In biomagnetic imaging, the magnetic field caused by electrical nerve impulses is measured and
used to form an estimate of the location and strength of the impulse. One complicating factor in forming
this estimate is the fact that the impulses induce current flow in the volume conductor surrounding the
nerve.17 In this presentation we explore the properties of these volume currents.
We first formulate the problem in the standard form using Ohm's law to relate the volume current
to the impressed (nerve impulse) current and the conductivity distribution. We then depart from the
usual derivation by making use of properties of the fourier-transformed maxwell8 and continuity
equations. In fourier space, the divergence operation in a vector field becomes a simple taking of the
radial component of the fourier-transformed field; the curl transforms into taking tangential components.
By decomposing the current densities and using the maxwell equations, we are able to arrive at a recursive
differential expression for the volume-current generated magnetic field. The driving term in the
expression is the current due to the divergence of the impressed current density.
We provide some examples of applying this expression to simply shaped conductors.