Electric and Magnetic Fields of the Brain

Electroencephalography (EEG) and Magnetoencephalography (MEG) provide two noninvasive methods to learn about the spatial and temporal behavior of neuronal currents. In this tutorial chapter we present the physics and mathematics needed to interpret such measurements. The frequencies present in neuronal activity are sufficiently low that Maxwell’s equations for electromagnetism can be approximated by omitting the terms involving time derivatives. In this ‘quasistatic’ approximation the electric and magnetic fields follow the time dependence of the neuronal current. The “Forward Problem” consists of solving for these fields on the surface of the scalp and just outside the head, for any assumed neuronal current distribution. It requires a knowledge of the ‘head model’, namely the shapes and electrical conductivities of the main head compartments, i.e., the brain, skull, and scalp, and possibly the cerebrospinal fluid. Analytical and numerical methods for doing this are discussed. In the “Inverse Problem” one tries to deduce the neuronal current distribution from EEG and/or MEG measurements on human subjects. The factors that contribute to the non-uniqueness of the solution are discussed, and the methods that are actually employed to obtain current distributions are described. The standard procedure is to assume one or more current distributions, solve the forward problem for each one, and compare them with the data. Various criteria for calculating how well they agree are discussed.