Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization

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

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

A novel ionic model for matured and paced atrial-like human iPSC-CMs integrating IKur and IKCa currents

This work introduces the first atrial-specific in-silico human induced pluripotent stem cells-derived cardiomyocytes (hiPSC-CMs) model, based on a set of phenotype-specific IKur,IKCa and IK1 membrane currents. This model is built on novel in-vitro experimental data recently published by some of the co-authors to simulate the paced action potential of matured atrial-like hiPSC-CMs. The model consists of a system of stiff ordinary differential equations depending on several parameters, which have been tuned by automatic optimization techniques to closely match selected experimental biomarkers. The new model effectively simulates the electronic in-vitro hiPSC-CMs maturation process, transitioning from an unstable depolarized membrane diastolic potential to a stable hyperpolarized resting potential, and exhibits spontaneous firing activity in unpaced conditions. Moreover, our model accurately reflects the experimental rate dependence data at different cycle length and demonstrates the expected response to a specific current blocker. This atrial-specific in-silico model provides a novel computational tool for electrophysiological studies of cardiac stem cells and their applications to drug evaluation and atrial fibrillation treatment.

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.

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.

Non-invasive estimation of atrial fibrillation driver position using long-short term memory neural networks and body surface potentials

BACKGROUND AND OBJECTIVE

Atrial Fibrillation (AF) is a supraventricular tachyarrhythmia that can lead to thromboembolism, hearlt failure, ischemic stroke, and a decreased quality of life. Characterizing the locations where the mechanisms of AF are initialized and maintained is key to accomplishing an effective ablation of the targets, hence restoring sinus rhythm. Many methods have been investigated to locate such targets in a non-invasive way, such as Electrocardiographic Imaging, which enables an on-invasive and panoramic characterization of cardiac electrical activity using recording Body Surface Potentials (BSP) and a torso model of the patient. Nonetheless, this technique entails some major issues stemming from solving the inverse problem, which is known to be severely ill-posed. In this context, many machine learning and deep learning approaches aim to tackle the characterization and classification of AF targets to improve AF diagnosis and treatment.

METHODS

In this work, we propose a method to locate AF drivers as a supervised classification problem. We employed a hybrid form of the convolutional-recurrent network which enables feature extraction and sequential data modeling utilizing labeled realistic computerized AF models. Thus, we used 16 AF electrograms, 1 atrium, and 10 torso geometries to compute the forward problem. Previously, the AF models were labeled by assigning each sample of the signals a region from the atria from 0 (no driver) to 7, according to the spatial location of the AF driver. The resulting 160 BSP signals, which resemble a 64-lead vest recording, are preprocessed and then introduced into the network following a 4-fold cross-validation in batches of 50 samples.

RESULTS

The results show a mean accuracy of 74.75% among the 4 folds, with a better performance in detecting sinus rhythm, and drivers near the left superior pulmonary vein (R1), and right superior pulmonary vein (R3) whose mean sensitivity bounds around 84%-87%. Significantly good results are obtained in mean sensitivity (87%) and specificity (83%) in R1.

CONCLUSIONS

Good results in R1 are highly convenient since AF drivers are commonly found in this area: the left atrial appendage, as suggested in some previous studies. These promising results indicate that using CNN-LSTM networks could lead to new strategies exploiting temporal correlations to address this challenge effectively.

Deciphering the roles of triiodothyronine (T3) and thyroid-stimulating hormone (TSH) on cardiac electrical remodeling in clinical and experimental hypothyroidism

Hypothyroidism is the most frequent endocrine pathology. Although clinical or overt hypothyroidism has been traditionally associated to low T3 / T4 and high thyrotropin (TSH) circulating levels, other forms exist such as subclinical hypothyroidism, characterized by normal blood T3 / T4 and high TSH. In its different forms is estimated to affect approximately 10% of the population, especially women, in a 5:1 ratio with respect to men. Among its consequences are alterations in cardiac electrical activity, especially in the repolarization phase, which is accompanied by an increased susceptibility to cardiac arrhythmias. Although these alterations have traditionally been attributed to thyroid hormone deficiency, recent studies, both clinical trials and experimental models, demonstrate a fundamental role of TSH in cardiac electrical remodeling. Thus, both metabolic thyroid hormones and TSH regulate cardiac ion channel expression in many and varied ways. This means that the different combinations of hormones that predominate in different types of hypothyroidism (overt, subclinic, primary, central) can generate different forms of cardiac electrical remodeling. These new findings are raising the relevant question of whether serum TSH reference ranges should be redefined.

