Coupled Networks, Patterns and Complexity - Abstract

Alonso, Sergio

Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue

Arrhythmias in cardiac tissue are related with breakup of the electrical wave propagating through the heart. Cardiac tissue is formed by a discrete network, which is far from homogeneous. We show numerically that a wave crossing an heterogeneous region of cardiac tissue may breakup and produce irregular patterns. Such type of patterns appear when the fraction of heterogeneites is close to the percolation threshold of the cell network. In cardiac tissue the reentry of an electrical wave generates a dangerous type of arrhythmia which may give rise to fibrillation, a fast reexcitation of the tissue which desynchronizes the whole heart. Cardiac tissue is heterogeneous, cells are inhomogeneously distributed and are connected by gap junctions. The presence of heterogeneities in the cardiac tissue perturbs the ideal homogeneous wave propagation and increases the risk of arrythmias. We study numerically the generation of reentries by a single action potential wave interacting with an heterogenous region surrounded by homogeneous tissue, mimicking a damaged region on the cardiac muscle. We restrict here to the study of a single wave and the relation with the percolation properties of the network of cells. We conclude that the statistical properties of the discrete network determines the breakup of the waves. The dependence of the reentry probability on the fraction of heterogeneities and on the system size can be inferred from the size distribution of non-conducting clusters near the percolation threshold.