The Na+/K+ pump is an important modulator of refractoriness and rotor dynamics in human atrial tissue

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Individual Contributions of Cardiac Ion Channels on Atrial Repolarization and Reentrant Waves: A Multiscale In-Silico Study

The excitation, contraction, and relaxation of an atrial cardiomyocyte are maintained by the activation and inactivation of numerous cardiac ion channels. Their collaborative efforts cause time-dependent changes of membrane potential, generating an action potential (AP), which is a surrogate marker of atrial arrhythmias. Recently, computational models of atrial electrophysiology emerged as a modality to investigate arrhythmia mechanisms and to predict the outcome of antiarrhythmic therapies. However, the individual contribution of atrial ion channels on atrial action potential and reentrant arrhythmia is not yet fully understood. Thus, in this multiscale in-silico study, perturbations of individual atrial ionic currents (I_Na, I_to, I_CaL, I_Kur, I_Kr, I_Ks, I_K1, I_NCX and I_NaK) in two in-silico models of human atrial cardiomyocyte (i.e., Courtemanche-1998 and Grandi-2011) were performed at both cellular and tissue levels. The results show that the inhibition of I_CaL and I_NCX resulted in AP shortening, while the inhibition of I_Kur, I_Kr, I_Ks, I_K1 and I_NaK prolonged AP duration (APD). Particularly, in-silico perturbations (inhibition and upregulation) of I_Kr and I_Ks only minorly affected atrial repolarization in the Grandi model. In contrast, in the Courtemanche model, the inhibition of I_Kr and I_Ks significantly prolonged APD and vice versa. Additionally, a 50% reduction of I_to density abbreviated APD in the Courtemanche model, while the same perturbation prolonged APD in the Grandi model. Similarly, a strong model dependence was also observed at tissue scale, with an observable I_K1-mediated reentry stabilizing effect in the Courtemanche model but not in the Grandi atrial model. Moreover, the Grandi model was highly sensitive to a change on intracellular Ca²⁺ concentration, promoting a repolarization failure in I_CaL upregulation above 150% and facilitating reentrant spiral waves stabilization by I_CaL inhibition. Finally, by incorporating the previously published atrial fibrillation (AF)-associated ionic remodeling in the Courtemanche atrial model, in-silico modeling revealed the antiarrhythmic effect of I_Kr inhibition in both acute and chronic settings. Overall, our multiscale computational study highlights the strong model-dependent effects of ionic perturbations which could affect the model’s accuracy, interpretability, and prediction. This observation also suggests the need for a careful selection of in-silico models of atrial electrophysiology to achieve specific research aims.

Efficacy of amiodarone for the prevention of atrial fibrillation recurrence after cardioversion

The restoration and maintenance of sinus rhythm is a desirable strategy for many patients with atrial fibrillation (AF) since it has been associated with improvement in symptoms and a better quality of life. Sinus rhythm can be achieved by pharmacological or electrical cardioversion or after catheter ablation of AF. Despite high rates of successful cardioversion, AF recurrence remains a major challenge. Anti-arrhythmic drug therapy currently plays a significant role in maintaining sinus rhythm after cardioversion. Amiodarone is the most commonly prescribed anti-arrhythmic drug for patients with AF. This is due to its particular electrophysiological properties and superior anti-arrhythmic effects in comparison with other anti-arrhythmic drugs. Understanding the cardiac electrophysiology and arrhythmogenesis mechanisms may result in identification of new targets for anti-arrhythmic therapy. The aim of this article was to review amiodarone's clinical pharmacology and evaluate evidence supporting amiodarone for treatment and prevention of AF recurrence after cardioversion.

Spatial Changes in the Atrial Fibrillation Wave-Dynamics After Using Antiarrhythmic Drugs: A Computational Modeling Study

Background: We previously reported that a computational modeling-guided antiarrhythmic drug (AAD) test was feasible for evaluating multiple AADs in patients with atrial fibrillation (AF). We explored the anti-AF mechanisms of AADs and spatial change in the AF wave-dynamics by a realistic computational model. Methods: We used realistic computational modeling of 25 AF patients (68% male, 59.8 ± 9.8 years old, 32.0% paroxysmal AF) reflecting the anatomy, histology, and electrophysiology of the left atrium (LA) to characterize the effects of five AADs (amiodarone, sotalol, dronedarone, flecainide, and propafenone). We evaluated the spatial change in the AF wave-dynamics by measuring the mean dominant frequency (DF) and its coefficient of variation [dominant frequency-coefficient of variation (DF-COV)] in 10 segments of the LA. The mean DF and DF-COV were compared according to the pulmonary vein (PV) vs. extra-PV, maximal slope of the restitution curves (Smax), and defragmentation of AF. Results: The mean DF decreased after the administration of AADs in the dose dependent manner (p < 0.001). Under AADs, the DF was significantly lower (p < 0.001) and COV-DF higher (p = 0.003) in the PV than extra-PV region. The mean DF was significantly lower at a high Smax (≥1.4) than a lower Smax condition under AADs. During the episodes of AF defragmentation, the mean DF was lower (p < 0.001), but the COV-DF was higher (p < 0.001) than that in those without defragmentation. Conclusions: The DF reduction with AADs is predominant in the PVs and during a high Smax condition and causes AF termination or defragmentation during a lower DF and spatially unstable (higher DF-COV) condition.