Integrative human atrial modelling unravels interactive protein kinase A and Ca2+/calmodulin-dependent protein kinase II signalling as key determinants of atrial arrhythmogenesis

AIMS

Atrial fibrillation (AF), the most prevalent clinical arrhythmia, is associated with atrial remodelling manifesting as acute and chronic alterations in expression, function, and regulation of atrial electrophysiological and Ca2+-handling processes. These AF-induced modifications crosstalk and propagate across spatial scales creating a complex pathophysiological network, which renders AF resistant to existing pharmacotherapies that predominantly target transmembrane ion channels. Developing innovative therapeutic strategies requires a systems approach to disentangle quantitatively the pro-arrhythmic contributions of individual AF-induced alterations.

METHODS AND RESULTS

Here, we built a novel computational framework for simulating electrophysiology and Ca2+-handling in human atrial cardiomyocytes and tissues, and their regulation by key upstream signalling pathways [i.e. protein kinase A (PKA), and Ca2+/calmodulin-dependent protein kinase II (CaMKII)] involved in AF-pathogenesis. Populations of atrial cardiomyocyte models were constructed to determine the influence of subcellular ionic processes, signalling components, and regulatory networks on atrial arrhythmogenesis. Our results reveal a novel synergistic crosstalk between PKA and CaMKII that promotes atrial cardiomyocyte electrical instability and arrhythmogenic triggered activity. Simulations of heterogeneous tissue demonstrate that this cellular triggered activity is further amplified by CaMKII- and PKA-dependent alterations of tissue properties, further exacerbating atrial arrhythmogenesis.

CONCLUSIONS

Our analysis reveals potential mechanisms by which the stress-associated adaptive changes turn into maladaptive pro-arrhythmic triggers at the cellular and tissue levels and identifies potential anti-AF targets. Collectively, our integrative approach is powerful and instrumental to assemble and reconcile existing knowledge into a systems network for identifying novel anti-AF targets and innovative approaches moving beyond the traditional ion channel-based strategy.

Towards Improved Human In Vitro Models for Cardiac Arrhythmia: Disease Mechanisms, Treatment, and Models of Atrial Fibrillation

Heart rhythm disorders, arrhythmias, place a huge economic burden on society and have a large impact on the quality of life of a vast number of people. Arrhythmias can have genetic causes but primarily arise from heart tissue remodeling during aging or heart disease. As current therapies do not address the causes of arrhythmias but only manage the symptoms, it is of paramount importance to generate innovative test models and platforms for gaining knowledge about the underlying disease mechanisms which are compatible with drug screening. In this review, we outline the most important features of atrial fibrillation (AFib), the most common cardiac arrhythmia. We will discuss the epidemiology, risk factors, underlying causes, and present therapies of AFib, as well as the shortcomings and opportunities of current models for cardiac arrhythmia, including animal models, in silico and in vitro models utilizing human pluripotent stem cell (hPSC)-derived cardiomyocytes.

Local Control Model of a Human Ventricular Myocyte: An Exploration of Frequency-Dependent Changes and Calcium Sparks

Calcium (Ca2+) sparks are the elementary events of excitation-contraction coupling, yet they are not explicitly represented in human ventricular myocyte models. A stochastic ventricular cardiomyocyte human model that adapts to intracellular Ca2+ ([Ca2+]i) dynamics, spark regulation, and frequency-dependent changes in the form of locally controlled Ca2+ release was developed. The 20,000 CRUs in this model are composed of 9 individual LCCs and 49 RyRs that function as couplons. The simulated action potential duration at 1 Hz steady-state pacing is ~0.280 s similar to human ventricular cell recordings. Rate-dependence experiments reveal that APD shortening mechanisms are largely contributed by the L-type calcium channel inactivation, RyR open fraction, and [Ca2+]myo concentrations. The dynamic slow-rapid-slow pacing protocol shows that RyR open probability during high pacing frequency (2.5 Hz) switches to an adapted "nonconducting" form of Ca2+-dependent transition state. The predicted force was also observed to be increased in high pacing, but the SR Ca2+ fractional release was lower due to the smaller difference between diastolic and systolic [Ca2+]SR. Restitution analysis through the S1S2 protocol and increased LCC Ca2+-dependent activation rate show that the duration of LCC opening helps modulate its effects on the APD restitution at different diastolic intervals. Ultimately, a longer duration of calcium sparks was observed in relation to the SR Ca2+ loading at high pacing rates. Overall, this study demonstrates the spontaneous Ca2+ release events and ion channel responses throughout various stimuli.

