PHASE-SENSITIVE CELLULAR AUTOMATA ON STOCHASTIC NETWORK AS A MODEL FOR CARDIAC PACEMAKER RHYTHMICITY

Oscillating cellular automata placed on two-dimensional stochastic lattice are proposed to model normal and abnormal cardiac pacemaker activity. In addition to Greenberg-Hasting approach, interactions which elongate the cellular period are proposed. Stationary states of the proposed system depend on density of intercellular connections, and thresholds for cell-to-cell interactions. The transition from expanding to collapsing wave patterns is observed at certain model parameters. A physiological meaning can be given to that transition, namely, as the arrhythmia phenomenon developing in the real heart due to abnormal high potassium concentration in the blood.