Quantifying the complex spatiotemporal chaos of cardiac fibrillation in ionic models across parameter regimes.

Characterizing the complexity of cardiac arrhythmias is essential for distinguishing different dynamical regimes, comparing rhythms across physiological and pathological conditions, and identifying transitions to life-threatening states such as fibrillation. In this work, we develop a comprehensive pipeline to quantify, for the first time, the degree of chaotic dynamics in mathematical cardiac models by calculating the largest Lyapunov exponent (LE) across a wide range of different dynamical regimes and parameter sets. This analysis was enabled by high-performance graphics processing unit-based 2D simulations implemented in WebGL, allowing fast systematic exploration of long-duration spatiotemporal dynamics across large parameter spaces. We show that both temporal and spatial LE (λT and λS) estimators can be effectively used with action potential duration (APD) data, even without full access to state variables. Specifically, a spatiotemporal algorithm and Wolf's algorithm are used to quantify LEs from APD data obtained from simulations exhibiting a broad range of complex reentrant spatiotemporal dynamics. Across different dynamical regimes and parameter variations, λT and λS generally track changes in chaotic complexity, while differences between them reflect distinct sensitivities to how the underlying instability is expressed in the spatiotemporal dynamics. We also identify the minimum data length and spatial density necessary to achieve robust and accurate LE estimation. In particular, the estimation of λS requires shorter recordings and fewer APD measurements and remains robust at lower spatial and temporal resolution, substantially reducing the data requirements compared with λT. Our results suggest that these APD-based methods can be applied not only to simulation data but also to clinical or experimental data, where access to complete state variables and long, high-resolution recordings is inherently limited. The ability of λS to track changes in chaotic complexity with substantially reduced data requirements, together with the complementary information obtained when both estimators are available, makes this framework particularly promising for quantifying chaotic dynamics in experimentally and clinically observed cardiac arrhythmias.