A computational modeling framework for pre-clinical evaluation of cardiac mapping systems

There are a variety of difficulties in evaluating clinical cardiac mapping systems, most notably the inability to record the transmembrane potential throughout the entire heart during patient procedures which prevents the comparison to a relevant "gold standard". Cardiac mapping systems are comprised of hardware and software elements including sophisticated mathematical algorithms, both of which continue to undergo rapid innovation. The purpose of this study is to develop a computational modeling framework to evaluate the performance of cardiac mapping systems. The framework enables rigorous evaluation of a mapping system's ability to localize and characterize (i.e., focal or reentrant) arrhythmogenic sources in the heart. The main component of our tool is a library of computer simulations of various dynamic patterns throughout the entire heart in which the type and location of the arrhythmogenic sources are known. Our framework allows for performance evaluation for various electrode configurations, heart geometries, arrhythmias, and electrogram noise levels and involves blind comparison of mapping systems against a "silver standard" comprised of computer simulations in which the precise transmembrane potential patterns throughout the heart are known. A feasibility study was performed using simulations of patterns in the human left atria and three hypothetical virtual catheter electrode arrays. Activation times (AcT) and patterns (AcP) were computed for three virtual electrode arrays: two basket arrays with good and poor contact and one high-resolution grid with uniform spacing. The average root mean squared difference of AcTs of electrograms and those of the nearest endocardial action potential was less than 1 ms and therefore appears to be a poor performance metric. In an effort to standardize performance evaluation of mapping systems a novel performance metric is introduced based on the number of AcPs identified correctly and those considered spurious as well as misclassifications of arrhythmia type; spatial and temporal localization accuracy of correctly identified patterns was also quantified. This approach provides a rigorous quantitative analysis of cardiac mapping system performance. Proof of concept of this computational evaluation framework suggests that it could help safeguard that mapping systems perform as expected as well as provide estimates of system accuracy.

Human atrial fibrillation and genetic defects in transient outward currents: mechanistic insights from multi-scale computational models

Previous studies have linked dysfunctional I_to arising from mutations to KCND3-encoded Kv4.3 and KCND2-encoded Kv4.2 to atrial fibrillation. Using computational models, this study aimed to investigate the mechanisms underlying pro-arrhythmic effects of the gain-of-function Kv4.3 (T361S, A545P) and Kv4.2 (S447R) mutations. Wild-type and mutant I_to formulations were developed from and validated against experimental data and incorporated into the Colman et al. model of human atrial cells. Single-cell models were incorporated into one- (1D) and two-dimensional (2D) models of atrial tissue, and a three-dimensional (3D) realistic model of the human atria. The three gain-of-function mutations had similar, albeit quantitatively different, effects: shortening of the action potential duration; lowering the plateau membrane potential, abbreviating the effective refractory period (ERP) and the wavelength (WL) of atrial excitation at the tissue level. Restitution curves for the WL, the ERP and the conduction velocity were leftward shifted, facilitating the conduction of atrial excitation waves at high excitation rates. The mutations also increased lifespan and stationarity of re-entry in both 2D and 3D simulations, which further highlighted a mutation-induced increase in spatial dispersion of repolarization. Collectively, these changes account for pro-arrhythmic effects of these Kv4.3 and Kv4.2 mutations in facilitating AF. This article is part of the theme issue 'The heartbeat: its molecular basis and physiological mechanisms'.

Generation of cardiomyocytes from human-induced pluripotent stem cells resembling atrial cells with ability to respond to adrenoceptor agonists

