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Aims: The mechanisms of transition from regular rhythms to ventricular fibrillation (VF) are poorly understood. The concordant to discordant repolarization alternans pathway is extensively studied; however, despite its theoretical centrality, cannot guide ablation. We hypothesize that complex repolarization dynamics, i.e. oscillations in the repolarization phase of action potentials with periods over two of classic alternans, is a marker of electrically unstable substrate, and ablation of these areas has a stabilizing effect and may reduce the risk of VF. To prove the existence of higher-order periodicities in human hearts., Methods and Results: We performed optical mapping of explanted human hearts obtained from recipients of heart transplantation at the time of surgery. Signals recorded from the right ventricle endocardial surface were processed to detect global and local repolarization dynamics during rapid pacing. A statistically significant global 1:4 peak was seen in three of six hearts. Local (pixel-wise) analysis revealed the spatially heterogeneous distribution of Periods 4, 6, and 8, with the regional presence of periods greater than two in all the hearts. There was no significant correlation between the underlying restitution properties and the period of each pixel., Conclusion: We present evidence of complex higher-order periodicities and the co-existence of such regions with stable non-chaotic areas in ex vivo human hearts. We infer that the oscillation of the calcium cycling machinery is the primary mechanism of higher-order dynamics. These higher-order regions may act as niduses of instability and may provide targets for substrate-based ablation of VF., Competing Interests: Conflict of interest: None declared., (© The Author(s) 2023. Published by Oxford University Press on behalf of the European Society of Cardiology.)

Cardiac Purkinje networks are a fundamental part of the conduction system and are known to initiate a variety of cardiac arrhythmias. However, patient-specific modeling of Purkinje networks remains a challenge due to their high morphological complexity. This work presents a novel method based on optimization principles for the generation of Purkinje networks that combines geometric and activation accuracy in branch size, bifurcation angles, and Purkinje-ventricular-junction activation times. Three biventricular meshes with increasing levels of complexity are used to evaluate the performance of our approach. Purkinje-tissue coupled monodomain simulations are executed to evaluate the generated networks in a realistic scenario using the most recent Purkinje/ventricular human cellular models and physiological values for the Purkinje-ventricular-junction characteristic delay. The results demonstrate that the new method can generate patient-specific Purkinje networks with controlled morphological metrics and specified local activation times at the Purkinje-ventricular junctions., (© 2023. The Author(s).)

Over the past two decades there has been a steady trend towards the development of realistic models of cardiac conduction with increasing levels of detail. However, making models more realistic complicates their personalization and use in clinical practice due to limited availability of tissue and cellular scale data. One such limitation is obtaining information about myocardial fiber organization in the clinical setting. In this study, we investigated a chimeric model of the left atrium utilizing clinically derived patient-specific atrial geometry and a realistic, yet foreign for a given patient fiber organization. We discovered that even significant variability of fiber organization had a relatively small effect on the spatio-temporal activation pattern during regular pacing. For a given pacing site, the activation maps were very similar across all fiber organizations tested.

Customization of cardiac action potential models has become increasingly important with the recognition of patient-specific models and virtual patient cohorts as valuable predictive tools. Nevertheless, developing customized models by fitting parameters to data poses technical and methodological challenges: despite noise and variability associated with real-world datasets, traditional optimization methods produce a single "best-fit" set of parameter values. Bayesian estimation methods seek distributions of parameter values given the data by obtaining samples from the target distribution, but in practice widely known Bayesian algorithms like Markov chain Monte Carlo tend to be computationally inefficient and scale poorly with the dimensionality of parameter space. In this paper, we consider two computationally efficient Bayesian approaches: the Hamiltonian Monte Carlo (HMC) algorithm and the approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithm. We find that both methods successfully identify distributions of model parameters for two cardiac action potential models using model-derived synthetic data and an experimental dataset from a zebrafish heart. Although both methods appear to converge to the same distribution family and are computationally efficient, HMC generally finds narrower marginal distributions, while ABC-SMC is less sensitive to the algorithmic settings including the prior distribution., (© 2022. International Federation for Medical and Biological Engineering.)

Epithelial-mesenchymal transition (EMT) is a biological process that plays a central role in embryonic development, tissue regeneration, and cancer metastasis. Transforming growth factor-β (TGFβ) is a potent inducer of this cellular transition, comprising transitions from an epithelial state to partial or hybrid EMT state(s), to a mesenchymal state. Recent experimental studies have shown that, within a population of epithelial cells, heterogeneous phenotypical profiles arise in response to different time- and TGFβ dose-dependent stimuli. This offers a challenge for computational models, as most model parameters are generally obtained to represent typical cell responses, not necessarily specific responses nor to capture population variability. In this study, we applied a data-assimilation approach that combines limited noisy observations with predictions from a computational model, paired with parameter estimation. Synthetic experiments mimic the biological heterogeneity in cell states that is observed in epithelial cell populations by generating a large population of model parameter sets. Analysis of the parameters for virtual epithelial cells with biologically significant characteristics (e.g., EMT prone or resistant) illustrates that these sub-populations have identifiable critical model parameters. We perform a series of in silico experiments in which a forecasting system reconstructs the EMT dynamics of each virtual cell within a heterogeneous population exposed to time-dependent exogenous TGFβ dose and either an EMT-suppressing or EMT-promoting perturbation. We find that estimating population-specific critical parameters significantly improved the prediction accuracy of cell responses. Thus, with appropriate protocol design, we demonstrate that a data-assimilation approach successfully reconstructs and predicts the dynamics of a heterogeneous virtual epithelial cell population in the presence of physiological model error and parameter uncertainty., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