Computational models of atrial fibrillation: achievements, challenges, and perspectives for improving clinical care

Despite significant advances in its detection, understanding and management, atrial fibrillation (AF) remains a highly prevalent cardiac arrhythmia with a major impact on morbidity and mortality of millions of patients. AF results from complex, dynamic interactions between risk factors and comorbidities that induce diverse atrial remodelling processes. Atrial remodelling increases AF vulnerability and persistence, while promoting disease progression. The variability in presentation and wide range of mechanisms involved in initiation, maintenance and progression of AF, as well as its associated adverse outcomes, make the early identification of causal factors modifiable with therapeutic interventions challenging, likely contributing to suboptimal efficacy of current AF management. Computational modelling facilitates the multilevel integration of multiple datasets and offers new opportunities for mechanistic understanding, risk prediction and personalized therapy. Mathematical simulations of cardiac electrophysiology have been around for 60 years and are being increasingly used to improve our understanding of AF mechanisms and guide AF therapy. This narrative review focuses on the emerging and future applications of computational modelling in AF management. We summarize clinical challenges that may benefit from computational modelling, provide an overview of the different in silico approaches that are available together with their notable achievements, and discuss the major limitations that hinder the routine clinical application of these approaches. Finally, future perspectives are addressed. With the rapid progress in electronic technologies including computing, clinical applications of computational modelling are advancing rapidly. We expect that their application will progressively increase in prominence, especially if their added value can be demonstrated in clinical trials.

Immediate and Delayed Response of Simulated Human Atrial Myocytes to Clinically-Relevant Hypokalemia

Although plasma electrolyte levels are quickly and precisely regulated in the mammalian cardiovascular system, even small transient changes in K⁺, Na⁺, Ca²⁺, and/or Mg²⁺ can significantly alter physiological responses in the heart, blood vessels, and intrinsic (intracardiac) autonomic nervous system. We have used mathematical models of the human atrial action potential (AP) to explore the electrophysiological mechanisms that underlie changes in resting potential (V_r) and the AP following decreases in plasma K⁺, [K⁺]_o, that were selected to mimic clinical hypokalemia. Such changes may be associated with arrhythmias and are commonly encountered in patients (i) in therapy for hypertension and heart failure; (ii) undergoing renal dialysis; (iii) with any disease with acid-base imbalance; or (iv) post-operatively. Our study emphasizes clinically-relevant hypokalemic conditions, corresponding to [K⁺]_o reductions of approximately 1.5 mM from the normal value of 4 to 4.5 mM. We show how the resulting electrophysiological responses in human atrial myocytes progress within two distinct time frames: (i) Immediately after [K⁺]_o is reduced, the K⁺-sensing mechanism of the background inward rectifier current (I_K1) responds. Specifically, its highly non-linear current-voltage relationship changes significantly as judged by the voltage dependence of its region of outward current. This rapidly alters, and sometimes even depolarizes, V_r and can also markedly prolong the final repolarization phase of the AP, thus modulating excitability and refractoriness. (ii) A second much slower electrophysiological response (developing 5-10 minutes after [K⁺]_o is reduced) results from alterations in the intracellular electrolyte balance. A progressive shift in intracellular [Na⁺]_i causes a change in the outward electrogenic current generated by the Na⁺/K⁺ pump, thereby modifying V_r and AP repolarization and changing the human atrial electrophysiological substrate. In this study, these two effects were investigated quantitatively, using seven published models of the human atrial AP. This highlighted the important role of I_K1 rectification when analyzing both the mechanisms by which [K⁺]_o regulates V_r and how the AP waveform may contribute to "trigger" mechanisms within the proarrhythmic substrate. Our simulations complement and extend previous studies aimed at understanding key factors by which decreases in [K⁺]_o can produce effects that are known to promote atrial arrhythmias in human hearts.

Linking cellular energy state to atrial fibrillation pathogenesis: Potential role of adenosine monophosphate-activated protein kinase

Adenosine monophosphate-activated protein kinase (AMPK) is the cellular stress-sensing molecule. Apart from maintaining cellular energy balance, AMPK controls expression and regulation of ion channels and ion transporters, including cytosolic Ca²⁺ handling proteins. Emerging evidence suggests that metabolic impairment plays a crucial role in the pathogenesis of atrial fibrillation. AMPK activation is thought to be protective by preventing metabolic stress, favorably modulating membrane electrophysiology including cytosolic Ca²⁺ dynamics; preventing cellular growth; and hypertrophic remodeling. This review considers current concepts and evidence from clinical and experimental studies regarding the role of AMPK in atrial fibrillation.

Understanding the Beat-to-Beat Variations of P-Waves Morphologies in AF Patients During Sinus Rhythm: A Scoping Review of the Atrial Simulation Studies

The remarkable advances in high-performance computing and the resulting increase of the computational power have the potential to leverage computational cardiology toward improving our understanding of the pathophysiological mechanisms of arrhythmias, such as Atrial Fibrillation (AF). In AF, a complex interaction between various triggers and the atrial substrate is considered to be the leading cause of AF initiation and perpetuation. In electrocardiography (ECG), P-wave is supposed to reflect atrial depolarization. It has been found that even during sinus rhythm (SR), multiple P-wave morphologies are present in AF patients with a history of AF, suggesting a higher dispersion of the conduction route in this population. In this scoping review, we focused on the mechanisms which modify the electrical substrate of the atria in AF patients, while investigating the existence of computational models that simulate the propagation of the electrical signal through different routes. The adopted review methodology is based on a structured analytical framework which includes the extraction of the keywords based on an initial limited bibliographic search, the extensive literature search and finally the identification of relevant articles based on the reference list of the studies. The leading mechanisms identified were classified according to their scale, spanning from mechanisms in the cell, tissue or organ level, and the produced outputs. The computational modeling approaches for each of the factors that influence the initiation and the perpetuation of AF are presented here to provide a clear overview of the existing literature. Several levels of categorization were adopted while the studies which aim to translate their findings to ECG phenotyping are highlighted. The results denote the availability of multiple models, which are appropriate under specific conditions. However, the consideration of complex scenarios taking into account multiple spatiotemporal scales, personalization of electrophysiological and anatomical models and the reproducibility in terms of ECG phenotyping has only partially been tackled so far.

