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

phase reset are that minimal energy is required to reset phase between
weakly coupled oscillators and phase reset occurs independent of amplitude.
In weakly coupled chaotic systems amplitude can vary randomly while
phase locking is stable.
Phase reset is defined as a significant positive or negative first
derivative of the time series of phase difference between two channels, i.e.,
d( ϕ
t
− ϕ′
t
_/t > 0 or < 0. Phase locked or phase synchrony is defined as that
period of time where there is a stable near zero first derivative of the
instantaneous phase difference between d( ϕ
t
− ϕ′
t
_/t ≈ 0. A high coherence
value is related to extended periods of phase locking. A significant positive
first derivative of the time series of coherence marks the onset of phase
locking and a significant negative first derivative of the time series of
coherence marks the onset of phase dispersion over an interval of time. The
significance level can be determined by computing the means and standard
deviations of the first derivative for each time series and then computing a Z
u − x
score for each time point with alpha at P < .05 or Z = where u = mean
SD
and x = the instantaneous first derivative at t and SD = standard deviation.
For example, depending on the method of computation, values near zero st.
dev. or < 1 st. dev may define the state of “Phase Locking”. Values > 2 st.
dev. may define the state of “Phase Transition” or “Phase Reset” (the alpha
threshold is a matter of observation and test).
Figure ten illustrates the concept of phase reset. Coherence is a
measure of phase consistency or phase clustering on the unit circle as
measured by the length of the unit vector r. The illustration in figure 10
shows that the resultant vector r 1 = r 2 and therefore coherence when
averaged over time is constant even though there can be a shift in the phase