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

Interactions between calcium-induced arrhythmia triggers and the electrophysiological-anatomical substrate underlying the induction of atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia and is sustained by spontaneous focal excitations and re-entry. Spontaneous electrical firing in the pulmonary vein (PV) sleeves is implicated in AF generation. The aim of this simulation study was to identify the mechanisms determining the localisation of AF triggers in the PVs and their contribution to the genesis of AF. A novel biophysical model of the canine atria was used that integrates stochastic, spontaneous subcellular Ca2+ release events (SCRE) with regional electrophysiological heterogeneity in ionic properties and a detailed three-dimensional model of atrial anatomy, microarchitecture and patchy fibrosis. Simulations highlighted the importance of the smaller inward rectifier potassium current (IK1 ) in PV cells compared to the surrounding atria, which enabled SCRE more readily to result in delayed-afterdepolarisations that induced triggered activity. There was a leftward shift in the dependence of the probability of triggered activity on sarcoplasmic reticulum Ca2+ load. This feature was accentuated in 3D tissue compared to single cells (Δ half-maximal [Ca2+ ]SR  = 58 μM vs. 22 μM). In 3D atria incorporating electrical heterogeneity, excitations preferentially emerged from the PV region. These triggered focal excitations resulted in transient re-entry in the left atrium. Addition of fibrotic patches promoted localised emergence of focal excitations and wavebreaks that had a more substantial impact on generating AF-like patterns than the PVs. Thus, a reduced IK1 , less negative resting membrane potential, and fibrosis-induced changes of the electrotonic load all contribute to the emergence of complex excitation patterns from spontaneous focal triggers. KEY POINTS: Focal excitations in the atria are most commonly associated with the pulmonary veins, but the mechanisms for this localisation are yet to be elucidated. We applied a multi-scale computational modelling approach to elucidate the mechanisms underlying such localisations. Myocytes in the pulmonary vein region of the atria have a less negative resting membrane potential and reduced time-independent potassium current; we demonstrate that both of these factors promote triggered activity in single cells and tissues. The less negative resting membrane potential also contributes to heterogeneous inactivation of the fast sodium current, which can enable re-entrant-like excitation patterns to emerge without traditional conduction block.

Exergy destruction in atrial fibrillation and a new 'Exergy Age Index'

The concept of exergy in living organisms has been widely used to explore correlations between exergy and different physiological conditions. Atrial fibrillation (AF) is an abnormal physiological condition that takes place inside the heart and is recognised as a common supraventricular arrhythmia. AF can significantly undermine heart function and subsequently circulatory system. Thus, exergy analysis of cardiac flow during AF is a procedure to quantify the long-term impact of persistent AF. The present study adopts the lumped modelling approach for considering cardiovascular circulation and thermoregulation of the body to evaluate the exergy consumption and destruction of the heart in AF. In order to assess the impact of AF, four common AF-associated characteristics including lack of atrial kick, left atrial remodelling, left ventricular systolic dysfunction, and high-frequency fibrillation are examined. The results show that among AF deficiencies, high-frequency fibrillation is the main cause of exergy destruction of the heart during AF. Moreover, a novel 'exergy age index' is proposed which has shown that high fibrillatory conditions in AF can significantly accelerate the heart ageing process, which in turn substantiates AF's adverse impact on the heart.

A detailed mathematical model of the human atrial cardiomyocyte: integration of electrophysiology and cardiomechanics

Mechano-electric regulations (MER) play an important role in the maintenance of cardiac performance. Mechano-calcium and mechano-electric feedback (MCF and MEF) pathways adjust the cardiomyocyte contractile force according to mechanical perturbations and affects electro-mechanical coupling. MER integrates all these regulations in one unit resulting in a complex phenomenon. Computational modelling is a useful tool to accelerate the mechanistic understanding of complex experimental phenomena. We have developed a novel model that integrates the MER loop for human atrial cardiomyocytes with proper consideration of feedforward and feedback pathways. The model couples a modified version of the action potential (AP) Koivumäki model with the contraction model by Quarteroni group. The model simulates iso-sarcometric and isometric twitches and the feedback effects on AP and Ca2+ -handling. The model showed a biphasic response of Ca2+ transient (CaT) peak to increasing pacing rates and highlights the possible mechanisms involved. The model has shown a shift of the threshold for AP and CaT alternans from 4.6 to 4 Hz under post-operative atrial fibrillation, induced by depressed SERCA activity. The alternans incidence was dependent on a chain of mechanisms including RyRs availability time, MCF coupling, CaMKII phosphorylation, and the stretch levels. As a result, the model predicted a 10% slowdown of conduction velocity for a 20% stretch, suggesting a role of stretch in creation of substrate formation for atrial fibrillation. Overall, we conclude that the developed model provides a physiological CaT followed by a physiological twitch. This model can open pathways for the future studies of human atrial electromechanics. KEY POINTS: With the availability of human atrial cellular data, interest in atrial-specific model integration has been enhanced. We have developed a detailed mathematical model of human atrial cardiomyocytes including the mechano-electric regulatory loop. The model has gone through calibration and evaluation phases against a wide collection of available human in-vitro data. The usefulness of the model for analysing clinical problems has been preliminaryly tested by simulating the increased incidence of Ca2+ transient and action potential alternans at high rates in post-operative atrial fibrillation condition. The model determines the possible role of mechano-electric feedback in alternans incidence, which can increase vulnerability to atrial arrhythmias by varying stretch levels. We found that our physiologically accurate description of Ca2+ handling can reproduce many experimental phenomena and can help to gain insights into the underlying pathophysiological mechanisms.