Atrial fibrillation (AF) is the most common chronic arrhythmia presenting a heavy disease burden. We report a new approach for generating cardiomyocytes (CMs) resembling atrial cells from human-induced pluripotent stem cells (hiPSCs) using a combination of Gremlin 2 and retinoic acid treatment. More than 40% of myocytes showed rod-shaped morphology, expression of CM proteins (including ryanodine receptor 2, α-actinin-2 and F-actin) and striated appearance, all of which were broadly similar to the characteristics of adult atrial myocytes (AMs). Isolated myocytes were electrically quiescent until stimulated to fire action potentials with an AM profile and an amplitude of approximately 100 mV, arising from a resting potential of approximately -70 mV. Single-cell RNA sequence analysis showed a high level of expression of several atrial-specific transcripts including NPPA, MYL7, HOXA3, SLN, KCNJ4, KCNJ5 and KCNA5. Amplitudes of calcium transients recorded from spontaneously beating cultures were increased by the stimulation of α-adrenoceptors (activated by phenylephrine and blocked by prazosin) or β-adrenoceptors (activated by isoproterenol and blocked by CGP20712A). Our new approach provides human AMs with mature characteristics from hiPSCs which will facilitate drug discovery by enabling the study of human atrial cell signalling pathways and AF. This article is part of the theme issue 'The heartbeat: its molecular basis and physiological mechanisms'.

Characterization of Experimentally Observed Complex Interplay between Pulse Duration, Electrical Field Strength, and Cell Orientation on Electroporation Outcome Using a Time-Dependent Nonlinear Numerical Model

Electroporation is a biophysical phenomenon involving an increase in cell membrane permeability to molecules after a high-pulsed electric field is applied to the tissue. Currently, electroporation is being developed for non-thermal ablation of cardiac tissue to treat arrhythmias. Cardiomyocytes have been shown to be more affected by electroporation when oriented with their long axis parallel to the applied electric field. However, recent studies demonstrate that the preferentially affected orientation depends on the pulse parameters. To gain better insight into the influence of cell orientation on electroporation with different pulse parameters, we developed a time-dependent nonlinear numerical model where we calculated the induced transmembrane voltage and pores creation in the membrane due to electroporation. The numerical results show that the onset of electroporation is observed at lower electric field strengths for cells oriented parallel to the electric field for pulse durations ≥10 µs, and cells oriented perpendicular for pulse durations ~100 ns. For pulses of ~1 µs duration, electroporation is not very sensitive to cell orientation. Interestingly, as the electric field strength increases beyond the onset of electroporation, perpendicular cells become more affected irrespective of pulse duration. The results obtained using the developed time-dependent nonlinear model are corroborated by in vitro experimental measurements. Our study will contribute to the process of further development and optimization of pulsed-field ablation and gene therapy in cardiac treatments.

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.

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.

An ECG generative model of myocardial infarction

Background and Objective Computer-aided diagnosis (CAD) of Myocardial Infarction (MI) using machine learning depends on a large amount of clinical Electrocardiogram (ECG) data. Existing infarct ECG databases face the problem of class imbalance. Data augmentation using generative simulation models is a new approach to effectively address this problem. Methods A multiscale ECG generative model was established for ECG data augmentation. In the cellular layer, an ischemic Action Potential (AP) model was established to generate APs in cardiomyocytes with different transmural regions of infraction or different ischemic durations. In the tissue layer, a probability-driven cellular automata excitation propagation model was established to simulate the propagation speed and direction of excitation. An infarct tissue model and a coronary artery model were established to describe the spatiotemporal diversity of MI. A ventricle model, a human torso model, and a computational model of surface ECG based on field source theory were established in the heart-torso layer. Results The model generated pathological 12-lead ECGs of MI with different topography and different extent. When simulating different ventricular wall infarction, the lesions appear in the same leads as the clinical 12-lead ECG. The ST-segment decreases and the T-wave amplitude decreases, similar to the clinical ECG features when simulating subendocardial ischemia. The average fidelity of the 12-lead ECG the model generated is 95.6%, according to the designed DTW-GRA distance algorithm. Conclusions The generative model considers the electrophysiological properties of the natural heart, the pathology of myocardial infarction, and the diversity of clinical ECGs. The model can provide many reliable samples for machine learning of MI.

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.