Transient outward K+ current can strongly modulate action potential duration and initiate alternans in the human atrium

Efforts to identify the mechanisms for the initiation and maintenance of human atrial fibrillation (AF) often focus on changes in specific elements of the atrial "substrate," i.e., its electrophysiological properties and/or structural components. We used experimentally validated mathematical models of the human atrial myocyte action potential (AP), both at baseline in sinus rhythm (SR) and in the setting of chronic AF, to identify significant contributions of the Ca2+-independent transient outward K+ current ( Ito) to electrophysiological instability and arrhythmia initiation. First, we explored whether changes in the recovery or restitution of the AP duration (APD) and/or its dynamic stability (alternans) can be modulated by Ito. Recent reports have identified disease-dependent spatial differences in expression levels of the specific K+ channel α-subunits that underlie Ito in the left atrium. Therefore, we studied the functional consequences of this by deletion of 50% of native Ito (Kv4.3) and its replacement with Kv1.4. Interestingly, significant changes in the short-term stability of the human atrial AP waveform were revealed. Specifically, this K+ channel isoform switch produced discontinuities in the initial slope of the APD restitution curve and appearance of APD alternans. This pattern of in silico results resembles some of the changes observed in high-resolution clinical electrophysiological recordings. Important insights into mechanisms for these changes emerged from known biophysical properties (reactivation kinetics) of Kv1.4 versus those of Kv4.3. These results suggest new approaches for pharmacological management of AF, based on molecular properties of specific K+ isoforms and their changed expression during progressive disease. NEW & NOTEWORTHY Clinical studies identify oscillations (alternans) in action potential (AP) duration as a predictor for atrial fibrillation (AF). The abbreviated AP in AF also involves changes in K+ currents and early repolarization of the AP. Our simulations illustrate how substitution of Kv1.4 for the native current, Kv4.3, alters the AP waveform and enhances alternans. Knowledge of this "isoform switch" and related dynamics in the AF substrate may guide new approaches for detection and management of AF.

Computational Modeling of Electrophysiology and Pharmacotherapy of Atrial Fibrillation: Recent Advances and Future Challenges

The pathophysiology of atrial fibrillation (AF) is broad, with components related to the unique and diverse cellular electrophysiology of atrial myocytes, structural complexity, and heterogeneity of atrial tissue, and pronounced disease-associated remodeling of both cells and tissue. A major challenge for rational design of AF therapy, particularly pharmacotherapy, is integrating these multiscale characteristics to identify approaches that are both efficacious and independent of ventricular contraindications. Computational modeling has long been touted as a basis for achieving such integration in a rapid, economical, and scalable manner. However, computational pipelines for AF-specific drug screening are in their infancy, and while the field is progressing quite rapidly, major challenges remain before computational approaches can fill the role of workhorse in rational design of AF pharmacotherapies. In this review, we briefly detail the unique aspects of AF pathophysiology that determine requirements for compounds targeting AF rhythm control, with emphasis on delimiting mechanisms that promote AF triggers from those providing substrate or supporting reentry. We then describe modeling approaches that have been used to assess the outcomes of drugs acting on established AF targets, as well as on novel promising targets including the ultra-rapidly activating delayed rectifier potassium current, the acetylcholine-activated potassium current and the small conductance calcium-activated potassium channel. Finally, we describe how heterogeneity and variability are being incorporated into AF-specific models, and how these approaches are yielding novel insights into the basic physiology of disease, as well as aiding identification of the important molecular players in the complex AF etiology.

Slow Recovery of Excitability Increases Ventricular Fibrillation Risk as Identified by Emulation

Purpose: Rotor stability and meandering are key mechanisms determining and sustaining cardiac fibrillation, with important implications for anti-arrhythmic drug development. However, little is yet known on how rotor dynamics are modulated by variability in cellular electrophysiology, particularly on kinetic properties of ion channel recovery.

Methods: We propose a novel emulation approach, based on Gaussian process regression augmented with machine learning, for data enrichment, automatic detection, classification, and analysis of re-entrant biomarkers in cardiac tissue. More than 5,000 monodomain simulations of long-lasting arrhythmic episodes with Fenton-Karma ionic dynamics, further enriched by emulation to 80 million electrophysiological scenarios, were conducted to investigate the role of variability in ion channel densities and kinetics in modulating rotor-driven arrhythmic behavior.

Results: Our methods predicted the class of excitation behavior with classification accuracy up to 96%, and emulation effectively predicted frequency, stability, and spatial biomarkers of functional re-entry. We demonstrate that the excitation wavelength interpretation of re-entrant behavior hides critical information about rotor persistence and devolution into fibrillation. In particular, whereas action potential duration directly modulates rotor frequency and meandering, critical windows of excitability are identified as the main determinants of breakup. Further novel electrophysiological insights of particular relevance for ventricular arrhythmias arise from our multivariate analysis, including the role of incomplete activation of slow inward currents in mediating tissue rate-dependence and dispersion of repolarization, and the emergence of slow recovery of excitability as a significant promoter of this mechanism of dispersion and increased arrhythmic risk.

