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

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.

Human induced pluripotent stem cell-derived atrial cardiomyocytes recapitulate contribution of the slowly activating delayed rectifier currents IKs to repolarization in the human atrium

AIMS

Human induced pluripotent stem cell-derived atrial cardiomyocytes (hiPSC-aCM) could be a helpful tool to study the physiology and diseases of the human atrium. To fulfil this expectation, the electrophysiology of hiPSC-aCM should closely resemble the situation in the human atrium. Data on the contribution of the slowly activating delayed rectifier currents (IKs) to repolarization are lacking for both human atrium and hiPSC-aCM.

METHODS AND RESULTS

Human atrial tissues were obtained from patients with sinus rhythm (SR) or atrial fibrillation (AF). Currents were measured in human atrial cardiomyocytes (aCM) and compared with hiPSC-aCM and used to model IKs contribution to action potential (AP) shape. Action potential was recorded by sharp microelectrodes. HMR-1556 (1 µM) was used to identify IKs and to estimate IKs contribution to repolarization. Less than 50% of hiPSC-aCM and aCM possessed IKs. Frequency of occurrence, current densities, activation/deactivation kinetics, and voltage dependency of IKs did not differ significantly between hiPSC-aCM and aCM, neither in SR nor AF. β-Adrenoceptor stimulation with isoprenaline did not increase IKs neither in aCM nor in hiPSC-aCM. In tissue from SR, block of IKs with HMR-1556 did not lengthen the action potential duration, even when repolarization reserve was reduced by block of the ultra-rapid repolarizing current with 4-aminopyridine or the rapidly activating delayed rectifier potassium outward current with E-4031.

CONCLUSION

I Ks exists in hiPSC-aCM with biophysics not different from aCM. As in adult human atrium (SR and AF), IKs does not appear to relevantly contribute to repolarization in hiPSC-aCM.

The spiral wave frequency effect in atrial fibrillation

A spiral wavefront (WF), generated by a cardiac rotor that drifts between surface electrodes during atrial fibrillation, exhibits frequency changes inconsistent with classical Doppler effect (CDE) phenomena. Recent clinical studies reveal three repeatedly observed events--1) side-dependent frequency changes across the path of the rotor, 2) one additional WF strike on the higher frequency side, and 3) a reversal of WF strike sequence--which constitute a diametrical property of spinning WF sources. A linear ray model is first used to reveal and develop the diametrical phenomena. Mathematical models of an Archimedean spiral and a spiral generated by the diffusion equation are developed and compared. Each formulation predicts the diametrical property that CDE does not capture and illuminates the occurrence of a strong side and weak side with respect to the rotor path. Whereas CDE exhibits higher and lower frequencies from approaching and receding sources of WFs, respectively, spiral rotors generate higher and lower frequencies on opposite sides of the migration path. This motivates the reconsideration of mapping and ablation strategies that have traditionally been based on identifying sites of the dominant frequency. While this research aims to characterize the path of a spiral rotor during atrial fibrillation accurately, the results are applicable in other fields of science and engineering in which rotating spiral waves occur.

The Dynamic Clamp Technique: A Robust Toolkit for Investigating Potassium Channel Function

The dynamic clamp technique has emerged as a powerful tool in the field of cardiac electrophysiology, enabling researchers to investigate the intricate dynamics of ion currents in cardiac cells. Potassium channels play a critical role in the functioning of cardiac cells and the overall electrical stability of the heart. This chapter provides a comprehensive overview of the methods and applications of dynamic clamp in the study of key potassium currents in cardiac cells. A step-by-step guide is presented, detailing the experimental setup and protocols required for implementing the dynamic clamp technique in cardiac cell studies. Special attention is given to the design and construction of a dynamic clamp setup with Real Time eXperimental Interface, configurations, and the incorporation of mathematical models to mimic ion channel behavior. The chapter's core focuses on applying dynamic clamp to elucidate the properties of various potassium channels in cardiac cells. It discusses how dynamic clamp can be used to investigate channel kinetics, voltage-dependent properties, and the impact of different potassium channel subtypes on cardiac electrophysiology. The chapter will also include examples of specific dynamic clamp experiments that studied potassium currents or their applications in cardiac cells.

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.

Building blocks of microphysiological system to model physiology and pathophysiology of human heart

Microphysiological systems (MPS) are drawing increasing interest from academia and from biomedical industry due to their improved capability to capture human physiology. MPS offer an advanced in vitro platform that can be used to study human organ and tissue level functions in health and in diseased states more accurately than traditional single cell cultures or even animal models. Key features in MPS include microenvironmental control and monitoring as well as high biological complexity of the target tissue. To reach these qualities, cross-disciplinary collaboration from multiple fields of science is required to build MPS. Here, we review different areas of expertise and describe essential building blocks of heart MPS including relevant cardiac cell types, supporting matrix, mechanical stimulation, functional measurements, and computational modelling. The review presents current methods in cardiac MPS and provides insights for future MPS development with improved recapitulation of human physiology.

