Oblique dipole layer potentials applied to electrocardiology

We study the properties of the potential field generated by an oblique dipole layer. This field arises, for instance, in describing the potential elicited by a depolarization wavefront spreading in the myocardium when a dependence of the potential on the cardiac fiber orientation is introduced. The representation of cardiac bioelectric sources by means of an oblique dipole layer leads to a mathematical structure which generalizes the classical solid angle theory used in electrocardiology, which has been challenged by recent experimental evidence, and links models previously proposed with a view to adequately reproduce the potential observed in experiments. We investigate also the relationship between our model and an intracellular current model and we derive potential jump formulae for some models which account for the anisotropic structure of the myocardium. The potential generated by an oblique dipole layer is considered both for unbounded and bounded domains. In the latter case an integral boundary equation is derived and we study its solvability. A numerical procedure for solving this integral equation by means of the finite element method with collocation is outlined.