Electric and magnetic fields of the brain computed by way of a discrete systems analytical approach: theory and...

It is shown how the stationary volume conduction phenomena in the brain, namely the electric and magnetic fields can be described in discrete terms. The volume conductor is sampled in space by introducing a sampling distance corresponding to the uncertainty in the measurements. In this way, a three-dimensional lattice is needed with equidistantly spaced nodes. The electric and magnetic properties of such a lattice are assumed to be equivalent to that of brain and other tissues. The electric and magnetic potential fields are calculated for each node as the output of a linear feedback system which has the impressed currents as the input. By way of the feedback loop the reflection phenomena at the boundaries between media of different conductivity can be taken into account. This discrete formalism has been implemented in a software system. To demonstrate the validity and accuracy of this system a number of analytically tractable problem in volume conduction has been evaluated.