Characterization of the Electrophysiological Characteristics of Chronic Atrial Fibrillation for Efficient Simulations

Atrial biophysical simulations have the potential to enhance outcomes by enabling the simulation of pharmacological and ablative strategies. However, the high computational times associated with such simulations render them unsuitable for diagnostic purposes. To address this challenge, discrete models such as cellular automata (CA) have been developed, which consider a finite number of states, thus significantly reducing computational times. Yet, there is a pressing need to determine whether CA can replicate pathological simulations with accuracy. The analysis of simulations under different degrees of electrical remodeling shows an expected increase of Action Potential Duration (APD) with the previous Diastolic Interval (DI) interval, indicating short-term memory of atrial cardiomyocytes: shorter APD0 provoked shorter APD+1, and previous DI has a similar effect on APD+1. Independent prediction using both APD0 and DI was found to provide a far better estimation of APD+1 values, compared to relying on DI alone (p<<0.01). Finally, the CA models were able to replicate reentrant patterns and cycle lengths of different states of atrial remodeling with a high degree of accuracy when compared to biophysical simulations. Overall, the use of atrial CA with short-term memory allows accurate reproduction of arrhythmic behavior in pathological tissue within a clinically relevant timeframe.Clinical Relevance- Discrete electrophysiological models simulate pathological self-sustained arrhythmias in diagnostic times.

A dynamic clamping approach using in silico IK1 current for discrimination of chamber-specific hiPSC-derived cardiomyocytes

Human induced pluripotent stem cell (hiPSC)-derived cardiomyocytes (CM) constitute a mixed population of ventricular-, atrial-, nodal-like cells, limiting the reliability for studying chamber-specific disease mechanisms. Previous studies characterised CM phenotype based on action potential (AP) morphology, but the classification criteria were still undefined. Our aim was to use in silico models to develop an automated approach for discriminating the electrophysiological differences between hiPSC-CM. We propose the dynamic clamp (DC) technique with the injection of a specific I_K1 current as a tool for deriving nine electrical biomarkers and blindly classifying differentiated CM. An unsupervised learning algorithm was applied to discriminate CM phenotypes and principal component analysis was used to visualise cell clustering. Pharmacological validation was performed by specific ion channel blocker and receptor agonist. The proposed approach improves the translational relevance of the hiPSC-CM model for studying mechanisms underlying inherited or acquired atrial arrhythmias in human CM, and for screening anti-arrhythmic agents.

PITX2 Knockout Induces Key Findings of Electrical Remodeling as Seen in Persistent Atrial Fibrillation

BACKGROUND

Electrical remodeling in human persistent atrial fibrillation is believed to result from rapid electrical activation of the atria, but underlying genetic causes may contribute. Indeed, common gene variants in an enhancer region close to PITX2 (paired-like homeodomain transcription factor 2) are strongly associated with atrial fibrillation, but the mechanism behind this association remains unknown. This study evaluated the consequences of PITX2 deletion (PITX2^-/-) in human induced pluripotent stem cell-derived atrial cardiomyocytes.

METHODS

CRISPR/Cas9 (clustered regularly interspaced short palindromic repeats/clustered regularly interspaced short palindromic repeat-associated 9) was used to delete PITX2 in a healthy human iPSC line that served as isogenic control. Human induced pluripotent stem cell-derived atrial cardiomyocytes were differentiated with unfiltered retinoic acid and cultured in atrial engineered heart tissue. Force and action potential were measured in atrial engineered heart tissues. Single human induced pluripotent stem cell-derived atrial cardiomyocytes were isolated from atrial engineered heart tissue for ion current measurements.

RESULTS

PITX2^-/- atrial engineered heart tissue beats slightly slower than isogenic control without irregularity. Force was lower in PITX2^-/- than in isogenic control (0.053±0.015 versus 0.131±0.017 mN, n=28/3 versus n=28/4, PITX2^-/- versus isogenic control; P<0.0001), accompanied by lower expression of CACNA1C and lower L-type Ca²⁺ current density. Early repolarization was weaker (action potential duration at 20% repolarization; 45.5±13.2 versus 8.6±5.3 ms, n=18/3 versus n=12/4, PITX2^-/- versus isogenic control; P<0.0001), and maximum diastolic potential was more negative (-78.3±3.1 versus -69.7±0.6 mV, n=18/3 versus n=12/4, PITX2^-/- versus isogenic control; P=0.001), despite normal inward rectifier currents (both I_K1 and I_K,ACh) and carbachol-induced shortening of action potential duration.

CONCLUSIONS

Complete PITX2 deficiency in human induced pluripotent stem cell-derived atrial cardiomyocytes recapitulates some findings of electrical remodeling of atrial fibrillation in the absence of fast beating, indicating that these abnormalities could be primary consequences of lower PITX2 levels.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Rotors Drift Toward and Stabilize in Low Power Regions in Heterogeneous Models of Atrial Fibrillation

Atrial fibrillation (AF) afflicts more than 33 million people worldwide. Success of therapy strategies remains poor and better understanding of the arrhythmia and how to device more effective therapies are needed. The aim of this work is to study the role of electric power distributions in rotors and AF dynamics. For this purpose, single cell and tissue simulations were performed to study the effect of ionic currents gradients and fibrosis in rotor's drifting. The root mean square of the ionic (Pion), capacitance (Pc) and electrotonic (Pele) power was computed over action potentials. Single cell simulations were performed for different values of IK1 and ICaL and number of coupled myofibroblasts. Tissue simulations were performed in presence of IK1 and ICaL gradients and diffused fibrosis. Single cell simulations showed that Pion and Pc increased with IK1, while decreased by increasing ICaL. Increasing the number of coupled myofibroblasts reduced Pion and Pc, whereas Pele increased. Finally, in tissue simulations rotors drifted to regions with low power and anchored in regions with higher density of blunted ionic induced power gradients.

