Relationships Among Green's Theorem, Helmholtz' Theorem, and Integral Equation Methods of Solving the Forward EGG Problem

Recent attempts to solve the forward problem of electrocardiography using approximation methods have proceeded from two distinct theoretical derivations, the Gelernter-Swihart procedure based on a Helmholtz Theorem approach and that of Barr et al. based on Green's Theorem. The Green's Theorem approach has not yet been satisfactorily placed on a physical basis, nor has it been interpreted in terms of what is acknowledged to be the most general formulation of time-invariant fields, Helmholtz's Theorem.