Stress-induced premature senescence is associated with a prolonged QT interval and recapitulates features of cardiac aging

Rationale: Aging in the heart is a gradual process, involving continuous changes in cardiovascular cells, including cardiomyocytes (CMs), namely cellular senescence. These changes finally lead to adverse organ remodeling and resulting in heart failure. This study exploits CMs from human induced pluripotent stem cells (iCMs) as a tool to model and characterize mechanisms involved in aging. Methods and Results: Human somatic cells were reprogrammed into human induced pluripotent stem cells and subsequently differentiated in iCMs. A senescent-like phenotype (SenCMs) was induced by short exposure (3 hours) to doxorubicin (Dox) at the sub-lethal concentration of 0.2 µM. Dox treatment induced expression of cyclin-dependent kinase inhibitors p21 and p16, and increased positivity to senescence-associated beta-galactosidase when compared to untreated iCMs. SenCMs showed increased oxidative stress, alteration in mitochondrial morphology and depolarized mitochondrial membrane potential, which resulted in decreased ATP production. Functionally, when compared to iCMs, SenCMs showed, prolonged multicellular QTc and single cell APD, with increased APD variability and delayed afterdepolarizations (DADs) incidence, two well-known arrhythmogenic indexes. These effects were largely ascribable to augmented late sodium current (I_NaL) and reduced delayed rectifier potassium current (Ikr). Moreover sarcoplasmic reticulum (SR) Ca²⁺ content was reduced because of downregulated SERCA2 and increased RyR2-mediated Ca²⁺ leak. Electrical and intracellular Ca²⁺ alterations were mostly justified by increased CaMKII activity in SenCMs. Finally, SenCMs phenotype was furtherly confirmed by analyzing physiological aging in CMs isolated from old mice in comparison to young ones. Conclusions: Overall, we showed that SenCMs recapitulate the phenotype of aged primary CMs in terms of senescence markers, electrical and Ca²⁺ handling properties and metabolic features. Thus, Dox-induced SenCMs can be considered a novel in vitro platform to study aging mechanisms and to envision cardiac specific anti-aging approach in humans.

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.

A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models

Computational models of the electrical potential across a cell membrane are longstanding and vital tools in electrophysiology research and applications. These models describe how ionic currents, internal fluxes, and buffering interact to determine membrane voltage and form action potentials (APs). Although this relationship is usually expressed as a differential equation, previous studies have shown it can be rewritten in an algebraic form, allowing direct calculation of membrane voltage. Rewriting in this form requires the introduction of a new parameter, called Γ0 in this manuscript, which represents the net concentration of all charges that influence membrane voltage but are not considered in the model. Although several studies have examined the impact of Γ0 on long-term stability and drift in model predictions, there has been little examination of its effects on model predictions, particularly when a model is refit to new data. In this study, we illustrate how Γ0 affects important physiological properties such as action potential duration restitution, and examine the effects of (in)correctly specifying Γ0 during model calibration. We show that, although physiologically plausible, the range of concentrations used in popular models leads to orders of magnitude differences in Γ0, which can lead to very different model predictions. In model calibration, we find that using an incorrect value of Γ0 can lead to biased estimates of the inferred parameters, but that the predictive power of these models can be restored by fitting Γ0 as a separate parameter. These results show the value of making Γ0 explicit in model formulations, as it forces modellers and experimenters to consider the effects of uncertainty and potential discrepancy in initial concentrations upon model predictions.

Basic Research Approaches to Evaluate Cardiac Arrhythmia in Heart Failure and Beyond

Patients with heart failure often develop cardiac arrhythmias. The mechanisms and interrelations linking heart failure and arrhythmias are not fully understood. Historically, research into arrhythmias has been performed on affected individuals or in vivo (animal) models. The latter however is constrained by interspecies variation, demands to reduce animal experiments and cost. Recent developments in in vitro induced pluripotent stem cell technology and in silico modelling have expanded the number of models available for the evaluation of heart failure and arrhythmia. An agnostic approach, combining the modalities discussed here, has the potential to improve our understanding for appraising the pathology and interactions between heart failure and arrhythmia and can provide robust and validated outcomes in a variety of research settings. This review discusses the state of the art models, methodologies and techniques used in the evaluation of heart failure and arrhythmia and will highlight the benefits of using them in combination. Special consideration is paid to assessing the pivotal role calcium handling has in the development of heart failure and arrhythmia.

Heart-on-Chip for Combined Cellular Dynamics Measurements and Computational Modeling Towards Clinical Applications

Organ-on-chip or micro-engineered three-dimensional cellular or tissue models are increasingly implemented in the study of cardiovascular pathophysiology as alternatives to traditional in vitro cell culture. Drug induced cardiotoxicity is a key issue in drug development pipelines, but the current in vitro and in vivo studies suffer from inter-species differences, high costs, and lack of reliability and accuracy in predicting cardiotoxicity. Microfluidic heart-on-chip devices can impose a paradigm shift to the current tools. They can not only recapitulate cardiac tissue level functionality and the communication between cells and extracellular matrices but also allow higher throughput studies conducive to drug screening especially with their added functionalities or sensors that extract disease-specific phenotypic, genotypic, and electrophysiological information in real-time. Such electrical and mechanical components can tailor the electrophysiology and mechanobiology of the experiment to better mimic the in vivo condition as well. Recent advancements and challenges are reviewed in the fabrication, functionalization and sensor assisted mechanical and electrophysiological measurements, numerical and computational modeling of cardiomyocytes' behavior, and the clinical applications in drug screening and disease modeling. This review concludes with the current challenges and perspectives on the future of such organ-on-chip platforms.