In recent years, machine-learning techniques, particularly deep learning, have outperformed traditional time-series forecasting approaches in many contexts, including univariate and multivariate predictions. This study aims to investigate the capability of (i) gated recurrent neural networks, including long short-term memory (LSTM) and gated recurrent unit (GRU) networks, (ii) reservoir computing (RC) techniques, such as echo state networks (ESNs) and hybrid physics-informed ESNs, and (iii) the nonlinear vector autoregression (NVAR) approach, which has recently been introduced as the next generation RC, for the prediction of chaotic time series and to compare their performance in terms of accuracy, efficiency, and robustness. We apply the methods to predict time series obtained from two widely used chaotic benchmarks, the Mackey-Glass and Lorenz-63 models, as well as two other chaotic datasets representing a bursting neuron and the dynamics of the El Niño Southern Oscillation, and to one experimental dataset representing a time series of cardiac voltage with complex dynamics. We find that even though gated RNN techniques have been successful in forecasting time series generally, they can fall short in predicting chaotic time series for the methods, datasets, and ranges of hyperparameter values considered here. In contrast, for the chaotic datasets studied, we found that reservoir computing and NVAR techniques are more computationally efficient and offer more promise in long-term prediction of chaotic time series., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Computational modeling and experimental/clinical prediction of the complex signals during cardiac arrhythmias have the potential to lead to new approaches for prevention and treatment. Machine-learning (ML) and deep-learning approaches can be used for time-series forecasting and have recently been applied to cardiac electrophysiology. While the high spatiotemporal nonlinearity of cardiac electrical dynamics has hindered application of these approaches, the fact that cardiac voltage time series are not random suggests that reliable and efficient ML methods have the potential to predict future action potentials. This work introduces and evaluates an integrated architecture in which a long short-term memory autoencoder (AE) is integrated into the echo state network (ESN) framework. In this approach, the AE learns a compressed representation of the input nonlinear time series. Then, the trained encoder serves as a feature-extraction component, feeding the learned features into the recurrent ESN reservoir. The proposed AE-ESN approach is evaluated using synthetic and experimental voltage time series from cardiac cells, which exhibit nonlinear and chaotic behavior. Compared to the baseline and physics-informed ESN approaches, the AE-ESN yields mean absolute errors in predicted voltage 6-14 times smaller when forecasting approximately 20 future action potentials for the datasets considered. The AE-ESN also demonstrates less sensitivity to algorithmic parameter settings. Furthermore, the representation provided by the feature-extraction component removes the requirement in previous work for explicitly introducing external stimulus currents, which may not be easily extracted from real-world datasets, as additional time series, thereby making the AE-ESN easier to apply to clinical data.

Venetoclax (ven) plus azacitidine (aza) is the standard of care for patients with newly diagnosed acute myeloid leukemia (AML) who are not candidates for intensive chemotherapy (IC). Some patients who are IC candidates instead receive ven/aza. We retrospectively analyzed patients with newly diagnosed AML who received ven/aza (n = 143) or IC (n = 149) to compare outcomes, seek variables that could predict response to 1 therapy or the other, and ascertain whether treatment recommendations could be refined. The response rates were 76.9% for ven/aza and 70.5% for IC. The median overall survival (OS) was 884 days for IC compared with 483 days for ven/aza (P = .0020). A propensity-matched cohort was used to compare outcomes in the setting of equivalent baseline variables, and when matched for age, biological risk, and transplantation, the median OS was 705 days for IC compared with not reached for ven/aza (P = .0667). Variables that favored response to ven/aza over IC included older age, secondary AML, and RUNX1 mutations. AML M5 favored response to IC over ven/aza. In the propensity-matched cohort analyzing OS, older age, adverse risk, and RUNX1 mutations favored ven/aza over IC, whereas intermediate risk favored IC over ven/aza. In conclusion, patients receiving IC have improved OS compared with those receiving ven/aza. However, in a propensity-matched cohort of patients with equivalent baseline factors, there was a trend toward favorable OS for ven/aza. Specific variables, such as RUNX1 mutations, reported here for the first time, can be identified that favor ven/aza or IC, helping to guide treatment decisions for patients who may be eligible candidates for either therapy., (© 2021 by The American Society of Hematology. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0), permitting only noncommercial, nonderivative use with attribution. All other rights reserved.)

The electrical signals triggering the heart's contraction are governed by non-linear processes that can produce complex irregular activity, especially during or preceding the onset of cardiac arrhythmias. Forecasts of cardiac voltage time series in such conditions could allow new opportunities for intervention and control but would require efficient computation of highly accurate predictions. Although machine-learning (ML) approaches hold promise for delivering such results, non-linear time-series forecasting poses significant challenges. In this manuscript, we study the performance of two recurrent neural network (RNN) approaches along with echo state networks (ESNs) from the reservoir computing (RC) paradigm in predicting cardiac voltage data in terms of accuracy, efficiency, and robustness. We show that these ML time-series prediction methods can forecast synthetic and experimental cardiac action potentials for at least 15-20 beats with a high degree of accuracy, with ESNs typically two orders of magnitude faster than RNN approaches for the same network size., 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 Shahi, Marcotte, Herndon, Fenton, Shiferaw and Cherry.)

Understanding cardiac arrhythmic mechanisms and developing new strategies to control and terminate them using computer simulations requires realistic physiological cell models with anatomically accurate heart structures. Furthermore, numerical simulations must be fast enough to study and validate model and structure parameters. Here, we present an interactive parallel approach for solving detailed cell dynamics in high-resolution human heart structures with a local PC's GPU. In vitro human heart MRI scans were manually segmented to produce 3D structures with anatomically realistic electrophysiology. The Abubu.js library was used to create an interactive code to solve the OVVR human ventricular cell model and the FDA extension of the model in the human MRI heart structures, allowing the simulation of reentrant waves and investigation of their dynamics in real time. Interactive simulations of a physiological cell model in a detailed anatomical human heart reveals propagation of waves through the fine structures of the trabeculae and pectinate muscle that can perpetuate arrhythmias, thereby giving new insights into effects that may need to be considered when planning ablation and other defibrillation methods.

The shape of the ECG depends on the lead positions but also on the distribution and dispersion of different cell types and their action potential (AP) durations and shapes. We present an interactive JavaScript program that allows fast simulations of the ECG by solving and displaying the dynamics of cardiac cells in tissue using a web browser. We use physiologically accurate ODE models of cardiac cells of different types including SA node, right and left atria, AV node, Purkinje, and right and left ventricular cells with dispersion that accounts for apex-to-base and epi-to-endo variations. The software allows for real-time variations for each cell type and their spatial range so as to identify how the shape of the ECG varies as a function of cell type, distribution, excitation duration and AP shape. The propagation of the wave is visualized in real time through all the regions as parameters are kept fixed or varied to modify ECG morphology. The code solves thousands of simulated cells in real time and is independent of operating system, so it can run on PCs, laptops, tablets and cellphones. This program can be used to teach students, fellows and the general public how and why lead positions and the different cell physiology in the heart affect the various features of the ECG.