Recurrence quantification analysis for fine-scale characterisation of arrhythmic patterns in cardiac tissue

This paper uses recurrence quantification analysis (RQA) combined with entropy measures and organization indices to characterize arrhythmic patterns and dynamics in computer simulations of cardiac tissue. We performed different simulations of cardiac tissues of sizes comparable to the human heart atrium. In these simulations, we observed four classic arrhythmic patterns: a spiral wave anchored to a highly fibrotic region resulting in sustained re-entry, a meandering spiral wave, fibrillation, and a spiral wave anchored to a scar region that breaks up into wavelets away from the main rotor. A detailed analysis revealed that, within the same simulation, maps of RQA metrics could differentiate regions with regular AP propagation from ones with chaotic activity. In particular, the combination of two RQA metrics, the length of the longest diagonal string of recurrence points and the mean length of diagonal lines, was able to identify the location of rotor tips, which are the active elements that maintain spiral waves and fibrillation. By proposing low-dimensional models based on the mean value and spatial correlation of metrics calculated from membrane potential time series, we identify RQA-based metrics that successfully separate the four different types of cardiac arrhythmia into distinct regions of the feature space, and thus might be used for automatic classification, in particular distinguishing between fibrillation driven by self-sustaining chaos and that created by a persistent rotor and wavebreak. We also discuss the practical applicability of such an approach.

Personalized biomechanical insights in atrial fibrillation: opportunities & challenges

INTRODUCTION

Atrial fibrillation (AF) is an increasingly prevalent and significant worldwide health problem. Manifested as an irregular atrial electrophysiological activation, it is associated with many serious health complications. AF affects the biomechanical function of the heart as contraction follows the electrical activation, subsequently leading to reduced blood flow. The underlying mechanisms behind AF are not fully understood, but it is known that AF is highly correlated with the presence of atrial fibrosis, and with a manifold increase in risk of stroke.

AREAS COVERED

In this review, we focus on biomechanical aspects in atrial fibrillation, current and emerging use of clinical images, and personalized computational models. We also discuss how these can be used to provide patient-specific care.

EXPERT OPINION

Understanding the connection betweenatrial fibrillation and atrial remodeling might lead to valuable understanding of stroke and heart failure pathophysiology. Established and emerging imaging modalities can bring us closer to this understanding, especially with continued advancements in processing accuracy, reproducibility, and clinical relevance of the associated technologies. Computational models of cardiac electromechanics can be used to glean additional insights on the roles of AF and remodeling in heart function.

Overview of Cardiac Arrhythmias and Treatment Strategies

Maintenance of normal cardiac rhythm requires coordinated activity of ion channels and transporters that allow well-ordered propagation of electrical impulses across the myocardium. Disruptions in this orderly process provoke cardiac arrhythmias that may be lethal in some patients. Risk of common acquired arrhythmias is increased markedly when structural heart disease caused by myocardial infarction (due to fibrotic scar formation) or left ventricular dysfunction is present. Genetic polymorphisms influence structure or excitability of the myocardial substrate, which increases vulnerability or risk of arrhythmias in patients. Similarly, genetic polymorphisms of drug-metabolizing enzymes give rise to distinct subgroups within the population that affect specific drug biotransformation reactions. Nonetheless, identification of triggers involved in initiation or maintenance of cardiac arrhythmias remains a major challenge. Herein, we provide an overview of knowledge regarding physiopathology of inherited and acquired cardiac arrhythmias along with a summary of treatments (pharmacologic or non-pharmacologic) used to limit their effect on morbidity and potential mortality. Improved understanding of molecular and cellular aspects of arrhythmogenesis and more epidemiologic studies (for a more accurate portrait of incidence and prevalence) are crucial for development of novel treatments and for management of cardiac arrhythmias and their consequences in patients, as their incidence is increasing worldwide.

