Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium

Effects of spatially dense adrenergic stimulation to rotor behaviour in simulated atrial sheets

Sympathetic hyperactivity via spatially dense adrenergic stimulation may create pro-arrhythmic substrates even without structural remodelling. However, the effect of sympathetic hyperactivity on arrhythmic activity, such as rotors, is unknown. Using simulations, we examined the effects of gradually increasing the spatial density of adrenergic stimulation (AS) in atrial sheets on rotors. We compared their characteristics against rotors hosted in atrial sheets with increasing spatial density of minimally conductive (MC) elements to simulate structural remodelling due to injury or disease. We generated rotors using an S1-S2 stimulation protocol. Then, we created phase maps to identify phase singularities and map their trajectory over time. We measured each rotor's duration (s), angular speed (rad/s), and spatiotemporal organization. We demonstrated that atrial sheets with increased AS spatial densities could maintain rotors longer than with MC elements (2.6 ± 0.1 s vs. 1.5 ± 0.2 s, p<0.001). Moreover, rotors have higher angular speed (70 ± 7 rads/s vs. 60 ± 15 rads/s, p<0.05) and better spatiotemporal organization (0.56 ± 0.05 vs. 0.58 ± 0.18, p<0.05) in atrial sheets with less than 25% AS elements compared to MC elements. Our findings may help elucidate electrophysiological potential alterations in atrial substrates due to sympathetic hyperactivity, particularly among individuals with autonomic derangements caused by chronic distress.

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Acetylcholine Reduces L-Type Calcium Current without Major Changes in Repolarization of Canine and Human Purkinje and Ventricular Tissue

Vagal nerve stimulation (VNS) holds a strong basis as a potentially effective treatment modality for chronic heart failure, which explains why a multicenter VNS study in heart failure with reduced ejection fraction is ongoing. However, more detailed information is required on the effect of acetylcholine (ACh) on repolarization in Purkinje and ventricular cardiac preparations to identify the advantages, risks, and underlying cellular mechanisms of VNS. Here, we studied the effect of ACh on the action potential (AP) of canine Purkinje fibers (PFs) and several human ventricular preparations. In addition, we characterized the effects of ACh on the L-type Ca²⁺ current (I_CaL) and AP of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) and performed computer simulations to explain the observed effects. Using microelectrode recordings, we found a small but significant AP prolongation in canine PFs. In the human myocardium, ACh slightly prolonged the AP in the midmyocardium but resulted in minor AP shortening in subepicardial tissue. Perforated patch-clamp experiments on hiPSC-CMs demonstrated that 5 µM ACh caused an ≈15% decrease in I_CaL density without changes in gating properties. Using dynamic clamp, we found that under blocked K⁺ currents, 5 µM ACh resulted in an ≈23% decrease in AP duration at 90% of repolarization in hiPSC-CMs. Computer simulations using the O'Hara-Rudy human ventricular cell model revealed that the overall effect of ACh on AP duration is a tight interplay between the ACh-induced reduction in I_CaL and ACh-induced changes in K⁺ currents. In conclusion, ACh results in minor changes in AP repolarization and duration of canine PFs and human ventricular myocardium due to the concomitant inhibition of inward I_CaL and outward K⁺ currents, which limits changes in net repolarizing current and thus prevents major changes in AP repolarization.

Effects of fibroblast on electromechanical dynamics of human atrial tissue-insights from a 2D discrete element model

Roughly 75% of normal myocardial tissue volume is comprised of myocytes, however, fibroblasts by number are the most predominant cells in cardiac tissue. Previous studies have shown distinctive differences in cellular electrophysiology and excitability between myocytes and fibroblasts. However, it is still unclear how the electrical coupling between the two and the increased population of fibroblasts affects the electromechanical dynamics of cardiac tissue. This paper focuses on investigating effects of fibroblast-myocyte electrical coupling (FMEC) and fibroblast population on atrial electrical conduction and mechanical contractility by using a two-dimensional Discrete Element Method (DEM) model of cardiac tissue that is different to finite element method (FEM). In the model, the electro-mechanics of atrial cells are modelled by a biophysically detailed model for atrial electrical action potentials and myofilament kinetics, and the atrial fibroblasts are modelled by an active model that considers four active membrane ionic channel currents. Our simulation results show that the FMEC impairs myocytes' electrical action potential and mechanical contractibility, manifested by reduced upstroke velocity, amplitude and duration of action potentials, as well as cell length shortening. At the tissue level, the FMEC slows down the conduction of excitation waves, and reduces strain of the tissue produced during a contraction course. These findings provide new insights into understandings of how FMEC impairs cardiac electrical and mechanical dynamics of the heart.

