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Objective: Accurate monitoring of fetal cardiac activity is paramount for the early detection of fetal pathologies during pregnancy. Non-invasive fetal ECG has shown promise, offering advantages over traditional fetal monitoring techniques such as cardiotocography. However, extracting fetal signals from maternal abdominal recordings poses challenges, particularly due to the presence of the vernix caseosa, a fatty layer surrounding the fetus. This study aims to investigate how vernix caseosa distribution influences ECG morphology in a novel computational framework., Methods: A multi-compartment volume conductor, integrating fetal and maternal hearts, fetal body, amniotic fluid, and vernix caseosa embedded in a maternal torso, is constructed. Vernix caseosa distribution is varied homogeneously and heterogeneously on the fetal body. Fetal cardiac activity is simulated using a pseudo-bidomain formulation. Resulting body surface potential and ECG is analysed in terms of RDM, lnMAG, QRS complex and T-wave morphology at six abdominal sensor placements., Results: Results indicate vernix caseosa conductive properties and presence on the fetal head do not notably interfere with ECG readings, except in rare instances where the signal strength is extremely low. Signal strength is reduced more when covering back compared to front of the fetus. Nonetheless, both scenarios have a notable impact on ECG signal and T/QRS ratio, aligning with earlier findings suggesting caution in interpreting T/QRS ratio when vernix caseosa is present., Conclusion: The presence of vernix caseosa warrants careful consideration regarding ECG and especially T/QRS ratio interpretation., Significance: The study contributes to advancing the understanding of non-invasive fetal ECG.

Background: The electrophysiological mechanism connecting mitral valve prolapse (MVP), premature ventricular complexes and life-threatening ventricular arrhythmia is unknown. A common hypothesis is that stretch activated channels (SACs) play a significant role. SACs can trigger depolarizations or shorten repolarization times in response to myocardial stretch. Through these mechanisms, pathological traction of the papillary muscle (PM), as has been observed in patients with MVP, may induce irregular electrical activity and result in reentrant arrhythmia., Methods: Based on a patient with MVP and mitral annulus disjunction, we modeled the effect of excessive PM traction in a detailed medical image-derived ventricular model by activating SACs in the PM insertion region. By systematically varying the onset of SAC activation following sinus pacing, we identified vulnerability windows for reentry with 1 ms resolution. We explored how reentry was affected by the SAC reversal potential ( E SAC ) and the size of the region with simulated stretch (SAC region). Finally, the effect of global or focal fibrosis, modeled as reduction in tissue conductivity or mesh splitting (fibrotic microstructure), was investigated., Results: In models with healthy tissue or fibrosis modeled solely as CV slowing, we observed two vulnerable periods of reentry: For E SAC of -10 and -30 mV, SAC activated during the T-wave could cause depolarization of the SAC region which lead to reentry. For E SAC of -40 and -70 mV, SAC activated during the QRS complex could result in early repolarization of the SAC region and subsequent reentry. In models with fibrotic microstructure in the SAC region, we observed micro-reentries and a larger variability in which times of SAC activation triggered reentry. In these models, 86% of reentries were triggered during the QRS complex or T-wave. We only observed reentry for sufficiently large SAC regions ( > = 8 mm radius in models with healthy tissue)., Conclusion: Stretch of the PM insertion region following sinus activation may initiate ventricular reentry in patients with MVP, with or without fibrosis. Depending on the SAC reversal potential and timing of stretch, reentry may be triggered by ectopy due to SAC-induced depolarizations or by early repolarization within the SAC region., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Myklebust, Monopoli, Balaban, Aabel, Ribe, Castrini, Hasselberg, Bugge, Five, Haugaa, Maleckar and Arevalo.)

Introduction: Patients with non-ischemic cardiomyopathy (NICM) are at risk for ventricular arrhythmias, but diagnosis and treatment planning remain a serious clinical challenge. Although computational modeling has provided valuable insight into arrhythmic mechanisms, the optimal method for simulating reentry in NICM patients with structural disease is unknown. Methods: Here, we compare the effects of fibrotic representation on both reentry initiation and reentry morphology in patient-specific cardiac models. We investigate models with heterogeneous networks of non-conducting structures (cleft models) and models where fibrosis is represented as a dense core with a surrounding border zone (non-cleft models). Using segmented cardiac magnetic resonance with late gadolinium enhancement (LGE) of five NICM patients, we created 185 3D ventricular electrophysiological models with different fibrotic representations (clefts, reduced conductivity and ionic remodeling). Results: Reentry was induced by electrical pacing in 647 out of 3,145 simulations. Both cleft and non-cleft models can give rise to double-loop reentries meandering through fibrotic regions (Type 1-reentry). When accounting for fibrotic volume, the initiation sites of these reentries are associated with high local fibrotic density (mean LGE in cleft models: p < 0.001, core volume in non-cleft models: p = 0.018, negative binomial regression). In non-cleft models, Type 1-reentries required slow conduction in core tissue (non-clefts c models) as opposed to total conduction block. Incorporating ionic remodeling in fibrotic regions can give rise to single- or double-loop rotors close to healthy-fibrotic interfaces (Type 2-reentry). Increasing the cleft density or core-to-border zone ratio in cleft and non-cleft c models, respectively, leads to increased inducibility and a change in reentry morphology from Type 2 to Type 1. Conclusions: By demonstrating how fibrotic representation affects reentry morphology and location, our findings can aid model selection for simulating arrhythmogenesis in NICM., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Myklebust, Maleckar and Arevalo.)

