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Background and Objective: Numerical simulations are valuable tools for studying cardiac arrhythmias. Not only do they complement experimental studies, but there is also an increasing expectation for their use in clinical applications to guide patient-specific procedures. However, numerical studies that solve the reaction-diffusion equations describing cardiac electrical activity remain challenging to set up, are time-consuming, and in many cases, are prohibitively computationally expensive for long studies. The computational cost of cardiac simulations of complex models on anatomically accurate structures necessitates parallel computing. Graphics processing units (GPUs), which have thousands of cores, have been introduced as a viable technology for carrying out fast cardiac simulations, sometimes including real-time interactivity. Our main objective is to increase the performance and accuracy of such GPU implementations while conserving computational resources., Methods: In this work, we present a compression algorithm that can be used to conserve GPU memory and improve efficiency by managing the sparsity that is inherent in using Cartesian grids to represent cardiac structures directly obtained from high-resolution MRI and mCT scans. Furthermore, we present a discretization scheme that includes the cross-diagonal terms in the computational cell to increase numerical accuracy, which is especially important for simulating thin tissue sections without the need for costly mesh refinement., Results: Interactive WebGL simulations of atrial/ventricular structures (on PCs, laptops, tablets, and phones) demonstrate the algorithm's ability to reduce memory demand by an order of magnitude and achieve calculations up to 20x faster. We further showcase its superiority in slender tissues and validate results against experiments performed in live explanted human hearts., Conclusions: In this work, we present a compression algorithm that accelerates electrical activity simulations on realistic anatomies by an order of magnitude (up to 20x), thereby allowing the use of finer grid resolutions while conserving GPU memory. Additionally, improved accuracy is achieved through cross-diagonal terms, which are essential for thin tissues, often found in heart structures such as pectinate muscles and trabeculae, as well as Purkinje fibers. Our method enables interactive simulations with even interactive domain boundary manipulation (unlike finite element/volume methods). Finally, agreement with experiments and ease of mesh import into WebGL paves the way for virtual cohorts and digital twins, aiding arrhythmia analysis and personalized therapies., 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., (Published by Elsevier B.V.)

Cardiac arrythmias are a form of heart disease that contributes toward making heart disease a significant cause of death globally. Irregular rhythms associated with cardiac arrythmias are thought to arise due to singularities in the heart tissue that generate reentrant waves in the underlying excitable medium. A normal approach to removing such singularities is to apply a high voltage electric shock, which effectively resets the phase of the cardiac cells. A concern with the use of this defibrillation technique is that the high-energy shock can cause lasting damage to the heart tissue. Various theoretical works have investigated lower-energy alternatives to defibrillation. In this work, we demonstrate the effectiveness of a low-energy defibrillation method in an experimental 2D Belousov-Zhabotinsky (BZ) system. When implemented as a 2D spatial reaction, the BZ reaction serves as an effective analog of general excitable media and supports regular and reentrant wave activity. The defibrillation technique employed involves targeted low-energy perturbations that can be used to "teleport" and/or annihilate singularities present in the excitable BZ medium., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Objective. Temperature plays a crucial role in influencing the spatiotemporal dynamics of the heart. Electrical instabilities due to specific thermal conditions typically lead to early period-doubling bifurcations and beat-to-beat alternans. These pro-arrhythmic phenomena manifest in voltage and calcium traces, resulting in compromised contractile behaviors. In such intricate scenario, dual optical mapping technique was used to uncover unexplored multi-scale and nonlinear couplings, essential for early detection and understanding of cardiac arrhythmia. Approach. We propose a methodological analysis of synchronized voltage-calcium signals for detecting alternans, restitution curves, and spatiotemporal alternans patterns under different thermal conditions, based on integral features calculation. To validate our approach, we conducted a cross-species investigation involving rabbit and guinea pig epicardial ventricular surfaces and human endocardial tissue under pacing-down protocols. Main results. We show that the proposed integral feature, as the area under the curve, could be an easily applicable indicator that may enhance the predictability of the onset and progression of cardiac alternans. Insights into spatiotemporal correlation analysis of characteristic spatial lengths across different heart species were further provided. Significance. Exploring cross-species thermoelectric features contributes to understanding temperature-dependent proarrhythmic regimes and their implications on coupled spatiotemporal voltage-calcium dynamics. The findings provide preliminary insights and potential strategies for enhancing arrhythmia detection and treatment., (Creative Commons Attribution license.)

