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Electroanatomic mapping as routinely acquired in ablation therapy of ventricular tachycardia is the gold standard method to identify the arrhythmogenic substrate. To reduce the acquisition time and still provide maps with high spatial resolution, we propose a novel deep learning method based on graph convolutional neural networks to estimate the depolarization time in the myocardium, given sparse catheter data on the left ventricular endocardium, ECG, and magnetic resonance images. The training set consists of data produced by a computational model of cardiac electrophysiology on a large cohort of synthetically generated geometries of ischemic hearts. The predicted depolarization pattern has good agreement with activation times computed by the cardiac electrophysiology model in a validation set of five swine heart geometries with complex scar and border zone morphologies. The mean absolute error hereby measures 8 ms on the entire myocardium when providing 50\% of the endocardial ground truth in over 500 computed depolarization patterns. Furthermore, when considering a complete animal data set with high density electroanatomic mapping data as reference, the neural network can accurately reproduce the endocardial depolarization pattern, even when a small percentage of measurements are provided as input features (mean absolute error of 7 ms with 50\% of input samples). The results show that the proposed method, trained on synthetically generated data, may generalize to real data., Comment: Accepted at the MICCAI 2020 Workshop Statistical Atlases and Computational Modeling of the Heart (STACOM)

Spiral waves are considered to be one of the potential mechanisms that maintains complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales. We simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of finite-time Lyapunov exponent (FTLE) between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. Both the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice. Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales., Comment: 13 pages, 4 figures

An example of phase transition in natural complex systems is the qualitative and sudden change in the heart rhythm between sinus rhythm and atrial fibrillation (AF), the most common irregular heart rhythm in humans. While the system behavior is centrally controlled by the behavior of the sinoatrial node in sinus rhythm, the macro-scale collective behavior of the heart causes the micro-scale behavior in AF. To quantitatively analyze this causation shift associated with phase transition in human heart, we evaluated the causal architecture of the human cardiac system using the time series of multi-lead intracardiac unipolar electrograms in a series of spatiotemporal scales by generating a stochastic renormalization group. We found that the phase transition between sinus rhythm and AF is associated with a significant shift of the peak causation from macroscopic to microscopic scales. Causal architecture analysis may improve our understanding of causality in phase transitions in other natural and social complex systems., Comment: 9 pages, 7 figures

Atrial fibrillation (AF) is the most common cardiac arrhythmia in human beings, and is associated with significant morbidity and mortality. The current standard of care includes interventional catheter ablation in selected patients, but the success rate is limited. The major limitation of the current approach to AF is the lack of fundamental understanding of its underlying mechanism. Specifically, it remains unclear whether human AF dynamics are a deterministic or a stochastic process. Here we assess for determinism in human AF by evaluating the properties of the symbolic representation of intracardiac electrical recordings obtained from patients. Specifically, we evaluate (a) the number of the missing ordinal patterns, (b) the rate of missing ordinal pattern decay for increased length of the time series, and (c) the causal-entropy complexity plane of the Bandt-Pompe symbolic representation. When used together, these are powerful tools to detect determinism, even in the presence of experimental noise and brief time series., Comment: 25 pages, 6 figures, 72 references

The heart exhibits complex systems behaviors during atrial fibrillation (AF), where the macroscopic collective behavior of the heart causes the microscopic behavior. However, the relationship between the downward causation and scale is nonlinear. We describe rotors in multiple spatiotemporal scales by generating a renormalization group from a numerical model of cardiac excitation, and evaluate the causal architecture of the system by quantifying causal emergence. Causal emergence is an information-theoretic metric that quantifies emergence or reduction between microscopic and macroscopic behaviors of a system by evaluating effective information at each spatiotemporal scale. We find that there is a spatiotemporal scale at which effective information peaks in the cardiac system with rotors. There is a positive correlation between the number of rotors and causal emergence up to the scale of peak causation. In conclusion, one can coarse-grain the cardiac system with rotors to identify a macroscopic scale at which the causal power reaches the maximum. This scale of peak causation should correspond to that of the AF driver, where networks of cardiomyocytes serve as the causal units. Those causal units, if identified, can be reasonable therapeutic targets of clinical intervention to cure AF., Comment: 19 pages, 9 figures. arXiv admin note: text overlap with arXiv:1711.10126

The mechanism that maintains atrial fibrillation (AF) remains elusive. One approach to understanding and controlling the mechanism ("AF driver") is to quantify inter-scale information flow from macroscopic to microscopic behaviors of the cardiac system as a surrogate for the downward causation of the AF driver. We use a numerical model of a cardiac system with one of the potential AF drivers, a rotor, the rotation center of spiral waves, and generate a renormalization group with system descriptions at multiple scales. We find that transfer entropy accurately quantifies the upward and downward information flow between microscopic and macroscopic descriptions of the cardiac system with spiral waves. Because the spatial profile of transfer entropy and intrinsic transfer entropy is identical, there are no synergistic effects in the system. We also find that inter-scale information flow significantly decreases as the description of the system becomes more macroscopic. The downward information flow is significantly smaller than the upward information flow. Lastly, we find that downward information flow from macroscopic to microscopic descriptions of the cardiac system is significantly correlated with the number of rotors, but the higher number of rotors is not necessarily associated with a higher downward information flow. This result contradicts the concept that the rotors are the AF driver, and may account for the conflicting evidence from clinical studies targeting rotors as the AF driver., Comment: 21 pages, 5 figures

To prevent sudden cardiac death, predicting where in the cardiac system an order-disorder phase transition into ventricular fibrillation begins is as important as when it begins. We present a computationally efficient, information-theoretic approach to predicting the locations of wavebreaks that initiate fibrillation in a cardiac system where the order-disorder behavior is controlled by a single driving component, mimicking electrical misfiring from the pulmonary veins or the Purkinje fibers. Communication analysis between the driving component and each component of the system reveals that channel capacity, mutual information and transfer entropy can locate the wavebreaks. This approach is applicable to interventional therapies to prevent sudden death, as well as to a wide range of systems to mitigate or prevent imminent phase transitions., Comment: 20 pages, 8 figures

A spiral wave is a macroscopic dynamic of excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise quantification can be challenging. Here we present a hybrid geometric and information-theoretic approach to quantifying spiral wave dynamics. We demonstrate the effectiveness of our approach by applying it to numerical simulations of a two-dimensional excitable medium with different numbers and spatial patterns of spiral waves. We show that, by defining information flow over the excitable medium, hidden coherent structures emerge that effectively quantify the information transport underlying spiral wave dynamics. Most importantly, we find that some coherent structures become more clearly defined over a longer observation period. These findings validate our approach to quantitatively characterize spiral wave dynamics by focusing on information transport. Our approach is computationally efficient and is applicable to many excitable media of interest in distinct physical, chemical and biological systems. Our approach could ultimately contribute to an improved therapy of clinical conditions such as seizures and cardiac arrhythmia by identifying potential targets of interventional therapies., Comment: 27 pages, 6 figures

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in 2-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry, and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques., Comment: 26 pages (including Appendix), 6 figures, 8 videos (not uploaded due to size limitation)