By sensing changes in intracellular Ca 2+ , small-conductance Ca 2+ -activated K + (SK) channels dynamically regulate the dynamics of the cardiac action potential (AP) on a beat-to-beat basis. Given their predominance in atria versus ventricles, SK channels are considered a promising atrial-selective pharmacological target against atrial fibrillation (AF), the most common cardiac arrhythmia. However, the precise contribution of SK current ( I SK ) to atrial arrhythmogenesis is poorly understood, and may potentially involve different mechanisms that depend on species, heart rates, and degree of AF-induced atrial remodeling. Both reduced and enhanced I SK have been linked to AF. Similarly, both SK channel up- and downregulation have been reported in chronic AF (cAF) versus normal sinus rhythm (nSR) patient samples. Here, we use our multiscale modeling framework to obtain mechanistic insights into the contribution of I SK in human atrial cardiomyocyte electrophysiology. We simulate several protocols to quantify how I SK modulation affects the regulation of AP duration (APD), Ca 2+ transient, refractoriness, and occurrence of alternans and delayed afterdepolarizations (DADs). Our simulations show that I SK activation shortens the APD and atrial effective refractory period, limits Ca 2+ cycling, and slightly increases the propensity for alternans in both nSR and cAF conditions. We also show that increasing I SK counteracts DAD development by enhancing the repolarization force that opposes the Ca 2+ -dependent depolarization. Taken together, our results suggest that increasing I SK in human atrial cardiomyocytes could promote reentry while protecting against triggered activity. Depending on the leading arrhythmogenic mechanism, I SK inhibition may thus be a beneficial or detrimental anti-AF strategy. NEW & NOTEWORTHY Using our established framework for human atrial myocyte simulations, we investigated the role of the small-conductance Ca 2+ -activated K + current ( I SK ) in the regulation of cell function and the development of Ca 2+ -driven arrhythmias. We found that I SK inhibition, a promising atrial-selective pharmacological strategy against atrial fibrillation, counteracts the reentry-promoting abbreviation of atrial refractoriness, but renders human atrial myocytes more vulnerable to delayed afterdepolarizations, thus potentially increasing the propensity for ectopic (triggered) activity.

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research., (© 2022 Scandinavian Physiological Society. Published by John Wiley & Sons Ltd.)

Background: Adverse events in COVID-19 are difficult to predict. Risk stratification is encumbered by the need to protect healthcare workers. We hypothesize that artificial intelligence (AI) can help identify subtle signs of myocardial involvement in the 12-lead electrocardiogram (ECG), which could help predict complications., Objective: Use intake ECGs from COVID-19 patients to train AI models to predict risk of mortality or major adverse cardiovascular events (MACE)., Methods: We studied intake ECGs from 1448 COVID-19 patients (60.5% male, aged 63.4 ± 16.9 years). Records were labeled by mortality (death vs discharge) or MACE (no events vs arrhythmic, heart failure [HF], or thromboembolic [TE] events), then used to train AI models; these were compared to conventional regression models developed using demographic and comorbidity data., Results: A total of 245 (17.7%) patients died (67.3% male, aged 74.5 ± 14.4 years); 352 (24.4%) experienced at least 1 MACE (119 arrhythmic, 107 HF, 130 TE). AI models predicted mortality and MACE with area under the curve (AUC) values of 0.60 ± 0.05 and 0.55 ± 0.07, respectively; these were comparable to AUC values for conventional models (0.73 ± 0.07 and 0.65 ± 0.10). There were no prominent temporal trends in mortality rate or MACE incidence in our cohort; holdout testing with data from after a cutoff date (June 9, 2020) did not degrade model performance., Conclusion: Using intake ECGs alone, our AI models had limited ability to predict hospitalized COVID-19 patients' risk of mortality or MACE. Our models' accuracy was comparable to that of conventional models built using more in-depth information, but translation to clinical use would require higher sensitivity and positive predictive value. In the future, we hope that mixed-input AI models utilizing both ECG and clinical data may be developed to enhance predictive accuracy., (© 2021 Heart Rhythm Society.)

We introduce a framework for end-to-end integrative modeling of 3D single-cell multi-channel fluorescent image data of diverse subcellular structures. We employ stacked conditional β-variational autoencoders to first learn a latent representation of cell morphology, and then learn a latent representation of subcellular structure localization which is conditioned on the learned cell morphology. Our model is flexible and can be trained on images of arbitrary subcellular structures and at varying degrees of sparsity and reconstruction fidelity. We train our full model on 3D cell image data and explore design trade-offs in the 2D setting. Once trained, our model can be used to predict plausible locations of structures in cells where these structures were not imaged. The trained model can also be used to quantify the variation in the location of subcellular structures by generating plausible instantiations of each structure in arbitrary cell geometries. We apply our trained model to a small drug perturbation screen to demonstrate its applicability to new data. We show how the latent representations of drugged cells differ from unperturbed cells as expected by on-target effects of the drugs., Competing Interests: The authors have declared that no competing interests exist.

Recent global developments underscore the prominent role big data have in modern medical science. But privacy issues constitute a prevalent problem for collecting and sharing data between researchers. However, synthetic data generated to represent real data carrying similar information and distribution may alleviate the privacy issue. In this study, we present generative adversarial networks (GANs) capable of generating realistic synthetic DeepFake 10-s 12-lead electrocardiograms (ECGs). We have developed and compared two methods, named WaveGAN* and Pulse2Pulse. We trained the GANs with 7,233 real normal ECGs to produce 121,977 DeepFake normal ECGs. By verifying the ECGs using a commercial ECG interpretation program (MUSE 12SL, GE Healthcare), we demonstrate that the Pulse2Pulse GAN was superior to the WaveGAN* to produce realistic ECGs. ECG intervals and amplitudes were similar between the DeepFake and real ECGs. Although these synthetic ECGs mimic the dataset used for creation, the ECGs are not linked to any individuals and may thus be used freely. The synthetic dataset will be available as open access for researchers at OSF.io and the DeepFake generator available at the Python Package Index (PyPI) for generating synthetic ECGs. In conclusion, we were able to generate realistic synthetic ECGs using generative adversarial neural networks on normal ECGs from two population studies, thereby addressing the relevant privacy issues in medical datasets., (© 2021. The Author(s).)