Conclusions: Our results mechanistically explain pro-arrhythmic effects of class Ic anti-arrhythmics in the ventricles despite their established role in the pharmacological management of atrial fibrillation. This is mediated by their slow recovery of excitability mode of action, promoting incomplete activation of slow inward currents and therefore increased dispersion of repolarization, given the larger influence of these currents in modulating the action potential in the ventricles compared to the atria. These results exemplify the potential of emulation techniques in elucidating novel mechanisms of arrhythmia and further application to cardiac electrophysiology.

Interpreting Activation Mapping of Atrial Fibrillation: A Hybrid Computational/Physiological Study

Atrial fibrillation is the most common rhythm disorder of the heart associated with a rapid and irregular beating of the upper chambers. Activation mapping remains the gold standard to diagnose and interpret atrial fibrillation. However, fibrillatory activation maps are highly sensitive to far-field effects, and often disagree with other optical mapping modalities. Here we show that computational modeling can identify spurious non-local components of atrial fibrillation electrograms and improve activation mapping. We motivate our approach with a cohort of patients with potential drivers of persistent atrial fibrillation. In a computational study using a monodomain Maleckar model, we demonstrate that in organized rhythms, electrograms successfully track local activation, whereas in atrial fibrillation, electrograms are sensitive to spiral wave distance and number, spiral tip trajectories, and effects of fibrosis. In a clinical study, we analyzed n = 15 patients with persistent atrial fibrillation that was terminated by limited ablation. In five cases, traditional activation maps revealed a spiral wave at sites of termination; in ten cases, electrogram timings were ambiguous and activation maps showed incomplete reentry. By adjusting electrogram timing through computational modeling, we found rotational activation, which was undetectable with conventional methods. Our results demonstrate that computational modeling can identify non-local deflections to improve activation mapping and explain how and where ablation can terminate persistent atrial fibrillation. Our hybrid computational/physiological approach has the potential to optimize map-guided ablation and improve ablation therapy in atrial fibrillation.

Unlocking data sets by calibrating populations of models to data density: A study in atrial electrophysiology

The understanding of complex physical or biological systems nearly always requires a characterization of the variability that underpins these processes. In addition, the data used to calibrate these models may also often exhibit considerable variability. A recent approach to deal with these issues has been to calibrate populations of models (POMs), multiple copies of a single mathematical model but with different parameter values, in response to experimental data. To date, this calibration has been largely limited to selecting models that produce outputs that fall within the ranges of the data set, ignoring any trends that might be present in the data. We present here a novel and general methodology for calibrating POMs to the distributions of a set of measured values in a data set. We demonstrate our technique using a data set from a cardiac electrophysiology study based on the differences in atrial action potential readings between patients exhibiting sinus rhythm (SR) or chronic atrial fibrillation (cAF) and the Courtemanche-Ramirez-Nattel model for human atrial action potentials. Not only does our approach accurately capture the variability inherent in the experimental population, but we also demonstrate how the POMs that it produces may be used to extract additional information from the data used for calibration, including improved identification of the differences underlying stratified data. We also show how our approach allows different hypotheses regarding the variability in complex systems to be quantitatively compared.

In Silico Assessment of Efficacy and Safety of IKur Inhibitors in Chronic Atrial Fibrillation: Role of Kinetics and State-Dependence of Drug Binding

Current pharmacological therapy against atrial fibrillation (AF), the most common cardiac arrhythmia, is limited by moderate efficacy and adverse side effects including ventricular proarrhythmia and organ toxicity. One way to circumvent the former is to target ion channels that are predominantly expressed in atria vs. ventricles, such as K_V1.5, carrying the ultra-rapid delayed-rectifier K⁺ current (I_Kur). Recently, we used an in silico strategy to define optimal K_V1.5-targeting drug characteristics, including kinetics and state-dependent binding, that maximize AF-selectivity in human atrial cardiomyocytes in normal sinus rhythm (nSR). However, because of evidence for I_Kur being strongly diminished in long-standing persistent (chronic) AF (cAF), the therapeutic potential of drugs targeting I_Kur may be limited in cAF patients. Here, we sought to simulate the efficacy (and safety) of I_Kur inhibitors in cAF conditions. To this end, we utilized sensitivity analysis of our human atrial cardiomyocyte model to assess the importance of I_Kur for atrial cardiomyocyte electrophysiological properties, simulated hundreds of theoretical drugs to reveal those exhibiting anti-AF selectivity, and compared the results obtained in cAF with those in nSR. We found that despite being downregulated, I_Kur contributes more prominently to action potential (AP) and effective refractory period (ERP) duration in cAF vs. nSR, with ideal drugs improving atrial electrophysiology (e.g., ERP prolongation) more in cAF than in nSR. Notably, the trajectory of the AP during cAF is such that more I_Kur is available during the more depolarized plateau potential. Furthermore, I_Kur block in cAF has less cardiotoxic effects (e.g., AP duration not exceeding nSR values) and can increase Ca²⁺ transient amplitude thereby enhancing atrial contractility. We propose that in silico strategies such as that presented here should be combined with in vitro and in vivo assays to validate model predictions and facilitate the ongoing search for novel agents against AF.

