The electroencephalographic (EEG) signal is the electric potential recorded on the scalp, and it is believed to originate from the combined activity of large populations of neurons. In forward models of EEG signals, one typically (i) represents neuronal sources in terms of effective current dipoles, (ii) defines a head model, which is a specification of the conductivity profile for the medium between the sources and the recording position (brain tissue, cerebrospinal fluid, skull, scalp), and (iii) uses volume-conductor theory to compute the resulting electric potential at the scalp. In this chapter, we introduce the key theory and computational frameworks for modeling EEG signals. We illustrate how biophysically detailed models of neurons can be reduced to approximate equivalent dipoles, and we discuss further ways to simplify neural simulations in order to reduce the computational cost. Using a combination of computational modeling and analytical approximations, we analyze how various factors are involved in shaping the EEG signal.

The magnetoencephalographic signal is the magnetic field recorded outside the scalp of the head. It is believed to originate from the combined activity of large populations of neurons. In forward models of MEG signals, the neural output is typically represented in terms of equivalent current dipoles. We here go through the mathematical equations for computing MEG signals from current dipoles, present computer simulations of MEG signals using simplified models of the head geometry, and show how the predicted MEG signals depend on the chosen head model and orientations of the dipoles. We also present a formalism for modeling the magnetic field inside brain tissue.