Forward-Solution Noninvasive Computational Arrhythmia Mapping: The VMAP Study

BACKGROUND

The accuracy of noninvasive arrhythmia source localization using a forward-solution computational mapping system has not yet been evaluated in blinded, multicenter analysis. This study tested the hypothesis that a computational mapping system incorporating a comprehensive arrhythmia simulation library would provide accurate localization of the site-of-origin for atrial and ventricular arrhythmias and pacing using 12-lead ECG data when compared with the gold standard of invasive electrophysiology study and ablation.

METHODS

The VMAP study (Vectorcardiographic Mapping of Arrhythmogenic Probability) was a blinded, multicenter evaluation with final data analysis performed by an independent core laboratory. Eligible episodes included atrial and ventricular: tachycardia, fibrillation, pacing, premature atrial and ventricular complexes, and orthodromic atrioventricular reentrant tachycardia. Mapping system results were compared with the gold standard site of successful ablation or pacing during electrophysiology study and ablation. Mapping time was assessed from time-stamped logs. Prespecified performance goals were used for statistical comparisons.

RESULTS

A total of 255 episodes from 225 patients were enrolled from 4 centers. Regional accuracy for ventricular tachycardia and premature ventricular complexes in patients without significant structural heart disease (n=75, primary end point) was 98.7% (95% CI, 96.0%-100%; P<0.001 to reject predefined H0 <0.80). Regional accuracy for all episodes (secondary end point 1) was 96.9% (95% CI, 94.7%-99.0%; P<0.001 to reject predefined H0 <0.75). Accuracy for the exact or neighboring segment for all episodes (secondary end point 2) was 97.3% (95% CI, 95.2%-99.3%; P<0.001 to reject predefined H0 <0.70). Median spatial accuracy was 15 mm (n=255, interquartile range, 7-25 mm). The mapping process was completed in a median of 0.8 minutes (interquartile range, 0.4-1.4 minutes).

CONCLUSIONS

Computational ECG mapping using a forward-solution approach exceeded prespecified accuracy goals for arrhythmia and pacing localization. Spatial accuracy analysis demonstrated clinically actionable results. This rapid, noninvasive mapping technology may facilitate catheter-based and noninvasive targeted arrhythmia therapies.

REGISTRATION

URL: https://www.

CLINICALTRIALS

gov; Unique identifier: NCT04559061.

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.

Arrhythmogenic influence of mutations in a myocyte-based computational model of the pulmonary vein sleeve

In the heart, electrophysiological dysregulation arises from defects at many biological levels (from point mutations in ion channel proteins to gross structural abnormalities). These defects disrupt the normal pattern of electrical activation, producing ectopic activity and reentrant arrhythmia. To interrogate mechanisms that link these primary biological defects to macroscopic electrophysiologic dysregulation most prior computational studies have utilized either (i) detailed models of myocyte ion channel dynamics at limited spatial scales, or (ii) homogenized models of action potential conduction that reproduce arrhythmic activity at tissue and organ levels. Here we apply our recent model (EMI), which integrates electrical activation and propagation across these scales, to study human atrial arrhythmias originating in the pulmonary vein (PV) sleeves. These small structures initiate most supraventricular arrhythmias and include pronounced myocyte-to-myocyte heterogeneities in ion channel expression and intercellular coupling. To test EMI's cell-based architecture in this physiological context we asked whether ion channel mutations known to underlie atrial fibrillation are capable of initiating arrhythmogenic behavior via increased excitability or reentry in a schematic PV sleeve geometry. Our results illustrate that EMI's improved spatial resolution can directly interrogate how electrophysiological changes at the individual myocyte level manifest in tissue and as arrhythmia in the PV sleeve.

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.

Computational modeling of atrial fibrillation

With the aging society, the prevalence of atrial fibrillation (AF) continues to increase. Nevertheless, there are still limitations in antiarrhythmic drugs (AAD) or catheter interventions for AF. If it is possible to predict the outcome of AF management according to various AADs or ablation lesion sets through computational modeling, it will be of great clinical help. AF computational modeling has been utilized for in-silico arrhythmia research and enabled high-density entire chamber mapping, reproducible condition control, virtual intervention, not possible clinically or experimentally, in-depth mechanistic research. With the recent development of computer science and technology, more sophisticated and faster computational modeling has become available for clinical application. In particular, it can be applied to determine the extra-PV target of persistent AF catheter ablation or to select the AAD with the best effect. AF computational modeling combined with artificial intelligence is expected to contribute to precision medicine for more diverse uses in the future. Therefore, in this review, we will deal with the history, development, and various applications of computation modeling.

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

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

The openCARP simulation environment for cardiac electrophysiology

BACKGROUND AND OBJECTIVE

Cardiac electrophysiology is a medical specialty with a long and rich tradition of computational modeling. Nevertheless, no community standard for cardiac electrophysiology simulation software has evolved yet. Here, we present the openCARP simulation environment as one solution that could foster the needs of large parts of this community.

METHODS AND RESULTS

openCARP and the Python-based carputils framework allow developing and sharing simulation pipelines which automate in silico experiments including all modeling and simulation steps to increase reproducibility and productivity. The continuously expanding openCARP user community is supported by tailored infrastructure. Documentation and training material facilitate access to this complementary research tool for new users. After a brief historic review, this paper summarizes requirements for a high-usability electrophysiology simulator and describes how openCARP fulfills them. We introduce the openCARP modeling workflow in a multi-scale example of atrial fibrillation simulations on single cell, tissue, organ and body level and finally outline future development potential.

CONCLUSION

As an open simulator, openCARP can advance the computational cardiac electrophysiology field by making state-of-the-art simulations accessible. In combination with the carputils framework, it offers a tailored software solution for the scientific community and contributes towards increasing use, transparency, standardization and reproducibility of in silico experiments.

