Abstract
In this work, we propose a mathematical model of the cardiac electrophysiology which takes into account time delays in signal transmission, in order to capture the whole activities of macro- to micro-scale transport processes, and use this model to analyze the propagation of electrophysiological waves in the heart. The propagation of electrical activity in the heart is mathematically modeled by a modified bidomain system. As transmembrane potential evolves, the domain has anisotropical properties which are transposed into intracellular and extracellular conductivity. The new bidomain system is a multi-scale, stiff and strongly nonlinear coupled reaction–diffusion model in the shape of a set of ordinary differential equations coupled with a set of partial differential equations with multiple time delays. First, the mathematical models are introduced. Afterward the existence and uniqueness of solution of the state equation are proved as well as stability result. A numerical calculation is performed by using a coupling Lattice Boltzmann Method.
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