State of the art paper: Cardiac computed tomography of the left atrium in atrial fibrillation

The clinical spectrum of atrial fibrillation means that a patient-individualized approach is required to ensure optimal treatment. Cardiac computed tomography can accurately delineate atrial structure and function and could contribute to a personalized care pathway for atrial fibrillation patients. The imaging modality offers excellent spatial resolution and has been utilised in pre-, peri- and post-procedural care for patients with atrial fibrillation. Advances in temporal resolution, acquisition times and analysis techniques suggest potential expanding roles for cardiac computed tomography in the future management of patients with atrial fibrillation. The aim of the current review is to discuss the use of cardiac computed tomography in atrial fibrillation in pre-, peri- and post-procedural settings. Potential future applications of cardiac computed tomography including atrial wall thickness assessment and epicardial fat volume quantification are discussed together with emerging analysis techniques including computational modelling and machine learning with attention paid to how these developments may contribute to a personalized approach to atrial fibrillation management.

Increased SERCA2a sub-cellular heterogeneity in right-ventricular heart failure inhibits excitation-contraction coupling and modulates arrhythmogenic dynamics

The intracellular calcium handling system of cardiomyocytes is responsible for controlling excitation-contraction coupling (ECC) and has been linked to pro-arrhythmogenic cellular phenomena in conditions such as heart failure (HF). SERCA2a, responsible for intracellular uptake, is a primary regulator of calcium homeostasis, and remodelling of its function has been proposed as a causal factor underlying cellular and tissue dysfunction in disease. Whereas adaptations to the global (i.e. whole-cell) expression of SERCA2a have been previously investigated in the context of multiple diseases, the role of its spatial profile in the sub-cellular volume has yet to be elucidated. We present an approach to characterize the sub-cellular heterogeneity of SERCA2a and apply this approach to quantify adaptations to the length-scale of heterogeneity (the distance over which expression is correlated) associated with right-ventricular (RV)-HF. These characterizations informed simulations to predict the functional implications of this heterogeneity, and its remodelling in disease, on ECC, the dynamics of calcium-transient alternans and the emergence of spontaneous triggered activity. Image analysis reveals that RV-HF is associated with an increase in length-scale and its inter-cellular variability; simulations predict that this increase in length-scale can reduce ECC and critically modulate the vulnerability to both alternans and triggered activity. This article is part of the theme issue 'The cardiomyocyte: new revelations on the interplay between architecture and function in growth, health, and disease'.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives

Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.

Quantitative cross-species translators of cardiac myocyte electrophysiology: Model training, experimental validation, and applications

Animal experimentation is key in the evaluation of cardiac efficacy and safety of novel therapeutic compounds. However, interspecies differences in the mechanisms regulating excitation-contraction coupling can limit the translation of experimental findings from animal models to human physiology and undermine the assessment of drugs’ efficacy and safety. Here, we built a suite of translators for quantitatively mapping electrophysiological responses in ventricular myocytes across species. We trained these statistical operators using a broad dataset obtained by simulating populations of our biophysically detailed computational models of action potential and Ca2+ transient in mouse, rabbit, and human. We then tested our translators against experimental data describing the response to stimuli, such as ion channel block, change in beating rate, and β-adrenergic challenge. We demonstrate that this approach is well suited to predicting the effects of perturbations across different species or experimental conditions and suggest its integration into mechanistic studies and drug development pipelines.

Electrophysiological Remodeling: Cardiac T-Tubules and ß-Adrenoceptors

Beta-adrenoceptors (βAR) are often viewed as archetypal G-protein coupled receptors. Over the past fifteen years, investigations in cardiovascular biology have provided remarkable insights into this receptor family. These studies have shifted pharmacological dogma, from one which centralized the receptor to a new focus on structural micro-domains such as caveolae and t-tubules. Important studies have examined, separately, the structural compartmentation of ion channels and βAR. Despite links being assumed, relatively few studies have specifically examined the direct link between structural remodeling and electrical remodeling with a focus on βAR. In this review, we will examine the nature of receptor and ion channel dysfunction on a substrate of cardiomyocyte microdomain remodeling, as well as the likely ramifications for cardiac electrophysiology. We will then discuss the advances in methodologies in this area with a specific focus on super-resolution microscopy, fluorescent imaging, and new approaches involving microdomain specific, polymer-based agonists. The advent of powerful computational modelling approaches has allowed the science to shift from purely empirical work, and may allow future investigations based on prediction. Issues such as the cross-reactivity of receptors and cellular heterogeneity will also be discussed. Finally, we will speculate as to the potential developments within this field over the next ten years.