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 electrical dynamics show complex space-time instabilities, like period-doubling bifurcation and beat-to-beat alternans, known to occur as pro-arrhythmic phenomena and linked to membrane voltage and intracellular calcium kinetics. Besides, cellular ionic dynamics are critically affected by temperature oscillations, further enhancing the complexity of such arrhythmias precursors that lead to irregular cardiac contraction. In this complex scenario, fluorescence dual optical mapping techniques allow the unveiling of nonlinear and multi-scale couplings. In this contribution, we propose a novel methodological analysis of synchronous dual voltage-calcium traces obtained from whole rabbit hearts for (i) detecting alternans onset and evolution, (ii) characterizing novel restitution curves, and (iii) defining spatio-temporal alternans patterns at four thermal states. We validate our approach against well-accepted analyses considering complete pacing-down restitution protocols. The proposed methodology computes integral features, e.g., area under the curve, suggesting that a novel, easy-to-use indicator, may advance predictability on alternans onset and evolution, further providing insights into spatio-temporal cardiac analyses.Clinical Relevance- This work introduces new methods for the early detection of cardiac alternans onset and development as precursors of arrhythmias and fibrillation at different temperatures.

Previous computer simulations have suggested that existing models of action potential wave propagation in the heart are not consistent with observed wave propagation behavior. Specifically, computer models cannot simultaneously reproduce the rapid wave speeds and small spatial scales of discordant alternans patterns measured experimentally in the same simulation. The discrepancy is important, because discordant alternans can be a key precursor to the development of abnormal and dangerous rapid rhythms in the heart. In this Letter, we show that this paradox can be resolved by allowing so-called ephaptic coupling to play a primary role in wave front propagation in place of conventional gap-junction coupling. With this modification, physiological wave speeds and small discordant alternans spatial scales both occur with gap-junction resistance values that are more in line with those observed in experiments. Our theory thus also provides support to the hypothesis that ephaptic coupling plays an important role in normal wave propagation.

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.

Discordant alternans, the spatially out-of-phase alternation of the durations of propagating action potentials in the heart, has been linked to the onset of fibrillation, a major cardiac rhythm disorder. The sizes of the regions, or domains, within which these alternations are synchronized are critical in this link. However, computer models employing standard gap junction-based coupling between cells have been unable to reproduce simultaneously the small domain sizes and rapid action potential propagation speeds seen in experiments. Here we use computational methods to show that rapid wave speeds and small domain sizes are possible when a more detailed model of intercellular coupling that accounts for so-called ephaptic effects is used. We provide evidence that the smaller domain sizes are possible, because different coupling strengths can exist on the wavefronts, for which both ephaptic and gap-junction coupling are involved, in contrast to the wavebacks, where only gap-junction coupling plays an active role. The differences in coupling strength are due to the high density of fast-inward (sodium) channels known to localize on the ends of cardiac cells, which are only active (and thus engage ephaptic coupling) during wavefront propagation. Thus, our results suggest that this distribution of fast-inward channels, as well as other factors responsible for the critical involvement of ephaptic coupling in wave propagation, including intercellular cleft spacing, play important roles in increasing the vulnerability of the heart to life-threatening tachyarrhythmias. Our results, combined with the absence of short-wavelength discordant alternans domains in standard gap-junction-dominated coupling models, also provide evidence that both gap-junction and ephaptic coupling are critical in wavefront propagation and waveback dynamics.