Background: Remodeling due to myocardial infarction (MI) significantly increases patient arrhythmic risk. Simulations using patient-specific models have shown promise in predicting personalized risk for arrhythmia. However, these are computationally- and time- intensive, hindering translation to clinical practice. Classical machine learning (ML) algorithms (such as K-nearest neighbors, Gaussian support vector machines, and decision trees) as well as neural network techniques, shown to increase prediction accuracy, can be used to predict occurrence of arrhythmia as predicted by simulations based solely on infarct and ventricular geometry. We present an initial combined image-based patient-specific in silico and machine learning methodology to assess risk for dangerous arrhythmia in post-infarct patients. Furthermore, we aim to demonstrate that simulation-supported data augmentation improves prediction models, combining patient data, computational simulation, and advanced statistical modeling, improving overall accuracy for arrhythmia risk assessment. Methods: MRI-based computational models were constructed from 30 patients 5 days post-MI (the "baseline" population). In order to assess the utility biophysical model-supported data augmentation for improving arrhythmia prediction, we augmented the virtual baseline patient population. Each patient ventricular and ischemic geometry in the baseline population was used to create a subfamily of geometric models, resulting in an expanded set of patient models (the "augmented" population). Arrhythmia induction was attempted via programmed stimulation at 17 sites for each virtual patient corresponding to AHA LV segments and simulation outcome, "arrhythmia," or "no-arrhythmia," were used as ground truth for subsequent statistical prediction (machine learning, ML) models. For each patient geometric model, we measured and used choice data features: the myocardial volume and ischemic volume, as well as the segment-specific myocardial volume and ischemia percentage, as input to ML algorithms. For classical ML techniques (ML), we trained k-nearest neighbors, support vector machine, logistic regression, xgboost, and decision tree models to predict the simulation outcome from these geometric features alone. To explore neural network ML techniques, we trained both a three - and a four-hidden layer multilayer perceptron feed forward neural networks (NN), again predicting simulation outcomes from these geometric features alone. ML and NN models were trained on 70% of randomly selected segments and the remaining 30% was used for validation for both baseline and augmented populations. Results: Stimulation in the baseline population (30 patient models) resulted in reentry in 21.8% of sites tested; in the augmented population (129 total patient models) reentry occurred in 13.0% of sites tested. ML and NN models ranged in mean accuracy from 0.83 to 0.86 for the baseline population, improving to 0.88 to 0.89 in all cases. Conclusion: Machine learning techniques, combined with patient-specific, image-based computational simulations, can provide key clinical insights with high accuracy rapidly and efficiently. In the case of sparse or missing patient data, simulation-supported data augmentation can be employed to further improve predictive results for patient benefit. This work paves the way for using data-driven simulations for prediction of dangerous arrhythmia in MI patients., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Maleckar, Myklebust, Uv, Florvaag, Strøm, Glinge, Jabbari, Vejlstrup, Engstrøm, Ahtarovski, Jespersen, Tfelt-Hansen, Naumova and Arevalo.)

Deep learning-based tools may annotate and interpret medical data more quickly, consistently, and accurately than medical doctors. However, as medical doctors are ultimately responsible for clinical decision-making, any deep learning-based prediction should be accompanied by an explanation that a human can understand. We present an approach called electrocardiogram gradient class activation map (ECGradCAM), which is used to generate attention maps and explain the reasoning behind deep learning-based decision-making in ECG analysis. Attention maps may be used in the clinic to aid diagnosis, discover new medical knowledge, and identify novel features and characteristics of medical tests. In this paper, we showcase how ECGradCAM attention maps can unmask how a novel deep learning model measures both amplitudes and intervals in 12-lead electrocardiograms, and we show an example of how attention maps may be used to develop novel ECG features.

Background: Although the chondrocyte is a nonexcitable cell, there is strong interest in gaining detailed knowledge of its ion pumps, channels, exchangers, and transporters. In combination, these transport mechanisms set the resting potential, regulate cell volume, and strongly modulate responses of the chondrocyte to endocrine agents and physicochemical alterations in the surrounding extracellular microenvironment. Materials and Methods: Mathematical modeling was used to assess the functional roles of energy-requiring active transport, the Na + /K + pump, in chondrocytes. Results: Our findings illustrate plausible physiological roles for the Na + /K + pump in regulating the resting membrane potential and suggest ways in which specific molecular components of pump can respond to the unique electrochemical environment of the chondrocyte. Conclusion: This analysis provides a basis for linking chondrocyte electrophysiology to metabolism and yields insights into novel ways of manipulating or regulating responsiveness to external stimuli both under baseline conditions and in chronic diseases such as osteoarthritis., Competing Interests: No competing financial interests exist. The authors do not have any financial conflicts of interest in relation to this work., (© Mary M. Maleckar et al. 2020; Published by Mary Ann Liebert, Inc.)

Using animal cells and tissues as precise measuring devices for developing new drugs presents a long-standing challenge for the pharmaceutical industry. Despite the very significant resources that continue to be dedicated to animal testing of new compounds, only qualitative results can be obtained. This often results in both false positives and false negatives. Here, we show how the effect of drugs applied to animal ventricular myocytes can be translated, quantitatively, to estimate a number of different effects of the same drug on human cardiomyocytes. We illustrate and validate our methodology by translating, from animal to human, the effect of dofetilide applied to dog cardiomyocytes, the effect of E-4031 applied to zebrafish cardiomyocytes, and, finally, the effect of sotalol applied to rabbit cardiomyocytes. In all cases, the accuracy of our quantitative estimates are demonstrated. Our computations reveal that, in principle, electrophysiological data from testing using animal ventricular myocytes, can give precise, quantitative estimates of the effect of new compounds on human cardiomyocytes.

Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) hold great potential for drug screening applications. However, their usefulness is limited by the relative immaturity of the cells' electrophysiological properties as compared to native cardiomyocytes in the adult human heart. In this work, we extend and improve on methodology to address this limitation, building on previously introduced computational procedures which predict drug effects for adult cells based on changes in optical measurements of action potentials and Ca 2+ transients made in stem cell derived cardiac microtissues. This methodology quantifies ion channel changes through the inversion of data into a mathematical model, and maps this response to an adult phenotype through the assumption of functional invariance of fundamental intracellular and membrane channels during maturation. Here, we utilize an updated action potential model to represent both hiPSC-CMs and adult cardiomyocytes, apply an IC50-based model of dose-dependent drug effects, and introduce a continuation-based optimization algorithm for analysis of dose escalation measurements using five drugs with known effects. The improved methodology can identify drug induced changes more efficiently, and quantitate important metrics such as IC50 in line with published values. Consequently, the updated methodology is a step towards employing computational procedures to elucidate drug effects in adult cardiomyocytes for new drugs using stem cell-derived experimental tissues., (Copyright © 2020 Jæger, Charwat, Charrez, Finsberg, Maleckar, Wall, Healy and Tveito.)

