Oblique double layer potentials for the direct and inverse problems of electrocardiology

A mathematical analysis of a model of the cardiac bioelectric sources generating the potential field in a bounded conducting volume is carried out. A boundary integral representation of the potential is given, which shows that, if the anisotropy of the cardiac muscle is taken into account, the bioelectric sources are characterized by an “oblique” double layer on the excitation wavefront. Boundedness conditions for the potential and jump relationships across the front are investigated. Uniqueness results for the inverse problem (i.e. the determination of the wavefront surface, given the potential on the volume boundary) are established.