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.

Quantitative roles of ion channel dynamics on ventricular action potential

Mathematical models for the action potential (AP) generation of the electrically excitable cells including the heart are involved different mechanisms including the voltage-dependent currents with nonlinear time- and voltage-gating properties. From the shape of the AP waveforms to the duration of the refractory periods or heart rhythms are greatly affected by the functions describing the features or the quantities of these ion channels. In this work, a mathematical measure to analyze the regional contributions of voltage-gated channels is defined by dividing the AP into phases, epochs, and intervals of interest. The contribution of each time-dependent current for the newly defined cardiomyocyte model is successfully calculated and it is found that the contribution of dominant ion channels changes substantially not only for each phase but also for different regions of the cardiac AP. Besides, the defined method can also be applied in all Hodgkin-Huxley types of electrically excitable cell models to be able to understand the underlying dynamics better.

Non-invasive Estimation of Atrial Fibrillation Driver Position With Convolutional Neural Networks and Body Surface Potentials

Atrial fibrillation (AF) is characterized by complex and irregular propagation patterns, and AF onset locations and drivers responsible for its perpetuation are the main targets for ablation procedures. ECG imaging (ECGI) has been demonstrated as a promising tool to identify AF drivers and guide ablation procedures, being able to reconstruct the electrophysiological activity on the heart surface by using a non-invasive recording of body surface potentials (BSP). However, the inverse problem of ECGI is ill-posed, and it requires accurate mathematical modeling of both atria and torso, mainly from CT or MR images. Several deep learning-based methods have been proposed to detect AF, but most of the AF-based studies do not include the estimation of ablation targets. In this study, we propose to model the location of AF drivers from BSP as a supervised classification problem using convolutional neural networks (CNN). Accuracy in the test set ranged between 0.75 (SNR = 5 dB) and 0.93 (SNR = 20 dB upward) when assuming time independence, but it worsened to 0.52 or lower when dividing AF models into blocks. Therefore, CNN could be a robust method that could help to non-invasively identify target regions for ablation in AF by using body surface potential mapping, avoiding the use of ECGI.

From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

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.

Optogenetic actuation in ChR2-transduced fibroblasts alter excitation-contraction coupling and mechano-electric feedback in coupled cardiomyocytes: a computational modeling study

With the help of the conventional electrical method and the growing optogenetic technology, cardiac fibroblasts (Fbs) have been verified to couple electrically with working myocytes and bring electrophysiological remodeling changes in them. The intrinsic properties of cardiac functional autoregulation represented by excitation-contraction coupling (ECC) and mechano-electric feedback (MEF) have also been extensively studied. However, the roles of optogenetic stimulation on the characteristics of ECC and MEF in cardiomyocytes (CMs) coupled with Fbs have been barely investigated. In this study, we proposed a combined model composed of three modules to explore these influences. Simulation results showed that (1) during ECC, an increased light duration (LD) strengthened the inflow of ChR2 current and prolonged action potential duration (APD), and extended durations of twitch and internal sarcomere deformation through the decreased dissociation of calcium with troponin C (CaTnC) complexes and the prolonged duration of Xb attachment-detachment; (2) during MEF, an increased LD was followed by a longer muscle twitch and deformation, and led to APD prolongation through the inward ChR2 current and its inward rectification kinetics, which far outweighed the effects of the delaying dissociation of CaTnC complexes and the prolonged reverse mode of Na⁺-Ca²⁺ exchange on AP shortening; (3) due to the ChR2 current's rectification feature, enhancing the light irradiance (LI) brought slight variations in peak or valley values of electrophysiological and mechanical parameters while did not change durations of AP and twitch and muscle deformation in both ECC and MEF. In conclusion, the inward ChR2 current and its inward rectification feature were found to affect significantly the durations of AP and twitch in both ECC and MEF. The roles of optogenetic actuation on both ECC and MEF should be considered in future cardiac computational optogenetics at the tissue and organ scale.