Computationally efficient model of myocardial electromechanics for multiscale simulations

A model of myocardial electromechanics is suggested. It combines modified and simplified versions of previously published models of cardiac electrophysiology, excitation-contraction coupling, and mechanics. The mechano-calcium and mechano-electrical feedbacks, including the strain-dependence of the propagation velocity of the action potential, are also accounted for. The model reproduces changes in the twitch amplitude and Ca2+-transients upon changes in muscle strain including the slow response. The model also reproduces the Bowditch effect and changes in the twitch amplitude and duration upon changes in the interstimulus interval, including accelerated relaxation at high stimulation frequency. Special efforts were taken to reduce the stiffness of the differential equations of the model. As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

A dual adaptive explicit time integration algorithm for efficiently solving the cardiac monodomain equation

The monodomain model is widely used in in-silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion term is solved implicitly with a large time step while the reaction term is solved by using an explicit method with adaptive time stepping. In this work, we propose a fully explicit method for the solution of the decoupled monodomain model. In contrast to semi-implicit methods, fully explicit methods present lower memory footprint and higher scalability. However, such methods are only conditionally stable. We overcome the conditional stability limitation by proposing a dual adaptive explicit method in which adaptive time integration is applied for the solution of both the reaction and diffusion terms. We perform a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions. Results show that the proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting-based methods.

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.

Model Systems for Addressing Mechanism of Arrhythmogenesis in Cardiac Repair

PURPOSE OF REVIEW

Cardiac cell-based therapy represents a promising approach for cardiac repair. However, one of the main challenges is cardiac arrhythmias associated with stem cell transplantation. The current review summarizes the recent progress in model systems for addressing mechanisms of arrhythmogenesis in cardiac repair.

RECENT FINDINGS

Animal models have been extensively developed for mechanistic studies of cardiac arrhythmogenesis. Advances in human induced pluripotent stem cells (hiPSCs), patient-specific disease models, tissue engineering, and gene editing have greatly enhanced our ability to probe the mechanistic bases of cardiac arrhythmias. Additionally, recent development in multiscale computational studies and machine learning provides yet another powerful tool to quantitatively decipher the mechanisms of cardiac arrhythmias. Advancing efforts towards the integrations of experimental and computational studies are critical to gain insights into novel mitigation strategies for cardiac arrhythmias in cell-based therapy.

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.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

Computational prediction of drug response in short QT syndrome type 1 based on measurements of compound effect in stem cell-derived cardiomyocytes

Short QT (SQT) syndrome is a genetic cardiac disorder characterized by an abbreviated QT interval of the patient's electrocardiogram. The syndrome is associated with increased risk of arrhythmia and sudden cardiac death and can arise from a number of ion channel mutations. Cardiomyocytes derived from induced pluripotent stem cells generated from SQT patients (SQT hiPSC-CMs) provide promising platforms for testing pharmacological treatments directly in human cardiac cells exhibiting mutations specific for the syndrome. However, a difficulty is posed by the relative immaturity of hiPSC-CMs, with the possibility that drug effects observed in SQT hiPSC-CMs could be very different from the corresponding drug effect in vivo. In this paper, we apply a multistep computational procedure for translating measured drug effects from these cells to human QT response. This process first detects drug effects on individual ion channels based on measurements of SQT hiPSC-CMs and then uses these results to estimate the drug effects on ventricular action potentials and QT intervals of adult SQT patients. We find that the procedure is able to identify IC50 values in line with measured values for the four drugs quinidine, ivabradine, ajmaline and mexiletine. In addition, the predicted effect of quinidine on the adult QT interval is in good agreement with measured effects of quinidine for adult patients. Consequently, the computational procedure appears to be a useful tool for helping predicting adult drug responses from pure in vitro measurements of patient derived cell lines.

