ABSTRACT
This chapter considers the properties of the volume conductor as it pertains to the evaluation of electric and magnetic fields arising therein. The sources of the aforementioned fields are described by J i , a function of position and time, which has the dimensions of current per unit area or dipole moment per unit volume. Such sources may arise from active endogenous electrophysiologic processes such as propagating action potentials, generator potentials, synaptic potentials, etc. Sources also may be established exogenously, as exemplified by electric or magnetic field stimulation. Details on how one may quantitatively evaluate a source function from an electrophysiologic process are found in other chapters. For our purposes here, we assume that such a source function J i is known and, furthermore, that it has well-behaved mathematical properties. Given such a source, we focus attention here on a description of the volume conductor as it affects the electric and magnetic fields that are established in it. As a loose definition, we consider the volume conductor to be the contiguous passive conducting medium that surrounds the region occupied by the source J i . (This may include a portion of the excitable tissue itself that is sufficiently far from J i to be described passively.)
Excitable tissue, when activated, will be found to generate currents both within itself and also in all surrounding conducting media. The latter passive region is characterized as a volume conductor. The adjective volume emphasizes that current flow is three-dimensional, in contrast to the confined onedimensional flow within insulated wires. The volume conductor is usually assumed to be a monodomain (whose meaning will be amplified later), isotropic, resistive, and (frequently) homogeneous. These are simply assumptions, as will be discussed subsequently. The permeability of biologic tissues is important
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when examining magnetic fields and is usually assumed to be that of free space. The permittivity is a more complicated property, but outside cell membranes (which have a high lipid content) it is also usually considered to be that of free space.