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.

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.

Revealing kinetics and state-dependent binding properties of IKur-targeting drugs that maximize atrial fibrillation selectivity

The K_V1.5 potassium channel, which underlies the ultra-rapid delayed-rectifier current (I_Kur) and is predominantly expressed in atria vs. ventricles, has emerged as a promising target to treat atrial fibrillation (AF). However, while numerous K_V1.5-selective compounds have been screened, characterized, and tested in various animal models of AF, evidence of antiarrhythmic efficacy in humans is still lacking. Moreover, current guidelines for pre-clinical assessment of candidate drugs heavily rely on steady-state concentration-response curves or IC₅₀ values, which can overlook adverse cardiotoxic effects. We sought to investigate the effects of kinetics and state-dependent binding of I_Kur-targeting drugs on atrial electrophysiology in silico and reveal the ideal properties of I_Kur blockers that maximize anti-AF efficacy and minimize pro-arrhythmic risk. To this aim, we developed a new Markov model of I_Kur that describes K_V1.5 gating based on experimental voltage-clamp data in atrial myocytes from patient right-atrial samples in normal sinus rhythm. We extended the I_Kur formulation to account for state-specificity and kinetics of K_V1.5-drug interactions and incorporated it into our human atrial cell model. We simulated 1- and 3-Hz pacing protocols in drug-free conditions and with a [drug] equal to the IC₅₀ value. The effects of binding and unbinding kinetics were determined by examining permutations of the forward (k_on) and reverse (k_off) binding rates to the closed, open, and inactivated states of the K_V1.5 channel. We identified a subset of ideal drugs exhibiting anti-AF electrophysiological parameter changes at fast pacing rates (effective refractory period prolongation), while having little effect on normal sinus rhythm (limited action potential prolongation). Our results highlight that accurately accounting for channel interactions with drugs, including kinetics and state-dependent binding, is critical for developing safer and more effective pharmacological anti-AF options.

Sensitivity analysis of ventricular activation and electrocardiogram in tailored models of heart-failure patients

Cardiac resynchronization therapy is not effective in a variable proportion of heart failure patients. An accurate knowledge of each patient's electroanatomical features could be helpful to determine the most appropriate treatment. The goal of this study was to analyze and quantify the sensitivity of left ventricular (LV) activation and the electrocardiogram (ECG) to changes in 39 parameters used to tune realistic anatomical-electrophysiological models of the heart. Electrical activity in the ventricles was simulated using a reaction-diffusion equation. To simulate cellular electrophysiology, the Ten Tusscher-Panfilov 2006 model was used. Intracardiac electrograms and 12-lead ECGs were computed by solving the bidomain equation. Parameters showing the highest sensitivity values were similar in the six patients studied. QRS complex and LV activation times were modulated by the sodium current, the cell surface-to-volume ratio in the LV, and tissue conductivities. The T-wave was modulated by the calcium and rectifier-potassium currents, and the cell surface-to-volume ratio in both ventricles. We conclude that homogeneous changes in ionic currents entail similar effects in all ECG leads, whereas the effects of changes in tissue properties show larger inter-lead variability. The effects of parameter variations are highly consistent between patients and most of the model tuning could be performed with only ~10 parameters.

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.

Serine/Threonine Phosphatases in Atrial Fibrillation

Serine/threonine protein phosphatases control dephosphorylation of numerous cardiac proteins, including a variety of ion channels and calcium-handling proteins, thereby providing precise post-translational regulation of cardiac electrophysiology and function. Accordingly, dysfunction of this regulation can contribute to the initiation, maintenance and progression of cardiac arrhythmias. Atrial fibrillation (AF) is the most common heart rhythm disorder and is characterized by electrical, autonomic, calcium-handling, contractile, and structural remodeling, which include, among other things, changes in the phosphorylation status of a wide range of proteins. Here, we review AF-associated alterations in the phosphorylation of atrial ion channels, calcium-handling and contractile proteins, and their role in AF-pathophysiology. We highlight the mechanisms controlling the phosphorylation of these proteins and focus on the role of altered dephosphorylation via local type-1, type-2A and type-2B phosphatases (PP1, PP2A, and PP2B, also known as calcineurin, respectively). Finally, we discuss the challenges for phosphatase research, potential therapeutic significance of altered phosphatase-mediated protein dephosphorylation in AF, as well as future directions.

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.

The Contribution of Ionic Currents to Rate-Dependent Action Potential Duration and Pattern of Reentry in a Mathematical Model of Human Atrial Fibrillation

Persistent atrial fibrillation (PeAF) in humans is characterized by shortening of action potential duration (APD) and attenuation of APD rate-adaptation. However, the quantitative influences of particular ionic current alterations on rate-dependent APD changes, and effects on patterns of reentry in atrial tissue, have not been systematically investigated. Using mathematical models of human atrial cells and tissue and performing parameter sensitivity analysis, we evaluated the quantitative contributions to action potential (AP) shortening and APD rate-adaptation of ionic current remodeling seen with PeAF. Ionic remodeling in PeAF was simulated by reducing L-type Ca²⁺ channel current (I_CaL), increasing inward rectifier K⁺ current (I_K1) and modulating five other ionic currents. Parameter sensitivity analysis, which quantified how each ionic current influenced APD in control and PeAF conditions, identified interesting results, including a negative effect of Na⁺/Ca²⁺ exchange on APD only in the PeAF condition. At high pacing rate (2 Hz), electrical remodeling in I_K1 alone accounts for the APD reduction of PeAF, but at slow pacing rate (0.5 Hz) both electrical remodeling in I_CaL alone (-70%) and I_K1 alone (+100%) contribute equally to the APD reduction. Furthermore, AP rate-adaptation was affected by I_Kur in control and by I_NaCa in the PeAF condition. In a 2D tissue model, a large reduction (-70%) of I_CaL becomes a dominant factor leading to a stable spiral wave in PeAF. Our study provides a quantitative and unifying understanding of the roles of ionic current remodeling in determining rate-dependent APD changes at the cellular level and spatial reentry patterns in tissue.