Cardiac transmembrane ion channels and action potentials: cellular physiology and arrhythmogenic behavior

Cardiac arrhythmias are among the leading causes of mortality. They often arise from alterations in the electrophysiological properties of cardiac cells and their underlying ionic mechanisms. It is therefore critical to further unravel the pathophysiology of the ionic basis of human cardiac electrophysiology in health and disease. In the first part of this review, current knowledge on the differences in ion channel expression and properties of the ionic processes that determine the morphology and properties of cardiac action potentials and calcium dynamics from cardiomyocytes in different regions of the heart are described. Then the cellular mechanisms promoting arrhythmias in congenital or acquired conditions of ion channel function (electrical remodeling) are discussed. The focus is on human-relevant findings obtained with clinical, experimental, and computational studies, given that interspecies differences make the extrapolation from animal experiments to human clinical settings difficult. Deepening the understanding of the diverse pathophysiology of human cellular electrophysiology will help in developing novel and effective antiarrhythmic strategies for specific subpopulations and disease conditions.

Afterdepolarizations and abnormal calcium handling in atrial myocytes with modulated SERCA uptake: a sensitivity analysis of calcium handling channels

Delayed afterdepolarizations (DADs) and spontaneous depolarizations (SDs) are typically triggered by spontaneous diastolic Ca²⁺ release from the sarcoplasmic reticulum (SR) which is caused by an elevated SR Ca²⁺-ATPase (SERCA) uptake and dysfunctional ryanodine receptors. However, recent studies on the T-box transcription factor gene (TBX5) demonstrated that abnormal depolarizations could occur despite a reduced SERCA uptake. Similar findings have also been reported in experimental or clinical studies of diabetes and heart failure. To investigate the sensitivity of SERCA in the genesis of DADs/SDs as well as its dependence on other Ca²⁺ handling channels, we performed systematic analyses using the Maleckar et al. model. Results showed that the modulation of SERCA alone cannot trigger abnormal depolarizations, but can instead affect the interdependency of other Ca²⁺ handling channels in triggering DADs/SDs. Furthermore, we discovered the existence of a threshold value for the intracellular concentration of Ca²⁺ ([Ca²⁺]_i) for abnormal depolarizations, which is modulated by the maximum SERCA uptake and the concentration of Ca²⁺ in the uptake and release compartments in the SR ([Ca²⁺]_up and [Ca²⁺]_rel). For the first time, our modelling study reconciles different mechanisms of abnormal depolarizations in the setting of 'lone' AF, reduced TBX5, diabetes and heart failure, and may lead to more targeted treatment for these patients. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Genetic variation in GNB5 causes bradycardia by augmenting the cholinergic response via increased acetylcholine-activated potassium current (I K,ACh)

Mutations in GNB5, encoding the G-protein β5 subunit (Gβ5), have recently been linked to a multisystem disorder that includes severe bradycardia. Here, we investigated the mechanism underlying bradycardia caused by the recessive p.S81L Gβ5 variant. Using CRISPR/Cas9-based targeting, we generated an isogenic series of human induced pluripotent stem cell (hiPSC) lines that were either wild type, heterozygous or homozygous for the GNB5 p.S81L variant. These were differentiated into cardiomyocytes (hiPSC-CMs) that robustly expressed the acetylcholine-activated potassium channel [I(KACh); also known as I_K,ACh]. Baseline electrophysiological properties of the lines did not differ. Upon application of carbachol (CCh), homozygous p.S81L hiPSC-CMs displayed an increased acetylcholine-activated potassium current (I _K,ACh) density and a more pronounced decrease of spontaneous activity as compared to wild-type and heterozygous p.S81L hiPSC-CMs, explaining the bradycardia in homozygous carriers. Application of the specific I(KACh) blocker XEN-R0703 resulted in near-complete reversal of the phenotype. Our results provide mechanistic insights and proof of principle for potential therapy in patients carrying GNB5 mutations.This article has an associated First Person interview with the first author of the paper.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Computational modeling: What does it tell us about atrial fibrillation therapy?

