Inverse problem solution in cardiomagnetism using a current multipole expansion of the primary sources

The equivalent current dipole (ECD) model is only the first-order approximation in modelling the primary sources of the magnetic field of the heart. From the experimental point of view this fact is particularly evident during the onset of ventricular depolarisation. In this paper we have tried to explain the departures of the experimental maps from the dipolar pattern in terms of the second-order component of the current multipole expansion for the primary source density. The antisymmetric part of this second-order component produces the external magnetic field and is equivalent to a magnetic dipole. To a first approximation it could represent circular currents flowing within the heart. We have derived the analytical expression for the magnetic field normal to the frontal plane produced by an equivalent current dipole and by an equivalent magnetic dipole (EMD) lying in a homogeneous conducting half-space. Using this expression in a least-squares fit computer program we have obtained the appropriate set of ECD and EMD parameters producing the best matching between theoretical and experimental field distributions in normal subjects. The results are in good agreement with the anatomical features of the heart and with the electrophysiology of ventricular activation. With previous theoretical considerations they strongly suggest the presence of divergence-free circular current sources within the heart.