Long-Time Prediction of Arrhythmic Cardiac Action Potentials Using Recurrent Neural Networks and Reservoir Computing

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.

Quantifying Distributions of Parameters for Cardiac Action Potential Models Using the Hamiltonian Monte Carlo Method

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.