Aims: Cardiac modeling in heart structures for the study of arrhythmia mechanisms requires the use of software that runs on supercomputers. Therefore, computational studies are limited to groups with access to computer clusters and personnel with high-performance computing experience. We present how to use and implement WebGL programs via a custom-written library to run and visualize simulations of the most complex ionic models in 2D and 3D, in real time, interactively using the multi-core GPU of a single computer., Methods: We use Abubu.js, a library we developed for solving partial differential equations such as those describing crystal growth and fluid flow, along with a newly implemented visualization algorithm, to simulate complex ionic cell models. By combining this library with JavaScript, we allow direct real-time interactions with simulations. We implemented: 1) modification of any model parameters and equations at any time, with direct access to the code while it runs, 2) electrode stimulation anywhere in the 2D/3D tissue with a mouse click, 3) saving the solution of the system at any time to re-initiate the dynamics from saved initial conditions, and 4) rotation/visualization of 3D structures at any angle., Results: As examples of this modeling platform, we implemented a phenomenological cell model and the human ventricular OVVR model (41 variables). In 2D we illustrate the dynamics in an annulus, disk, and square tissue; in 2D and 3D porcine ventricles, we show the initiation of functional/anatomical reentry, spiral wave dynamics in different regimes, initiation of early afterdepolarizations (EADs), and the effects of model parameter variations in real time., Conclusions: We present the first simulations of complex models in anatomical structures with enhanced visualization and extended interactivity that run on a single PC, without software downloads, and as fast as in real-time even for 3D full ventricles.

Aims: Cardiac action potential (AP) models are typically given with a single set of parameter values; however, this approach does not consider variability and uncertainty across individuals and experimental conditions. As an alternative to single-value parameter fitting, we sought to use a Bayesian approach, the Hamiltonian Monte Carlo (HMC) algorithm, to find distributions of physiological parameter values for cardiac AP models across a range of cycle lengths (CLs) and dynamics., Methods: To assess HMC's accuracy for cardiac data, we applied it to synthetic APs from the Mitchell-Shaeffer (MS) and Fenton-Karma (FK) models with added noise over a range of physiological CLs, some of which included alternans. To show the applicability of HMC to experimental data, we calculated parameter distributions for both models using micro-electrode recordings of zebrafish APs from a range of CLs., Results: For synthetic APs generated from three CLs using the MS (FK) models, HMC produced unimodal quasi-symmetric distributions for all five (13) parameters. APs generated by setting all parameters in the MS (FK) model to the modes of their corresponding marginal distributions yielded errors in voltage traces below 5.0% (0.6%). We also obtained distributions for the MS (FK) model parameters using zebrafish data to construct the first minimal model of the zebrafish AP, with voltage trace errors below 4.8% (3.4%)., Conclusion: We have shown that HMC can identify not only a single set of parameter values but also viable distributions for cardiac AP model parameters using synthetic and experimental data. Because HMC generates samples from the parameter distributions based on input data, it can produce families of parameterizations that can be used in population-based modeling approaches without the need for rejecting a large number of randomly generated candidate parameterizations. HMC also has the potential to provide quantitative measures of spatial/individual variability and uncertainty.

Time series of spatially-extended two-dimensional recordings are the cornerstone of basic and clinical cardiac electrophysiology. The data source may be either multipolar catheters, multi-electrode arrays, optical mapping with the help of voltage and calcium-sensitive fluorescent dyes, or the output of simulation studies. The resulting data cubes (usually two spatial and one temporal dimension) are shared either as movie files or, after additional processing, various graphs and tables. However, such data products can only convey a limited view of the data. It will be beneficial if the data consumers can interactively process the data, explore different processing options and change its visualization. This paper presents the Unified Electrophysiology Mapping Framework (Unimapper) to facilitate the exchange of electrophysiology data. Its pedigree includes a Java-based optical mapping application. The core of Unimapper is a website and a collection of JavaScript utility functions for data import and visualization (including multi-channel visualization for simultaneous voltage/calcium mapping), basic image processing (e.g., smoothing), basic signal processing (e.g., signal detrending), and advanced processing (e.g., phase calculation using the Hilbert transform). Additionally, Unimapper can optionally use graphics processing units (GPUs) for computationally intensive operations. The Unimapper ecosystem also includes utility libraries for commonly used scientific programming languages (MATLAB, Python, and Julia) that allow the data producers to convert images and recorded signals into a standard format readable by Unimapper. Unimapper can act as a nexus to share electrophysiology data - whether recorded experimentally, clinically or generated by simulation - and enhance communication and collaboration among researchers.

Long-QT is commonly associated with an increased risk of polymorphic ventricular tachycardia from drug therapy. However, not all drugs prolonging QT interval are proarrhythmic. This study aimed to characterize cellular and tissue mechanisms under which QT-interval prolonging drugs and their combination are proarrhythmic, examining arrhythmia susceptibility due to action potential (AP) triangulation and spatial dispersion of action potential duration (APD). Additionally, we aimed to elucidate that Torsades de Pointe (TdP) associated with long-QT are not necessarily caused by early-after-depolarization (EADs) but are related to the presence of AP alternans in both time and space. Isolated Guinea Pig hearts were Langendorff perfused, and optical mapping was done with a voltage dye-sensitive dye. Two commonly used drugs at the beginning of the COVID-19 pandemic, hydroxychloroquine (HCQ) and Azithromycin (AZM), were added to study the effects of QT interval prolongation. Alternans in time and space were characterized by performing restitution pacing protocols. Comparing APs, HCQ prolongs APD during phase-III repolarization, resulting in a higher triangulation ratio than AZM alone or AZM combined with HCQ. Lower triangulation ratios with AZM are associated with phase-II prolongation, lower arrhythmia, and lower incidence of spatially discordant alternans.

