Field Theory of Electromagnetic Brain Activity.

The brain is considered as a complex, physical, and open system that exhibits spatiotemporal behavior at various time and length scales. A necessary condition for this pattern forming character of the brain is a nonlinear dynamics and a spatial interconnection of its elements, the neurons. The functional behavior of the brain is encoded in these spatiotemporal structures and can, at least partly, be extracted from the dynamics of the macroscopic quantities measured by the EEG and MEG. According to synergetics [1], this extraction contains all the relevant information about the spatiotemporal behavior of the brain and has, in general, a small number of degrees of freedom. This idea has been formalized to the order parameter concept based on circular causality: The order parameters are determined and created by the cooperation of microscopic quantities, but at the same time the order parameters govern the behavior of the whole system. Based on this approach phenomenological models were set up in the past for different experiments in order to find evolution equations that describe the experimentally observed macroscopic dynamics [2]. The purpose of this Letter is twofold: First, we derive a nonlinear partial differential equation from simple properties of neural populations. This field equation governs the dynamics of the macroscopic quantities measured by EEG and MEG. Second, with respect to a particular MEG experiment by Kelso et al. [3] we discuss the obtained field equation analytically and numerically and prove that it reproduces the experimentally observed phenomena. An explicit derivation and discussion of the field equation will be published elsewhere. Single neurons have two main state variables: (1) Dendritic currents are generated by active synapses that serve as current sources causing the waves of extracellular fields. These waves mainly correspond to the quantities measured by EEG and MEG [4]. (2) Action potentials are generated at the somas of neurons and correspond to pulses. See [5] for a detailed discussion of these quantities and their experimental measurements. The conversion of pulses to current amplitude occurs at synapses, the dendritic wave amplitude is converted to a pulse frequency at the somas. In contrast to single