Volume Conduction & Source Localization (EEG/MEG Forward & Inverse)

Quasi-static approximation

At the frequencies relevant to EEG and MEG (below a few kilohertz), the electromagnetic field in head tissue is well described by the quasi-static approximation of Maxwell's equations: capacitive, inductive and wave-propagation terms are negligible, so the fields at each instant depend only on the source configuration at that same instant. Formally this reduces the electric problem to Poisson's equation, div(sigma grad V) = -div(J_primary), with sigma the tissue conductivity and J_primary the impressed neural current.

The practical payoffs are large. The forward mapping from sources to sensors becomes a linear, memoryless operator (the lead field), and propagation delays through tissue can be ignored, so any measured lag between channels reflects neural timing rather than conduction time. The approximation holds because, at these frequencies, the electromagnetic wavelength is enormous compared with the size of the head.

The quasi-static approximation is precisely why volume conduction produces zero-lag mixing. It is an assumption, not an exact truth, but its error at EEG/MEG frequencies is negligible.

Also called
quasistatic Maxwell approximation準靜電磁近似