Cell shapes and connectivities evolve over time as the colony changes shape or embryos develop. Shapes of intercellular interfaces are closely coupled with the forces resulting from actomyosin interactions, membrane tension, or cell-cell adhesions. Although it is possible to computationally infer cell-cell forces from a mechanical model of collective cell behavior, doing so for temporally evolving forces in a manner robust to digitization difficulties is challenging. Here, we introduce a method for dynamic local intercellular tension estimation (DLITE) that infers such evolution in temporal force with less sensitivity to digitization ambiguities or errors. This method builds upon previous work on single time points (cellular force-inference toolkit). We validate our method using synthetic geometries. DLITE's inferred cell colony tension evolutions correlate better with ground truth for these synthetic geometries as compared to tension values inferred from methods that consider each time point in isolation. We introduce cell connectivity errors, angle estimate errors, connection mislocalization, and connection topological changes to synthetic data and show that DLITE has reduced sensitivity to these conditions. Finally, we apply DLITE to time series of human-induced pluripotent stem cell colonies with endogenously expressed GFP-tagged zonulae occludentes-1. We show that DLITE offers improved stability in the inference of cell-cell tensions and supports a correlation between the dynamics of cell-cell forces and colony rearrangement., (Copyright © 2019 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Understanding cells as integrated systems is central to modern biology. Although fluorescence microscopy can resolve subcellular structure in living cells, it is expensive, is slow, and can damage cells. We present a label-free method for predicting three-dimensional fluorescence directly from transmitted-light images and demonstrate that it can be used to generate multi-structure, integrated images. The method can also predict immunofluorescence (IF) from electron micrograph (EM) inputs, extending the potential applications.

Human transplant programs provide significant opportunities for detailed in vitro assessments of physiological properties of selected tissues and cell types. We present a semi-quantitative study of the fundamental electrophysiological/biophysical characteristics of human chondrocytes, focused on K + transport mechanisms, and their ability to regulate to the resting membrane potential, E m . Patch clamp studies on these enzymatically isolated human chondrocytes reveal consistent expression of at least three functionally distinct K + currents, as well as transient receptor potential (TRP) currents. The small size of these cells and their exceptionally low current densities present significant technical challenges for electrophysiological recordings. These limitations have been addressed by parallel development of a mathematical model of these K + and TRP channel ion transfer mechanisms in an attempt to reveal their contributions to E m. In combination, these experimental results and simulations yield new insights into: (i) the ionic basis for E m and its expected range of values; (ii) modulation of E m by the unique articular joint extracellular milieu; (iii) some aspects of TRP channel mediated depolarization-secretion coupling; (iv) some of the essential biophysical principles that regulate K + channel function in "chondrons." The chondron denotes the chondrocyte and its immediate extracellular compartment. The presence of discrete localized surface charges and associated zeta potentials at the chondrocyte surface are regulated by cell metabolism and can modulate interactions of chondrocytes with the extracellular matrix. Semi-quantitative analysis of these factors in chondrocyte/chondron function may yield insights into progressive osteoarthritis.

Computational modeling may provide a quantitative framework for integrating multiscale data to gain insight into mechanisms of heart disease, identify and test pharmacological and electrical therapy and interventions, and support clinical decisions. Patient-specific computational cardiac models can help guide such procedures, and cardiac inverse modeling is a promising alternative to adequately personalize these models. Indeed, full cardiac inverse modeling is currently becoming computationally feasible; however, fundamental work to assess the feasibility of emerging techniques is still needed. In this study, we use a partial differential equation-constrained optimal control approach to numerically investigate the identifiability of an initial activation sequence from synthetic (partial) observations of the extracellular potential using the bidomain approximation and 2D representations of cardiac tissue. Our results demonstrate that activation times and duration of several stimuli can be recovered even with high levels of noise, that it is sufficient to sample the observations at the electrocardiogram-relevant sampling frequency of 1 kHz, and that spatial resolutions that are coarser than the standard in electrophysiological simulations can be used. The optimization of activation times is still effective when synthetic data are generated with a different cell membrane kinetics model than optimized for. The findings thus indicate that the presented approach has potential for finding activation sequences from clinical data modalities, as an extension to existing cardiac imaging approaches., (Copyright © 2017 John Wiley & Sons, Ltd.)

Models of cardiac cell electrophysiology are complex non-linear systems which can be used to gain insight into mechanisms of cardiac dynamics in both healthy and pathological conditions. However, the complexity of cardiac models can make mechanistic insight difficult. Moreover, these are typically fitted to averaged experimental data which do not incorporate the variability in observations. Recently, building populations of models to incorporate inter- and intra-subject variability in simulations has been combined with sensitivity analysis (SA) to uncover novel ionic mechanisms and potentially clarify arrhythmogenic behaviors. We used the Koivumäki human atrial cell model to create two populations, representing normal Sinus Rhythm (nSR) and chronic Atrial Fibrillation (cAF), by varying 22 key model parameters. In each population, 14 biomarkers related to the action potential and dynamic restitution were extracted. Populations were calibrated based on distributions of biomarkers to obtain reasonable physiological behavior, and subjected to SA to quantify correlations between model parameters and pro-arrhythmia markers. The two populations showed distinct behaviors under steady state and dynamic pacing. The nSR population revealed greater variability, and more unstable dynamic restitution, as compared to the cAF population, suggesting that simulated cAF remodeling rendered cells more stable to parameter variation and rate adaptation. SA revealed that the biomarkers depended mainly on five ionic currents, with noted differences in sensitivities to these between nSR and cAF. Also, parameters could be selected to produce a model variant with no alternans and unaltered action potential morphology, highlighting that unstable dynamical behavior may be driven by specific cell parameter settings. These results ultimately suggest that arrhythmia maintenance in cAF may not be due to instability in cell membrane excitability, but rather due to tissue-level effects which promote initiation and maintenance of reentrant arrhythmia.