Artificial intelligence in the diagnosis and management of arrhythmias

The field of cardiac electrophysiology (EP) had adopted simple artificial intelligence (AI) methodologies for decades. Recent renewed interest in deep learning techniques has opened new frontiers in electrocardiography analysis including signature identification of diseased states. Artificial intelligence advances coupled with simultaneous rapid growth in computational power, sensor technology, and availability of web-based platforms have seen the rapid growth of AI-aided applications and big data research. Changing lifestyles with an expansion of the concept of internet of things and advancements in telecommunication technology have opened doors to population-based detection of atrial fibrillation in ways, which were previously unimaginable. Artificial intelligence-aided advances in 3D cardiac imaging heralded the concept of virtual hearts and the simulation of cardiac arrhythmias. Robotics, completely non-invasive ablation therapy, and the concept of extended realities show promise to revolutionize the future of EP. In this review, we discuss the impact of AI and recent technological advances in all aspects of arrhythmia care.

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.

Statistical Approach to Incorporating Experimental Variability into a Mathematical Model of the Voltage-Gated Na+ Channel and Human Atrial Action Potential

The voltage-gated Na⁺ channel Na_v1.5 is critical for normal cardiac myocyte excitability. Mathematical models have been widely used to study Na_v1.5 function and link to a range of cardiac arrhythmias. There is growing appreciation for the importance of incorporating physiological heterogeneity observed even in a healthy population into mathematical models of the cardiac action potential. Here, we apply methods from Bayesian statistics to capture the variability in experimental measurements on human atrial Na_v1.5 across experimental protocols and labs. This variability was used to define a physiological distribution for model parameters in a novel model formulation of Na_v1.5, which was then incorporated into an existing human atrial action potential model. Model validation was performed by comparing the simulated distribution of action potential upstroke velocity measurements to experimental measurements from several different sources. Going forward, we hope to apply this approach to other major atrial ion channels to create a comprehensive model of the human atrial AP. We anticipate that such a model will be useful for understanding excitability at the population level, including variable drug response and penetrance of variants linked to inherited cardiac arrhythmia syndromes.

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.

Patch-Clamp Recordings of Action Potentials From Human Atrial Myocytes: Optimization Through Dynamic Clamp

Introduction: Atrial fibrillation (AF) is the most common cardiac arrhythmia. Consequently, novel therapies are being developed. Ultimately, the impact of compounds on the action potential (AP) needs to be tested in freshly isolated human atrial myocytes. However, the frequent depolarized state of these cells upon isolation seriously hampers reliable AP recordings.

Purpose: We assessed whether AP recordings from single human atrial myocytes could be improved by providing these cells with a proper inward rectifier K⁺ current (I_K1), and consequently with a regular, non-depolarized resting membrane potential (RMP), through “dynamic clamp”.

Methods: Single myocytes were enzymatically isolated from left atrial appendage tissue obtained from patients with paroxysmal AF undergoing minimally invasive surgical ablation. APs were elicited at 1 Hz and measured using perforated patch-clamp methodology, injecting a synthetic I_K1 to generate a regular RMP. The injected I_K1 had strong or moderate rectification. For comparison, a regular RMP was forced through injection of a constant outward current. A wide variety of ion channel blockers was tested to assess their modulatory effects on AP characteristics.

Results: Without any current injection, RMPs ranged from −9.6 to −86.2 mV in 58 cells. In depolarized cells (RMP positive to −60 mV), RMP could be set at −80 mV using I_K1 or constant current injection and APs could be evoked upon stimulation. AP duration differed significantly between current injection methods (p < 0.05) and was shortest with constant current injection and longest with injection of I_K1 with strong rectification. With moderate rectification, AP duration at 90% repolarization (APD₉₀) was similar to myocytes with regular non-depolarized RMP, suggesting that a synthetic I_K1 with moderate rectification is the most appropriate for human atrial myocytes. Importantly, APs evoked using each injection method were still sensitive to all drugs tested (lidocaine, nifedipine, E-4031, low dose 4-aminopyridine, barium, and apamin), suggesting that the major ionic currents of the atrial cells remained functional. However, certain drug effects were quantitatively dependent on the current injection approach used.

Conclusion: Injection of a synthetic I_K1 with moderate rectification facilitates detailed AP measurements in human atrial myocytes. Therefore, dynamic clamp represents a promising tool for testing novel antiarrhythmic drugs.

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.

Mechanisms underlying pro-arrhythmic abnormalities arising from Pitx2-induced electrical remodelling: an in silico intersubject variability study

Background

Electrical remodelling as a result of the homeodomain transcription factor 2 (Pitx2)-dependent gene regulation induces atrial fibrillation (AF) with different mechanisms. The purpose of this study was to identify Pitx2-induced changes in ionic currents that cause action potential (AP) shortening and lead to triggered activity.

Methods

Populations of computational atrial AP models were developed based on AP recordings from sinus rhythm (SR) and AF patients. Models in the AF population were divided into triggered and untriggered AP groups to evaluate the relationship between each ion current regulated by Pitx2 and triggered APs. Untriggered AP models were then divided into shortened and unshortened AP groups to determine which Pitx2-dependent ion currents contribute to AP shortening.