Understanding PITX2-Dependent Atrial Fibrillation Mechanisms through Computational Models

Atrial fibrillation (AF) is a common arrhythmia. Better prevention and treatment of AF are needed to reduce AF-associated morbidity and mortality. Several major mechanisms cause AF in patients, including genetic predispositions to AF development. Genome-wide association studies have identified a number of genetic variants in association with AF populations, with the strongest hits clustering on chromosome 4q25, close to the gene for the homeobox transcription PITX2. Because of the inherent complexity of the human heart, experimental and basic research is insufficient for understanding the functional impacts of PITX2 variants on AF. Linking PITX2 properties to ion channels, cells, tissues, atriums and the whole heart, computational models provide a supplementary tool for achieving a quantitative understanding of the functional role of PITX2 in remodelling atrial structure and function to predispose to AF. It is hoped that computational approaches incorporating all we know about PITX2-related structural and electrical remodelling would provide better understanding into its proarrhythmic effects leading to development of improved anti-AF therapies. In the present review, we discuss advances in atrial modelling and focus on the mechanistic links between PITX2 and AF. Challenges in applying models for improving patient health are described, as well as a summary of future perspectives.

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.

A Computational Study of the Effects of Tachycardia-Induced Remodeling on Calcium Wave Propagation in Rabbit Atrial Myocytes

In atrial cardiomyocytes without a well-developed T-tubule system, calcium diffuses from the periphery toward the center creating a centripetal wave pattern. During atrial fibrillation, rapid activation of atrial myocytes induces complex remodeling in diffusion properties that result in failure of calcium to propagate in a fully regenerative manner toward the center; a phenomenon termed “calcium silencing.” This has been observed in rabbit atrial myocytes after exposure to prolonged rapid pacing. Although experimental studies have pointed to possible mechanisms underlying calcium silencing, their individual effects and relative importance remain largely unknown. In this study we used computational modeling of the rabbit atrial cardiomyocyte to query the individual and combined effects of the proposed mechanisms leading to calcium silencing and abnormal calcium wave propagation. We employed a population of models obtained from a newly developed model of the rabbit atrial myocyte with spatial representation of intracellular calcium handling. We selected parameters in the model that represent experimentally observed cellular remodeling which have been implicated in calcium silencing, and scaled their values in the population to match experimental observations. In particular, we changed the maximum conductances of ICaL, INCX, and INaK, RyR open probability, RyR density, Serca2a density, and calcium buffering strength. We incorporated remodeling in a population of 16 models by independently varying parameters that reproduce experimentally observed cellular remodeling, and quantified the resulting alterations in calcium dynamics and wave propagation patterns. The results show a strong effect of ICaL in driving calcium silencing, with INCX, INaK, and RyR density also resulting in calcium silencing in some models. Calcium alternans was observed in some models where INCX and Serca2a density had been changed. Simultaneously incorporating changes in all remodeled parameters resulted in calcium silencing in all models, indicating the predominant role of decreasing ICaL in the population phenotype.

Latest Insights into Mechanisms behind Atrial Cardiomyopathy: It Is Not always about Ventricular Function

Atrial cardiomyopathy (ACM) represents a constantly evolving concept, with increasing importance in contemporary research and clinical practice. A better understanding of the mechanisms involved in atrial remodeling and its clinical correlations especially with atrial fibrillation (AF) and other cardiometabolic comorbidities may induce a significant impact on the diagnosis, prognosis, and therapeutic approach of ACM-related comorbidities. Although initially described several decades ago, investigators have only recently highlighted that several renal, metabolic, and cardiovascular diseases are determining factors for atrial remodeling and subsequent ACM. Based on data from multiple recent studies, our research emphasizes the correlations between ACM and other coexisting pathologies including cardiovascular, respiratory, or metabolic diseases, with fibrosis being the most incriminated pathophysiological mechanism. In addition to the usual tests, the paraclinical assessment of ACM is increasingly based on the use of various cardiac biomarkers, while the cardiac magnetic resonance (CMR) has become an increasingly tempting diagnostic too for describing morphofunctional aspects of the heart chambers, with the gadolinium contrast enhanced CMR (LGE-CMR) emerging as a commonly used technique aiming to identify and quantify the precise extent of atrial fibrosis. Further research should be conducted in order to clarify our knowledge regarding atrial remodeling and, therefore, to develop new and improved therapeutic approaches in these patients.

