On the magnetic field generated outside an inhomogeneous volume conductor by internal current sources

Abstract

The magnetocardiogram results from the detection of magnetic fields generated outside the body by electric current sources in the heart. Let the source current dipole moment per unit volume be Ji, the conductivityg, the electric potentialV, and the electric field intensityE. Then it may be shown that the magnetic fieldHis given by eitherH = (1/4\pi) \int J^{i} \times \nabla(1/r) dv + \sum_{i} \int (g' - g")(E \times dS_{i}/r), orH = (1/4\pi) \int J^{i} \times \nabla(1/r) dv + \sum_{i} \int (g' - g")V\nabla(1/r) \times dS_{i}, where the surface integral is over all surfaces Siseparating regions of different conductivity, i.e.,g' andg", andris the distance from the point of measurement to the element of volume or surface. The magnetic dipole momentmis given bym = \frac{1}{2} \int r_{1} \times J^{i}dv - \frac{1}{2} \sum_{i} \int (g'-g")Vr_{1} \times dS_{i}, where r1is a radius vector from an arbitrary origin.