Results

According to the physiological range of AP biomarkers measured experimentally, populations of 2,885 SR and 4,781 AF models out of the initial pool of 30,000 models were selected. Models in the AF population predicted AP shortening and triggered activity observed in experiments in Pitx2-induced remodelling conditions. The AF models included 925 triggered AP models, 1,412 shortened AP models and 2,444 unshortened AP models. Intersubject variability in I_Ks and I_CaL primarily modulated variability in AP duration (APD) in all shortened and unshortened AP models, whereas intersubject variability in I_K1 and SERCA mainly contributed to the variability in AP morphology in all triggered and untriggered AP models. The incidence of shortened AP was positively correlated with I_Ks and I_K1 and was negatively correlated with I_Na , I_CaL and SERCA, whereas the incidence of triggered AP was negatively correlated with I_Ks and I_K1 and was positively correlated with I_Na , I_CaL and SERCA.

Conclusions

Electrical remodelling due to Pitx2 upregulation may increase the incidence of shortened AP, whereas electrical remodelling arising from Pitx2 downregulation may favor to the genesis of triggered AP.

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.

Using cardiac ionic cell models to interpret clinical data

For over 100 years cardiac electrophysiology has been measured in the clinic. The electrical signals that can be measured span from noninvasive ECG and body surface potentials measurements through to detailed invasive measurements of local tissue electrophysiology. These electrophysiological measurements form a crucial component of patient diagnosis and monitoring; however, it remains challenging to quantitatively link changes in clinical electrophysiology measurements to biophysical cellular function. Multi-scale biophysical computational models represent one solution to this problem. These models provide a formal framework for linking cellular function through to emergent whole organ function and routine clinical diagnostic signals. In this review, we describe recent work on the use of computational models to interpret clinical electrophysiology signals. We review the simulation of human cardiac myocyte electrophysiology in the atria and the ventricles and how these models are being used to link organ scale function to patient disease mechanisms and therapy response in patients receiving implanted defibrillators, \cardiac resynchronisation therapy or suffering from atrial fibrillation and ventricular tachycardia. There is a growing use of multi-scale biophysical models to interpret clinical data. This allows cardiologists to link clinical observations with cellular mechanisms to better understand cardiopathophysiology and identify novel treatment strategies. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Calibration of ionic and cellular cardiac electrophysiology models

Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

Simulation of the Effects of Extracellular Calcium Changes Leads to a Novel Computational Model of Human Ventricular Action Potential With a Revised Calcium Handling

The importance of electrolyte concentrations for cardiac function is well established. Electrolyte variations can lead to arrhythmias onset, due to their important role in the action potential (AP) genesis and in maintaining cell homeostasis. However, most of the human AP computer models available in literature were developed with constant electrolyte concentrations, and fail to simulate physiological changes induced by electrolyte variations. This is especially true for Ca2+, even in the O'Hara-Rudy model (ORd), one of the most widely used models in cardiac electrophysiology. Therefore, the present work develops a new human ventricular model (BPS2020), based on ORd, able to simulate the inverse dependence of AP duration (APD) on extracellular Ca2+ concentration ([Ca2+]o), and APD rate dependence at 4 mM extracellular K+. The main changes needed with respect to ORd are: (i) an increased sensitivity of L-type Ca2+ current inactivation to [Ca2+]o; (ii) a single compartment description of the sarcoplasmic reticulum; iii) the replacement of Ca2+ release. BPS2020 is able to simulate the physiological APD-[Ca2+]o relationship, while also retaining the well-reproduced properties of ORd (APD rate dependence, restitution, accommodation and current block effects). We also used BPS2020 to generate an experimentally-calibrated population of models to investigate: (i) the occurrence of repolarization abnormalities in response to hERG current block; (ii) the rate adaptation variability; (iii) the occurrence of alternans and delayed after-depolarizations at fast pacing. Our results indicate that we successfully developed an improved version of ORd, which can be used to investigate electrophysiological changes and pro-arrhythmic abnormalities induced by electrolyte variations and current block at multiple rates and at the population level.

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.

A compartmentalized mathematical model of mouse atrial myocytes

Various experimental mouse models are extensively used to research human diseases, including atrial fibrillation, the most common cardiac rhythm disorder. Despite this, there are no comprehensive mathematical models that describe the complex behavior of the action potential and [Ca²⁺]_i transients in mouse atrial myocytes. Here, we develop a novel compartmentalized mathematical model of mouse atrial myocytes that combines the action potential, [Ca²⁺]_i dynamics, and β-adrenergic signaling cascade for a subpopulation of right atrial myocytes with developed transverse-axial tubule system. The model consists of three compartments related to β-adrenergic signaling (caveolae, extracaveolae, and cytosol) and employs local control of Ca²⁺ release. It also simulates ionic mechanisms of action potential generation and describes atrial-specific Ca²⁺ handling as well as frequency dependences of the action potential and [Ca²⁺]_i transients. The model showed that the T-type Ca²⁺ current significantly affects the later stage of the action potential, with little effect on [Ca²⁺]_i transients. The block of the small-conductance Ca²⁺-activated K⁺ current leads to a prolongation of the action potential at high intracellular Ca²⁺. Simulation results obtained from the atrial model cells were compared with those from ventricular myocytes. The developed model represents a useful tool to study complex electrical properties in the mouse atria and could be applied to enhance the understanding of atrial physiology and arrhythmogenesis.NEW & NOTEWORTHY A new compartmentalized mathematical model of mouse right atrial myocytes was developed. The model simulated action potential and Ca²⁺ dynamics at baseline and after stimulation of the β-adrenergic signaling system. Simulations showed that the T-type Ca²⁺ current markedly prolonged the later stage of atrial action potential repolarization, with a minor effect on [Ca²⁺]_i transients. The small-conductance Ca²⁺-activated K⁺ current block resulted in prolongation of the action potential only at the relatively high intracellular Ca²⁺.