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.)

Conduction velocity (CV) slowing is associated with atrial fibrillation (AF) and reentrant ventricular tachycardia (VT). Clinical electroanatomical mapping systems used to localize AF or VT sources as ablation targets remain limited by the number of measuring electrodes and signal processing methods to generate high-density local activation time (LAT) and CV maps of heterogeneous atrial or trabeculated ventricular endocardium. The morphology and amplitude of bipolar electrograms depend on the direction of propagating electrical wavefront, making identification of low-amplitude signal sources commonly associated with fibrotic area difficulty. In comparison, unipolar electrograms are not sensitive to wavefront direction, but measurements are susceptible to distal activity. This study proposes a method for local CV calculation from optical mapping measurements, termed the circle method (CM). The local CV is obtained as a weighted sum of CV values calculated along different chords spanning a circle of predefined radius centered at a CV measurement location. As a distinct maximum in LAT differences is along the chord normal to the propagating wavefront, the method is adaptive to the propagating wavefront direction changes, suitable for electrical conductivity characterization of heterogeneous myocardium. In numerical simulations, CM was validated characterizing modeled ablated areas as zones of distinct CV slowing. Experimentally, CM was used to characterize lesions created by radiofrequency ablation (RFA) on isolated hearts of rats, guinea pig, and explanted human hearts. To infer the depth of RFA-created lesions, excitation light bands of different penetration depths were used, and a beat-to-beat CV difference analysis was performed to identify CV alternans. Despite being limited to laboratory research, studies based on CM with optical mapping may lead to new translational insights into better-guided ablation 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 © 2022 Siles-Paredes, Crowley, Fenton, Bhatia, Iravanian, Sandoval, Pollnow, Dössel, Salinet and Uzelac.)

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.

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

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.

Understanding and predicting the mechanisms promoting the onset and sustainability of cardiac arrhythmias represent a primary concern in the scientific and medical communities still today. Despite the long-lasting effort in clinical and physico-mathematical research, a critical aspect to be fully characterized and unveiled is represented by spatiotemporal alternans patterns of cardiac excitation. The identification of discordant alternans and higher-order alternating rhythms by advanced data analyses as well as their prediction by reliable mathematical models represents a major avenue of research for a broad and multidisciplinary scientific community. Current limitations concern two primary aspects: 1) robust and general-purpose feature extraction techniques and 2) in silico data assimilation within reliable and predictive mathematical models. Here, we address both aspects. At first, we extend our previous works on Fourier transformation imaging (FFI), applying the technique to whole-ventricle fluorescence optical mapping. Overall, we identify complex spatial patterns of voltage alternans and characterize higher-order rhythms by a frequency-series analysis. Then, we integrate the optical ultrastructure obtained by FFI analysis within a fine-tuned electrophysiological mathematical model of the cardiac action potential. We build up a novel data assimilation procedure demonstrating its reliability in reproducing complex alternans patterns in two-dimensional computational domains. Finally, we prove that the FFI approach applied to both experimental and simulated signals recovers the same information, thus closing the loop between the experiment, data analysis, and numerical simulations., 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 © 2022 Loppini, Erhardt, Fenton, Filippi, Hörning and Gizzi.)

Most cardiac arrhythmias at the whole heart level result from alteration of cell membrane ionic channels and intracellular calcium concentration ([Ca 2+ ] i ) cycling with emerging spatiotemporal behavior through tissue-level coupling. For example, dynamically induced spatial dispersion of action potential duration, QT prolongation, and alternans are clinical markers for arrhythmia susceptibility in regular and heart-failure patients that originate due to changes of the transmembrane voltage ( V m ) and [Ca 2+ ] i . We present an optical-mapping methodology that permits simultaneous measurements of the V m - [Ca 2+ ] i signals using a single-camera without cross-talk, allowing quantitative characterization of favorable/adverse cell and tissue dynamical effects occurring from remodeling and/or drugs in heart failure. We demonstrate theoretically and experimentally in six different species the existence of a family of excitation wavelengths, we termed semasbestic, that give no change in signal for one dye, and thus can be used to record signals from another dye, guaranteeing zero cross-talk., Competing Interests: IU is the owner of Aleksa Tech Inc., a manufacturer of power sources for LED illumination in optical mapping measurements. The remaining 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 © 2022 Uzelac, Crowley, Iravanian, Kim, Cho and Fenton.)

