Cluster synchronization and spatio-temporal dynamics in networks of oscillatory and excitable Luo-Rudy cells
We study collective phenomena in nonhomogeneous cardiac cell culture models, including one-and two-dimensional lattices of oscillatory cells and mixtures of oscillatory and excitable cells. Individual cell dynamics is described by a modified Luo-Rudy model with depolarizing current. We focus on the transition from incoherent behavior to global synchronization via cluster synchronization regimes as coupling strength is increased. These regimes are characterized qualitatively by space-time plots
... y space-time plots and quantitatively by profiles of local frequencies and distributions of cluster sizes in dependence upon coupling strength. We describe spatio-temporal patterns arising during this transition, including pacemakers, spiral waves, and complicated irregular activity. Processes of generation and propagation of cell excitation waves in cardiac tissues are a matter of topical interest because of their importance for understanding normal and pathological types of heart activity. The dynamics of heart tissues has been studied quite extensively in recent years, both experimentally and by means of numerical modeling. A special class of studies is concerned with cardiac cell cultures-thin layers of cells grown in Petri dishes. Characteristic features of such systems are spontaneous oscillatory activity, spatial inhomogeneity and variability of intercellular coupling strength due to an increasing number of cell junctions. The present paper is devoted to modeling the dynamics of spatio-temporal patterns of excitation in such inhomogeneous cultures in dependence upon the coupling strength. The model of a culture is based on the paradigmatic Luo-Rudy model of an isolated cardiac cell. The results of modeling are interpreted in terms of synchronization theory. In particular, cluster synchronization regimes are studied, in which the ensemble of cells gets split into several subgroups (clusters), each characterized by its own oscillation frequency. Several available experimental results (formation of target and spiral waves in cultures) are reproduced by modeling.