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.

Towards chamber specific heart-on-a-chip for drug testing applications

Modeling of human organs has long been a task for scientists in order to lower the costs of therapeutic development and understand the pathological onset of human disease. For decades, despite marked differences in genetics and etiology, animal models remained the norm for drug discovery and disease modeling. Innovative biofabrication techniques have facilitated the development of organ-on-a-chip technology that has great potential to complement conventional animal models. However, human organ as a whole, more specifically the human heart, is difficult to regenerate in vitro, in terms of its chamber specific orientation and its electrical functional complexity. Recent progress with the development of induced pluripotent stem cell differentiation protocols, made recapitulating the complexity of the human heart possible through the generation of cells representative of atrial & ventricular tissue, the sinoatrial node, atrioventricular node and Purkinje fibers. Current heart-on-a-chip approaches incorporate biological, electrical, mechanical, and topographical cues to facilitate tissue maturation, therefore improving the predictive power for the chamber-specific therapeutic effects targeting adult human. In this review, we will give a summary of current advances in heart-on-a-chip technology and provide a comprehensive outlook on the challenges involved in the development of human physiologically relevant heart-on-a-chip.

Differential Modulation of IK and ICa,L Channels in High-Fat Diet-Induced Obese Guinea Pig Atria

Obesity mechanisms that make atrial tissue vulnerable to arrhythmia are poorly understood. Voltage-dependent potassium (I_K, I_Kur, and I_K1) and L-type calcium currents (I_Ca,L) are electrically relevant and represent key substrates for modulation in obesity. We investigated whether electrical remodeling produced by high-fat diet (HFD) alone or in concert with acute atrial stimulation were different. Electrophysiology was used to assess atrial electrical function after short-term HFD-feeding in guinea pigs. HFD atria displayed spontaneous beats, increased I_K (I_Kr + I_Ks) and decreased I_Ca,L densities. Only with pacing did a reduction in I_Kur and increased I_K1 phenotype emerge, leading to a further shortening of action potential duration. Computer modeling studies further indicate that the measured changes in potassium and calcium current densities contribute prominently to shortened atrial action potential duration in human heart. Our data are the first to show that multiple mechanisms (shortened action potential duration, early afterdepolarizations and increased incidence of spontaneous beats) may underlie initiation of supraventricular arrhythmias in obese guinea pig hearts. These results offer different mechanistic insights with implications for obese patients harboring supraventricular arrhythmias.

Chaotic tip trajectories of a single spiral wave in the presence of heterogeneities

Spiral waves have been observed in a variety of physical, chemical, and biological systems. They play a major role in cardiac arrhythmias, including fibrillation, where the observed irregular activation patterns are generally thought to arise from the continuous breakup of multiple unstable spiral waves. Using spatially extended simulations of different electrophysiological models of cardiac tissue, we show that a single spiral wave in the presence of heterogeneities can display chaotic tip trajectories, consistent with fibrillation. We also show that the simulated spiral tip dynamics, including chaotic trajectories, can be captured by a simple particle model which only describes the dynamics of the spiral tip. This shows that spiral wave breakup, or interactions with other waves, are not necessary to initiate chaos in spiral waves.

Diminished inhibition and facilitated activation of RyR2-mediated Ca2+ release is a common defect of arrhythmogenic calmodulin mutations

A number of calmodulin (CaM) mutations cause severe cardiac arrhythmias, but their arrhythmogenic mechanisms are unclear. While some of the arrhythmogenic CaM mutations have been shown to impair CaM-dependent inhibition of intracellular Ca²⁺ release through the ryanodine receptor type 2 (RyR2), the impact of a majority of these mutations on RyR2 function is unknown. Here, we investigated the effect of 14 arrhythmogenic CaM mutations on the CaM-dependent RyR2 inhibition. We found that all the arrhythmogenic CaM mutations tested diminished CaM-dependent inhibition of RyR2-mediated Ca²⁺ release and increased store-overload induced Ca²⁺ release (SOICR) in HEK293 cells. Moreover, all the arrhythmogenic CaM mutations tested either failed to inhibit or even promoted RyR2-mediated Ca²⁺ release in permeabilized HEK293 cells with elevated cytosolic Ca²⁺ , which was markedly different from the inhibitory action of CaM wild-type. The CaM mutations also altered the Ca²⁺ -dependency of CaM binding to the RyR2 CaM-binding domain. These results demonstrate that diminished inhibition, and even facilitated activation, of RyR2-mediated Ca²⁺ release is a common defect of arrhythmogenic CaM mutations.

Heterogeneous Effects of Fibroblast-Myocyte Coupling in Different Regions of the Human Atria Under Conditions of Atrial Fibrillation

Background: Atrial fibrillation (AF), the most common cardiac arrhythmia, is characterized by alteration of the action potential (AP) propagation. Under persistent AF, myocytes undergo electrophysiological and structural remodeling, which involves fibroblast proliferation and differentiation, modifying the substrate for AP propagation. The aim of this study was to analyze the effects on the AP of fibroblast-myocyte coupling during AF and its propagation in different regions of the atria.

Methods: Isolated myocytes were coupled to different numbers of fibroblasts using the established AP models and tissue simulations were performed by randomly distributing fibroblasts. Fibroblast formulations were updated to match recent experimental data. Major ion current conductances of the myocyte model were modified to simulate AP heterogeneity in four different atrial regions (right atrium posterior wall, crista terminalis, left atrium posterior wall, and pulmonary vein) according to experimental and computational studies.