Isolation of a recombinant antibody specific for a surface marker of the corneal endothelium by phage display

Cell surface antigens are important targets for monoclonal antibodies, but they are often difficult to work with due to their association with the cell membrane. Phage display is a versatile technique that can be applied to generate binders against difficult targets. Here we used antibody phage display to isolate a binder for a rare and specialized cell, the human corneal endothelial cell. The human corneal endothelium is a medically important cell layer; defects in this layer account for about half of all corneal transplants. Despite its importance, no specific antigens have been found to mark this cell type. By panning a phage library directly on human corneal endothelial cells, we isolated an antibody that bound to these cells and not the other types of corneal cells. Subsequently, we identified the antibody's putative target to be CD166 by immunoprecipitation and mass spectrometry. This approach can be used to isolate antibodies against other poorly-characterized cell types, such as stem cells or cancer cells, without any prior knowledge of their discriminating markers.

QT Adaptation and Intrinsic QT Variability in Congenital Long QT Syndrome

BACKGROUND

Increased variability of QT interval (QTV) has been linked to arrhythmias in animal experiments and multiple clinical situations. Congenital long QT syndrome (LQTS), a pure repolarization disease, may provide important information on the relationship between delayed repolarization and QTV.

METHODS AND RESULTS

Twenty-four-hour Holter monitor tracings from 78 genotyped congenital LQTS patients (52 females; 51 LQT1, 23 LQT2, 2 LQT5, 2 JLN, 27 symptomatic; age, 35.2±12.3 years) were evaluated with computer-assisted annotation of RR and QT intervals. Several models of RR-QT relationship were tested in all patients. A model assuming exponential decrease of past RR interval contributions to QT duration with 60-second time constant provided the best data fit. This model was used to calculate QTc and residual "intrinsic" QTV, which cannot be explained by heart rate change. The intrinsic QTV was higher in patients with long QTc (r=0.68; P<10(-4)), and in LQT2 than in LQT1/5 patients (5.65±1.28 vs 4.46±0.82; P<0.0002). Both QTc and intrinsic QTV were similar in symptomatic and asymptomatic patients (467±52 vs 459±53 ms and 5.10±1.19 vs 4.74±1.09, respectively).

CONCLUSIONS

In LQTS patients, QT interval adaptation to heart rate changes occurs with time constant ≈60 seconds, similar to results reported in control subjects. Intrinsic QTV correlates with the degree of repolarization delay and might reflect action potential instability observed in animal models of LQTS.

A Computer Simulation Study of Anatomy Induced Drift of Spiral Waves in the Human Atrium

The interaction of spiral waves of excitation with atrial anatomy remains unclear. This simulation study isolates the role of atrial anatomical structures on spiral wave spontaneous drift in the human atrium. We implemented realistic and idealised 3D human atria models to investigate the functional impact of anatomical structures on the long-term (∼40 s) behaviour of spiral waves. The drift of a spiral wave was quantified by tracing its tip trajectory, which was correlated to atrial anatomical features. The interaction of spiral waves with the following idealised geometries was investigated: (a) a wedge-like structure with a continuously varying atrial wall thickness; (b) a ridge-like structure with a sudden change in atrial wall thickness; (c) multiple bridge-like structures consisting of a bridge connected to the atrial wall. Spiral waves drifted from thicker to thinner regions and along ridge-like structures. Breakthrough patterns caused by pectinate muscles (PM) bridges were also observed, albeit infrequently. Apparent anchoring close to PM-atrial wall junctions was observed. These observations were similar in both the realistic and the idealised models. We conclude that spatially altering atrial wall thickness is a significant cause of drift of spiral waves. PM bridges cause breakthrough patterns and induce transient anchoring of spiral waves.

A patient-specific model of virtual ablation for atrial fibrillation

The purpose of this study was to propose a patient-specific model of atrial fibrillation (AF) and apply it to virtual radiofrequency ablation (RFA). We obtained patient-specific geometries of the left atrium (LA) from CT data and constructed three-dimensional (3D) simulation models. A bidomain Courtemanche model was used to simulate the 3D electric waves on the LA surface, and an S1-S2 protocol was applied to induce AF in the model. To identify scar areas in the models, we converted clinically measured voltage data on the LA surface to the scar maps of the simulation model. Then, after initiation of AF, we applied the virtual ablation scheme to the model and investigated whether the AF was terminated by the scheme. The computed results of AF and ablation were similar to those of clinical observation, providing a clinically important simulation method for preclinical virtual trials of AF treatment.

