This leads to a reduction of Maxwell's equations to one of two forms. The more general form is a reduction to Poisson's equation for electrical conduction:
where is the electrical conductivity tensor, is the electrostatic potential, is the current source per unit volume, and is the solution domain. In this form, one includes the source region and an understanding of the primary bioelectric sources, , usually in the form of a simplified mathematical model. Alternatively, one can define a surface bounding the region which includes the sources and recast the formulation in terms of information on that surface, yielding Laplace's equation:
One then solves these equations subject to an appropriate set of boundary conditions. At first glance, this seems simple: we know the governing equation and we know how to solve Poisson's and Laplace's equations. However, as we shall see, there are some significant challenges when one tries to solve a large scale, inhomogeneous, anisotropic, inverse volume conductor problem that exhibits the complicated geometry of the human body.