Results: The results of the coupled myocyte-fibroblast simulations suggest that a more depolarized membrane potential and higher fibroblast membrane capacitance have a greater impact on AP duration and myocyte maximum depolarization velocity. The number of coupled fibroblasts and the stimulation frequency are determining factors in altering myocyte AP. Strand simulations show that conduction velocity tends to homogenize in all regions, while the left atrium is more likely to be affected by fibroblast and AP propagation block is more likely to occur. The pulmonary vein is the most affected region, even at low fibroblast densities. In 2D sheets with randomly placed fibroblasts, wavebreaks are observed in the low density (10%) central fibrotic zone and when fibroblast density increases (40%) propagation in the fibrotic region is practically blocked. At densities of 10 and 20% the width of the vulnerable window increases with respect to control but is decreased at 40%.

Conclusion: Myocyte-fibroblast coupling characteristics heterogeneously affect AP propagation and features in the different atrial zones, and myocytes from the left atria are more sensitive to fibroblast coupling.

Understanding AF Mechanisms Through Computational Modelling and Simulations

AF is a progressive disease of the atria, involving complex mechanisms related to its initiation, maintenance and progression. Computational modelling provides a framework for integration of experimental and clinical findings, and has emerged as an essential part of mechanistic research in AF. The authors summarise recent advancements in development of multi-scale AF models and focus on the mechanistic links between alternations in atrial structure and electrophysiology with AF. Key AF mechanisms that have been explored using atrial modelling are pulmonary vein ectopy; atrial fibrosis and fibrosis distribution; atrial wall thickness heterogeneity; atrial adipose tissue infiltration; development of repolarisation alternans; cardiac ion channel mutations; and atrial stretch with mechano-electrical feedback. They review modelling approaches that capture variability at the cohort level and provide cohort-specific mechanistic insights. The authors conclude with a summary of future perspectives, as envisioned for the contributions of atrial modelling in the mechanistic understanding of AF.

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

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

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.

Computational Model of Calcium Signaling in Cardiac Atrial Cells at the Submicron Scale

In cardiac cells, calcium is the mediator of excitation-contraction coupling. Dysfunctions in calcium handling have been identified as the origin of some cardiac arrhythmias. In the particular case of atrial myocytes, recent available experimental data has found links between these dysfunctions and structural changes in the calcium handling machinery (ryanodine cluster size and distribution, t-tubular network, etc). To address this issue, we have developed a computational model of an atrial myocyte that takes into account the detailed intracellular structure. The homogenized macroscopic behavior is described with a two-concentration field model, using effective diffusion coefficients of calcium in the sarcoplasmic reticulum (SR) and in the cytoplasm. The model reproduces the right calcium transients and dependence with pacing frequency. Under basal conditions, the calcium rise is mostly restricted to the periphery of the cell, with a large concentration ratio between the periphery and the interior. We have then studied the dependence of the speed of the calcium wave on cytosolic and SR diffusion coefficients, finding an almost linear relation with the former, in agreement with a diffusive and fire mechanism of propagation, and little dependence on the latter. Finally, we have studied the effect of a change in RyR cluster microstructure. We find that, under resting conditions, the spark frequency decreases slightly with RyR cluster spatial dispersion, but markedly increases when the RyRs are distributed in clusters of larger size, stressing the importance of RyR cluster organization to understand atrial arrhythmias, as recent experimental results suggest (Macquaide et al., 2015).

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.

Description of the Human Atrial Action Potential Derived From a Single, Congruent Data Source: Novel Computational Models for Integrated Experimental-Numerical Study of Atrial Arrhythmia Mechanisms

Introduction: The development of improved diagnosis, management, and treatment strategies for human atrial fibrillation (AF) is a significant and important challenge in order to improve quality of life for millions and reduce the substantial social-economic costs of the condition. As a complex condition demonstrating high variability and relation to other cardiac conditions, the study of AF requires approaches from multiple disciplines including single-cell experimental electrophysiology and computational modeling. Models of human atrial cells are less well parameterized than those of the human ventricle or other mammal species, largely due to the inherent challenges in patch clamping human atrial cells. Such challenges include, frequently, unphysiologically depolarized resting potentials and thus injection of a compensatory hyperpolarizing current, as well as detecting certain ion currents which may be disrupted by the cell isolation process. The aim of this study was to develop a laboratory specific model of human atrial electrophysiology which reproduces exactly the conditions of isolated-cell experiments, including testing of multiple experimental interventions. Methods: Formulations for the primary ion currents characterized by isolated-cell experiments in the Workman laboratory were fit directly to voltage-clamp data; the fast sodium-current was parameterized based on experiments relating resting membrane potential to maximal action potential upstroke velocity; compensatory hyperpolarizing current was included as a constant applied current. These formulations were integrated with three independent human atrial cell models to provide a family of novel models. Extrapolated intact-cell models were developed through removal of the hyperpolarizing current and introduction of terminal repolarization potassium currents. Results: The isolated-cell models quantitatively reproduced experimentally measured properties of excitation in both control and pharmacological and dynamic-clamp interventions. Comparison of isolated and intact-cell models highlighted the importance of reproducing this cellular environment when comparing experimental and simulation data. Conclusion: We have developed a laboratory specific model of the human atrial cell which directly reproduces the experimental isolated-cell conditions and captures human atrial excitation properties. The model may be particularly useful for directly relating model to experiment, and offers a complementary tool to the available set of human atrial cell models with specific advantages resulting from the congruent input data source.

