Cardiac action potential models allow examination of a variety of cardiac dynamics, including how behaviour may change under specific interventions. To study a specific scenario, including patient-specific cases, model parameter sets must be found that accurately reproduce the dynamics of interest. To facilitate this complex and time-consuming process, we present CardioFit, an interactive browser-based tool that uses the particle swarm optimization (PSO) algorithm implemented in JavaScript and takes advantage of the WebGL API for hardware acceleration. Our tool allows rapid customization and can find low-error fittings to user-provided voltage time series or action potential duration data from multiple cycle lengths in a few iterations (10-32), corresponding to a runtime of a few seconds on most machines. Additionally, our tool focuses on ease of use and flexibility, providing a webpage interface that allows users to select a subset of parameters to fit, set the range of values each parameter is allowed to assume, and control the PSO algorithm hyperparameters. We demonstrate our tool's utility by fitting a variety of models to different datasets, showing how convergence is affected by model choice, dataset properties and PSO algorithmic settings, and explaining new insights gained about the physiological and dynamical roles of the model parameters.

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.

Cardiac ventricular myocyte action potential dynamics are regulated by intricate and nonlinear interactions between the cell transmembrane potential and ionic currents and concentrations. Present technology limits the ability to measure transmembrane potential and multiple ionic currents simultaneously, which narrows the scope of experiments to provide a complete snapshot of the cardiac myocyte state. This limitation presents an obstacle for understanding how perturbations can trigger arrhythmias and more broadly how the myocyte responds to different conditions, such as changes in pacing rate or responses to drug treatment. In this study, we demonstrate that a data-assimilation approach can successfully reconstruct and predict the dynamics of a heterogeneous virtual cardiac ventricular myocyte population in the presence of parameter uncertainty. A population of heterogeneous cardiac ventricular myocytes is generated by varying ionic current conductance parameters, and additional observational uncertainty is mimicked by the addition of Gaussian noise to the transmembrane potential. We demonstrate that the data-assimilation approach accurately reconstructs transmembrane potential, with error less than the magnitude of the noise. Further, the data-assimilation approach successfully estimates the conductances of ionic currents generally with high accuracy and requiring low computational time. As a proof of concept, we apply the data-assimilation approach to reconstruct action potential dynamics from optical mapping experiments in an ex vivo isolated guinea pig heart. Critically, we demonstrate that the ionic conductance parameters estimated from a recording at one pacing frequency can accurately predict action potential dynamics at different rates.

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.

Papillary muscles (PMs) are known triggers of ventricular arrhythmia, especially nonsustained ventricular tachycardia (VT) and sustained recurrent VT, and may play a role as triggers of ventricular fibrillation. Catheter ablation of PM is challenging and results in high VT recurrence rates.

The two-variable Fitzhugh-Nagumo (FHN) model is widely used due to its simplicity; however, it lacks many of the dynamics observed in cardiac experiments that can be reproduced by complex ionic cell models, such as the 19-variable Ten Tusscher et. al (TNNP) model. We aim to parameterize a modified version of the FHN model that re-produces the dynamics in space of more complex cardiac cell models. We combined a series of modifications that previously were applied to the FHN model - mainly, the addition of a nullcline at zero voltage for the fast variable, that eliminates the hyperpolarization of the traditional FHN model and the modification of the slow nullcline from linear to quadratic, which allows alternans behavior and a better fit to experiments and other models. This new model is fitted using particle swarm optimization (PSO) to fit the action potential for a large number of pacing periods so that the restitution of the action potential is matched between the two models. We created a modified FHN model that matches most of the action potential (AP) shape of the TNNP model for a large range of periods and dynamics in space. This model allows for faster proof of concept investigations that can then help guide the more time-consuming simulations from using complex ionic models.