Atrial fibrillation (AF) is a complex cardiac arrhythmia with diverse etiology that negatively affects morbidity and mortality of millions of patients. Technological and experimental advances have provided a wealth of information on the pathogenesis of AF, highlighting a multitude of mechanisms involved in arrhythmia initiation and maintenance, and disease progression. However, it remains challenging to identify the predominant mechanisms for specific subgroups of AF patients, which, together with an incomplete understanding of the pleiotropic effects of antiarrhythmic therapies, likely contributes to the suboptimal efficacy of current antiarrhythmic approaches. Computer modeling of cardiac electrophysiology has advanced in parallel to experimental research and provides an integrative framework to attempt to overcome some of these challenges. Multi-scale cardiac modeling and simulation integrate structural and functional data from experimental and clinical work with knowledge of atrial electrophysiological mechanisms and dynamics, thereby improving our understanding of AF mechanisms and therapy. In this review, we describe recent advances in our quantitative understanding of AF through mathematical models. We discuss computational modeling of AF mechanisms and therapy using detailed, mechanistic cell/tissue-level models, including approaches to incorporate variability in patient populations. We also highlight efforts using whole-atria models to improve catheter ablation therapies. Finally, we describe recent efforts and suggest future extensions to model clinical concepts of AF using patient-level models.

Cellular Mechanisms of Sinus Node Dysfunction in Carriers of the SCN5A-E161K Mutation and Role of the H558R Polymorphism

Background: Carriers of the E161K mutation in the SCN5A gene, encoding the Na_V1.5 pore-forming α-subunit of the ion channel carrying the fast sodium current (I_Na), show sinus bradycardia and occasional exit block. Voltage clamp experiments in mammalian expression systems revealed a mutation-induced 2.5- to 4-fold reduction in I_Na peak current density as well as a +19 mV shift and reduced steepness of the steady-state activation curve. The highly common H558R polymorphism in Na_V1.5 limits this shift to +13 mV, but also introduces a -10 mV shift in steady-state inactivation. Aim: We assessed the cellular mechanism by which the E161K mutation causes sinus node dysfunction in heterozygous mutation carriers as well as the potential role of the H558R polymorphism. Methods: We incorporated the mutation-induced changes in I_Na into the Fabbri-Severi model of a single human sinoatrial node cell and the Maleckar et al. human atrial cell model, and carried out simulations under control conditions and over a wide range of acetylcholine levels. Results: In absence of the H558R polymorphism, the E161K mutation increased the basic cycle length of the sinoatrial node cell from 813 to 866 ms. In the simulated presence of 10 and 25 nM acetylcholine, basic cycle length increased from 1027 to 1131 and from 1448 to 1795 ms, respectively. The increase in cycle length was the result of a significant slowing of diastolic depolarization. The mutation-induced reduction in I_Na window current had reduced the contribution of the mutant component of I_Na to the net membrane current during diastolic depolarization to effectively zero. Highly similar results were obtained in presence of the H558R polymorphism. Atrial excitability was reduced, both in absence and presence of the H558R polymorphism, as reflected by an increase in threshold stimulus current and a concomitant decrease in capacitive current of the atrial cell. Conclusion: We conclude that the experimentally identified mutation-induced changes in I_Na can explain the clinically observed sinus bradycardia and potentially the occasional exit block. Furthermore, we conclude that the common H558R polymorphism does not significantly alter the effects of the E161K mutation and can thus not explain the reduced penetrance of the E161K mutation.

Ionic and cellular mechanisms underlying TBX5/PITX2 insufficiency-induced atrial fibrillation: Insights from mathematical models of human atrial cells

Transcription factors TBX5 and PITX2 involve in the regulation of gene expression of ion channels and are closely associated with atrial fibrillation (AF), the most common cardiac arrhythmia in developed countries. The exact cellular and molecular mechanisms underlying the increased susceptibility to AF in patients with TBX5/PITX2 insufficiency remain unclear. In this study, we have developed and validated a novel human left atrial cellular model (TPA) based on the ten Tusscher-Panfilov ventricular cell model to systematically investigate how electrical remodeling induced by TBX5/PITX2 insufficiency leads to AF. Using our TPA model, we have demonstrated that spontaneous diastolic depolarization observed in atrial myocytes with TBX5-deletion can be explained by altered intracellular calcium handling and suppression of inward-rectifier potassium current (IK1). Additionally, our computer simulation results shed new light on the novel cellular mechanism underlying AF by indicating that the imbalance between suppressed outward current IK1 and increased inward sodium-calcium exchanger current (INCX) resulted from SR calcium leak leads to spontaneous depolarizations. Furthermore, our simulation results suggest that these arrhythmogenic triggers can be potentially suppressed by inhibiting sarcoplasmic reticulum (SR) calcium leak and reversing remodeled IK1. More importantly, this study has clinically significant implications on the drugs used for maintaining SR calcium homeostasis, whereby drugs such as dantrolene may confer significant improvement for the treatment of AF patients with TBX5/PITX2 insufficiency.

