Mathematical models and problems in electrocardiology

Some mathematical models and problems, arising in electrocardiology, are reviewed. The excitation process, characterized by a front of the transmembrane potential spreading through the myocardium is examined. It is an evolution problem exhibiting considerable numerical difficulties for its solution and the eikonal approximation is introduced. Some aspects of these problems are described and we derive under subsequent assumptions different models for the far-field potential approximation yielding the model of the oblique dipole layer imbedded into an anisotropic or in a uniform isotropic medium. Also the classical model of a uniform normal double layer is considered.