Fibrillation is characterized by complex spatiotemporal electrical dynamics often driven by the continuous creation and annihilation of reentrant waves. While it has been shown that this dynamics can be chaotic and deterministic, it is hard to describe its evolution, which could help define for example the best times to defibrillate using the lowest energy. To date it has been impossible to predict the dynamics of reentrant waves once initiated in space, not only in experiments but also in simulations using the most up-to-date ionic cell models.

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.

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.

Background:Repolarization alternans, defined as period-2 oscillation in the repolarization phase of the action potentials, is one of the cornerstones of cardiac electrophysiology as it provides a mechanistic link between cellular dynamics and ventricular fibrillation (VF). Theoretically, higher-order periodicities (e.g., period-4, period-8,...) are expected but have very limited experimental evidence.Methods:We studied explanted human hearts, obtained from the recipients of heart transplantation at the time of surgery, using optical mapping technique with transmembrane voltage-sensitive fluorescent dyes. The hearts were stimulated at an increasing rate until VF was induced. The signals recorded from the right ventricle endocardial surface just before the induction of VF and in the presence of 1:1 conduction were processed using the Principal Component Analysis and a combinatorial algorithm to detect and quantify higher-order dynamics.Results:A prominent and statistically significant 1:4 peak (corresponding to period-4 dynamics) was seen in three of the six studied hearts. Local analysis revealed the spatiotemporal distribution of higher-order periods. Period-4 was localized to temporally stable islands. Higher-order oscillations (period-5, 6, and 8) were transient and primarily occurred in arcs parallel to the activation isochrones.Discussion:We present evidence of higher-order periodicities and the co-existence of such regions with stable non-chaotic areas in ex-vivo human hearts before VF induction. This result is consistent with the period-doubling route to chaos as a possible mechanism of VF initiation, which complements the concordant to discordant alternans mechanism. The presence of higher-order regions may act as niduses of instability that can degenerate into chaotic fibrillation.

Cardiac modeling on supercomputers has limited arrhythmia studies to groups with specialized access and expertise. We previously showed that WebGL programs can simulate complex ionic models in 2D and 3D cardiac geometries in real time without the need for a supercomputer by utilizing parallel hardware through the graphics processing unit (GPU). In this work, we use sparse Cartesian grids to balance GPU load, conserve memory, and avoid unnecessary read/write operations, speeding up 3D simulations by up to a factor of 20. We also present a simple mapping technique to compress sparse data structures into compact structures, which allows us to access texture memory efficiently during the time-stepping portion of the computation. As examples, we present the implementation of phenomenological models for 3D atrial and ventricular simulations, as well as the 41-state-variable OVVR human ventricular cell model on 3D ventricular human anatomical structures. We show how our programs can be used to initiate and terminate scroll waves in 3D interactively.

Background:Repolarization alternans, defined as period-2 oscillation in the repolarization phase of the action potentials, provides a mechanistic link between cellular dynamics and ventricular fibrillation (VF). Theoretically, higher-order periodicities (e.g., periods 4, 6, 8,...) are expected but have minimal experimental evidence.Methods:We studied explanted human hearts obtained from recipients of heart transplantation at the time of surgery. Optical mapping of the transmembrane potential was performed after staining the hearts with voltage-sensitive fluorescent dyes. Hearts were stimulated at an increasing rate until VF was induced. Signals recorded from the right ventricle endocardial surface prior to induction of VF and in the presence of 1:1 conduction were processed using the Principal Component Analysis and a combinatorial algorithm to detect and quantify higher-order dynamics. Results were correlated to the underlying electrophysiological characteristics as quantified by restitution curves and conduction velocity.Results:A prominent and statistically significant global 1:4 peak (corresponding to period-4 dynamics) was seen in three of the six studied 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.Discussion:We present evidence of higher-order periodicities and the co-existence of such regions with stable non-chaotic areas in ex-vivo human hearts. We infer from the independence of the period to the underlying restitution properties that the oscillation of the excitation-contraction coupling and calcium cycling mechanisms is the primary mechanism of higher-order dynamics. These higher-order regions may act as niduses of instability that can degenerate into chaotic fibrillation and may provide targets for substrate-based ablation of VF.

