increases SR Ca(2+) uptake. For this reason, PLN is one of the major determinants of cardiac contractility and relaxation. In this review, we attempted to highlight the functional significance of PLN in vertebrate cardiac physiology. We will refer to the huge literature on mammals in order to describe the molecular characteristics of this protein, its interaction with SERCA2a and its role in the regulation of the mechanic and the electric performance of the heart under basal conditions, in the presence of chemical and physical stresses, such as β-adrenergic stimulation, response to stretch, force-frequency relationship and intracellular acidosis. Our aim is to provide the basis to discuss the role of PLN also on the cardiac function of nonmammalian vertebrates, because so far this aspect has been almost neglected. Accordingly, when possible, the literature on PLN will be analysed taking into account the nonuniform cardiac structural and functional characteristics encountered in ectothermic vertebrates, such as the peculiar and variable organization of the SR, the large spectrum of response to stresses and the disaptive absence of crucial proteins (i.e. haemoglobinless and myoglobinless species).

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.

Subcellular calcium dynamics in a whole-cell model of an atrial myocyte

In this study, we present an innovative mathematical modeling approach that allows detailed characterization of Ca(2+) movement within the three-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic representation of Ca(2+) release sites and physiological Ca(2+) flux parameters, coupled with a computationally inexpensive framework. By translating nonlinear Ca(2+) excitability into threshold dynamics, we avoid the computationally demanding time stepping of the partial differential equations that are often used to model Ca(2+) transport. Our approach successfully reproduces key features of atrial myocyte Ca(2+) signaling observed using confocal imaging. In particular, the model displays the centripetal Ca(2+) waves that occur within atrial myocytes during excitation-contraction coupling, and the effect of positive inotropic stimulation on the spatial profile of the Ca(2+) signals. Beyond this validation of the model, our simulation reveals unexpected observations about the spread of Ca(2+) within an atrial myocyte. In particular, the model describes the movement of Ca(2+) between ryanodine receptor clusters within a specific z disk of an atrial myocyte. Furthermore, we demonstrate that altering the strength of Ca(2+) release, ryanodine receptor refractoriness, the magnitude of initiating stimulus, or the introduction of stochastic Ca(2+) channel activity can cause the nucleation of proarrhythmic traveling Ca(2+) waves. The model provides clinically relevant insights into the initiation and propagation of subcellular Ca(2+) signals that are currently beyond the scope of imaging technology.

Human atrial action potential and Ca2+ model: sinus rhythm and chronic atrial fibrillation

RATIONALE

Understanding atrial fibrillation (AF) requires integrated understanding of ionic currents and Ca2+ transport in remodeled human atrium, but appropriate models are limited.

OBJECTIVE

To study AF, we developed a new human atrial action potential (AP) model, derived from atrial experimental results and our human ventricular myocyte model.

METHODS AND RESULTS

Atria versus ventricles have lower I(K1), resulting in more depolarized resting membrane potential (≈7 mV). We used higher I(to,fast) density in atrium, removed I(to,slow), and included an atrial-specific I(Kur). I(NCX) and I(NaK) densities were reduced in atrial versus ventricular myocytes according to experimental results. SERCA function was altered to reproduce human atrial myocyte Ca2+ transients. To simulate chronic AF, we reduced I(CaL), I(to), I(Kur) and SERCA, and increased I(K1),I(Ks) and I(NCX). We also investigated the link between Kv1.5 channelopathy, [Ca2+]i, and AF. The sinus rhythm model showed a typical human atrial AP morphology. Consistent with experiments, the model showed shorter APs and reduced AP duration shortening at increasing pacing frequencies in AF or when I(CaL) was partially blocked, suggesting a crucial role of Ca2+ and Na+ in this effect. This also explained blunted Ca2+ transient and rate-adaptation of [Ca2+]i and [Na+]i in chronic AF. Moreover, increasing [Na+]i and altered I(NaK) and I(NCX) causes rate-dependent atrial AP shortening. Blocking I(Kur) to mimic Kv1.5 loss-of-function increased [Ca2+]i and caused early afterdepolarizations under adrenergic stress, as observed experimentally.