Patient-specific estimates of the stress distribution in the left ventricles (LV) may have important applications for therapy planning, but computing the stress generally requires knowledge of the material behaviour. The passive stress-strain relation of myocardial tissue has been characterized by a number of models, but material parameters (MPs) remain difficult to estimate. The aim of this study is to implement a zero-pressure algorithm to reconstruct numerically the stress distribution in the LV without precise knowledge of MPs. We investigate the sensitivity of the stress distribution to variations in the different sets of constitutive parameters. We show that the sensitivity of the LV stresses to MPs can be marginal for an isotropic constitutive model. However, when using a transversely isotropic exponential strain energy function, the LV stresses become sensitive to MPs, especially to the linear elastic coefficient before the exponential function. This indicates that in-vivo identification efforts should focus mostly on this MP for the development of patient-specific finite-element analysis.

There is pressing clinical need to identify developing heart attack (infarction) in patients as early as possible. However, current state-of-the-art tools in clinical practice, underpinned by the evaluation of elevation of the ST segment of the 12-lead electrocardiogram (ECG), do not identify all patients suffering from lack of blood flow to the heart muscle (cardiac ischemia), worsening the risk for further adverse events and patient outcome overall. In this study, we aimed to explore and compare the portions of cardiac repolarization in the ECG that best capture the electrophysiological changes associated with ischemia. We developed three-dimensional electrophysiological models of the human ventricles and torso, incorporating biophysically-based membrane kinetics and realistic activation sequence, to compute simulated ECGs and their alteration with the application of simulated ischemia of differing severity in diverse regions of the heart. Results suggest that metrics based on the T-wave in addition to the ST segment may be more sensitive to detecting ischemia than those using the ST segment alone. Further research into how such simulation-aided risk assessment methods may aid workflows in extant clinical practice, with the ultimate goal of multimodality clinical support, is warranted.

Excitation-contraction coupling in cardiac myocytes requires calcium influx through L-type calcium channels in the sarcolemma, which gates calcium release through sarcoplasmic reticulum ryanodine receptors in a process known as calcium-induced calcium release, producing a myoplasmic calcium transient and enabling cardiomyocyte contraction. The spatio-temporal dynamics of calcium release, buffering, and reuptake into the sarcoplasmic reticulum play a central role in excitation-contraction coupling in both normal and diseased cardiac myocytes. However, further quantitative understanding of these cells' calcium machinery and the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease requires accurate knowledge of cardiac ultrastructure, protein distribution and subcellular function. As current imaging techniques are limited in spatial resolution, limiting insight into changes in calcium handling, computational models of excitation-contraction coupling have been increasingly employed to probe these structure-function relationships. This review will focus on the development of structural models of cardiac calcium dynamics at the subcellular level, orienting the reader broadly towards the development of models of subcellular calcium handling in cardiomyocytes. Specific focus will be given to progress in recent years in terms of multi-scale modeling employing resolved spatial models of subcellular calcium machinery. A review of the state-of-the-art will be followed by a review of emergent insights into calcium-dependent etiologies in heart disease and, finally, we will offer a perspective on future directions for related computational modeling and simulation efforts., Competing Interests: DECLARATION OF CONFLICTING INTERESTS: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Background: Refractoriness of cardiac cells limits maximum frequency of electrical activity and protects the heart from tonic contractions. Short refractory periods support major arrhythmogenic substrates and augmentation of refractoriness is therefore seen as a main mechanism of antiarrhythmic drugs. Cardiomyocyte excitability depends on availability of sodium channels, which involves both time- and voltage-dependent recovery from inactivation. This study therefore aims to characterise how sodium channel inactivation affects refractoriness in human atria., Methods and Results: Steady-state activation and inactivation parameters of sodium channels measured in vitro in isolated human atrial cardiomyocytes were used to parameterise a mathematical human atrial cell model. Action potential data were acquired from human atrial trabeculae of patients in either sinus rhythm or chronic atrial fibrillation. The ex vivo measurements of action potential duration, effective refractory period and resting membrane potential were well-replicated in simulations using this new in silico model. Notably, the voltage threshold potential at which refractoriness was observed was not different between sinus rhythm and chronic atrial fibrillation tissues and was neither affected by changes in frequency (1 vs. 3Hz)., Conclusions: Our results suggest a preferentially voltage-dependent, rather than time-dependent, effect with respect to refractoriness at physiologically relevant rates in human atria. However, as the resting membrane potential is hyperpolarized in chronic atrial fibrillation, the voltage-dependence of excitability dominates, profoundly increasing the risk for arrhythmia re-initiation and maintenance in fibrillating atria. Our results thereby highlight resting membrane potential as a potential target in pharmacological management of chronic atrial fibrillation., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Atrial fibrillation (AF), the most common cardiac arrhythmia, is associated with increased risk of cerebrovascular stroke, and with several other pathologies, including heart failure. Current therapies for AF are targeted at reducing risk of stroke (anticoagulation) and tachycardia-induced cardiomyopathy (rate or rhythm control). Rate control, typically achieved by atrioventricular nodal blocking drugs, is often insufficient to alleviate symptoms. Rhythm control approaches include antiarrhythmic drugs, electrical cardioversion, and ablation strategies. Here, we offer several examples of how computational modeling can provide a quantitative framework for integrating multiscale data to: (a) gain insight into multiscale mechanisms of AF; (b) identify and test pharmacological and electrical therapy and interventions; and (c) support clinical decisions. We review how modeling approaches have evolved and contributed to the research pipeline and preclinical development and discuss future directions and challenges in the field., (Copyright © 2016 Elsevier Inc. All rights reserved.)