Influence of atrial contraction dynamics on cardiac function

In recent years, there has been a move from monoventricular or biventricular models of the heart, to more complex models that incorporate the electromechanical function in all 4 chambers. However, the biophysical foundation is still underdeveloped, with most work in atrial cellular models having focused on electrophysiological properties. Here, we present a biophysical model of human atrial contraction at body temperature and use it to study the effects of atrial contraction on whole organ function and a study of the effects of remodelling due to atrial fibrillation on atrial and ventricular function.

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.

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.

An integrative appraisal of mechano-electric feedback mechanisms in the heart

Mechanically-induced alterations in cardiac electrophysiology are referred to as mechano-electric feedback (MEF), and play an important role in electrical regulation of cardiac performance. The influence of mechanical stress and strain on electrophysiology has been investigated at all levels, however the role of MEF in arrhythmia remains poorly understood. During the normal contraction of the heart, mechano-sensitive processes are an implicit component of cardiac activity. Under abnormal mechanical events, stretch-activated mechanisms may contribute to local or global changes in electrophysiology (EP). While such mechanisms have been hypothesised to be involved in mechanically-initiated arrhythmias, the details of these mechanisms and their importance remain elusive. We assess the theoretical role of stretch mechanisms using coupled models of cellular electrophysiology and sarcomere contraction dynamics. Using models of single ventricular myocytes, we first investigated the potential MEF contributions of stretch-activated currents (SAC), and stretch-induced myofilament calcium release, to test how strain and fibrosis may alter cellular electrophysiology. For all models investigated, SACs were alone not sufficient to create a pro-arrhythmic perturbation of the action potential with stretch. However, when combined with stretch-induced myofilament calcium release, the action potential could be shortened depending on the timing of the strain. This effect was highly model dependent, with a canine epicardial EP model being the most sensitive. These model results suggest that known mechanisms of mechano-electric coupling in cardiac myocyte may be sufficient to be pro-arrhythmic, but only in combination and under specific strain patterns.

In Silico Evaluation of the Potential Antiarrhythmic Effect of Epigallocatechin-3-Gallate on Cardiac Channelopathies

Ion channels are transmembrane proteins that allow the passage of ions according to the direction of their electrochemical gradients. Mutations in more than 30 genes encoding ion channels have been associated with an increasingly wide range of inherited cardiac arrhythmias. In this line, ion channels become one of the most important molecular targets for several classes of drugs, including antiarrhythmics. Nevertheless, antiarrhythmic drugs are usually accompanied by some serious side effects. Thus, developing new approaches could offer added values to prevent and treat the episodes of arrhythmia. In this sense, green tea catechins seem to be a promising alternative because of the significant effect of Epigallocatechin-3-Gallate (E3G) on the electrocardiographic wave forms of guinea pig hearts. Thus, the aim of this study was to evaluate the benefits-risks balance of E3G consumption in the setting of ion channel mutations linked with aberrant cardiac excitability phenotypes. Two gain-of-function mutations, Na_v1.5-p.R222Q and Na_v1.5-p.I141V, which are linked with cardiac hyperexcitability phenotypes were studied. Computer simulations of action potentials (APs) show that 30 μM E3G reduces and suppresses AP abnormalities characteristics of these phenotypes. These results suggest that E3G may have a beneficial effect in the setting of cardiac sodium channelopathies displaying a hyperexcitability phenotype.

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.