Background: In March 2020, hydroxychloroquine (HCQ) alone or combined with azithromycin (AZM) was authorized as a treatment for COVID-19 in many countries. The therapy proved ineffective with long QT and deadly cardiac arrhythmia risks, illustrating challenges to determine the new safety profile of repurposed drugs., Objective: To investigate proarrhythmic effects and mechanism of HCQ and AZM (combined and alone) with high doses of HCQ as in the COVID-19 clinical trials., Methods: Proarrhythmic effects of HCQ and AZM are quantified using optical mapping with voltage-sensitive dyes in ex vivo Langendorff-perfused guinea pig (GP) hearts and with numerical simulations of a GP Luo-Rudy and a human O'Hara-Virag-Varro-Rudy models, for Epi, Endo, and M cells, in cell and tissue, incorporating the drug's effect on cell membrane ionic currents., Results: Experimentally, HCQ alone and combined with AZM leads to long QT intervals by prolonging the action potential duration and increased spatial dispersion of action potential (AP) repolarization across the heart, leading to proarrhythmic discordant alternans. AZM alone had a lesser arrhythmic effect with less triangulation of the AP shape. Mathematical cardiac models fail to reproduce most of the arrhythmic effects observed experimentally., Conclusions: During public health crises, the risks and benefits of new and repurposed drugs could be better assessed with alternative experimental and computational approaches to identify proarrhythmic mechanisms. Optical mapping is an effective framework suitable to investigate the drug's adverse effects on cardiac cell membrane ionic channels at the cellular level and arrhythmia mechanisms at the tissue and whole-organ level., (© 2021 Heart Rhythm Society. Published by Elsevier Inc.)

Genetic mutations in genes encoding for potassium channel protein structures have been recently associated with episodes of atrial fibrillation in asymptomatic patients. The aim of this study is to investigate the potential arrhythmogenicity of three gain-of-function mutations related to atrial fibrillation-namely, KCNH2 T895M, KCNH2 T436M, and KCNE3-V17M-using modeling and simulation of the electrophysiological activity of the heart. A genetic algorithm was used to tune the parameters' value of the original ionic currents to reproduce the alterations experimentally observed caused by the mutations. The effects on action potentials, ionic currents, and restitution properties were analyzed using versions of the Courtemanche human atrial myocyte model in different tissues: pulmonary vein, right, and left atrium. Atrial susceptibility of the tissues to spiral wave generation was also investigated studying the temporal vulnerability. The presence of the three mutations resulted in an overall more arrhythmogenic substrate. Higher current density, action potential duration shortening, and flattening of the restitution curves were the major effects of the three mutations at the single-cell level. The genetic mutations at the tissue level induced a higher temporal vulnerability to the rotor's initiation and progression, by sustaining spiral waves that perpetuate until the end of the simulation. The mutation with the highest pro-arrhythmic effects, exhibiting the widest sustained VW and the smallest meandering rotor's tip areas, was KCNE3-V17M. Moreover, the increased susceptibility to arrhythmias and rotor's stability was tissue-dependent. Pulmonary vein tissues were more prone to rotor's initiation, while in left atrium tissues rotors were more easily sustained. Re-entries were also progressively more stable in pulmonary vein tissue, followed by the left atrium, and finally the right atrium. The presence of the genetic mutations increased the susceptibility to arrhythmias by promoting the rotor's initiation and maintenance. The study provides useful insights into the mechanisms underlying fibrillatory events caused by KCNH2 T895M, KCNH2 T436M, and KCNE3-V17M and might aid the planning of patient-specific targeted therapies., 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 Belletti, Romero, Martinez-Mateu, Cherry, Fenton and Saiz.)

Certain cardiac arrhythmias are preceded by electrical alternans, a state characterized by beat-to-beat alternation in cellular action potential duration. Cardiac alternans may arise from different mechanisms including instabilities in voltage or intracellular calcium cycling. Although a number of techniques have been proposed to suppress alternans, these methods have mainly been tested using models that do not support calcium-driven alternans. Therefore, it is important to understand how control methods may perform when alternans is driven by instabilities in calcium cycling. In this study, we applied controllability analysis to a discrete map of alternans dynamics in a cardiac cell. We compared two different controllability measures to determine to what extent different control strategies could suppress alternans and tested these predictions using three feedback controllers. We found a modal controllability measure, unlike the minimum singular value of the controllability matrix, consistently indicated the control strategies requiring the least control effort and yielding the smallest closed-loop eigenvalue. In addition, action potential duration was identified as the most effective variable through which control can be applied, regardless of alternans mechanism, although sarcoplasmic reticulum calcium load was also useful for the calcium-driven alternans cases.

Reconstructions of excitation patterns in cardiac tissue must contend with uncertainties due to model error, observation error, and hidden state variables. The accuracy of these state reconstructions may be improved by efforts to account for each of these sources of uncertainty, in particular, through the incorporation of uncertainty in model specification and model dynamics. To this end, we introduce stochastic modeling methods in the context of ensemble-based data assimilation and state reconstruction for cardiac dynamics in one- and three-dimensional cardiac systems. We propose two classes of methods, one following the canonical stochastic differential equation formalism, and another perturbing the ensemble evolution in the parameter space of the model, which are further characterized according to the details of the models used in the ensemble. The stochastic methods are applied to a simple model of cardiac dynamics with fast-slow time-scale separation, which permits tuning the form of effective stochastic assimilation schemes based on a similar separation of dynamical time scales. We find that the selection of slow or fast time scales in the formulation of stochastic forcing terms can be understood analogously to existing ensemble inflation techniques for accounting for finite-size effects in ensemble Kalman filter methods; however, like existing inflation methods, care must be taken in choosing relevant parameters to avoid over-driving the data assimilation process. In particular, we find that a combination of stochastic processes-analogously to the combination of additive and multiplicative inflation methods-yields improvements to the assimilation error and ensemble spread over these classical methods.

Background: Early during the current coronavirus disease 19 (COVID-19) pandemic, hydroxychloroquine (HCQ) received a significant amount of attention as a potential antiviral treatment, such that it became one of the most commonly prescribed medications for COVID-19 patients. However, not only has the effectiveness of HCQ remained questionable, but mainly based on preclinical and a few small clinical studies, HCQ is known to be potentially arrhythmogenic, especially as a result of QT prolongation., Objective: The purpose of this study was to investigate the arrhythmic effects of HCQ, as the heightened risk is especially relevant to COVID-19 patients, who are at higher risk for cardiac complications and arrhythmias at baseline., Methods: An optical mapping technique utilizing voltage-sensitive fluorescent dyes was used to determine the arrhythmic effects of HCQ in ex vivo guinea pig and rabbit hearts perfused with the upper therapeutic serum dose of HCQ (1000 ng/mL)., Results: HCQ markedly increased action potential dispersion, resulted in development of repolarization alternans, and initiated polymorphic ventricular tachycardia., Conclusion: The study results further highlight the proarrhythmic effects of HCQ., (Copyright © 2020 Heart Rhythm Society. Published by Elsevier Inc. All rights reserved.)