Effects of Ageing on Aortic Circulation During Atrial Fibrillation; a Numerical Study on Different Aortic Morphologies

Atrial fibrillation (AF) can alter intra-cardiac flow and cardiac output that subsequently affects aortic flow circulation. These changes may become more significant where they occur concomitantly with ageing. Aortic ageing is accompanied with morphological changes such as dilation, lengthening, and arch unfolding. While the recognition of AF mechanism has been the subject of numerous studies, less focus has been devoted to the aortic circulation during the AF and there is a lack of such investigation at different ages. The current work aims to address the present gap. First, we analyse aortic flow distribution in three configurations, which attribute to young, middle and old people, using geometries constructed via clinical data. We then introduce two transient inlet flow conditions representative of key AF-associated defects. Results demonstrate that both AF and ageing negatively affect flow circulation. The main consequence of concomitant occurrence is enhancement of endothelial cell activation potential (ECAP) throughout the vascular domain, mainly at aortic arch and descending thoracic aorta, which is consistent with some clinical observations. The outcome of the current study suggests that AF exacerbates the vascular defects occurred due to the ageing, which increases the possibility of cardiovascular diseases per se.

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.

Short P-Wave Duration is a Marker of Higher Rate of Atrial Fibrillation Recurrences after Pulmonary Vein Isolation: New Insights into the Pathophysiological Mechanisms Through Computer Simulations

Background Short ECG P-wave duration has recently been demonstrated to be associated with higher risk of atrial fibrillation (AF). The aim of this study was to assess the rate of AF recurrence after pulmonary vein isolation in patients with a short P wave, and to mechanistically elucidate the observation by computer modeling. Methods and Results A total of 282 consecutive patients undergoing a first single-pulmonary vein isolation procedure for paroxysmal or persistent AF were included. Computational models studied the effect of adenosine and sodium conductance on action potential duration and P-wave duration (PWD). About 16% of the patients had a PWD of 110 ms or shorter (median PWD 126 ms, interquartile range, 115 ms-138 ms; range, 71 ms-180 ms). At Cox regression, PWD was significantly associated with AF recurrence (P=0.012). Patients with a PWD <110 ms (hazard ratio [HR], 2.20; 95% CI, 1.24-3.88; P=0.007) and patients with a PWD ≥140 (HR, 1.87, 95% CI, 1.06-3.30; P=0.031) had a nearly 2-fold increase in risk with respect to the other group. In the computational model, adenosine yielded a significant reduction of action potential duration 90 (52%) and PWD (7%). An increased sodium conductance (up to 200%) was robustly accompanied by an increase in conduction velocity (26%), a reduction in action potential duration 90 (28%), and PWD (22%). Conclusions One out of 5 patients referred for pulmonary vein isolation has a short PWD which was associated with a higher rate of AF after the index procedure. Computer simulations suggest that shortening of atrial action potential duration leading to a faster atrial conduction may be the cause of this clinical observation.

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.

A Novel Computational Model of the Rabbit Atrial Cardiomyocyte With Spatial Calcium Dynamics

Models of cardiac electrophysiology are widely used to supplement experimental results and to provide insight into mechanisms of cardiac function and pathology. The rabbit has been a particularly important animal model for studying mechanisms of atrial pathophysiology and atrial fibrillation, which has motivated the development of models for the rabbit atrial cardiomyocyte electrophysiology. Previously developed models include detailed representations of membrane currents and intracellular ionic concentrations, but these so-called “common-pool” models lack a spatially distributed description of the calcium handling system, which reflects the detailed ultrastructure likely found in cells in vivo. Because of the less well-developed T-tubular system in atrial compared to ventricular cardiomyocytes, spatial gradients in intracellular calcium concentrations may play a more significant role in atrial cardiomyocyte pathophysiology, rendering common-pool models less suitable for investigating underlying electrophysiological mechanisms. In this study, we developed a novel computational model of the rabbit atrial cardiomyocyte incorporating detailed compartmentalization of intracellular calcium dynamics, in addition to a description of membrane currents and intracellular processes. The spatial representation of calcium was based on dividing the intracellular space into eighteen different compartments in the transversal direction, each with separate systems for internal calcium storage and release, and tracking ionic fluxes between compartments in addition to the dynamics driven by membrane currents and calcium release. The model was parameterized employing a population-of-models approach using experimental data from different sources. The parameterization of this novel model resulted in a reduced population of models with inherent variability in calcium dynamics and electrophysiological properties, all of which fall within the range of observed experimental values. As such, the population of models may represent natural variability in cardiomyocyte electrophysiology or inherent uncertainty in the underlying experimental data. The ionic model population was also able to reproduce the U-shaped waveform observed in line-scans of triggered calcium waves in atrial cardiomyocytes, characteristic of the absence of T-tubules, resulting in a centripetal calcium wave due to subcellular calcium diffusion. This novel spatial model of the rabbit atrial cardiomyocyte can be used to integrate experimental findings, offering the potential to enhance our understanding of the pathophysiological role of calcium-handling abnormalities under diseased conditions, such as atrial fibrillation.

