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.