Myokit: A simple interface to cardiac cellular electrophysiology

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

Virtual electrophysiological study of atrial fibrillation in fibrotic remodeling

Research has indicated that atrial fibrillation (AF) ablation failure is related to the presence of atrial fibrosis. However it remains unclear whether this information can be successfully used in predicting the optimal ablation targets for AF termination. We aimed to provide a proof-of-concept that patient-specific virtual electrophysiological study that combines i) atrial structure and fibrosis distribution from clinical MRI and ii) modeling of atrial electrophysiology, could be used to predict: (1) how fibrosis distribution determines the locations from which paced beats degrade into AF; (2) the dynamic behavior of persistent AF rotors; and (3) the optimal ablation targets in each patient. Four MRI-based patient-specific models of fibrotic left atria were generated, ranging in fibrosis amount. Virtual electrophysiological studies were performed in these models, and where AF was inducible, the dynamics of AF were used to determine the ablation locations that render AF non-inducible. In 2 of the 4 models patient-specific models AF was induced; in these models the distance between a given pacing location and the closest fibrotic region determined whether AF was inducible from that particular location, with only the mid-range distances resulting in arrhythmia. Phase singularities of persistent rotors were found to move within restricted regions of tissue, which were independent of the pacing location from which AF was induced. Electrophysiological sensitivity analysis demonstrated that these regions changed little with variations in electrophysiological parameters. Patient-specific distribution of fibrosis was thus found to be a critical component of AF initiation and maintenance. When the restricted regions encompassing the meander of the persistent phase singularities were modeled as ablation lesions, AF could no longer be induced. The study demonstrates that a patient-specific modeling approach to identify non-invasively AF ablation targets prior to the clinical procedure is feasible.

Cellular cardiac electrophysiology modeling with Chaste and CellML

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

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.

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.

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.

Cross talk between cardiac myocytes and fibroblasts: from multiscale investigative approaches to mechanisms and functional consequences

The heart is comprised of a syncytium of cardiac myocytes (CM) and surrounding nonmyocytes, the majority of which are cardiac fibroblasts (CF). CM and CF are highly interspersed in the myocardium with one CM being surrounded by one or more CF. Bidirectional cross talk between CM and CF plays important roles in determining cardiac mechanical and electrical function in both normal and diseased hearts. Genetically engineered animal models and in vitro studies have provided evidence that CM and CF can regulate each other's function. Their cross talk contributes to structural and electrical remodeling in both atria and ventricles and appears to be involved in the pathogenesis of various heart diseases that lead to heart failure and arrhythmia disorders. Mechanisms of CM-CF cross talk, which are not yet fully understood, include release of paracrine factors, direct cell-cell interactions via gap junctions and potentially adherens junctions and nanotubes, and cell interactions with the extracellular matrix. In this article, we provide an overview of the existing multiscale experimental and computational approaches for the investigation of cross talk between CM and CF and review recent progress in our understanding of the functional consequences and underlying mechanisms. Targeting cross talk between CM and CF could potentially be used therapeutically for the modulation of the cardiac remodeling response in the diseased heart and may lead to new strategies for the treatment of heart failure or rhythm disturbances.

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.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

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

Measurement of the membrane potential in small cells using patch clamp methods

The resting membrane potential, E(m), of mammalian cells is a fundamental physiological parameter. Even small changes in E(m) can modulate excitability, contractility and rates of cell migration. At present accurate, reproducible measurements of E(m) and determination of its ionic basis remain significant challenges when patch clamp methods are applied to small cells. In this study, a mathematical model has been developed which incorporates many of the main biophysical principles which govern recordings of the resting potential of 'small cells'. Such a prototypical cell (approx. capacitance, 6 pF; input resistance 5 GΩ) is representative of neonatal cardiac myocytes, and other cells in the cardiovascular system (endothelium, fibroblasts) and small cells in other tissues, e.g. bone (osteoclasts) articular joints (chondrocytes) and the pancreas (β cells). Two common experimental conditions have been examined: (1) when the background K(+) conductance is linear; and (2) when this K(+) conductance is highly nonlinear and shows pronounced inward rectification. In the case of a linear K(+) conductance, the presence of a "leakage" current through the seal resistance between the cell membrane and the patch pipette always depolarizes E(m). Our calculations confirm that accurate characterization of E(m) is possible when the seal resistance is at least 5 times larger than the input resistance of the targeted cell. Measurement of E(m) under conditions in which the main background current includes a markedly nonlinear K(+) conductance (due to inward rectification) yields complex and somewhat counter-intuitive findings. In fact, there are at least two possible stable values of resting membrane potential for a cell when the nonlinear, inwardly rectifying K(+) conductance interacts with the seal current. This type of bistable behavior has been reported in a variety of small mammalian cells, including those from the heart, endothelium, smooth muscle and bone. Our theoretical treatment of these two common experimental situations provides useful mechanistic insights, and suggests practical methods by which these significant limitations, and their impact, can be minimized.

