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

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Fig. 2- Illustration of the “In-Phase” volume conduction vs. “Out-of-Phase” connectivity components of the Cross-Spectrum. See section 9 for more details. In NeuroGuide it is simple to test the “In-Phase” vs “Out-of-Phase” analyses by using sine waves and shifting one sine wave with respect to a second sign wave and then computing the cospectrum and quadspectrum. To test the cospectrum and quadspectrum download NeuroGuide from http://www.appliedneuroscience.com/Contact%20Download1.htm and after launching NeuroGuide click File > Open > Signal Generation and then enter sine waves at different phase shifts for a given frequency and then compute the cospectrum and quadspectrum. Figure 3 shows an example of the
Fig. 3- Example of cospectrum (in-phase) and quadspectrum (out-of-phase) power using two 5 Hz sine waves shifted by 10 degrees from 0 to 180 degrees. Blue diamonds are the in-phase cospectrum values and the red squares are the out-of-phase quadspectrum power values. The use of the quadspectrum or “Out-of-Phase” computation is a method to remove zero phase lag from the computation of coherence and thus is volume conduction corrected coherence also referred to as Zerophase lag removed coherence (Nolte et al, 2004; Pascual-Marqui, 2007). 4- How is network zero phase lag different from volume conduction? Spatially distributed neurons exhibit near zero phase difference, referred to as a “binding” or “synchrony” within a network of neurons, which is independent of volume conduction (Ekhorn et al, 1988; Gray et al, 1989, John, 2005; Thatcher et al, 1994). The thalamus is the master synchronizer of the EEG and “binding” at zero phase lag can easily be produced by the centrally located thalamus (see Steriade, 1995). Multiple unit recordings and Magnetic electroencephalography (MEG) which is invisible to volume conduction have firmly established the scientific validity of network zero phase lag independent of volume conduction (Rogers,
Page 1 and 2: (unpublished manuscript - Version 1
Page 3 and 4: 29- Definition of the Cross Channel
Page 5 and 6: possible and this is why the cospec
Page 7 and 8: is because there are relatively lon
Page 9: Fig. 1 - Illustration of volume con
Page 13 and 14: coefficient is a valid and importan
Page 15 and 16: Eq. 1- r = ∑ N ∑ N ( X ( X −
Page 17 and 18: Fig. 5 - Comparisons between the Br
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Page 21 and 22: constitute the basis for all spectr
Page 23 and 24: The frequency analysis of a time se
Page 25 and 26: That is, the cross-spectrum power i
Page 27 and 28: Demo). 11- Third Compute Coherence
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Page 31 and 32: frame” of consciousness (Thatcher
Page 33 and 34: Fig. 9 - Various degrees and types
Page 35 and 36: Fig. 10 - Illustrations of phase re
Page 37 and 38: when the 1 st derivative of the pha
Page 39 and 40: Fig. 13 shows an example of two 10
Page 41 and 42: Figure 15 - The x-axis are differen
Page 43 and 44: Fig - 16. Top is coherence (y-axis)
Page 45 and 46: Coherence inflation is defined as a
Page 47 and 48: time over which the average is comp
Page 49 and 50: Nonetheless, “instantaneous” ph
Page 51 and 52: Example of conventional digital EEG
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Page 57 and 58: Multiple frequencies and multiple m
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advantage of imaging of non-cortica
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where n is the number of observatio
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Fig. 22 - Illustration of phase str
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measure of the area under the curve
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Fig. 24 - Top is filtered EEG at 25
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Fig. 26 - Top is the spontaneous EE
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27- How to compute Auto-channel Cro
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30- Cross-Channel Cross-Frequency C
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degrees or radians and is “normal
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exhibits statistically significant
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www.appliedneuroscience.com 37 - Co
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elationships as defined by the phas
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Fig. 33 - Example of phase differen
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Fig. 35 - Example of 4 different fr
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Fig. 37 - Example of a measure of c
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Fig. 39- Illustration of how cross-
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Fig. 41- Example of cross-frequency
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Gray, C.M., Konig, P., Engle, A.K.
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localization and functional connect
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35 - 48, 2007. Thatcher, R.W., Bive
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Cannon, R., Lubar, J., Sokhadze, E.
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Lubar, J., Congedo, M. and Askew, J
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Yoo, S. S. et al. Increasing cortic
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F and likewise, F iω0t iϕ t [ y e
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6- Phase Delay or phase difference
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EEG and Brain Connectivity: A Tutorial - Bio-Medical Instruments, Inc.

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