A wide range of atrial arrythmias are caused by molecular defects in proteins that regulate calcium (Ca) cycling. In many cases, these defects promote the propagation of subcellular Ca waves in the cell, which can perturb the voltage time course and induce dangerous perturbations of the action potential (AP). However, subcellular Ca waves occur randomly in cells and, therefore, electrical coupling between cells substantially decreases their effect on the AP. In this study, we present evidence that Ca waves in atrial tissue can synchronize in-phase owing to an order-disorder phase transition. In particular, we show that, below a critical pacing rate, Ca waves are desynchronized and therefore do not induce substantial AP fluctuations in tissue. However, above this critical pacing rate, Ca waves gradually synchronize over millions of cells, which leads to a dramatic amplification of AP fluctuations. We exploit an underlying Ising symmetry of paced cardiac tissue to show that this transition exhibits universal properties common to a wide range of physical systems in nature. Finally, we show that in the heart, phase synchronization induces spatially out-of-phase AP duration alternans which drives wave break and reentry. These results suggest that cardiac tissue exhibits a phase transition that is required for subcellular Ca cycling defects to induce a life-threatening arrhythmia., (Copyright © 2021 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine them to visualize the spread of electrophysiological wave phenomena across the heart surface. However, low spatial resolution, sparse measurement locations, noise and other artifacts make it challenging to accurately visualize spatio-temporal activity. For instance, electro-anatomical catheter mapping is severely limited by the sparsity of the measurements, and optical mapping is prone to noise and motion artifacts. In the past, several approaches have been proposed to create more reliable maps from noisy or sparse mapping data. Here, we demonstrate that deep learning can be used to compute phase maps and detect phase singularities in optical mapping videos of ventricular fibrillation, as well as in very noisy, low-resolution and extremely sparse simulated data of reentrant wave chaos mimicking catheter mapping data. The self-supervised deep learning approach is fundamentally different from classical phase mapping techniques. Rather than encoding a phase signal from time-series data, a deep neural network instead learns to directly associate phase maps and the positions of phase singularities with short spatio-temporal sequences of electrical data. We tested several neural network architectures, based on a convolutional neural network (CNN) with an encoding and decoding structure, to predict phase maps or rotor core positions either directly or indirectly via the prediction of phase maps and a subsequent classical calculation of phase singularities. Predictions can be performed across different data, with models being trained on one species and then successfully applied to another, or being trained solely on simulated data and then applied to experimental data. Neural networks provide a promising alternative to conventional phase mapping and rotor core localization methods. Future uses may include the analysis of optical mapping studies in basic cardiovascular research, as well as the mapping of atrial fibrillation in the clinical setting., 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 Lebert, Ravi, Fenton and Christoph.)

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.)

Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)PREHBM2470-004510.1103/PhysRevE.100.020201] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.