Role of ion channels in chronic intermittent hypoxia-induced atrial remodeling in rats

AIMS

Atrial remodeling, including structural and electrical remodeling, is considered as the substrate in the development of atrial fibrillation (AF). Structural remodeling mainly involves atrial fibrosis, and electrical remodeling is closely related to the changes of ion channels in atrial myocytes. In this study, we aimed to investigate the changes of ion channels in atrial remodeling induced by CIH in rats, which provide the explication for the mechanisms of AF.

MATERIALS AND METHODS

80 male Sprague-Dawley rats were randomized into two groups: Control and CIH group (n = 40). CIH rats were subjected to CIH 8 h/d for 30 days. Atrial epicardial conduction velocity, conduction inhomogeneity and AF inducibility were examined. Masson's trichrome staining was used to evaluate the extent of atrial fibrosis, and the expression levels of ion channel subunits were measured by RT-qPCR, Western blot, and IHC, respectively. The remaining 40 rats were used for whole-cell patch clamp experiments. Action potential, I_Na, I_Ca-L, I_to were recorded and compared between two groups.

KEY FINDINGS

CIH rats showed increased AF inducibility, atrial interstitial collagen deposition, APD, expression levels of RyR2, p-RyR2, CaMKII, p-CaMKII, and decreased atrial epicardial conduction velocity, expression levels of Na_v1.5, Ca_v1.2, K_v1.5, K_v4.2, K_v4.3 compared to the Control rats, and the current density of I_Na, I_Ca-L, I_to were significantly decreased in CIH group.

SIGNIFICANCE

We observed significant atrial remodeling induced by CIH in our rat model, which was characterized by changes in ion channels. These changes may be the mechanisms of CIH promoting AF.

Cardiomyocyte calcium handling in health and disease: Insights from in vitro and in silico studies

Calcium (Ca²⁺) plays a central role in cardiomyocyte excitation-contraction coupling. To ensure an optimal electrical impulse propagation and cardiac contraction, Ca²⁺ levels are regulated by a variety of Ca²⁺-handling proteins. In turn, Ca²⁺ modulates numerous electrophysiological processes. Accordingly, Ca²⁺-handling abnormalities can promote cardiac arrhythmias via various mechanisms, including the promotion of afterdepolarizations, ion-channel modulation and structural remodeling. In the last 30 years, significant improvements have been made in the computational modeling of cardiomyocyte Ca²⁺ handling under physiological and pathological conditions. However, numerous questions involving the Ca²⁺-dependent regulation of different macromolecular complexes, cross-talk between Ca²⁺-dependent regulatory pathways operating over a wide range of time scales, and bidirectional interactions between electrophysiology and mechanics remain to be addressed by in vitro and in silico studies. A better understanding of disease-specific Ca²⁺-dependent proarrhythmic mechanisms may facilitate the development of improved therapeutic strategies. In this review, we describe the fundamental mechanisms of cardiomyocyte Ca²⁺ handling in health and disease, and provide an overview of currently available computational models for cardiomyocyte Ca²⁺ handling. Finally, we discuss important uncertainties and open questions about cardiomyocyte Ca²⁺ handling and highlight how synergy between in vitro and in silico studies may help to answer several of these issues.

PITX2 upregulation increases the risk of chronic atrial fibrillation in a dose-dependent manner by modulating IKs and ICaL -insights from human atrial modelling

Background

Functional analysis has shown that the paired-like homeodomain transcription factor 2 (PITX2) overexpression associated with atrial fibrillation (AF) leads to the slow delayed rectifier K⁺ current (I_Ks) increase and the L-type Ca²⁺ current (I_CaL) reduction observed in isolated right atrial myocytes from chronic AF (CAF) patients. Through multiscale computational models, this study aimed to investigate the functional impact of the PITX2 overexpression on atrial electrical activity.

Methods

The well-known Courtemanche-Ramirez-Nattel (CRN) model of human atrial action potentials (APs) was updated to incorporate experimental data on alterations in I_Ks and I_CaL due to the PITX2 overexpression. These cell models for sinus rhythm (SR) and CAF were then incorporated into homogeneous multicellular one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) tissue models. The proarrhythmic effects of the PITX2 overexpression were quantified with ion current profiles, AP morphology, AP duration (APD) restitution, conduction velocity restitution (CVR), wavelength (WL), vulnerable window (VW) for unidirectional conduction block, and minimal substrate size required to induce re-entry. Dynamic behaviors of spiral waves were characterized by measuring lifespan (LS), tip patterns and dominant frequencies.