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.

Model Systems for Addressing Mechanism of Arrhythmogenesis in Cardiac Repair

PURPOSE OF REVIEW

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

RECENT FINDINGS

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

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

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

Evolution of mathematical models of cardiomyocyte electrophysiology

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

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.

Electric discharge of electrocytes: Modelling, analysis and simulation

In this paper, we investigate the electric discharge of electrocytes by extending our previous work on the generation of electric potential. We first give a complete formulation of a single cell unit consisting of an electrocyte and a resistor, based on a Poisson-Nernst-Planck (PNP) system with various membrane currents as interfacial conditions for the electrocyte and a Maxwell's model for the resistor. Our previous work can be treated as a special case with an infinite resistor (or open circuit). Using asymptotic analysis, we simplify our PNP system and reduce it to an ordinary differential equation (ODE) based model. Unlike the case of an infinite resistor, our numerical simulations of the new model reveal several distinct features. A finite current is generated, which leads to non-constant electric potentials in the bulk of intracellular and extracellular regions. Furthermore, the current induces an additional action potential (AP) at the non-innervated membrane, contrary to the case of an open circuit where an AP is generated only at the innervated membrane. The voltage drop inside the electrocyte is caused by an internal resistance due to mobile ions. We show that our single cell model can be used as the basis for a system with stacked electrocytes and the total current during the discharge of an electric eel can be estimated by using our model.

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.

Role of Oxidation-Dependent CaMKII Activation in the Genesis of Abnormal Action Potentials in Atrial Cardiomyocytes: A Simulation Study

Atrial fibrillation is a common cardiac arrhythmia with an increasing incidence rate. Particularly for the aging population, understanding the underlying mechanisms of atrial arrhythmia is important in designing clinical treatment. Recently, experiments have shown that atrial arrhythmia is associated with oxidative stress. In this study, an atrial cell model including oxidative-dependent Ca²⁺/calmodulin- (CaM-) dependent protein kinase II (CaMKII) activation was developed to explore the intrinsic mechanisms of atrial arrhythmia induced by oxidative stress. The simulation results showed that oxidative stress caused early afterdepolarizations (EADs) of action potentials by altering the dynamics of transmembrane currents and intracellular calcium cycling. Oxidative stress gradually elevated the concentration of calcium ions in the cytoplasm by enhancing the L-type Ca²⁺ current and sarcoplasmic reticulum (SR) calcium release. Owing to increased intracellular calcium concentration, the inward Na⁺/Ca²⁺ exchange current was elevated which slowed down the repolarization of the action potential. Thus, the action potential was prolonged and the L-type Ca²⁺ current was reactivated, resulting in the genesis of EAD. Furthermore, based on the atrial single-cell model, a two-dimensional (2D) ideal tissue model was developed to explore the effect of oxidative stress on the electrical excitation wave conduction in 2D tissue. Simulation results demonstrated that, under oxidative stress conditions, EAD hindered the conduction of electrical excitation and caused an unstable spiral wave, which could disrupt normal cardiac rhythm and cause atrial arrhythmia. This study showed the effects of excess reactive oxygen species on calcium cycling and action potential in atrial myocytes and provided insights regarding atrial arrhythmia induced by oxidative stress.

Reducing complexity and unidentifiability when modelling human atrial cells

Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

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

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

Reducing complexity and unidentifiability when modelling human atrial cells

Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Atrial fibrillation source area probability mapping using electrogram patterns of multipole catheters

BACKGROUND

Catheter ablation therapy involving isolation of pulmonary veins (PVs) from the left atrium is performed to terminate atrial fibrillation (AF). Unfortunately, standalone PV isolation procedure has shown to be a suboptimal success with AF continuation or recurrence. One reason, especially in patients with persistent or high-burden paroxysmal AF, is known to be due to the formation of repeating-pattern AF sources with a meandering core inside the atria. However, there is a need for accurate mapping and localization of these sources during catheter ablation.

