Here, the direct problem would be to solve
(3) for 
with a known description of 
and the
Neumann boundary condition:
which says that
the normal component of the electric field is zero on the surface
interfacing with air (here denoted by 
). This problem can
be used to solve two well known problems in medicine, the direct EEG
(electroencephioliography) and ECG (electrocardiography) volume
conductor problems. In the direct EEG problem, one usually discretizes
the brain and surrounding tissue and skull. One then assumes a
description of the bioelectric current source within the brain (this
usually takes the form of dipoles or multipoles) and calculates the
field within the brain and on the surface of the scalp. Similarly, in
one version of the direct ECG problem, one utilizes descriptions of the
current sources in the heart (either dipoles or membrane current source
models such as the FitzHugh Nagumo and Beeler Reuter, among others) and
calculates the currents and voltages within the volume conductor of the
chest and voltages on the surface of the torso.