Cardiovascular safety risk assessment for new candidate drugs from functional and pathological data: Conference report

This is a report on a 2-day joint meeting between the British Society of Toxicological Pathology (BSTP) and the Safety Pharmacology Society (SPS) held in the UK in November 2013. Drug induced adverse effects on the cardiovascular system are associated with the attrition of more marketed and candidate drugs than any other safety issue. The objectives of this meeting were to foster inter-disciplinary approaches to address cardiovascular risk assessment, improve understanding of the respective disciplines, and increase awareness of new technologies. These aims were achieved. This well attended meeting covered both 'purely functional' cardiovascular adverse effects of drugs (e.g., electrophysiological and haemodynamic changes) as well as adverse effects encompassing both functional and pathological changes. Most of the presentations focused on nonclinical safety data, with information on translation to human where known. To reflect the content of the presentations we have cited key references and review articles.

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.

Inter-subject variability in human atrial action potential in sinus rhythm versus chronic atrial fibrillation

AIMS

Human atrial electrophysiology exhibits high inter-subject variability in both sinus rhythm (SR) and chronic atrial fibrillation (cAF) patients. Variability is however rarely investigated in experimental and theoretical electrophysiological studies, thus hampering the understanding of its underlying causes but also its implications in explaining differences in the response to disease and treatment. In our study, we aim at investigating the ability of populations of human atrial cell models to capture the inter-subject variability in action potential (AP) recorded in 363 patients both under SR and cAF conditions.

METHODS AND RESULTS

Human AP recordings in atrial trabeculae (n = 469) from SR and cAF patients were used to calibrate populations of computational SR and cAF atrial AP models. Three populations of over 2000 sampled models were generated, based on three different human atrial AP models. Experimental calibration selected populations of AP models yielding AP with morphology and duration in range with experimental recordings. Populations using the three original models can mimic variability in experimental AP in both SR and cAF, with median conductance values in SR for most ionic currents deviating less than 30% from their original peak values. All cAF populations show similar variations in G(K1), G(Kur) and G(to), consistent with AF-related remodeling as reported in experiments. In all SR and cAF model populations, inter-subject variability in I(K1) and I(NaK) underlies variability in APD90, variability in I(Kur), I(CaL) and I(NaK) modulates variability in APD50 and combined variability in Ito and I(Kur) determines variability in APD20. The large variability in human atrial AP triangulation is mostly determined by I(K1) and either I(NaK) or I(NaCa) depending on the model.

CONCLUSION

Experimentally-calibrated human atrial AP models populations mimic AP variability in SR and cAF patient recordings, and identify potential ionic determinants of inter-subject variability in human atrial AP duration and morphology in SR versus cAF.

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.

A simple model of the right atrium of the human heart with the sinoatrial and atrioventricular nodes included

Existing atrial models with detailed anatomical structure and multi-variable cardiac transmembrane current models are too complex to allow to combine an investigation of long time dycal properties of the heart rhythm with the ability to effectively simulate cardiac electrical activity during arrhythmia. Other ways of modeling need to be investigated. Moreover, many state-of-the-art models of the right atrium do not include an atrioventricular node (AVN) and only rarely--the sinoatrial node (SAN). A model of the heart tissue within the right atrium including the SAN and AVN nodes was developed. Looking for a minimal model, currently we are testing our approach on chosen well-known arrhythmias, which were until now obtained only using much more complicated models, or were only observed in a clinical setting. Ultimately, the goal is to obtain a model able to generate sequences of RR intervals specific for the arrhythmias involving the AV junction as well as for other phenomena occurring within the atrium. The model should be fast enough to allow the study of heart rate variability and arrhythmias at a time scale of thousands of heart beats in real-time. In the model of the right atrium proposed here, different kinds of cardiac tissues are described by sets of different equations, with most of them belonging to the class of Liénard nonlinear dynamical systems. We have developed a series of models of the right atrium with differing anatomical simplifications, in the form of a 2D mapping of the atrium or of an idealized cylindrical geometry, including only those anatomical details required to reproduce a given physiological phenomenon. The simulations allowed to reconstruct the phase relations between the sinus rhythm and the location and properties of a parasystolic source together with the effect of this source on the resultant heart rhythm. We model the action potential conduction time alternans through the atrioventricular AVN junction observed in cardiac tissue in electrophysiological studies during the ventricular-triggered atrial tachycardia. A simulation of the atrio-ventricular nodal reentry tachycardia was performed together with an entrainment procedure in which the arrhythmia circuit was located by measuring the post-pacing interval (PPI) at simulated mapping catheters. The generation and interpretation of RR times series is the ultimate goal of our research. However, to reach that goal we need first to (1) somehow verify the validity of the model of the atrium with the nodes included and (2) include in the model the effect of the sympathetic and vagal ANS. The current paper serves as a partial solution of the 1). In particular we show, that measuring the PPI-TCL entrainment response in proximal (possibly-the slow-conducting pathway), the distal and at a mid-distance from CS could help in rapid distinction of AVNRT from other atrial tachycardias. Our simulations support the hypothesis that the alternans of the conduction time between the atria and the ventricles in the AV orthodromic reciprocating tachycardia can occur within a single pathway. In the atrial parasystole simulation, we found a mathematical condition which allows for a rough estimation of the location of the parasystolic source within the atrium, both for simplified (planar) and the cylindrical geometry of the atrium. The planar and the cylindrical geometry yielded practically the same results of simulations.

