Quantifying The Complex Spatiotemporal Chaos of Cardiac Fibrillation in Ionic Models Across Parameter Regimes

Abstract

Quantifying the complexity of cardiac systems is fundamental to understanding the onset of rhythm disorders, from mild arrhythmias to life-threatening fibrillation. In this work, we investigate how chaos shows up and evolves in simplified cardiac models by calculating the Lyapunov exponent (LE) across different parameter sets. We show that both temporal and spatial LE estimators can be effectively applied to action potential duration (APD) data, even without full access to state variables. Specifically, the spatial-temporal algorithm and Wolf's algorithm are used in quantifying the complexity, with experiments demonstrating their distinct behaviors on various single-spiral patterns. We also identify the minimum data length and sampling density necessary to achieve robust and accurate estimation. Overall, our results suggest that these APD-based methods can be applied not only to simulation data but also to future clinical or experimental data, particularly when observations are limited, such as when only APD data are available for analysis.