EEG and Brain Connectivity: A Tutorial - Bio-Medical Instruments, Inc.

degrees or radians and is “normalized” with respect to frequency (i.e.,
independent of frequency because r = 1). For example, a phase difference of
45 0 is the same for the standard EEG frequency bands of delta, theta, alpha,
beta, gamma, etc. Because of this fact and because of the physics of
superposition of waves the bi-spectral phase measure is a useful measure of
local and distant coupling by frequency and phase locking. The first and
second derivatives of bi-phase coupling are useful measures of “transition
states” or bifurcation points and stability measures of homeostatic systems
(similar to their application to phase reset described in section 9).
The equation for use with a hand calculator to compute Cross Bi-Spectral
Phase or CCP is:
Eq. 31-
CCP =
Arc tan
∑
N
∑
N
(( a(
x'
f ) v(
y'
f ) − b(
x'
f ) u(
y'
f ))
1
(( a(
x'
f ) u(
y'
f ) + b(
x'
f ) v(
y'
f ))
1
2
2
1
1
2
2
34- Coherence of Coherence
Defined as the average Coherence between two time series of
instantaneous coherence for a pair of electrodes with a common reference.
The importance of a common reference is because algebraic subtraction
occurs only by virtue of a common reference whereas an average reference
or a Laplacian reference mixes signals from all leads into each of the
remaining leads thus eliminating valid and meaningful algebra. A view of
all pair wise combinations of “Coherence of Coherence” for 19 leads = 171
combinations using Cz as the reference electrode is in Figure 28.