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

29- Definition of the Cross Channel Cross-Frequency Coherence
30- Generic Bi-Spectral Phase
31- Definition of the Auto Channel Cross-Frequency Phase Difference
32- Definition of the Cross Channel Cross-Frequency Phase Difference
33- Coherence of Coherences
34 – Phase Difference of Coherences
35 – Coherence of Phase Differences
36 – Coherence of Phase Resets
37 – Phase Difference of Phase Differences
38 – Phase Difference of Phase Resets
39- Bi-Spectrum Cross-Frequency Power Correlations
40- Bi-Spectrum Cross-Frequency Phase Synchrony & Phase Reset
41 – References
42 – Appendix A – General Time & Frequency Issues
43- Appendix B – Instantaneous Coherence, Phase and Bi-Spectra
44- Appendix C – Listing of Equations
1 - Introduction
Measurements of real-time and off-line electrodynamics of the human
brain have evolved over the years and one purpose of this paper is to provide
simple hand calculator equations to facilitate standardization and the
implementation of standardized methods. We begin with the fact that the
brain weighs approximately 2.5 pounds and consumes approximately 60%
of blood glucose (Tryer, 1988) and consumes as much oxygen as our
muscles consume during active contraction, 24 hours a day. How is this
disproportionate amount of energy used? The answer is that it is used to
produce electricity including synchronized and collective actions of small
and large groups of neurons linked by axonal and dendritic connections.
Each neuron is like a dynamically oscillating battery that is continually
being recharged (Steriade, 1995). Locally connected neurons recruit
neighboring neurons with a sequential build up of electrical potential
referred to as the recruiting response and the augmenting response also
called EEG “burst activity” and “spindles” (Thatcher and John, 1977;
Steriade, 1995). EEG burst activity is recognized by spindle shaped waves
that wax and wane (i.e., augmenting by sequential build up, then asymptote
and then decline to repeat as a waxing and waning pattern) are universal and
are present in delta (1 – 4 Hz) theta (4-7.5Hz), alpha (8 to 12 Hz), beta (12.5
Hz to 30 Hz) and gamma (30 Hz – 100 Hz) frequency bands during waking
in normal functioning people. Another fundamental fact is that only