Aims: The study investigates how increased Ito, as mediated by the activator NS5806, affects excitation-contraction coupling in chronic heart failure (HF). We hypothesized that restoring spike-and-dome morphology of the action potential (AP) to a healthy phenotype would be insufficient to restore the intracellular Ca(2) (+) transient (CaT), due to HF-induced remodelling of Ca(2+) handling., Methods and Results: An existing mathematical model of the canine ventricular myocyte was modified to incorporate recent experimental data from healthy and failing myocytes, resulting in models of both healthy and HF epicardial, midmyocardial, and endocardial cell variants. Affects of NS5806 were also included in HF models through its direct interaction with Kv4.3 and Kv1.4. Single-cell simulations performed in all models (control, HF, and HF + drug) and variants (epi, mid, and endo) assessed AP morphology and underlying ionic processes with a focus on calcium transients (CaT), how these were altered in HF across the ventricular wall, and the subsequent effects of varying compound concentration in HF. Heart failure model variants recapitulated a characteristic increase in AP duration (APD) in the disease. The qualitative effects of application of half-maximal effective concentration (EC50) of NS5806 on APs and CaT are heterogeneous and non-linear. Deepening in the AP notch with drug is a direct effect of the activation of Ito; both Ito and consequent alteration of IK1 kinetics cause decrease in AP plateau potential. Decreased APD50 and APD90 are both due to altered IK1. Analysis revealed that drug effects depend on transmurality. Ca(2+) transient morphology changes-increased amplitude and shorter time to peak-are due to direct increase in ICa,L and indirect larger SR Ca(2+) release subsequent to Ito activation., Conclusions: Downstream effects of a compound acting exclusively on sarcolemmal ion channels are difficult to predict. Remediation of APD to pre-failing state does not ameliorate dysfunction in CaT; however, restoration of notch depth appears to impart modest benefit and a likelihood of therapeutic value in modulating early repolarization., (Published on behalf of the European Society of Cardiology. All rights reserved. © The Author 2014. For permissions please email: journals.permissions@oup.com.)

Although t-tubules have traditionally been thought to be absent in atrial cardiomyocytes, recent studies have suggested that t-tubules exist in the atria of large mammals. However, it is unclear whether regional differences in t-tubule organization exist that define cardiomyocyte function across the atria. We sought to investigate regional t-tubule density in pig and rat atria and the consequences for cardiomyocyte Ca(2+) homeostasis. We observed t-tubules in approximately one-third of rat atrial cardiomyocytes, in both tissue cryosections and isolated cardiomyocytes. In a minority (≈10%) of atrial cardiomyocytes, the t-tubular network was well organized, with a transverse structure resembling that of ventricular cardiomyocytes. In both rat and pig atrial tissue, we observed higher t-tubule density in the epicardium than in the endocardium. Consistent with high variability in the distribution of t-tubules and Ca(2+) channels among cells, L-type Ca(2+) current amplitude was also highly variable and steeply dependent on capacitance and t-tubule density. Accordingly, Ca(2+) transients showed great variability in Ca(2+) release synchrony. Simultaneous imaging of the cell membrane and Ca(2+) transients confirmed t-tubule functionality. Results from mathematical modeling indicated that a transmural gradient in t-tubule organization and Ca(2+) release kinetics supports synchronization of contraction across the atrial wall and may underlie transmural differences in the refractory period. In conclusion, our results indicate that t-tubule density is highly variable across the atria. We propose that higher t-tubule density in cells localized in the epicardium may promote synchronization of contraction across the atrial wall., (Copyright © 2014 the American Physiological Society.)

In the mammalian heart fibroblasts have important functional roles in both healthy conditions and diseased states. During pathophysiological challenges, a closely related myofibroblast cell population emerges, and can have distinct, significant roles. Recently, it has been reported that human atrial myofibroblasts can express a Na(+) current, INa. Some of the biophysical properties and molecular features suggest that this INa is due to expression of Nav 1.5, the same Na(+) channel α subunit that generates the predominant INa in myocytes from adult mammalian heart. In principle, expression of Nav 1.5 could give rise to regenerative action potentials in the fibroblasts/myofibroblasts. This would suggest an active as opposed to passive role for fibroblasts/myofibroblasts in both the "trigger" and the "substrate" components of cardiac rhythm disturbances. Our goals in this preliminary study were: (i) to confirm and extend the electrophysiological characterization of INa in a human atrial fibroblast/myofibroblast cell population maintained in conventional 2-D tissue culture; (ii) to identify key molecular properties of the α and β subunits of these Na(+) channel(s); (iii) to define the biophysical and pharmacological properties of this INa; (iv) to integrate the available multi-disciplinary data, and attempt to illustrate its functional consequences, using a mathematical model in which the human atrial myocyte is coupled via connexins to fixed numbers of fibroblasts/myofibroblasts in a syncytial arrangement. Our experimental findings confirm that a significant fraction (approximately 40-50%) of these human atrial myofibroblasts can express INa. However, our data suggest that INa may be generated by a combination of Nav 1.9, Nav 1.2, and Nav 1.5. Our results, when complemented with mathematical modeling, provide a background for re-evaluating pharmacological management of supraventricular rhythm disorders, e.g., persistent atrial fibrillation.

Chronic atrial fibrillation (AF) is a complex disease with underlying changes in electrophysiology, calcium signaling and the structure of atrial myocytes. How these individual remodeling targets and their emergent interactions contribute to cell physiology in chronic AF is not well understood. To approach this problem, we performed in silico experiments in a computational model of the human atrial myocyte. The remodeled function of cellular components was based on a broad literature review of in vitro findings in chronic AF, and these were integrated into the model to define a cohort of virtual cells. Simulation results indicate that while the altered function of calcium and potassium ion channels alone causes a pronounced decrease in action potential duration, remodeling of intracellular calcium handling also has a substantial impact on the chronic AF phenotype. We additionally found that the reduction in amplitude of the calcium transient in chronic AF as compared to normal sinus rhythm is primarily due to the remodeling of calcium channel function, calcium handling and cellular geometry. Finally, we found that decreased electrical resistance of the membrane together with remodeled calcium handling synergistically decreased cellular excitability and the subsequent inducibility of repolarization abnormalities in the human atrial myocyte in chronic AF. We conclude that the presented results highlight the complexity of both intrinsic cellular interactions and emergent properties of human atrial myocytes in chronic AF. Therefore, reversing remodeling for a single remodeled component does little to restore the normal sinus rhythm phenotype. These findings may have important implications for developing novel therapeutic approaches for chronic AF.