The dynamics of the cardiac ventricular myocyte action potential (AP) is regulated by intricate and nonlinear interactions between the cell transmembrane potential, and ionic currents and concentrations. Present technology limits the ability to simultaneously measuring multiple ionic currents and concentration during an AP in in vitro single cell experiments, which limits the scope of experimental data to provide a complete snapshot of the cardiac myocyte system state. This limitation presents an obstacle for understanding how cellular perturbations can trigger arrhythmogenic conditions. In this study, we applied a data assimilation approach, which combines limited noisy observations with predictions from a computational model, paired with a parameter estimation to minimize the effects of parameter uncertainty and model error. We performed a series of in silico experiments, in which a forecasting system was tasked with reconstructing AP dynamics of a virtual ventricular myocyte in the presence varying degrees of parameter and model error. With appropriate protocol design, we find that a data assimilation approach can successfully reconstruct and predict the dynamics of not only the directly observed state variables (such as the transmembrane potential and a selected ionic current), but also unobserved state variables, such as unmeasured ionic currents and concentrations. As an extension of the results of these series of in silico experiments, we generated simulations to assess which ionic currents, when measured, offer greater predictive ability using the data assimilation algorithm. This can offer valuable information for the design of single cardiac in vitro experiments, as it is not feasible to measure all ionic currents and concentrations across time within the same cell during an AP. Future work will investigate the longer-term accuracy of this approach predicting potentially pro-arrhythmic perturbations for arrhythmia risk assessment.

Both experimental and clinical cardiac electrophysiology data often are recorded with limited spatial resolution or inconsistent spatial distribution. Rather than interpolating such data, which neglects constraints imposed by dynamics, data assimilation can be used to mitigate the effects of low-resolution data by providing estimates of voltage in unmapped areas. Here, we investigate the effects of different spatial distributions of observation data on cardiac voltage reconstructions over time using data assimilation. We used an ensemble Kalman filter method to reconstruct complete, uniform voltage data from observational data with different spatial distributions. Stable spiral-wave and sustained spiral-wave breakup cases from the modified Mitchell-Schaeffer model were analyzed. Coarse uniform observations and observations restricted to half the domain were considered. Stable spiral wave dynamics could be reconstructed well, with some lag at the coarsest resolutions and for half-domain observations far from the spiral core. Breakup cases were more difficult to match quantitatively; scenarios with fewer spirals or greater observation coverage of the most intense breakup regions could be reconstructed more accurately. Overall, we found that accurate voltage reconstructions could be generated for stable waves and breakup cases using data assimilation, provided that observations include regions driving breakup.

The study of arrhythmia formation is impeded by limitations in sensor technology, since not all quantities of interest can be measured directly from the same cell or tissue preparation. Data assimilation algorithms can reconstruct unmeasured quantities by combining model predictions with available data. However, it is not clear which types of measurements are best for reconstructing data, or how abnormal action-potential patterns, such as alternans, affect the informativeness of measurements. To address these issues, we examined the Shiferaw-Sato-Karma (SSK) cardiac myocyte model, which can be used to simulate multiple alternans mechanisms. We conducted a numerical study in which each SSK dynamical variable was considered to be a source of simulated data, and computed observability measures, where observability is a control-theoretic model property that indicates whether unmeasured quantities can be reconstructed from a measured variable. Although the best measurements (in the sense of maximizing observability) varied depending on alternans mechanism (voltage- or calcium-driven), we found that some patterns held for both mechanisms, such as intracellular calcium concentration yielding stronger observability than membrane potential. Observability strengths also typically predicted the relative performances of Kalman-filter-based assimilators for different measurement types.