Results

The I_Ks increase and the I_CaL decrease arising from the PITX2 overexpression abbreviated APD and flattened APD restitution (APDR) curves in single cells. It reduced WL and increased CV at high excitation rates at the 1D tissue level. Although it had no effects on VW for initiating spiral waves, it decreased the minimal substrate size necessary to sustain re-entry. It also stabilized and accelerated spiral waves in 2D and 3D tissue models.

Conclusions

Electrical remodeling (I_Ks and I_CaL) due to the PITX2 overexpression increases susceptibility to AF due to increased tissue vulnerability, abbreviated APD, shortened WL and altered CV, which, in combination, facilitate initiation and maintenance of spiral waves.

Multi-scale approaches for the simulation of cardiac electrophysiology: I - Sub-cellular and stochastic calcium dynamics from cell to organ

Computational models of the heart at multiple spatial scales, from sub-cellular nanodomains to the whole-organ, are a powerful tool for the simulation of cardiac electrophysiology. Application of these models has provided remarkable insight into the normal and pathological functioning of the heart. In these two articles, we present methods for modelling cardiac electrophysiology at all of these spatial scales. In part one, presented here, we discuss methods and approaches for modelling sub-cellular calcium dynamics at the whole-cell and organ scales, valuable for modelling excitation-contraction coupling and mechanisms of arrhythmia triggers.

Doxycycline Improves Fibrosis-Induced Abnormalities in Atrial Conduction and Vulnerability to Atrial Fibrillation in Chronic Intermittent Hypoxia Rats

Background

The structural remodeling of atrial architecture, especially increased amounts of fibrosis, is a critical substrate to atrial fibrillation (AF). Doxycycline (Doxy) has recently been shown to exert protective effects against fibrogenic response. This study investigated whether doxycycline (Doxy) can sufficiently ameliorate the fibrosis-induced changes of atrial conduction and AF vulnerability in a chronic intermittent hypoxia (CIH) rat model.

Material/Methods

Sixty rats were randomized into 3 groups: Control, CIH, and CIH with Doxy treatment (DOXY) group. CIH rats were exposed to CIH (6 h/d) and Doxy-treated rats were treated with Doxy during processing CIH. After 6 weeks, echocardiographic and hemodynamic parameters were measured. Isolated atrial epicardial activation mapping and heart electrophysiology were performed. The extent of atrial interstitial fibrosis were estimated by Masson’s trichrome staining. The expression levels of TGF-β1 and downstream factors were determined by real-Time PCR, immunohistochemistry, and Western blot analysis.

Results

Compared to Control rats, the CIH rats showed significant atrial interstitial fibrosis, longer inter-atrial conduction time, and elevated conduction inhomogeneity and AF inducibility, and the expression of TGF-β1, TGF-βRI, TGF-βRII, P-Smad2/3, α-SMA, CTGF, and Collagen I were significantly increased, whereas the velocity of atrial conduction and the expression of miR-30c were dramatically decreased. All of these changes were significantly improved by Doxy treatment.

Conclusions

The findings suggested that Doxy can profoundly mitigate atrial fibrosis, conduction inhomogeneity as well as high AF inducibility secondary to fibrosis in a CIH rat model through suppressing the TGF-β1 signaling pathway.

Numerical Study of Atrial Fibrillation Effects on Flow Distribution in Aortic Circulation

Atrial fibrillation (AF) is the most common type of arrhythmia, which undermines cardiac function. Atrial fibrillation is a multi-facet malady and it may occur as a result of other diseases or it may trigger other problems. One of the main complications of AF is stroke due to the possibility of clot formation inside the atrium. However, the possibility of stroke occurrence due to the AF and the location from which an embolus dispatches are subject of debate. Another hypothesis about the embolus formation during AF is thrombus formation in aorta and carotid arteries, embolus detachment and its movement. To investigate the possibility of the latter postulation, the current work suggests a parametric study to quantify the sensitivity of aortic flow to four common AF traits including lack of atrial kick, atrial remodelling, left ventricle systolic dysfunction, and high frequency fibrillation. The simulation was carried out by coupling several in-house codes and ANSYS-CFX module. The results reveal that AF traits lower flow rate at left ventricular outflow tract, which in general lowers blood perfusion to systemic, cerebral and coronary circulations. Consequently, it leads to endothelial cell activation potential (ECAP) increase and variation of flow structure that both suggest predisposed areas to atherogenesis and thrombus formation in different regions in ascending aorta, aortic arch and descending thoracic aorta.

