A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics

The purpose of this paper is twofold: First, we present a semi-quantitative nonlinear field theory of the brain under realistic anatomical connectivity conditions describing the interaction between functional units within the brain. This macroscopic field theory is derived from the quasi microscopic conversion properties of neural populations occurring at synapses and somas. The quasi-microscopic models by Wilson-Cowan (1972,1973) and Nunez (1974) can be derived from these. Functional units are treated as inhomogeneities within a nonlinear one-dimensional neural tissue. Second, for the case of the Kelso experiment the field equation is treated analytically and numerically and can be reduced to a set of ordinary differential equations which corresponds to a model by Jirsa et al. (1994,1995). This phenomenological model reproduces the spatio-temporal phenomena experimentally observed. Here the most prominent property of the neural tissue is the parametric excitation. The macroscopic field parameters can be expressed by quasi-microscopic neural parameters.