Mathematical modeling of cardiac electrophysiology is an insightful method to investigate the underlying mechanisms responsible for arrhythmias such as atrial fibrillation (AF). In past years, five models of human atrial electrophysiology with different formulations of ionic currents, and consequently diverging properties, have been published. The aim of this work is to give an overview of strengths and weaknesses of these models depending on the purpose and the general requirements of simulations. Therefore, these models were systematically benchmarked with respect to general mathematical properties and their ability to reproduce certain electrophysiological phenomena, such as action potential (AP) alternans. To assess the models' ability to replicate modified properties of human myocytes and tissue in cardiac disease, electrical remodeling in chronic atrial fibrillation (cAF) was chosen as test case. The healthy and remodeled model variants were compared with experimental results in single-cell, 1D and 2D tissue simulations to investigate AP and restitution properties, as well as the initiation of reentrant circuits.

Intercellular calcium waves in cardiac myocytes are a well-recognized, if incompletely understood, phenomenon. In a variety of preparations, investigators have reported multi-cellular calcium waves or triggered propagated contractions, but the mechanisms of propagation and pathological importance of these events remain unclear. Here, we review existing experimental data and present a computational approach to investigate the mechanisms of multi-cellular calcium wave propagation. Over the past 50 years, the standard modeling paradigm for excitable cardiac tissue has seen increasingly detailed models of the dynamics of individual cells coupled in tissue solely by intercellular and interstitial current flow. Although very successful, this modeling regime has been unable to capture two important phenomena: 1) the slow intercellular calcium waves observed experimentally, and 2) how intercellular calcium events resulting in delayed after depolarizations at the cellular level could overcome a source-sink mismatch to initiate depolarization waves in tissue. In this paper, we introduce a mathematical model with subcellular spatial resolution, in which we allow both inter- and intracellular current flow and calcium diffusion. In simulations of coupled cells employing this model, we observe: a) slow inter-cellular calcium waves propagating at about 0.1 mm/s, b) faster Calcium-Depolarization-Calcium (CDC) waves, traveling at about 1 mm/s, and c) CDC-waves that can set off fast depolarization-waves (50 cm/s) in tissue with varying gap-junction conductivity., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Reduced conduction velocity (CV) in the myocardium is well known to increase the probability of arrhythmia and can be caused by structural changes, reduced excitability of individual myocytes, or decreased electrical coupling in the tissue. Recently, investigators have developed antiarrhythmic drugs that target the connections between individual myocytes with the goal of restoring tissue CV, specifically through increasing gap-junction coupling. In a simple but qualitatively relevant mathematical model, we show here that the introduction of a drug that improves intercellular conductance will indeed increase the CV. However, conditions that would require such a drug, such as fibrotic remodeling, may also increase the load of fibroblasts. Fibroblasts may couple to myocytes in much the same way as myocytes couple to each other, and therefore the use of such an agent may also improve coupling between myocytes and fibroblasts. We present numerical examples illustrating that when the load of coupled fibroblasts on myocytes is low or nonexistent, the drug works as expected, i.e., the drug increases CV. On the other hand, when the fibroblast load is high, changes in CV are nonmonotonic, i.e., the CV first increases and then decreases with an increase in dosage. The existence of coupled fibroblasts may therefore impair the effect of the drug, and under unfortunate conditions may be proarrhythmic., (Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Fibroblasts are electrophysiologically quiescent in the healthy heart. Evidence suggests that remodeling following myocardial infarction may include coupling of myofibroblasts (Mfbs) among themselves and with myocytes via gap junctions. We use a magnetic resonance imaging-based, three-dimensional computational model of the chronically infarcted rabbit ventricles to characterize the arrhythmogenic substrate resulting from Mfb infiltration as a function of Mfb density. Mfbs forming gap junctions were incorporated into both infarct regions, the periinfarct zone (PZ) and the scar; six scenarios were modeled: 0%, 10%, and 30% Mfbs in the PZ, with either 80% or 0% Mfbs in the scar. Ionic current remodeling in PZ was also included. All preparations exhibited elevated resting membrane potential within and near the PZ and action potential duration shortening throughout the ventricles. The unique combination of PZ ionic current remodeling and different degrees of Mfb infiltration in the infarcted ventricles determines susceptibility to arrhythmia. At low densities, Mfbs do not alter arrhythmia propensity; the latter arises predominantly from ionic current remodeling in PZ. At intermediate densities, Mfbs cause additional action potential shortening and exacerbate arrhythmia propensity. At high densities, Mfbs protect against arrhythmia by causing resting depolarization and blocking propagation, thus overcoming the arrhythmogenic effects of PZ ionic current remodeling., (Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The well-organized contraction of each heartbeat is enabled by an electrical wave traversing and exciting the myocardium in a regular manner. Perturbations to this wave, referred to as arrhythmias, can lead to lethal fibrillation if not treated within minutes. One manner in which arrhythmias originate is an ill-fated interaction of the regular electrical signal controlling the heartbeat, the sinus wave, with an ectopic stimulus. It is not fully understood how and when ectopic waves are generated. Based on mathematical models, we show that ectopic beats can be characterized in terms of unstable eigenmodes of the resting state.

We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the collection. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts. The numerical experiments demonstrate that there is a region of instability of the form observed in the simplified model analysis., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Atrial fibrosis has been implicated in the development and maintenance of atrial arrhythmias, and is characterized by expansion of the extracellular matrix and an increased number of fibroblasts (Fbs). Electrotonic coupling between atrial myocytes and Fbs may contribute to the formation of an arrhythmogenic substrate. However, the role of these cell-cell interactions in the function of both normal and diseased atria remains poorly understood. The goal of this study was to gain mechanistic insight into the role of electrotonic Fb-myocyte coupling on myocyte excitability and repolarization. To represent the system, a human atrial myocyte (hAM) coupled to a variable number of Fbs, we employed a new ionic model of the hAM, and a variety of membrane representations for atrial Fbs. Simulations elucidated the effects of altering the intercellular coupling conductance, electrophysiological Fb properties, and stimulation rate on the myocyte action potential. The results demonstrate that the myocyte resting potential and action potential waveform are modulated strongly by the properties and number of coupled Fbs, the degree of coupling, and the pacing frequency. Our model provides mechanistic insight into the consequences of heterologous cell coupling on hAM electrophysiology, and can be extended to evaluate these implications at both tissue and organ levels.