Effective cardiac contraction during each heartbeat relies on the coordination of an electrical wave of excitation propagating across the heart. Dynamically induced heterogeneous wave propagation may fracture and initiate reentry-based cardiac arrhythmias, during which fast-rotating electrical waves lead to repeated self-excitation that compromises cardiac function and potentially results in sudden cardiac death. Species which function effectively over a large range of heart temperatures must balance the many interacting, temperature-sensitive biochemical processes to maintain normal wave propagation at all temperatures. To investigate how these species avoid dangerous states across temperatures, we optically mapped the electrical activity across the surfaces of alligator ( Alligator mississippiensis ) hearts at 23°C and 38°C over a range of physiological heart rates and compare them with that of rabbits ( Oryctolagus cuniculus ). We find that unlike rabbits, alligators show minimal changes in wave parameters (action potential duration and conduction velocity) which complement each other to retain similar electrophysiological wavelengths across temperatures and pacing frequencies. The cardiac electrophysiology of rabbits accommodates the high heart rates necessary to sustain an active and endothermic metabolism at the cost of increased risk of cardiac arrhythmia and critical vulnerability to temperature changes, whereas that of alligators allows for effective function over a range of heart temperatures without risk of cardiac electrical arrhythmias such as fibrillation, but is restricted to low heart rates. Synopsis La contracción cardíaca efectiva durante cada latido del corazón depende de la coordinación de una onda eléctrica de excitación que se propaga a través del corazón. Heterogéidades inducidas dinámicamente por ondas de propagación pueden resultar en fracturas de las ondas e iniciar arritmias cardíacas basadas en ondas de reingreso, durante las cuales ondas espirales eléctricas de rotación rápida producen una autoexcitación repetida que afecta la función cardíaca y pude resultar en muerte súbita cardíaca. Las especies que funcionan eficazmente en una amplia gama de temperaturas cardíacas deben equilibrar los varios procesos bioquímicos que interactúan, sensibles a la temperatura para mantener la propagación normal de ondas a todas las temperaturas. Para investigar cómo estas especies evitan los estados peligrosos a través de las temperaturas, mapeamos ópticamente la actividad eléctrica a través de las superficies de los corazones de caimanes ( Alligator mississippiensis ) a 23°C and 38°C sobre un rango de frecuencias fisiológicas del corazón y comparamos con el de los conejos ( Oryctolagus cuniculus ). Encontramos que a diferencia de los conejos, los caimanes muestran cambios mínimos en los parámetros de onda (duración potencial de acción y velocidad de conducción) que se complementan entre sí para retener longitudes de onda electrofisiológicas similares a través de los rangos de temperaturas y frecuencias de ritmo. La electrofisiología cardíaca de los conejos acomoda las altas frecuencias cardíacas necesarias para mantener un metabolismo activo y endotérmico a costa de un mayor riesgo de arritmia cardíaca y vulnerabilidad crítica a los cambios de temperatura, mientras que la de los caimanes permite un funcionamiento eficaz en una serie de temperaturas cardíacas sin riesgo de arritmias eléctricas cardíacas como la fibrilación, pero está restringida a bajas frecuencias cardíacas., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology.)

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.

Computational modeling of cardiac electrophysiology (EP) has recently transitioned from a scientific research tool to clinical applications. To ensure reliability of clinical or regulatory decisions made using cardiac EP models, it is vital to evaluate the uncertainty in model predictions. Model predictions are uncertain because there is typically substantial uncertainty in model input parameters, due to measurement error or natural variability. While there has been much recent uncertainty quantification (UQ) research for cardiac EP models, all previous work has been limited by either: (i) considering uncertainty in only a subset of the full set of parameters; and/or (ii) assigning arbitrary variation to parameters (e.g., ±10 or 50% around mean value) rather than basing the parameter uncertainty on experimental data. In our recent work we overcame the first limitation by performing UQ and sensitivity analysis using a novel canine action potential model, allowing all parameters to be uncertain, but with arbitrary variation. Here, we address the second limitation by extending our previous work to use data-driven estimates of parameter uncertainty. Overall, we estimated uncertainty due to population variability in all parameters in five currents active during repolarization: inward potassium rectifier, transient outward potassium, L-type calcium, rapidly and slowly activating delayed potassium rectifier; 25 parameters in total (all model parameters except fast sodium current parameters). A variety of methods was used to estimate the variability in these parameters. We then propagated the uncertainties through the model to determine their impact on predictions of action potential shape, action potential duration (APD) prolongation due to drug block, and spiral wave dynamics. Parameter uncertainty had a significant effect on model predictions, especially L-type calcium current parameters. Correlation between physiological parameters was determined to play a role in physiological realism of action potentials. Surprisingly, even model outputs that were relative differences, specifically drug-induced APD prolongation, were heavily impacted by the underlying uncertainty. This is the first data-driven end-to-end UQ analysis in cardiac EP accounting for uncertainty in the vast majority of parameters, including first in tissue, and demonstrates how future UQ could be used to ensure model-based decisions are robust to all underlying parameter uncertainties., (Copyright © 2020 Pathmanathan, Galappaththige, Cordeiro, Kaboudian, Fenton and Gray.)

