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

Increase in current density (14–18 Hz) from three different ROIs, resulting from training
of the Anterior Cingulate gyrus (AC). LPFC = left pre-frontal cortex; RPFC = right prefrontal
cortex. The AC appears to influence increases in the LPFC & RPFC higher than
the increase for itself although all three ROIs increased current density as a function of
training. Corresponding improvements in working memory and attention were also
measured. From Cannon et al, 2009.
21 – Coherence, Phase and Circular Statistics
Phase angle has an intrinsic discontinuity, for example consider the
linear and circular distributions of 360 equidistant points. In the linear
distribution 0 and 360 are at opposite ends while in the circular distribution
0 0 = 360 0 (Jammalamadaka and SenGupta, 2001). To evaluate phase angles
it is necessary to use vector algebra and compute a mean vector with
magnitude or length r, and a direction Θ and to calculate the average x and y
components of the mean vector:
1
n
n
Eq. 21 - x = ∑[ sin( α ) + sin( α ) + sin( α ) + ... sin( α )]
1 2
3
n
i−1
1
n
n
Eq. 22 - y = ∑[ cos( α ) + cos( α ) + cos( α ) + ... cos( α )]
1 2
3
n
i−1