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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. 

Abstract BackgroundRepolarization 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. MethodsWe 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. ResultsA 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. DiscussionWe 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. 

Abstract AimsThe 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 resultsWe 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. ConclusionWe 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.