Theoretical Studies on the Inverse Problem in Electrocardiography and the Uniqueness of the Solution

This paper focuses on the theoretical formulation of the inverse problem in electrocardiography under a general inhomogeneous and anisotropic configuration of the torso conductor. The following points are especially considered: 1) derivation of the Fredholm integral equation of the first kind which relates epicardial to body surface potentials, 2) specification of the conditions which its kernel must satisfy, 3) general solution method for the inverse problem by using the vector space theory, taking into consideration the ill condition of this inverse problem, and 4) proof of the uniqueness of the epicardial potentials.