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm's sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

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.

Epithelial-mesenchymal transition (EMT) is a fundamental biological process that plays a central role in embryonic development, tissue regeneration, and cancer metastasis. Transforming growth factor-β (TGFβ) is a potent inducer of this cellular transition, which is composed of transitions from an epithelial state to intermediate or partial EMT state(s) to a mesenchymal state. Using computational models to predict cell state transitions in a specific experiment is inherently difficult for reasons including model parameter uncertainty and error associated with experimental observations. In this study, we demonstrate that a data-assimilation approach using an ensemble Kalman filter, which combines limited noisy observations with predictions from a computational model of TGFβ-induced EMT, can reconstruct the cell state and predict the timing of state transitions. We used our approach in proof-of-concept "synthetic" in silico experiments, in which experimental observations were produced from a known computational model with the addition of noise. We mimic parameter uncertainty in in vitro experiments by incorporating model error that shifts the TGFβ doses associated with the state transitions and reproduces experimentally observed variability in cell state by either shifting a single parameter or generating "populations" of model parameters. We performed synthetic experiments for a wide range of TGFβ doses, investigating different cell steady-state conditions, and conducted parameter studies varying properties of the data-assimilation approach including the time interval between observations and incorporating multiplicative inflation, a technique to compensate for underestimation of the model uncertainty and mitigate the influence of model error. We find that cell state can be successfully reconstructed and the future cell state predicted in synthetic experiments, even in the setting of model error, when experimental observations are performed at a sufficiently short time interval and incorporate multiplicative inflation. Our study demonstrates the feasibility and utility of a data-assimilation approach to forecasting the fate of cells undergoing EMT., (Copyright © 2020 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Delay differential equations (DDEs) recently have been used in models of cardiac electrophysiology, particularly in studies focusing on electrical alternans, instabilities, and chaos. A number of processes within cardiac cells involve delays, and DDEs can potentially represent mechanisms that result in complex dynamics both at the cellular level and at the tissue level, including cardiac arrhythmias. However, DDE-based formulations introduce new computational challenges due to the need for storing and retrieving past values of variables at each spatial location. Cardiac tissue simulations that use DDEs may require over 28 GB of memory if the history of variables is not managed carefully. This paper addresses both computational and dynamical issues. First, we present new methods for the numerical solution of DDEs in tissue to mitigate the memory requirements associated with the history of variables. The new methods exploit the different time scales of an action potential to dynamically optimize history size. We find that the proposed methods decrease memory usage by up to 95% in cardiac tissue simulations compared to straightforward history-management algorithms. Second, we use the optimized methods to analyze for the first time the dynamics of wave propagation in two-dimensional cardiac tissue for models that include DDEs. In particular, we study the effects of DDEs on spiral-wave dynamics, including wave breakup and chaos, using a canine myocyte model. We find that by introducing delays to the gating variables governing the calcium current, DDEs can induce spiral-wave breakup in 2D cardiac tissue domains.

Complex spatiotemporal patterns of action potential duration have been shown to occur in many mammalian hearts due to period-doubling bifurcations that develop with increasing frequency of stimulation. Here, through high-resolution optical mapping experiments and mathematical modeling, we introduce a characteristic spatial length of cardiac activity in canine ventricular wedges via a spatiotemporal correlation analysis, at different stimulation frequencies and during fibrillation. We show that the characteristic length ranges from 40 to 20 cm during one-to-one responses and it decreases to a specific value of about 3 cm at the transition from period-doubling bifurcation to fibrillation. We further show that during fibrillation, the characteristic length is about 1 cm. Another significant outcome of our analysis is the finding of a constitutive phenomenological law obtained from a nonlinear fitting of experimental data which relates the conduction velocity restitution curve with the characteristic length of the system. The fractional exponent of 3/2 in our phenomenological law is in agreement with the domain size remapping required to reproduce experimental fibrillation dynamics within a realistic cardiac domain via accurate mathematical models.

Purpose: Multi-polar diagnostic catheters are used to construct the 3D electro-anatomic mapping of the atrium during atrial fibrillation (AF) ablation procedures; however, it remains unclear how to use the electrograms recorded by these catheters to locate AF-driving sites known as focal and rotor source types. The purpose of this study is to present the first algorithm to iteratively navigate a circular multi-polar catheter to locate AF focal and rotor sources without the need to map the entire atria., Methods: Starting from an initial location, the algorithm, which was blinded to the location and type of the AF source, iteratively advanced a Lasso catheter based on its electrogram characteristics. The algorithm stopped the catheter when it located of an AF source and identified the type. The efficiency of the algorithm is validated using a set of simulated focal and rotor-driven arrhythmias in fibrotic human 2D and 3D atrial tissue., Results: Our study shows the feasibility of locating AF sources with a success rate of greater than 95.25% within average 7.56 ± 2.28 placements independently of the initial position of the catheter and the source type., Conclusions: The algorithm could play a critical role in clinical electrophysiology laboratories for mapping patient-specific ablation of AF sources located outside the pulmonary veins and improving the procedure success.

Introduction: Targeting repeating-pattern atrial fibrillation (AF) sources (reentry or focal drivers) can help in patient-specific ablation therapy for AF; however, the development of reliable and accurate tools for locating such sources remains a major challenge. We describe iterative catheter navigation (ICAN) algorithm to locate AF drivers using a conventional circular Lasso catheter., Methods and Results: At each step, the algorithm analyzes 10 bipolar electrograms recoded at a given catheter location and the history of previous catheter movements to determine if the source is inside the catheter loop. If not, it calculates new coordinates and selects a new position for the catheter. The process continues until a source is located. The algorithm was evaluated in a computer model of atrial tissue with various degrees of fibrosis under a broad range of arrhythmia scenarios. The latter included slow and fast reentry, macroreentry, figure-of-eight reentry, and fibrillatory conduction. Depending on the initial distance of the catheter from the source and scenario, it took about 3 to 16 steps to localize an AF source. In 94% of cases, the identified location was within 4 mm from the source, independently of the initial position of the catheter. The algorithm worked equally well in the presence of patchy fibrosis, low-voltage areas, fragmented electrograms, and dominant-frequency gradients., Conclusions: AF repeating-pattern sources can be localized using circular catheters without the need to map the entire tissue. The proposed algorithm has the potential to become a useful tool for patient-specific ablation of AF sources located outside the pulmonary veins., (© 2019 The Authors. Journal of Cardiovascular Electrophysiology Published by Wiley Periodicals, Inc.)