Cardiac models are an important tool for understanding the causes of arrhythmias and other types of heart disease. Numerical simulations of these models require small time steps to make accurate predictions, leading to long simulation times even with programs parallelized over space. Parallelization over time presents a promising approach to increase the speed of cardiac simulations and to fully utilize highly parallel modern architectures. This study evaluates the use of the parareal algorithm, a parallel-in-time integration method for solving differential equations, for simulations of cardiac cells and tissue. The parareal algorithm estimates the system state at fixed times, then iteratively refines these estimates by solving from the previous time estimate in parallel. Thus, fast convergence to an accurate solution is necessary for this method to be viable. We perform simulations of the Beeler-Reuter (BR) model to evaluate the accuracy and speed of this method in comparison to sequential algorithms. We demonstrate that the parareal algorithm converges exponentially to the true solution in the single-cell case and accurately reproduces APD dynamics in tissue simulations, while attaining speedup relative to the serial algorithm in both cases.

Models of cardiac electrophysiology can be useful for assessing the behavior of the heart when subjected to in-terventions like pacing, defibrillation, or drugs. However, for patient-specific predictions, models must be customized to match the electrophysiological properties of individu-als. We present a browser-based tool for customizing models of cardiac action potentials by fitting parameter values to user-provided datasets. The tool uses a particle swarm optimization algorithm accelerated by the user's graphics card, which can support a large particle population and typically finds a low-error solution within a small number of iterations (10–32), computed within seconds. The interface allows all model parameters or a user-specified subset to be selected for fitting, and the user can set bounds for all parameters to constrain their values. We demonstrate the effectiveness of this tool by creating parameterizations of a four-variable human ventricular model to match human cardiac action potential data taken from tissue exhibiting Brugada syndrome. We expect this tool will be useful for tuning models to match data recorded from individual ex-periments and patients under normal and diseased conditions.

Repolarization alternans is one of the mainstays of theoretical cardiac electrophysiology and provides a link between cellular dynamics and fibrillation. Action potential duration (APD) alternans is the simplest manifestation of repolarization dynamics. However, excitation-contraction coupling can generate higher-order periodicities that are precursors to chaotic rhythms. Higher-order periods have been experimentally elusive and only detected in a few cases. We detect higher-order periods using a combinatorial algorithm. The key idea of the algorithm is to set up a weighted-directed graph, where the vertices correspond to the beats, and the links are assigned according to the distance metric function between the beats. The shortest path between the first and last beats in the graph determines the optimal periodicity of each beat. We applied the algorithm to optical-mapping signals recorded using voltage-sensitive fluorescent dyes to six human heart transplantation recipients. We detected periods 4, 6, and 8, and higher (chaotic areas) with heterogeneous spatial distribution. Our graph-based algorithm is a valuable tool to probe the complex dynamics of cardiac tissue by looking beyond classic alternans, especially at fast rates and before the transition to chaotic fibrillation.

The reconstruction of electrical excitation patterns through the unobserved depth of the tissue is essential to realizing the potential of computational models in cardiac medicine. We have utilized experimental optical-mapping recordings of cardiac electrical excitation on the epicardial and endocardial surfaces of a canine ventricle as observations directing a local ensemble transform Kalman Filter (LETKF) data assimilation scheme. We demonstrate that the inclusion of explicit information about the stimulation protocol can marginally improve the confidence of the ensemble reconstruction and the reliability of the assimilation over time. Likewise, we consider the efficacy of stochastic modeling additions to the assimilation scheme in the context of experimentally derived observation sets. Approximation error is addressed at both the observation and modeling stages, through the uncertainty of observations and the specification of the model used in the assimilation ensemble. We find that perturbative modifications to the observations have marginal to deleterious effects on the accuracy and robustness of the state reconstruction. Further, we find that incorporating additional information from the observations into the model itself (in the case of stimulus and stochastic currents) has a marginal improvement on the reconstruction accuracy over a fully autonomous model, while complicating the model itself and thus introducing potential for new types of model error. That the inclusion of explicit modeling information has negligible to negative effects on the reconstruction implies the need for new avenues for optimization of data assimilation schemes applied to cardiac electrical excitation.