Ongoing investigation of the electrophysiology and pathophysiology of the human atria requires an accurate representation of the membrane dynamics of the human atrial myocyte. However, existing models of the human atrial myocyte action potential do not accurately reproduce experimental observations with respect to the kinetics of key repolarizing currents or rate dependence of the action potential and fail to properly enforce charge conservation, an essential characteristic in any model of the cardiac membrane. In addition, recent advances in experimental methods have resulted in new data regarding the kinetics of repolarizing currents in the human atria. The goal of this study was to develop a new model of the human atrial action potential, based on the Nygren et al. model of the human atrial myocyte and newly available experimental data, that ensures an accurate representation of repolarization processes and reproduction of action potential rate dependence and enforces charge conservation. Specifically, the transient outward K(+) current (I(t)) and ultrarapid rectifier K(+) current (I(Kur)) were newly formulated. The inwardly recitifying K(+) current (I(K1)) was also reanalyzed and implemented appropriately. Simulations of the human atrial myocyte action potential with this new model demonstrated that early repolarization is dependent on the relative conductances of I(t) and I(Kur), whereas densities of both I(Kur) and I(K1) underlie later repolarization. In addition, this model reproduces experimental measurements of rate dependence of I(t), I(Kur), and action potential duration. This new model constitutes an improved representation of excitability and repolarization reserve in the human atrial myocyte and, therefore, provides a useful computational tool for future studies involving the human atrium in both health and disease.

To fully characterize the mechanisms of defibrillation, it is necessary to understand the response, within the three-dimensional (3D) volume of the ventricles, to shocks given in diastole. Studies that have examined diastolic responses conducted measurements on the epicardium or on a transmural surface of the left ventricular (LV) wall only. The goal of this study was to use optical imaging experiments and 3D bidomain simulations, including a model of optical mapping, to ascertain the shock-induced virtual electrode and activation patterns throughout the rabbit ventricles following diastolic shocks. We tested the hypothesis that the locations of shock-induced regions of hyperpolarization govern the different diastolic activation patterns for shocks of reversed polarity. In model and experiment, uniform-field monophasic shocks of reversed polarities (cathode over the right ventricle is RV-, reverse polarity is LV-) were applied to the ventricles in diastole. Experiments and simulations revealed that RV- shocks resulted in longer activation times compared with LV- shocks of the same strength. 3D simulations demonstrated that RV- shocks induced a greater volume of hyperpolarization at shock end compared with LV- shocks; most of these hyperpolarized regions were located in the LV. The results of this study indicate that ventricular geometry plays an important role in both the location and size of the shock-induced virtual anodes that determine activation delay during the shock and subsequently affect shock-induced propagation. If regions of hyperpolarization that develop during the shock are sufficiently large, activation delay may persist until shock end.

In the mammalian heart, myocytes and fibroblasts can communicate via gap junction, or connexin-mediated current flow. Some of the effects of this electrotonic coupling on the action potential waveform of the human ventricular myocyte have been analyzed in detail. The present study employs a recently developed mathematical model of the human atrial myocyte to investigate the consequences of this heterogeneous cell-cell interaction on the action potential of the human atrium. Two independent physiological processes which alter the physiology of the human atrium have been studied. i) The effects of the autonomic transmitter acetylcholine on the atrial action potential have been investigated by inclusion of a time-independent, acetylcholine-activated K(+) current in this mathematical model of the atrial myocyte. ii) A non-selective cation current which is activated by natriuretic peptides has been incorporated into a previously published mathematical model of the cardiac fibroblast. These results identify subtle effects of acetylcholine, which arise from the nonlinear interactions between ionic currents in the human atrial myocyte. They also illustrate marked alterations in the action potential waveform arising from fibroblast-myocyte source-sink principles when the natriuretic peptide-mediated cation conductance is activated. Additional calculations also illustrate the effects of simultaneous activation of both of these cell-type specific conductances within the atrial myocardium. This study provides a basis for beginning to assess the utility of mathematical modeling in understanding detailed cell-cell interactions within the complex paracrine environment of the human atrial myocardium.

Ventricular dilatation increases the defibrillation threshold (DFT). In order to elucidate the mechanisms responsible for this increase, the present article investigates changes in the postshock behavior of the myocardium upon stretch. A two-dimensional electro-mechanical model of cardiac tissue incorporating heterogeneous fiber orientation was used to explore the effect of sustained stretch on postshock behavior via (a) recruitment of mechanosensitive channels (MSC) and (b) tissue deformation and concomitant changes in tissue conductivities. Recruitment of MSC had no influence on vulnerability to electric shocks as compared to control, but increased the complexity of postshock VF patterns. Stretch-induced deformation and changes in tissue conductivities resulted in a decrease in vulnerability to electric shocks.

The goal of this study is to investigate the mechanisms responsible for the increase in the upper limit of vulnerability (ULV; highest shock strength that induces arrhythmia) following the increase in pacing rate. To accomplish this goal, the study employs a three-dimensional bidomain finite element model of a slice through the canine ventricles. The preparation was paced eight times at a basic cycle length (BCL) of either 80 or 150ms followed by delivery of shocks of various strengths and timings. Our results demonstrate that the shock strength, which induced an arrhythmia 50% of the time, increased 20% for the faster pacing compared to the slower pacing. Analysis of the mechanisms underlying the increased vulnerability revealed that delayed post-shock activations originating in the tissue depths appear as breakthrough activations on the surfaces of the preparation following an isoelectric window (IW). However, the IW duration was consistently shorter in the faster-paced preparation. Consequently, breakthrough activations appeared on the surfaces of this preparation earlier, when the tissue was less recovered, resulting in higher probability of unidirectional block and reentry. This explains why shocks of the same strength were more likely to result in arrhythmia induction when delivered to a preparation that was rapidly paced.