High throughput gene expression analysis identifies reliable expression markers of human corneal endothelial cells

Considerable interest has been generated for the development of suitable corneal endothelial graft alternatives through cell-tissue engineering, which can potentially alleviate the shortage of corneal transplant material. The advent of less invasive suture-less key-hole surgery options such as Descemet’s Stripping Endothelial Keratoplasty (DSEK) and Descemet’s Membrane Endothelial Keratoplasty (DMEK), which involve transplantation of solely the endothelial layer instead of full thickness cornea, provide further impetus for the development of alternative endothelial grafts for clinical applications. A major challenge for this endeavor is the lack of specific markers for this cell type. To identify genes that reliably mark corneal endothelial cells (CECs) in vivo and in vitro, we performed RNA-sequencing on freshly isolated human CECs (from both young and old donors), CEC cultures, and corneal stroma. Gene expression of these corneal cell types was also compared to that of other human tissue types. Based on high throughput comparative gene expression analysis, we identified a panel of markers that are: i) highly expressed in CECs from both young donors and old donors; ii) expressed in CECs in vivo and in vitro; and iii) not expressed in corneal stroma keratocytes and the activated corneal stroma fibroblasts. These were SLC4A11, COL8A2 and CYYR1. The use of this panel of genes in combination reliably ascertains the identity of the CEC cell type.

Computational assessment of drug-induced effects on the electrocardiogram: from ion channel to body surface potentials

Background and Purpose

Understanding drug effects on the heart is key to safety pharmacology assessment and anti-arrhythmic therapy development. Here our goal is to demonstrate the ability of computational models to simulate the effect of drug action on the electrical activity of the heart, at the level of the ion-channel, cell, heart and ECG body surface potential.

Experimental Approach

We use the state-of-the-art mathematical models governing the electrical activity of the heart. A drug model is introduced using an ion channel conductance block for the hERG and fast sodium channels, depending on the IC₅₀ value and the drug dose. We simulate the ECG measurements at the body surface and compare biomarkers under different drug actions.

Key Results

Introducing a 50% hERG-channel current block results in 8% prolongation of the APD₉₀ and 6% QT interval prolongation, hERG block does not affect the QRS interval. Introducing 50% fast sodium current block prolongs the QRS and the QT intervals by 12% and 5% respectively, and delays activation times, whereas APD₉₀ is not affected.

Conclusions and Implications

Both potassium and sodium blocks prolong the QT interval, but the underlying mechanism is different: for potassium it is due to APD prolongation; while for sodium it is due to a reduction of electrical wave velocity. This study shows the applicability of in silico models for the investigation of drug effects on the heart, from the ion channel to the ECG-based biomarkers.

Na/K pump regulation of cardiac repolarization: insights from a systems biology approach

The sodium-potassium pump is widely recognized as the principal mechanism for active ion transport across the cellular membrane of cardiac tissue, being responsible for the creation and maintenance of the transarcolemmal sodium and potassium gradients, crucial for cardiac cell electrophysiology. Importantly, sodium-potassium pump activity is impaired in a number of major diseased conditions, including ischemia and heart failure. However, its subtle ways of action on cardiac electrophysiology, both directly through its electrogenic nature and indirectly via the regulation of cell homeostasis, make it hard to predict the electrophysiological consequences of reduced sodium-potassium pump activity in cardiac repolarization. In this review, we discuss how recent studies adopting the systems biology approach, through the integration of experimental and modeling methodologies, have identified the sodium-potassium pump as one of the most important ionic mechanisms in regulating key properties of cardiac repolarization and its rate dependence, from subcellular to whole organ levels. These include the role of the pump in the biphasic modulation of cellular repolarization and refractoriness, the rate control of intracellular sodium and calcium dynamics and therefore of the adaptation of repolarization to changes in heart rate, as well as its importance in regulating pro-arrhythmic substrates through modulation of dispersion of repolarization and restitution. Theoretical findings are consistent across a variety of cell types and species including human, and widely in agreement with experimental findings. The novel insights and hypotheses on the role of the pump in cardiac electrophysiology obtained through this integrative approach could eventually lead to novel therapeutic and diagnostic strategies.

A three-dimensional human atrial model with fiber orientation. Electrograms and arrhythmic activation patterns relationship

The most common sustained cardiac arrhythmias in humans are atrial tachyarrhythmias, mainly atrial fibrillation. Areas of complex fractionated atrial electrograms and high dominant frequency have been proposed as critical regions for maintaining atrial fibrillation; however, there is a paucity of data on the relationship between the characteristics of electrograms and the propagation pattern underlying them. In this study, a realistic 3D computer model of the human atria has been developed to investigate this relationship. The model includes a realistic geometry with fiber orientation, anisotropic conductivity and electrophysiological heterogeneity. We simulated different tachyarrhythmic episodes applying both transient and continuous ectopic activity. Electrograms and their dominant frequency and organization index values were calculated over the entire atrial surface. Our simulations show electrograms with simple potentials, with little or no cycle length variations, narrow frequency peaks and high organization index values during stable and regular activity as the observed in atrial flutter, atrial tachycardia (except in areas of conduction block) and in areas closer to ectopic activity during focal atrial fibrillation. By contrast, cycle length variations and polymorphic electrograms with single, double and fragmented potentials were observed in areas of irregular and unstable activity during atrial fibrillation episodes. Our results also show: (1) electrograms with potentials without negative deflection related to spiral or curved wavefronts that pass over the recording point and move away, (2) potentials with a much greater proportion of positive deflection than negative in areas of wave collisions, (3) double potentials related with wave fragmentations or blocking lines and (4) fragmented electrograms associated with pivot points. Our model is the first human atrial model with realistic fiber orientation used to investigate the relationship between different atrial arrhythmic propagation patterns and the electrograms observed at more than 43000 points on the atrial surface.

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.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

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

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