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

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

Automatic Optimization of an in Silico Model of Human iPSC Derived Cardiomyocytes Recapitulating Calcium Handling Abnormalities

The growing importance of human induced pluripotent stem cell-derived cardiomyoyctes (hiPSC-CMs), as patient-specific and disease-specific models for studying cellular cardiac electrophysiology or for preliminary cardiotoxicity tests, generated better understanding of hiPSC-CM biophysical mechanisms and great amount of action potential and calcium transient data. In this paper, we propose a new hiPSC-CM in silico model, with particular attention to Ca²⁺ handling. We used (i) the hiPSC-CM Paci2013 model as starting point, (ii) a new dataset of Ca²⁺ transient measurements to tune the parameters of the inward and outward Ca²⁺ fluxes of sarcoplasmic reticulum, and (iii) an automatic parameter optimization to fit action potentials and Ca²⁺ transients. The Paci2018 model simulates, together with the typical hiPSC-CM spontaneous action potentials, more refined Ca²⁺ transients and delayed afterdepolarizations-like abnormalities, which the old Paci2013 was not able to predict due to its mathematical formulation. The Paci2018 model was validated against (i) the same current blocking experiments used to validate the Paci2013 model, and (ii) recently published data about effects of different extracellular ionic concentrations. In conclusion, we present a new and more versatile in silico model, which will provide a platform for modeling the effects of drugs or mutations that affect Ca²⁺ handling in hiPSC-CMs.

Is human atrial fibrillation stochastic or deterministic?-Insights from missing ordinal patterns and causal entropy-complexity plane analysis

The mechanism of atrial fibrillation (AF) maintenance in humans is yet to be determined. It remains controversial whether cardiac fibrillatory dynamics are the result of a deterministic or a stochastic process. Traditional methods to differentiate deterministic from stochastic processes have several limitations and are not reliably applied to short and noisy data obtained during clinical studies. The appearance of missing ordinal patterns (MOPs) using the Bandt-Pompe (BP) symbolization is indicative of deterministic dynamics and is robust to brief time series and experimental noise. Our aim was to evaluate whether human AF dynamics is the result of a stochastic or a deterministic process. We used 38 intracardiac atrial electrograms during AF from the coronary sinus of 10 patients undergoing catheter ablation of AF. We extracted the intervals between consecutive atrial depolarizations (AA interval) and converted the AA interval time series to their BP symbolic representation (embedding dimension 5, time delay 1). We generated 40 iterative amplitude-adjusted, Fourier-transform (IAAFT) surrogate data for each of the AA time series. IAAFT surrogates have the same frequency spectrum, autocorrelation, and probability distribution with the original time series. Using the BP symbolization, we compared the number of MOPs and the rate of MOP decay in the first 1000 timepoints of the original time series with that of the surrogate data. We calculated permutation entropy and permutation statistical complexity and represented each time series on the causal entropy-complexity plane. We demonstrated that (a) the number of MOPs in human AF is significantly higher compared to the surrogate data (2.7 ± 1.18 vs. 0.39 ± 0.28, p < 0.001); (b) the median rate of MOP decay in human AF was significantly lower compared with the surrogate data (6.58 × 10^-3 vs. 7.79 × 10^-3, p < 0.001); and (c) 81.6% of the individual recordings had a rate of decay lower than the 95% confidence intervals of their corresponding surrogates. On the causal entropy-complexity plane, human AF lay on the deterministic part of the plane that was located above the trajectory of fractional Brownian motion with different Hurst exponents on the plane. This analysis demonstrates that human AF dynamics does not arise from a rescaled linear stochastic process or a fractional noise, but either a deterministic or a nonlinear stochastic process. Our results justify the development and application of mathematical analysis and modeling tools to enable predictive control of human AF.

The expression of the rare caveolin-3 variant T78M alters cardiac ion channels function and membrane excitability

Aims

Caveolinopathies are a family of genetic disorders arising from alterations of the caveolin-3 (cav-3) gene. The T78M cav-3 variant has been associated with both skeletal and cardiac muscle pathologies but its functional contribution, especially to cardiac diseases, is still controversial. Here, we evaluated the effect of the T78M cav-3 variant on cardiac ion channel function and membrane excitability.

Methods and results

We transfected either the wild type (WT) or T78M cav-3 in caveolin-1 knock-out mouse embryonic fibroblasts and found by immunofluorescence and electron microscopy that both are expressed at the plasma membrane and form caveolae. Two ion channels known to interact and co-immunoprecipitate with the cav-3, hKv1.5 and hHCN4, interact also with T78M cav-3 and reside in lipid rafts. Electrophysiological analysis showed that the T78M cav-3 causes hKv1.5 channels to activate and inactivate at more hyperpolarized potentials and the hHCN4 channels to activate at more depolarized potentials, in a dominant way. In spontaneously beating neonatal cardiomyocytes, the expression of the T78M cav-3 significantly increased action potential peak-to-peak variability without altering neither the mean rate nor the maximum diastolic potential. We also found that in a small cohort of patients with supraventricular arrhythmias, the T78M cav-3 variant is more frequent than in the general population. Finally, in silico analysis of both sinoatrial and atrial cell models confirmed that the T78M-dependent changes are compatible with a pro-arrhythmic effect.

Conclusion

This study demonstrates that the T78M cav-3 induces complex modifications in ion channel function that ultimately alter membrane excitability. The presence of the T78M cav-3 can thus generate a susceptible substrate that, in concert with other structural alterations and/or genetic mutations, may become arrhythmogenic.

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.