Biomagnetic Fourier imaging (current density reconstruction)

A technique for reconstructing a current density distribution from measurements of its magnetic field is described. The technique assumes that the current distribution is confined to a single plane. The data it requires are measurements of the magnetic flux on a plane. These can be provided by an integrated planar array of superconducting quantum interference device magnetometers. The approach is based on the magnetic lead field which is derived in a simple way based on energy concepts. Using the lead field and conservation of charge conditions provides two linear, spatially invariant imaging equations relating the current density and flux measurements. These equations are solved using Fourier techniques. The validity of the resulting reconstruction technique is shown both analytically and with a computer model. The effects of not satisfying the planar assumption are described for the case where the currents are parallel but not in the same plane.