METHODS

A novel AF source area probability (ASAP) mapping algorithm was developed and evaluated in 2D and 3D atrial simulated tissues with various arrhythmia scenarios and a retrospective study with three cases of clinical human AF. The ASAP mapping analyzes the electrograms collected from a multipole diagnostic catheter that is commonly used during catheter ablation procedure to intelligently sample the atria and delineate the trajectory path of a meandering repeating-pattern AF source. ASAP starts by placing the diagnostic catheter at an arbitrary location in the atria. It analyzes the recorded bipolar electrograms to build an ASAP map over the atrium anatomy and suggests an optimal location for the subsequent catheter location. ASAP then determines from the constructed ASAP map if an AF source has been delineated. If so, the catheter navigation is stopped and the algorithm provides the area of the AF source. Otherwise, the catheter is navigated to the suggested location, and the process is continued until an AF-source area is delineated.

RESULTS

ASAP delineated the AF source in over 95% of the simulated human AF cases within less than eight catheter placements regardless of the initial catheter placement. The success of ASAP in the clinical AF was confirmed by the ablation outcomes and the electrogram patterns at the delineated area.

CONCLUSION

Our analysis indicates the potential of the ASAP mapping to provide accurate information about the area of the meandering repeating-pattern AF sources as AF ablation targets for effective AF termination. Our algorithm could improve the success of AF catheter ablation therapy by locating and subsequently targeting patient-specific and repeating-pattern AF sources inside the atria.

Sensitivity and Uncertainty Analysis of Two Human Atrial Cardiac Cell Models Using Gaussian Process Emulators

Biophysically detailed cardiac cell models reconstruct the action potential and calcium dynamics of cardiac myocytes. They aim to capture the biophysics of current flow through ion channels, pumps, and exchangers in the cell membrane, and are highly detailed. However, the relationship between model parameters and model outputs is difficult to establish because the models are both complex and non-linear. The consequences of uncertainty and variability in model parameters are therefore difficult to determine without undertaking large numbers of model evaluations. The aim of the present study was to demonstrate how sensitivity and uncertainty analysis using Gaussian process emulators can be used for a systematic and quantitive analysis of biophysically detailed cardiac cell models. We selected the Courtemanche and Maleckar models of the human atrial action potential for analysis because these models describe a similar set of currents, with different formulations. In our approach Gaussian processes emulate the main features of the action potential and calcium transient. The emulators were trained with a set of design data comprising samples from parameter space and corresponding model outputs, initially obtained from 300 model evaluations. Variance based sensitivity indices were calculated using the emulators, and first order and total effect indices were calculated for each combination of parameter and output. The differences between the first order and total effect indices indicated that the effect of interactions between parameters was small. A second set of emulators were then trained using a new set of design data with a subset of the model parameters with a sensitivity index of more than 0.1 (10%). This second stage analysis enabled comparison of mechanisms in the two models. The second stage sensitivity indices enabled the relationship between the L-type Ca 2+ current and the action potential plateau to be quantified in each model. Our quantitative analysis predicted that changes in maximum conductance of the ultra-rapid K + channel I Kur would have opposite effects on action potential duration in the two models, and this prediction was confirmed by additional simulations. This study has demonstrated that Gaussian process emulators are an effective tool for sensitivity and uncertainty analysis of biophysically detailed cardiac cell models.

Validation of quantitative measure of repolarization reserve as a novel marker of drug induced proarrhythmia

Repolarization reserve, the robustness of a cell to repolarize even when one of the repolarization mechanisms is failing, has been described qualitatively in terms of ionic currents, but has not been quantified by a generic metric that is applicable to drug screening. Prolonged repolarization leading to repolarization failure is highly arrhythmogenic. It may lead to ventricular tachycardia caused by triggered activity from early afterdepolarizations (EADs), or it may promote the occurrence of unidirectional conduction block and reentry. Both types of arrhythmia may deteriorate into ventricular fibrillation (VF) and death. We define the Repolarization Reserve Current (RRC) as the minimum constant current necessary to prevent normal repolarization of a cell. After developing and testing RRC for nine computational ionic models of various species, we applied it experimentally to atrial and ventricular human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM), and isolated guinea-pig ventricular cardiomyocytes. In simulations, repolarization was all-or-none with a precise, model-dependent critical RRC, resulting in a discrete shift in the Action Potential Duration (APD) - RRC relation, in the occurrence of EADs and repolarization failure. These data were faithfully reproduced in cellular experiments. RRC allows simple, fast, unambiguous quantification of the arrhythmogenic propensity in cardiac cells of various origins and species without the need of prior knowledge of underlying currents and is suitable for high throughput applications, and personalized medicine applications.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.