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

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Dr. Thomas Collura recently evaluated the commonalities and differences between “comodulation” and the Lexicor application of the Pearson product correlation (Collura, 2006). It was shown that the difference between the “co-modulation” and Lexicor methods is primarily in terms of the number of degrees of freedom as well as the evaluation of covariance of spectral energies over time in the former application of the Pearson Product correlation versus within frequency band covariation across channels in the Lexicor method of applying the Pearson product correlation. Below is a hand calculator example of a Lexicor application of the Pearson product correlation coefficient for the alpha frequency band (8 – 12 Hz column on the left) between channel X and channel Y using easy numbers for a hand calculator using equation 2 with N = 5 (i.e., number of spectral bins within a band and the number of degrees of freedom = 4). Table I X (uV) Y (uV) X 2 (uV 2 ) Y 2 (uV 2 ) XY 8Hz 1 2 1 4 2 9Hz 2 1 4 1 2 10Hz 3 2 9 4 6 11Hz 3 1 9 1 3 12Hz 4 2 16 4 8 ∑X = 13 ∑Y = 8 ∑X 2 = 39 ∑Y 2 = 18 ∑XY = 21 r r = = ( N N∑ XY − ∑ X∑Y 2 2 2 ∑ X − ( ∑ X ) )( N∑Y − ( ∑ 5 × 21 − 13 × 8 2 2 (5 × 39 − 13 )(5 × 18 −8 ) Y ) 2 ) r = 1 26 × 26 = + 0.001479 Figure 5 shows the results of the BrainMaster implementation of the Lexicor spectral correlation method in which very high correlation values are present because of the low number of degrees of freedom and especially the divergent differences at higher frequencies because of slight differences in filtering. This figure emphasizes that extreme caution should be used when computing a correlation coefficient using the Lexicor method with low degrees of freedom.
Fig. 5 - Comparisons between the BrainMaster and Lexicor implementation of the spectral correlation method. The correlation values are all very high due to the low degrees of freedom and miss-match of calculation occurs at the higher frequencies depending on the filter parameters (From Collura, 2006). LORETA source correlations are another example of the application of the Pearson product correlation coefficient (Thatcher et al, 2006). Below are examples of the relationship between cortico-cortical connectivity and distance from a point source using LORETA current sources and the Pearson product correlation coefficient (PCC) as applied to sequential epochs of time. The degrees of freedom ranged from 29 to 60 in which a correlation of 0.367 to 0.254 is necessary for P < .05. This analysis is a cross-frequency correlation as well as a cross-region of interest correlation. The time series analyses of cross-channel and cross-frequency coherence and phase synchrony is discussed in sections 25 to 39.
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 and 10: Fig. 1 - Illustration of volume con
Page 11 and 12: Fig. 3- Example of cospectrum (in-p
Page 13 and 14: coefficient is a valid and importan
Page 15: Eq. 1- r = ∑ N ∑ N ( X ( X −
Page 19 and 20: to a Pearson product-moment correla
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
Page 59 and 60: Example of one of the progress char
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Page 63 and 64: where n is the number of observatio
Page 65 and 66: 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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