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Cable theory and active equivalent circuits have been used to simulate the propagation of action potentials along a single nerve or muscle fiber by representing the cell as a unidimensional cable composed of isopotential segments. We extended this method to a two-dimensional sheet of cells which in many ways represents the atrium. Our method consisted of solving for the potential profile of a sheet composed of a large number of isopotential membrane patches, each of which was represented by an active equivalent circuit in which the ionic conductances were functions of voltage and time. The patches were arranged in a rectangular array with resistive interconnections that could be varied over the sheet. We used this model to study the effect of various inhomogeneities on conduction velocity and the resulting wave fronts in a sheet of excitable tissue. Some of these inhomogeneities included different effective internal resistances in the x and y directions, preferential pathways, and discrete regions of changing resistive connections. The results showed that very localized changes in membrane properties or cellular interconnections produce changes in the wave front over broad areas. This model provides a method for computing the wave fronts of action potential propagation in any two-dimensional inhomogeneous sheet of coupled excitable cells.

Simulation of action potential propagation in an inhomogeneous sheet of coupled excitable cells.