  The problem of determining the neuronal current inside the brain from
measurements of the induced magnetic field outside the head is discussed under
the assumption that the space occupied by the brain is approximately spherical.
By inverting the Geselowitz equation, the part of the current which can be
reconstructed from the measurements is precisely determined. This actually
consists of only certain moments of one of the two functions specifying the
tangential part of the current. The other function specifying the tangential
part of the current as well as the radial part of the current are completely
arbitrary. However, it is also shown that with the assumption of energy
minimization, the current can be reconstructed uniquely. A numerical
implementation of this unique reconstruction is also presented.