Ca²⁺-induced delayed afterdepolarizations are triggered by dyadic subspace Ca2²⁺ affirming that increasing SERCA reduces aftercontractions

Ca(2+)-induced delayed afterdepolarizations (DADs) are depolarizations that occur after full repolarization. They have been observed across multiple species and cell types. Experimental results have indicated that the main cause of DADs is Ca(2+) overload. The main hypothesis as to their initiation has been Ca(2+) overflow from the overloaded sarcoplasmic reticulum (SR). Our results using 37 previously published mathematical models provide evidence that Ca(2+)-induced DADs are initiated by the same mechanism as Ca(2+)-induced Ca(2+) release, i.e., the modulation of the opening of ryanodine receptors (RyR) by Ca(2+) in the dyadic subspace; an SR overflow mechanism was not necessary for the induction of DADs in any of the models. The SR Ca(2+) level is better viewed as a modulator of the appearance of DADs and the magnitude of Ca(2+) release. The threshold for the total Ca(2+) level within the cell (not only the SR) at which Ca(2+) oscillations arise in the models is close to their baseline level (∼1- to 3-fold). It is most sensitive to changes in the maximum sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA) pump rate (directly proportional), the opening probability of RyRs, and the Ca(2+) diffusion rate from the dyadic subspace into the cytosol (both indirectly proportional), indicating that the appearance of DADs is multifactorial. This shift in emphasis away from SR overload as the trigger for DADs toward a multifactorial analysis could explain why SERCA overexpression has been shown to suppress DADs (while increasing contractility) and why DADs appear during heart failure (at low SR Ca(2+) levels).

Stiffness analysis of cardiac electrophysiological models

The electrophysiology in a cardiac cell can be modeled as a system of ordinary differential equations (ODEs). The efficient solution of these systems is important because they must be solved many times as sub-problems of tissue- or organ-level simulations of cardiac electrophysiology. The wide variety of existing cardiac cell models encompasses many different properties, including the complexity of the model and the degree of stiffness. Accordingly, no single numerical method can be expected to be the most efficient for every model. In this article, we study the stiffness properties of a range of cardiac cell models and discuss the implications for their numerical solution. This analysis allows us to select or design numerical methods that are highly effective for a given model and hence outperform commonly used methods.

Effects of fibroblast-myocyte coupling on cardiac conduction and vulnerability to reentry: A computational study

BACKGROUND

Recent experimental studies have documented that functional gap junctions form between fibroblasts and myocytes, raising the possibility that fibroblasts play roles in cardiac electrophysiology that extend beyond acting as passive electrical insulators.

OBJECTIVE

The purpose of this study was to use computational models to investigate how fibroblasts may affect cardiac conduction and vulnerability to reentry under different fibroblast-myocyte coupling conditions and tissue structures.

METHODS

Computational models of two-dimensional tissue with fibroblast-myocyte coupling were developed and numerically simulated. Myocytes were modeled by the phase I of the Luo-Rudy model, and fibroblasts were modeled by a passive model.

RESULTS

Besides slowing conduction by cardiomyocyte decoupling and electrotonic loading, fibroblast coupling to myocytes elevates myocyte resting membrane potential, causing conduction velocity to first increase and then decrease as fibroblast content increases, until conduction failure occurs. Fibroblast-myocyte coupling can also enhance conduction by connecting uncoupled myocytes. These competing effects of fibroblasts on conduction give rise to different conduction patterns under different fibroblast-myocyte coupling conditions and tissue structures. Elevation of myocyte resting potential due to fibroblast-myocyte coupling slows sodium channel recovery, which extends postrepolarization refractoriness. Owing to this prolongation of the myocyte refractory period, reentry was more readily induced by a premature stimulation in heterogeneous tissue models when fibroblasts were electrotonically coupled to myocytes compared with uncoupled fibroblasts acting as pure passive electrical insulators.

CONCLUSIONS

Fibroblasts affect cardiac conduction by acting as obstacles or by creating electrotonic loading and elevating myocyte resting potential. Functional fibroblast-myocyte coupling prolongs the myocyte refractory period, which may facilitate induction of reentry in cardiac tissue with fibrosis.