Aims: Defibrillation shocks may cause AV node burnout, scar formation, and pain. In this study, we present a real-time feedback-based control of ventricular fibrillation (VF) with a series of low-energy shocks using ventricular electrical activity as the feedback input., Methods: Isolated rabbit hearts were Langendorff perfused and stained with a fluorescent V m dye. The ventricular activity was measured with a pair of photodiodes, and processed with a feedback controller to calculate defibrillation shock parameters in real-time. Shock timing was based on desynchronized activation of the left and right ventricles during VF, and the strength was proportional to the amplitude difference of the photodiode signals. Shocks were delivered with a custom-developed arbitrary waveform trans-conductance amplifier., Results: Feedback based resynchronization therapy converts VT to MT before sinus rhythm is restored with a reduction of defibrillation energy, compared to a single biphasic shock., Conclusions: Feedback based resynchronization therapy is based on real-time sensing of ventricular activity, while a series of low-energy shocks are delivered, reducing the risk of associated side effects.

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.)

The monophasic action potential (MAP) is a near replica of the transmembrane potential recorded when an electrode is pushed firmly against cardiac tissue. Despite its many practical uses, the mechanism of MAP signal generation and the reason it is so different from unipolar recordings are not completely known and are a matter of controversy. In this work, we describe a method to simulate realistic MAP and intermediate forms, which are multiphasic electrograms different from an ideal MAP. The key ideas of our method are the formation of compressed zones and junctional spaces-regions of the extracellular and bath or blood pool directly in contact with electrodes that exhibit a pressure-induced reduction in electrical conductivity-and the presence of a complex network of passive components that acts as a high-pass filter to distort and attenuate the signal that reaches the recording amplifier. The network is formed by the interaction between the passive tissue properties and the double-layer capacitance of electrodes. The MAP and intermediate forms reside on a continuum of signals, which can be generated by the change of the model parameters. Our model helps to decipher the mechanisms of signal generation and can lead to a better design for electrodes, recording amplifiers, and experimental setups., (Copyright © 2020 Biophysical 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'.

Microscopic structural features of cardiac tissue play a fundamental role in determining complex spatio-temporal excitation dynamics at the macroscopic level. Recent efforts have been devoted to the development of mathematical models accounting for non-local spatio-temporal coupling able to capture these complex dynamics without the need of resolving tissue heterogeneities down to the micro-scale. In this work, we analyse in detail several important aspects affecting the overall predictive power of these modelling tools and provide some guidelines for an effective use of space-fractional models of cardiac electrophysiology in practical applications. Through an extensive computational study in simplified computational domains, we highlight the robustness of models belonging to different categories, i.e., physiological and phenomenological descriptions, against the introduction of non-locality, and lay down the foundations for future research and model validation against experimental data. A modern genetic algorithm framework is used to investigate proper parameterisations of the considered models, and the crucial role played by the boundary assumptions in the considered settings is discussed. Several numerical results are provided to support our claims.

