Comparison of Complexity and Predictability of a Cellular Automaton Model in Excitable Media Cardiac Wave Propagation Compared with a FitzHugh-Nagumo Model

Abstract

Background: Excitable media are spatially distributed systems that propagate signals without damping. Examples include fire propagating through a forest, the Belousov-Zhabotinsky reaction, and cardiac tissue. (1) Excitable media generate waves which synchronize cardiac muscle contraction with each heartbeat. Spatiotemporal patterns formed by excitation waves distinguish healthy heart tissues from diseased ones. (3) Discrete Greenberg-Hastings Cellular- Automaton (CA) (1) and the continuous FitzHugh- Nagumo (FHN) model (7) are two methods used to simulate cardiac wave propagation. However, previous observations have shown that these models are not accurately predictive of experimental results as a function of time. We hypothesize that cardiac simulations deviate from the experimental data at a rate that depends on the complexity of the experimental data’s initial conditions (I.C.).

Methods: To test this hypothesis, we investigated two types of propagating waves with different complexities: a planar (i.e. simple) and a spiral wave (i.e. complex). With the same I.C., we first compared simulation results of a Greenberg-Hastings Cellular Automaton (GH-CA) model to that a FitzHugh-Nagumo (FHN) continuous model which we used as a surrogate for experimental data. We then used median-filtered real-time cardiac tissue experimental data to initialize the GH-CA model and observe the divergence of wave propagation in the simulation and the experiment.

Results: The alignment between the CA model of a planar wave and the FHN model remains constant, while the degree of overlap between the CA and FHN models decreases for a spiral wave as a function of time. CA simulation initialized by a planar wave real-time cardiac tissue data propagates like the experimental data, however, this is not the case for the spiral wave experimental data.

Conclusion: We were able to confirm our hypothesis that the divergence between the two models is due to initial condition (I.C.) complexity.

Discussion: We discuss a promising strategy to represent a GH-CA model as a Convolutional Neural Network (CNN) to enhance predictability of the model when an initial condition is given by the experimental data with a higher level of complexity.