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.
Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular ...(MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher–Noble–Noble–Panfilov (TNNP), and the Iyer–Mazhari–Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.
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.
Alternans of action potential duration has been associated with T wave alternans and the development of arrhythmias because it produces large gradients of repolarization. However, little is known ...about alternans dynamics in large mammalian hearts. Using optical mapping to record electrical activations simultaneously from the epicardium and endocardium of 9 canine right ventricles, we demonstrate novel arrhythmogenic complex spatiotemporal dynamics. (i) Alternans predominantly develops first on the endocardium. (ii) The postulated simple progression from normal rhythm to concordant to discordant alternans is not always observed; concordant alternans can develop from discordant alternans as the pacing period is decreased. (iii) In contrast to smaller tissue preparations, multiple stationary nodal lines may exist and need not be perpendicular to the pacing site or to each other. (iv) Alternans has fully three-dimensional dynamics and the epicardium and endocardium can show significantly different dynamics: multiple nodal surfaces can be transmural or intramural and can form concave/convex surfaces resulting in islands of discordant alternans. (v) The complex spatiotemporal patterns observed during alternans are very sensitive to both the site of stimulation and the stimulation history. Alternans in canine ventricles not only exhibit larger amplitudes and persist for longer cycle length regimes compared to those found in smaller mammalian hearts, but also show novel dynamics not previously described that enhance dispersion and show high sensitivity to initial conditions. This indicates some underlying predisposition to chaos and can help to guide the design of new drugs and devices controlling and preventing arrhythmic events.
Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves ...in a heterogeneous anatomical substrate. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation. Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ E(α). These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.
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.
Computer studies are often used to study mechanisms of cardiac arrhythmias, including atrial fibrillation (AF). A crucial component in these studies is the electrophysiological model that describes ...the membrane potential of myocytes. The models vary from detailed, describing numerous ion channels, to simplified, grouping ionic channels into a minimal set of variables. The parameters of these models, however, are determined across different experiments in varied species. Furthermore, a single set of parameters may not describe variations across patients, and models have rarely been shown to recapitulate critical features of AF in a given patient. In this study we develop physiologically accurate computational human atrial models by fitting parameters of a detailed and of a simplified model to clinical data for five patients undergoing ablation therapy. Parameters were simultaneously fitted to action potential (AP) morphology, action potential duration (APD) restitution and conduction velocity (CV) restitution curves in these patients. For both models, our fitting procedure generated parameter sets that accurately reproduced clinical data, but differed markedly from published sets and between patients, emphasizing the need for patient-specific adjustment. Both models produced two-dimensional spiral wave dynamics for that were similar for each patient. These results show that simplified, computationally efficient models are an attractive choice for simulations of human atrial electrophysiology in spatially extended domains. This study motivates the development and validation of patient-specific model-based mechanistic studies to target therapy.
The study of complex systems has emerged as an important field with many discoveries still to be made. Computer simulation and visualization provide important tools for studying complex dynamics ...including chaos, solitons, and fractals, but available computing power has been a limiting factor. In this work, we describe a novel and highly efficient computing and visualization paradigm using a Web Graphics Library (WebGL 2.0) methodology along with our newly developed library (Abubu.js). Our approach harnesses the power of widely available and highly parallel graphics cards while maintaining ease of use by simplifying programming through hiding implementation details, running in a web browser without the need for compilation, and avoiding the use of plugins. At the same time, it allows for interactivity, such as changing parameter values on the fly, and its computing is so fast that zooming in on a region of a fractal like the Mandelbrot set can incur no delay despite having to recalculate values for the entire plane. We demonstrate our approach using a wide range of complex systems that display dynamics from fractals to standing and propagating waves in 1, 2 and 3 dimensions. We also include some models with instabilities that can lead to chaotic dynamics. For all the examples shown here we provide links to the codes for anyone to use, modify and further develop with other models. Overall, the enhanced visualization and computation capabilities provided by WebGL together with Abubu.js have great potential to facilitate new discoveries about complex systems.
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.
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.
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).
HCQ markedly increased action potential dispersion, resulted in development of repolarization alternans, and initiated polymorphic ventricular tachycardia.
The study results further highlight the proarrhythmic effects of HCQ.
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.
•We forecast synthetic and experimental chaotic and highly nonlinear time series.•Gated recurrent neural networks frequently perform poorly in this setting.•Echo state networks can provide accurate chaotic signal prediction in less time.•Nonlinear vector autoregression is an efficient alternative for signal prediction
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