CONCLUSIONS

Our study provides a novel tool and insights into ionic bases of atrioventricular AP differences, and shows how Na+ and Ca2+ homeostases critically mediate abnormal repolarization in AF.

Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation

Cellular electrophysiology experiments, important for understanding cardiac arrhythmia mechanisms, are usually performed with channels expressed in non myocytes, or with non-human myocytes. Differences between cell types and species affect results. Thus, an accurate model for the undiseased human ventricular action potential (AP) which reproduces a broad range of physiological behaviors is needed. Such a model requires extensive experimental data, but essential elements have been unavailable. Here, we develop a human ventricular AP model using new undiseased human ventricular data: Ca(2+) versus voltage dependent inactivation of L-type Ca(2+) current (I(CaL)); kinetics for the transient outward, rapid delayed rectifier (I(Kr)), Na(+)/Ca(2+) exchange (I(NaCa)), and inward rectifier currents; AP recordings at all physiological cycle lengths; and rate dependence and restitution of AP duration (APD) with and without a variety of specific channel blockers. Simulated APs reproduced the experimental AP morphology, APD rate dependence, and restitution. Using undiseased human mRNA and protein data, models for different transmural cell types were developed. Experiments for rate dependence of Ca(2+) (including peak and decay) and intracellular sodium ([Na(+)](i)) in undiseased human myocytes were quantitatively reproduced by the model. Early afterdepolarizations were induced by I(Kr) block during slow pacing, and AP and Ca(2+) alternans appeared at rates >200 bpm, as observed in the nonfailing human ventricle. Ca(2+)/calmodulin-dependent protein kinase II (CaMK) modulated rate dependence of Ca(2+) cycling. I(NaCa) linked Ca(2+) alternation to AP alternans. CaMK suppression or SERCA upregulation eliminated alternans. Steady state APD rate dependence was caused primarily by changes in [Na(+)](i), via its modulation of the electrogenic Na(+)/K(+) ATPase current. At fast pacing rates, late Na(+) current and I(CaL) were also contributors. APD shortening during restitution was primarily dependent on reduced late Na(+) and I(CaL) currents due to inactivation at short diastolic intervals, with additional contribution from elevated I(Kr) due to incomplete deactivation.

An ion-insensitive cAMP biosensor for long term quantitative ratiometric fluorescence resonance energy transfer (FRET) measurements under variable physiological conditions

Ratiometric measurements with FRET-based biosensors in living cells using a single fluorescence excitation wavelength are often affected by a significant ion sensitivity and the aggregation behavior of the FRET pair. This is an important problem for quantitative approaches. Here we report on the influence of physiological ion concentration changes on quantitative ratiometric measurements by comparing different FRET pairs for a cAMP-detecting biosensor. We exchanged the enhanced CFP/enhanced YFP FRET pair of an established Epac1-based biosensor by the fluorophores mCerulean/mCitrine. In the case of enhanced CFP/enhanced YFP, we showed that changes in proton, and (to a lesser extent) chloride ion concentrations result in incorrect ratiometric FRET signals, which may exceed the dynamic range of the biosensor. Calcium ions have no direct, but an indirect pH-driven effect by mobilizing protons. These ion dependences were greatly eliminated when mCerulean/mCitrine fluorophores were used. For such advanced FRET pairs the biosensor is less sensitive to changes in ion concentration and allows consistent cAMP concentration measurements under different physiological conditions, as occur in metabolically active cells. In addition, we verified that the described FRET pair exchange increased the dynamic range of the FRET efficiency response. The time window for stable experimental conditions was also prolonged by a faster biosensor expression rate in transfected cells and a greatly reduced tendency to aggregate, which reduces cytotoxicity. These properties were verified in functional tests in single cells co-expressing the biosensor and the 5-HT(1A) receptor.