An algorithm for the EEG frequency architecture of consciousness and brain body coupling

Abstract

THE FREQUENCY ARCHITECTURE OF THE CONSCIOUS HUMAN BRAIN The EEG is traditionally categorized into a handful of different frequency bands (δ, θ, α, β, γ; c.f. Schomer and Lopes da Silva, 2011). This implies that EEG frequencies do not represent an unstructured continuum. But what could be the reasons for that? One obvious reason is that frequency bands such as e.g., θ and α exhibit a clear task and event related behavior (Klimesch, 1999, 2012; Buzsaki, 2006). But here the emphasis is on a formal aspect, which is to avoid unwanted “spurious” phase synchronization. If the numerical ratio between two frequencies (f1, f2; f1 < f2) is harmonic (f2 = I ∗ f1; I = integer), the excitatory phases of the two frequencies can meet and synchronize according to a strict and regular pattern. This is of great advantage when phase coupling between frequencies is an important aspect of neuronal communication. If the ratio differs from a harmonic, spurious (unwanted) phase synchronization will appear in an uncontrolled way. Pletzer et al. (2010) have shown mathematically that the golden mean (g = 1.618 . . ..) is the best possible ratio to avoid spurious phase synchronization (see also Roopun et al., 2008). These aspects of phase synchronization can be summarized by two assumptions. (a) The center frequency of each EEG band is harmonically related to those of neighboring bands. A good estimate for δ, θ, α, β and γ is 2.5, 5, 10, 20, and 40Hz. (b) The width of a band is defined on the basis of the “golden mean role” (Klimesch, 2012; for an illustration, see Figure 1A left panel) to guarantee minimal interference between bands. EEG center frequencies which have these properties are termed frequency domains in the following. When considering the numerical relation between δ, θ, α, γ as described by assumption (a) it can easily be recognized that each center frequency is twice as high than its (lower) neighbor. An exponential function with base 2 defines that property.