Dipole density instead of potentials in electrocardiology

We discuss the forward and inverse problems between the potential V(x) measured in a heart chamber and its sources represented by a dipole density d(y) located on the heart wall. We show that the mapping from d(y) to V(x) is a compact integral operator. Its inverse is unbounded which makes the inverse problem ill-posed in the mathematical sense. We investigate methods to solve the inverse problem approximately in view of the mapping of complicated cardiac arrhythmias. We point out an analogy between phase mapping and 2-dimensional hydrodynamics.