Models of extracellular potentials are typically based on treating brain tissue as a continuous volume conductor. An important parameter, or sometimes variable, in volume-conductor theory is the conductivity. Here, we present both theoretical and experimental estimates of the conductivity of brain tissue. A common modeling approximation is to assume that the conductivity does not vary with position, is the same in all directions, and does not depend on the frequency of the electric signal. With references to both experimental and theoretical studies, we discuss whether these approximations are reasonable, and we introduce ways to relax these approximations in models.

The standard two-step scheme for modeling extracellular signals is to first compute the neural membrane currents using multicompartment neuron models (step 1) and next use volume-conductor theory to compute the extracellular potential resulting from these membrane currents (step 2). Here, we present the volume-conductor theory used in step 2. The neural output from step 1 can be represented in terms of (i) a set of point sources, (ii) a set of line sources, (iii) a current-source density, or (iv) one or several current dipoles. We derive equations for the extracellular potential under the approximations (i–iv), discuss the validity and applicability of the different approximations, and explain how they are related. We also discuss how to model the effects that the electrode itself can have on the measured extracellular potential.