Simulations of cardiac electrophysiological models in tissue, particularly in 3D require the solutions of billions of differential equations even for just a couple of milliseconds, thus highly demanding in computational resources. In fact, even studies in small domains with very complex models may take several hours to reproduce seconds of electrical cardiac behavior. Today's Graphics Processor Units (GPUs) are becoming a way to accelerate such simulations, and give the added possibilities to run them locally without the need for supercomputers. Nevertheless, when using GPUs, bottlenecks related to global memory access caused by the spatial discretization of the large tissue domains being simulated, become a big challenge. For simulations in a single GPU, we propose a strategy to accelerate the computation of the diffusion term through a data-structure and memory access pattern designed to maximize coalescent memory transactions and minimize branch divergence, achieving results approximately 1.4 times faster than a standard GPU method. We also combine this data structure with a designed communication strategy to take advantage in the case of simulations in multi-GPU platforms. We demonstrate that, in the multi-GPU approach performs, simulations in 3D tissue can be just 4× slower than real time., Competing Interests: CONFLICT OF INTEREST The authors declare no potential conflict of interests.

The spatiotemporal dynamics of complex systems have been studied traditionally and visualized numerically using high-end computers. However, due to advances in microcontrollers, it is now possible to run what once were considered large-scale simulations using a very small and inexpensive single integrated circuit that can furthermore send and receive information to and from the outside world in real time. In this paper, we show how microcontrollers can be used to perform simulations of nonlinear ordinary differential equations with spatial coupling and to visualize their dynamics using arrays of light-emitting diodes and/or touchscreens. We demonstrate these abilities using three different models: two reaction-diffusion models (one neural and one cardiac) and a generic model of network oscillators. These models are commonly used to simulate various phenomena in biophysical systems, including bifurcations, waves, chaos, and synchronization. We also demonstrate how simple it is to integrate real-time user interaction with the simulations by showing examples with a light sensor, touchscreen, and web browser.

Every heartbeat originates from a tiny tissue in the heart called the sinoatrial node (SAN). The SAN harbors only ≈10 000 cardiac pacemaker cells, initiating an electrical impulse that captures the entire heart, consisting of billions of cardiomyocytes for each cardiac contraction. How these rare cardiac pacemaker cells (the electrical source) can overcome the electrically hyperpolarizing and quiescent myocardium (the electrical sink) is incompletely understood. Due to the scarcity of native pacemaker cells, this concept of source-sink mismatch cannot be tested directly with live cardiac tissue constructs. By exploiting TBX18 induced pacemaker cells by somatic gene transfer, 3D cardiac pacemaker spheroids can be tissue-engineered. The TBX18 induced pacemakers (sphTBX18) pace autonomously and drive the contraction of neighboring myocardium in vitro. TBX18 spheroids demonstrate the need for reduced electrical coupling and physical separation from the neighboring ventricular myocytes, successfully recapitulating a key design principle of the native SAN. β-Adrenergic stimulation as well as electrical uncoupling significantly increase sphTBX18s' ability to pace-and-drive the neighboring myocardium. This model represents the first platform to test design principles of the SAN for mechanistic understanding and to better engineer biological pacemakers for therapeutic translation., Competing Interests: The authors declare no conflict of interest., (© 2019 The Authors. Published by WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim.)

Optical mapping methods utilize fluorescence dyes to measure dynamic response of cardiac tissue such as changes in transmembrane potential (V m ). For the commonly used V m sensitive dyes, a dye absorption and emission spectra shift as V m changes. Signals relevant to V m are calculated as a relative fluorescence change with respect to the fluorescence baseline. The amplitude of the change depends on the long-pass (LP) filter cut-on wavelength, placed on the sensor side, and the excitation wavelength. An excitation wavelength near the absorption peak, termed the isosbestic point, results in minimal absorption coefficient change as absorption spectra shifts. Consequentially the fluorescence intensity virtually does not change, when fluorescence across the entire emission spectra is measured, irrelevant of V m changes. In this study we experimentally determined the isosbestic point for a near infrared dye Di-4-ANBDQPQ. We then present a theoretical study examining the dye linear or non-linear response as the fractional fluorescence change of V m change, due to emission spectra shift and amplitude change, over a range of excitation wavelengths and LP filters. Linear "optical" response is important to quantify certain aspects of cardiac dynamics such as the action potential (AP) shape and duration, especially when studying drug effects and dynamical substrates for arrhythmia development.

