Generation of anisotropic networks for simulations of signals spreading in excitable cell systems.

Abstract

We describe a technique of constructing an anisotropic lattice of coupled subunits and apply it to assemblages of excitable myocardial cells conducting an electric impulse. The cells are assumed arranged in a planar network comprising a few thousands of cells, each having at most eight connections to neighbors. The connections are characterized as being one of four kinds: horizontal, vertical, diagonal and inversely diagonal. The connectivity in the cellular network is constructed randomly with prescribed fractions of each of the four kinds of connections. These fractions are taken from literature and characterize certain types of cardiac tissues, the left ventricle in particular. The nodes in the network correspond to cells, which are treated as point objects described by ordinary differential equations. For the model of the left ventricle we study spreading of the action potential initiated by an impulse stimulus of a small cluster of cells.