Brain potential is described using the mesocolumnar averaged excitatory and inhibitory neuron firings of neocortex. Lagrangian is constructed based on SMNI(Statistical Mechanics of Neocortical Interaction) and then Euler Lagrange equation is obtained. It is assumed that excitatory neuron firing is amplitude-modulated dominantly by the sum of two modes of frequency ω and 2ω. Time series of this neuron firing is calculated numerically. IωL related to low frequency distribution of power spectrum, IωH high frequency, and Sd(standard deviation) are introduced for the effective extraction of the dynamic property in this simulated brain potential. The behavior of IωL, IωH, and Sd due to ε and γ parameters is found. Experimentally, IωL, IωH, and Sd are obtained from EEG of 4 persons in rest state and of canis familiaris in deep sleep state and are compared with theoretical results.
It is very important in many fields related to human well-being such as comfort-pursued industrial design, psychology, medicine to characterize emotional states by EEG analysis. The pleasant and unpleasant sensation among various emotional states could be characterized by ranges of ε, γ parameters estimated by the simulated IωL-IωH-Sd relations.