Optical mapping measurements on hearts stained with fluorescent dyes is imagining method widely accepted and recognized as a tool to study complex spatial-temporal dynamics of cardiac electro-physiology. One shortcoming of the method is baseline wandering in obtained fluorescence signals as signals relevant to transmembrane potential (V m ) change and free intracellular calcium concentration ([Ca] i +2 ), the two most used dyes, are calculated as a relative signal change in respect to the fluorescence baseline. These changes are small fractional changes often smaller than 10 %. Baseline fluorescence drifts due to dye photo-bleaching, heart contraction/movement artifacts, and stability of the excitation light source over time. Depending on experimental instrumentation, recording duration, signal to noise levels and study aims of the optical imagining, many research groups adopted their own techniques tailored to a specific experimental data. Here we present a technique based on finite impulse response (FIR) filters with paralleled acceleration implemented on GPUs and multi-core CPU, in MATLAB.

Optical imaging methods on ex-vivo hearts have had large impact in furthering our understanding of cardiac electrophysiology. One common problem in this method is a baseline wandering of the fluorescence signals over time, caused by dye photo-bleaching, small variation of the excitation light source, or other similar artifacts. Due to its relative magnitude, the removal of baseline wandering can be a nontrivial task and has major implications for analyzing important physiological dynamics such as traveling waves and alternans. Here we present a computational technique for the removal of such baseline wandering based on Proportional-Integral-Derivative (PID) closed loop feedback. The PID method applied a continuous control stimulus to the input V m based on an error value which is defined by Euclidean distance from a pre-computed setpoint in phase space. We quantify and validate the PID control method by adding a linear combination of arbitrary sinusoidal drift, of frequency less than the signal pacing frequency, to the system signal V m . The PID control loop effectively removed the baseline wandering with minimal degradation to the input V m , and thus provides a viable tool for baseline wandering removal when implemented in an appropriate phase space. The computational simplicity of the method also lends itself to implementation in embedded systems, such as Arduinos and Raspberry-Pis.

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.

Theoretical cardiac electrophysiology focuses on the dynamics of the membrane and sarcoplasmic reticulum ion currents; however, passive (e.g., membrane capacitance) and quasi-active (response to small signals) properties of the cardiac sarcolemma, which are quantified by impedance, are also important in determining the behavior of cardiac tissue. Theoretically, impedance varies in the different phases of a cardiac cycle. Our goal in this study was to numerically predict and experimentally validate these phasic changes. We calculated the expected impedance signal using analytic methods (for generic ionic models) and numerical computation (for a rabbit ventricular ionic model). Cardiac impedance is dependent on the phase of the action potential, with multiple deflections caused by a sequential activation and inactivation of various membrane channels. The two main channels shaping the impedance signal are the sodium channel causing a sharp and transient drop at the onset of action potential and the inward rectifying potassium channel causing an increase in impedance during the plateau phase. This dip and dome pattern was confirmed in an ex-vivo rabbit heart model using high-frequency sampling through a monophasic action potential electrode. The hearts were immobilized using a myosin-inhibitor to minimize motion artifacts. We observed phasic impedance changes in three out of four hearts with a dome amplitude of 2 - 4Ω. Measurement of phasic impedance modulation using an extracellular electrode is feasible and provides a non-invasive way to gain insight into the state of cardiac cells and membrane ionic channels. The observed impedance recordings are consistent with the dip and dome pattern predicted analytically.

Competing Interests: Conflict of Interest Statement: 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.