The study of complex systems has emerged as an important field with many discoveries still to be made. Computer simulation and visualization provide important tools for studying complex dynamics including chaos, solitons, and fractals, but available computing power has been a limiting factor. In this work, we describe a novel and highly efficient computing and visualization paradigm using a Web Graphics Library (WebGL 2.0) methodology along with our newly developed library (Abubu.js). Our approach harnesses the power of widely available and highly parallel graphics cards while maintaining ease of use by simplifying programming through hiding implementation details, running in a web browser without the need for compilation, and avoiding the use of plugins. At the same time, it allows for interactivity, such as changing parameter values on the fly, and its computing is so fast that zooming in on a region of a fractal like the Mandelbrot set can incur no delay despite having to recalculate values for the entire plane. We demonstrate our approach using a wide range of complex systems that display dynamics from fractals to standing and propagating waves in 1, 2 and 3 dimensions. We also include some models with instabilities that can lead to chaotic dynamics. For all the examples shown here we provide links to the codes for anyone to use, modify and further develop with other models. Overall, the enhanced visualization and computation capabilities provided by WebGL together with Abubu.js have great potential to facilitate new discoveries about complex systems.

Cardiac dynamics modeling has been useful for studying and treating arrhythmias. However, it is a multiscale problem requiring the solution of billions of differential equations describing the complex electrophysiology of interconnected cells. Therefore, large-scale cardiac modeling has been limited to groups with access to supercomputers and clusters. Many areas of computational science face similar problems where computational costs are too high for personal computers so that supercomputers or clusters currently are necessary. Here, we introduce a new approach that makes high-performance simulation of cardiac dynamics and other large-scale systems like fluid flow and crystal growth accessible to virtually anyone with a modest computer. For cardiac dynamics, this approach will allow not only scientists and students but also physicians to use physiologically accurate modeling and simulation tools that are interactive in real time, thereby making diagnostics, research, and education available to a broader audience and pushing the boundaries of cardiac science.

Objective: This work presents a new algorithm for the construction of a model for the Purkinje network (PN) of the heart., Methods: The algorithm is based on a method called constructive constrained optimization (CCO), which was reformulated for the specific case of automatic PN generation. The proposed optimization-based algorithm is referred to as constructive optimization (CO). The CO method iteratively constructs the PN by minimizing the total length of the generated PN tree. In addition, it can take into account some important topological information of the PN, such as the location of the Purkinje-muscle junctions and the average bifurcation angle found in the literature., Results: To validate the model, the new method was compared with the classical L-system method for generating PN models and to a recently proposed image-based technique., Conclusion: The results show that the CO is able to construct PNs with geometric features and activation times that are in good agreement with those reported in the literature and to those obtained by the other aforementioned alternatives.

Catheter ablation therapy involving isolation of pulmonary veins (PVs) remains the cornerstone procedure to treat AF. However, due to the sub-optimal success rates of PV isolation, there is a need for new ablation techniques to locate AF ablation targets known as rotors, outside of the PVs. In this paper, we developed a novel rotor-mapping algorithm that uses a conventional diagnostic catheter, Lasso, to locate a rotor source. The algorithm, called the Region of Rotor (ROR) Mapping, utilizes the characteristics of local bipolar electrograms to navigate the catheter's iterative placements while generating a map, overlaid on the atrial anatomy, that displays the potential rotor region. We evaluated the developed ROR mapping algorithm using a 2D simulation of AF on a tissue with heterogeneous conduction properties. The results demonstrated a significant success rate of 93% in accurately locating the region of the rotor with a mean distance of 1.4mm from the ground truth trajectory. The algorithm could play a critical role in mapping non-PV AF ablation targets and improving the outcome of AF ablation.

Locating atrial fibrillation (AF) rotor sources can help target ablation therapy for AF. Our aim was to develop a catheter-tracking algorithm to locate AF rotor sources using a conventional 20-electrode circular catheter. We simulated rotor-driven arrhythmias in homogeneous and fibrotic human atrial tissue and evaluated the algorithm for different initial catheter positions. The algorithm guided and detected a rotor with a success rate of greater than 97.9% independently of the initial position of the catheter with an accuracy of greater than 2.3±1.4 mm.

Rationale: Discordant alternans, a phenomenon in which the action potential duration (APDs) and/or intracellular calcium transient durations (CaDs) in different spatial regions of cardiac tissue are out of phase, present a dynamical instability for complex spatial dispersion that can be associated with long-QT syndrome (LQTS) and the initiation of reentrant arrhythmias. Because the use of numerical simulations to investigate arrhythmic effects, such as acquired LQTS by drugs is beginning to be studied by the FDA, it is crucial to validate mathematical models that may be used during this process. Objective: In this study, we characterized with high spatio-temporal resolution the development of discordant alternans patterns in transmembrane voltage (V m ) and intracellular calcium concentration ([Ca i ] +2 ) as a function of pacing period in rabbit hearts. Then we compared the dynamics to that of the latest state-of-the-art model for ventricular action potentials and calcium transients to better understand the underlying mechanisms of discordant alternans and compared the experimental data to the mathematical models representing V m and [Ca i ] +2 dynamics. Methods and Results: We performed simultaneous dual optical mapping imaging of V m and [Ca i ] +2 in Langendorff-perfused rabbit hearts with higher spatial resolutions compared with previous studies. The rabbit hearts developed discordant alternans through decreased pacing period protocols and we quantified the presence of multiple nodal points along the direction of wave propagation, both in APD and CaD, and compared these findings with results from theoretical models. In experiments, the nodal lines of CaD alternans have a steeper slope than those of APD alternans, but not as steep as predicted by numerical simulations in rabbit models. We further quantified several additional discrepancies between models and experiments. Conclusions: Alternans in CaD have nodal lines that are about an order of magnitude steeper compared to those of APD alternans. Current action potential models lack the necessary coupling between voltage and calcium compared to experiments and fail to reproduce some key dynamics such as, voltage amplitude alternans, smooth development of calcium alternans in time, conduction velocity and the steepness of the nodal lines of APD and CaD.