How personalized heart modeling can help treatment of lethal arrhythmias: A focus on ventricular tachycardia ablation strategies in post-infarction patients

Precision Cardiology is a targeted strategy for cardiovascular disease prevention and treatment that accounts for individual variability. Computational heart modeling is one of the novel approaches that have been developed under the umbrella of Precision Cardiology. Personalized computational modeling of patient hearts has made strides in the development of models that incorporate the individual geometry and structure of the heart as well as other patient-specific information. Of these developments, one of the potentially most impactful is the research aimed at noninvasively predicting the targets of ablation of lethal arrhythmia, ventricular tachycardia (VT), using patient-specific models. The approach has been successfully applied to patients with ischemic cardiomyopathy in proof-of-concept studies. The goal of this paper is to review the strategies for computational VT ablation guidance in ischemic cardiomyopathy patients, from model developments to the intricacies of the actual clinical application. To provide context in describing the road these computational modeling applications have undertaken, we first review the state of the art in VT ablation in the clinic, emphasizing the benefits that personalized computational prediction of ablation targets could bring to the clinical electrophysiology practice. This article is characterized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine.

Arrhythmia mechanisms and spontaneous calcium release: Bi-directional coupling between re-entrant and focal excitation

Spontaneous sub-cellular calcium release events (SCRE) are conjectured to promote rapid arrhythmias associated with conditions such as heart failure and atrial fibrillation: they can underlie the emergence of spontaneous action potentials in single cells which can lead to arrhythmogenic triggers in tissue. The multi-scale mechanisms of the development of SCRE into arrhythmia triggers, and their dynamic interaction with the tissue substrate, remain elusive; rigorous and simultaneous study of dynamics from the nanometre to the centimetre scale is a major challenge. The aim of this study was to develop a computational approach to overcome this challenge and study potential bi-directional coupling between sub-cellular and tissue-scale arrhythmia phenomena. A framework comprising a hierarchy of computational models was developed, which includes detailed single-cell models describing spatio-temporal calcium dynamics in 3D, efficient non-spatial cell models, and both idealised and realistic tissue models. A phenomenological approach was implemented to reproduce SCRE morphology and variability in the efficient cell models, comprising the definition of analytical Spontaneous Release Functions (SRF) whose parameters may be randomly sampled from appropriate distributions in order to match either the 3D cell models or experimental data. Pro-arrhythmogenic pacing protocols were applied to initiate re-entry and promote calcium overload, leading to the emergence of SCRE. The SRF accurately reproduced the dynamics of SCRE and its dependence on environment variables under multiple different conditions. Sustained re-entrant excitation promoted calcium overload, and led to the emergence of focal excitations after termination. A purely functional mechanism of re-entry and focal activity localisation was demonstrated, related to the unexcited spiral wave core. In conclusion, a novel approach has been developed to dynamically model SCRE at the tissue scale, which facilitates novel, detailed multi-scale mechanistic analysis. It was revealed that complex re-entrant excitation patterns and SCRE may be bi-directionally coupled, promoting novel mechanisms of arrhythmia perpetuation.

Biophysical Psychiatry-How Computational Neuroscience Can Help to Understand the Complex Mechanisms of Mental Disorders

The brain is the most complex of human organs, and the pathophysiology underlying abnormal brain function in psychiatric disorders is largely unknown. Despite the rapid development of diagnostic tools and treatments in most areas of medicine, our understanding of mental disorders and their treatment has made limited progress during the last decades. While recent advances in genetics and neuroscience have a large potential, the complexity and multidimensionality of the brain processes hinder the discovery of disease mechanisms that would link genetic findings to clinical symptoms and behavior. This applies also to schizophrenia, for which genome-wide association studies have identified a large number of genetic risk loci, spanning hundreds of genes with diverse functionalities. Importantly, the multitude of the associated variants and their prevalence in the healthy population limit the potential of a reductionist functional genetics approach as a stand-alone solution to discover the disease pathology. In this review, we outline the key concepts of a "biophysical psychiatry," an approach that employs large-scale mechanistic, biophysics-founded computational modelling to increase transdisciplinary understanding of the pathophysiology and strive toward robust predictions. We discuss recent scientific advances that allow a synthesis of previously disparate fields of psychiatry, neurophysiology, functional genomics, and computational modelling to tackle open questions regarding the pathophysiology of heritable mental disorders. We argue that the complexity of the increasing amount of genetic data exceeds the capabilities of classical experimental assays and requires computational approaches. Biophysical psychiatry, based on modelling diseased brain networks using existing and future knowledge of basic genetic, biochemical, and functional properties on a single neuron to a microcircuit level, may allow a leap forward in deriving interpretable biomarkers and move the field toward novel treatment options.