Most bioelectric field problems (volume conductor problems) can be formulated in terms of either the Poisson or Laplace equation for electrical conduction. Since Laplace's equation is the homogeneous counterpart of the Poisson equation, we will develop the treatment for a general three-dimensional Poisson problem and discuss simplifications and special cases when necessary.
As we noted previously, a typical bioelectric volume conductor can be posed as the following boundary value problem:
The associated boundary conditions depend on what type of problem one wishes to solve. There are usually considered to be two different types of direct and inverse volume conductor problems. One type deals with the interplay between the description of the bioelectric volume source currents and the resulting volume currents and volume and surface voltages.