Alternans, a proarrhythmic dynamical state in which cardiac action potentials alternate between long and short durations despite a constant pacing period, traditionally has been explained at the cellular level using nonlinear dynamics principles under the assumption that the action potential duration (APD) is determined solely by the time elapsed since the end of the previous action potential, called the diastolic interval (DI). In this scenario, APDs at a steady state should be the same provided that the preceding DIs are the same. Nevertheless, experiments attempting to eliminate alternans by dynamically adjusting the timing of pacing stimuli to keep the DI constant showed that alternans persisted, contradicting the traditional theory. It is now widely known that alternans also can arise from a different mechanism associated with intracellular calcium cycling. Our goal is to determine whether intracellular calcium dynamics can explain the experimental findings regarding the persistence of alternans despite a constant DI. For this, we use mathematical models capable of producing alternans through both voltage- and calcium-mediated mechanisms. We show that for voltage-driven alternans, action potentials elicited from a constant-DI protocol are always the same. However, in the case of calcium-driven alternans, the constant-DI protocol can result in alternans. Reducing the strength of the calcium instability progressively reduces and finally eliminates constant-DI alternans. Our findings suggest that screening for the presence of alternans using a constant-DI protocol has the potential for differentiating between voltage-driven and calcium-driven alternans.

Finding appropriate values for parameters in mathematical models of cardiac cells is a challenging task. Here, we show that it is possible to obtain good parameterizations in as little as 30-40 s when as many as 27 parameters are fit simultaneously using a genetic algorithm and two flexible phenomenological models of cardiac action potentials. We demonstrate how our implementation works by considering cases of "model recovery" in which we attempt to find parameter values that match model-derived action potential data from several cycle lengths. We assess performance by evaluating the parameter values obtained, action potentials at fit and non-fit cycle lengths, and bifurcation plots for fidelity to the truth as well as consistency across different runs of the algorithm. We also fit the models to action potentials recorded experimentally using microelectrodes and analyze performance. We find that our implementation can efficiently obtain model parameterizations that are in good agreement with the dynamics exhibited by the underlying systems that are included in the fitting process. However, the parameter values obtained in good parameterizations can exhibit a significant amount of variability, raising issues of parameter identifiability and sensitivity. Along similar lines, we also find that the two models differ in terms of the ease of obtaining parameterizations that reproduce model dynamics accurately, most likely reflecting different levels of parameter identifiability for the two models.

Reentrant electrical scroll waves have been shown to underlie many cardiac arrhythmias, but the inability to observe locations away from the heart surfaces and the restriction of observations to only one or two state variables have made understanding arrhythmia mechanisms challenging. Recently, we showed that data assimilation from spatiotemporally sparse surrogate observations could be used to reconstruct a reliable time series of state estimates of reentrant cardiac electrical waves including unobserved variables in one and three spatial dimensions. However, real cardiac tissue is unlikely to be described accurately by mathematical models because of errors in model formulation and parameterization as well as intrinsic but poorly described spatial heterogeneity of electrophysiological properties in the heart. Here, we extend our previous work to assess how model error affects the accuracy of cardiac state estimates achieved using data assimilation with the Local Ensemble Transform Kalman Filter. We focus on one-dimensional states of discordant alternans characterized by significant wavelength oscillations. We demonstrate that data assimilation can provide high-quality estimates under a wide range of model error conditions, ranging from varying one or more parameter values to using an entirely different model to generate the truth state. We illustrate how multiplicative and additive inflation can be used to reduce error in the state estimates. Even when the truth state contains underlying spatial heterogeneity, we show that using a homogeneous model in the data assimilation algorithm can achieve good results. Overall, we find data assimilation to be a robust approach for reconstructing complex cardiac electrical states corresponding to arrhythmias even in the presence of model error.

Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.

Background: Low-energy anti-fibrillation pacing (LEAP) has been suggested as an alternative treatment in symptomatic fibrillation patients. It significantly lowers the energy required compared with standard 1-shock defibrillation., Objective: In this study, we investigated the mechanism of arrhythmia termination by LEAP and systematically analyzed the influence of shock period and timing on the success rate of LEAP., Methods: We induced atrial and ventricular fibrillation in isolated canine hearts and applied LEAP and standard 1-shock defibrillation to terminate the arrhythmia. We simulated the arrhythmia and LEAP using a 2-dimensional bidomain human atrial model., Results: The ex vivo experiments showed successful termination of atrial fibrillation and ventricular fibrillation using LEAP, with an average 88% and 81% energy reduction, respectively, and both experiments and simulations verified that synchronization from virtual electrodes is the key mechanism for termination of arrhythmia by LEAP using modified Kuramoto phase plots and fraction of tissue excited (FTE) plots. We also observed in simulations that LEAP is more effective when the shock period is close to the dominant period and the first shock is delivered when FTE is decreasing., Conclusions: Our results support synchronization as the mechanism for arrhythmia termination by LEAP, and its effectiveness can be improved by adjusting shock period and timing., (Copyright © 2017 Heart Rhythm Society. Published by Elsevier Inc. All rights reserved.)

Objective: It has long been known that variations in temperature can facilitate the development of cardiac arrhythmias. Here, we aim to quantify the effects of temperature on cardiac alternans properties., Approach: in this work, we use optical mapping recordings of canine ventricular epicardial preparations to demonstrate that hypothermia can promote the formation of alternans, which is an important precursor to potentially lethal arrhythmias like fibrillation. We then present a novel quantification of alternans properties for a broad range of cycle lengths under different thermal states. Specifically, we apply the recently developed multi-band-decomposition analysis (MBDA) in the context of cardiac action potential dynamics., Main Results: We show that the MBDA offers several advantages compared with traditional analysis of action potential durations. First, MBDA allows a depiction and quantification of the magnitude of alternans at all threshold values simultaneously and thus offers more information about how alternans relates to the action potential morphology while also removing the necessity of choosing a single threshold value. Second, the MBDA technique offers simple ways for assessing action potential amplitude alternans. Finally, MBDA provides a quantification of signal quality without any additional processing., Significance: We find that the MBDA technique shows promise in leading to a deeper understanding of cardiac alternans properties.

