Quantifying the Complexity of Cardiac System by Analyzing its APD Sequence

The study of chaotic dynamics in cardiac systems has gained significant importance due to its presence during irregular arrhythmic heart conditions like Tachycardia and fibrillation. We calculate the Lyapunov exponent in time and as a function of space to quantify the amount of chaos in a wide regime of spiral wave dynamics, from meander to breakup (fibrillation), using Action Potential Duration (APD) data from both simulations and experiments. We employ techniques like Wolf's Algorithm and the Spatial-Temporal Algorithm to quantify the chaotic and non-chaotic regions during single and multiple spiral wave regimes with large degrees of spatiotemporal complexity. We first quantify the methods with the simulation results, including noise, which then allows us to test experimental results with measurement noise. In this talk, I show temporal and spatial quantification of chaotic transition in cardiac mathematical models as a function of main model parameters that affect excitability and wave duration. We are able to address the complexity in the chaotic dynamics for different regimes of spiral wave meander and breakup using Lyapunov exponents first in models and then from optical mapping experiments obtained in live animal hearts such as rabbits and pigs.