Spatial Networks of Hybrid I/O Automata for Modeling Excitable Tissue

We propose a new biological framework, spatial networks of hybrid input/output automata (SNHIOA), for the efficient modeling and simulation of excitable-cell tissue. Within this framework, we view an excitable tissue as a network of interacting cells disposed according to a 2D spatial lattice, with the electrical behavior of a single cell modeled as a hybrid input/ouput automaton. To capture the phenomenon that the strength of communication between automata depends on their relative positions within the lattice, we introduce a new, weighted parallel composition operator to specify the influence of one automata over another. The purpose of the SNHIOA model is to efficiently capture the spatiotemporal behavior of wave propagation in 2D excitable media. To validate this claim, we show how SNHIOA can be used to model and capture different spatiotemporal behavior of wave propagation in 2D isotropic cardiac tissue, including normal planar wave propagation, spiral creation, the breakup of spirals into more complex (potentially lethal) spatiotemporal patterns, and the recovery of the tissue to the rest via defibrillation.