Cardiac electrical alternans is a period-2 dynamical behavior with alternating long and short action potential durations (APD) that often precedes dangerous arrhythmias associated with cardiac arrest. Despite the importance of alternans, many current ordinary differential equations models of cardiac electrophysiology do not produce alternans, thereby limiting the use of these models for studying the mechanisms that underlie this condition. Because delay differential equations (DDEs) commonly induce complex dynamics in other biological systems, we investigate whether incorporating DDEs can lead to alternans development in cardiac models by studying the Fox et al. canine ventricular action potential model. After suppressing the alternans in the original model, we show that alternans can be obtained by introducing DDEs in the model gating variables, and we quantitatively compare the DDE-induced alternans with the alternans present in the original model. We analyze the behavior of the voltage, currents, and gating variables of the model to study the effects of the delays and to determine how alternans develops in that setting, and we discuss the mathematical and physiological implications of our findings. In future work, we aim to apply our approach to induce alternans in models that do not naturally exhibit such dynamics., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Atrial fibrillation (AF) is an irregular heart rhythm that can lead to stroke and other heart-related complications. Catheter ablation has been commonly used to destroy triggering sources of AF in the atria and consequently terminate the arrhythmia. However, efficient and accurate localization of the AF sustaining sources known as rotors is a major challenge in catheter ablation. In this paper, we developed a novel probabilistic algorithm that can adaptively guide a Lasso diagnostic catheter to locate the center of a rotor. Our algorithm uses a Bayesian updating approach to search for and locate rotors based on the characteristics of electrogram signals collected at every catheter placement. The algorithm was evaluated using a 10 × 10 cm 2 D atrial tissue simulation of the Nygren human atrial cell model and was able to successfully guide the catheter to the rotor center in 3.37 ± 1.05 (mean±std) steps (including placement at the center) when starting from any location on the tissue. Our novel automated algorithm can potentially play a significant role in patient-specific ablation of AF sources and increase the success of AF elimination procedures.

Simulations are excellent tools for assessing new therapeutic strategies and are often conducted before implementing new therapy options in a clinical practice. For patients suffering from a heart arrhythmia, the main source of information comes from an intracardiac catheter. One of the common catheters is a Lasso multi-pole diagnostic catheter, which is a catheter that has 20 electrodes in a circular pattern. In this paper, we developed algorithm and simulation software that allows the users to place a multi-pole catheter on the atrial endocardial surface and record electrograms. In 3D atrial tissue, the plane of principal curvature is determined using eigenvectors of catheter vertices, from where the normals are projected and registered to the surface using 3D geodesic distance. This tool provides a platform for performing customized virtual cardiac experiments.

Locating atrial fibrillation (AF) focal and rotor sources can help improve target ablation therapy for AF. However, it remains unclear how to use the information provided by multi-polar diagnostic catheters (MPDC) to locate AF sources. Our aim was to develop a catheter-guidance algorithm to locate AF focal and rotor sources using a conventional MPDC. We simulated a 10 cm × 10 cm atrial tissue with focal and rotor sources using the Nygren et al. ionic model. We modeled a Lasso MPDC with 20-unipole electrodes placed with a spacing of 4.5-1-4.5 mm (diameter, d=15 mm) along a circle to obtain 10-bipole electrograms. Staring from an initial location, the algorithm, which was blinded to the location and type of the AF source, iteratively advanced the MPDC by moving its center to the location of the first activated bipole (FAB). The algorithm located an AF source if a stopping condition for either source was satisfied using bipole electrogram characteristics extracted from the MPDC placement. We tested the algorithm for a single rotor and focal source for all possible initial positions on the simulated tissue and repeated it for a random placement with a maximum of 20 possible placements at every trial. The algorithm located the AF source for 100% of trials and on average required 5.99 ± 1.92 placements to an AF source. This algorithm may be used to iteratively direct an MPDC towards an AF source and allow the AF source to be localized for customized AF ablation.

For many years, reentrant scroll waves have been predicted and studied as an underlying mechanism for cardiac arrhythmias using numerical techniques, and high-resolution mapping studies using fluorescence recordings from the surfaces of cardiac tissue preparations have confirmed the presence of visible spiral waves. However, assessing the three-dimensional dynamics of these reentrant waves using experimental techniques has been limited to verifying stable scroll-wave dynamics in relatively thin preparations. We propose a different approach to recovering the three-dimensional dynamics of reentrant waves in the heart. By applying techniques commonly used in weather forecasting, we combine dual-surface observations from a particular experiment with predictions from a numerical model to reconstruct the full three-dimensional time series of the experiment. Here, we use model-generated surrogate observations from a numerical experiment to evaluate the performance of the ensemble Kalman filter in reconstructing such time series for a discordant alternans state in one spatial dimension and for scroll waves in three dimensions. We show that our approach is able to recover time series of both observed and unobserved variables matching the truth. Where nearby observations are available, the error is reduced below the synthetic observation error, with a smaller reduction with increased distance from observations. Our findings demonstrate that state reconstruction for spatiotemporally complex cardiac electrical dynamics is possible and will lead naturally to applications using real experimental data.

During heart failure (HF) at the cellular level, the electrophysiological properties of single myocytes get remodeled, which can trigger the occurrence of ventricular arrhythmias that could be manifested in many forms such as early afterdepolarizations (EADs) and alternans (ALTs). In this paper, based on experimentally observed human HF data, specific ionic and exchanger current strengths are modified from a recently developed human ventricular cell model: the O'Hara-Virág-Varró-Rudy (OVVR) model. A new transmural HF-OVVR model is developed that incorporates HF changes and variability of the observed remodeling. This new heterogeneous HF-OVVR model is able to replicate many of the failing action potential (AP) properties and the dynamics of both [Ca(2+)]i and [Na(+)]i in accordance with experimental data. Moreover, it is able to generate EADs for different cell types and exhibits ALTs at modest pacing rate for transmural cell types. We have assessed the HF-OVVR model through the examination of the AP duration and the major ionic currents' rate dependence in single myocytes. The evaluation of the model comes from utilizing the steady-state (S-S) and S1-S2 restitution curves and from probing the accommodation of the HF-OVVR model to an abrupt change in cycle length. In addition, we have investigated the effect of chosen currents on the AP properties, such as blocking the slow sodium current to shorten the AP duration and suppress the EADs, and have found good agreement with experimental observations. This study should help elucidate arrhythmogenic mechanisms at the cellular level and predict unseen properties under HF conditions. In addition, this AP cell model might be useful for modeling and simulating HF at the tissue and organ levels.