This document discusses neural networks in the brain and various methods for analyzing functional connectivity between brain areas using electrophysiology data. It introduces several measures of neural synchronization such as coherence, phase locking value, pairwise phase consistency, phase slope index, and Granger causality. It also discusses issues like the common reference problem, common input problem, and volume conduction that need to be addressed when applying these methods. The document provides references for further reading on graph analysis techniques and interpreting results.

1. Neural networks in the
brain
Ilya Zakharov
Research associate
Developmental behavioral genetics lab
Psychological Institute
Russian Academy of Education

2. Neural networks

4. Networks on different levels.
Spikes

5. Networks on different levels.
Brain areas

6. Networks on different levels.
Electrophysiology

7. Neural coupling

8. Measures

9. Phase synchrony

10. Perfect synchronization
Synchronization with
time lag
No synchronization

11. Coherence coefficient
Coherence - the frequency domain
equivalent to the time domain cross-
correlation function.
*Phase Locking Value
Coherence for normalized Fourier-
transformed signals

12. Phase lag index
The PLI is a metric that evaluates the distribution of phase
differences across observations.
Stam et al., 2007
the PPC is computed from the distribution of all pairwise
differences (between pairs of observations) of the relative
phases.
Pairwise phase consistency
Vinck et al., 2010
Non-directed

13. Phase slope index
Granger causality
Computed from the complex-valued coherency, and
quantifies the consistency of the direction of the change
in the phase difference across. The sign of the PSI
informs about which signal is temporally leading the
other
Nolte et al., 2008
Directed
Represents the result of a model comparison. It is rooted in the autoregressive
modeling framework, where future values of time series are modeled as a
weighted combination of past values of time series. Specifically, the quality of an
AR-model can be quantified by the variance of the model’s residuals, and Granger
causality is defined as the natural logarithm of a ratio of residual variances,
obtained from two different AR-models.
Ding et al., 2006

14. Common reference problem
Bipolar referencing?

15. Common input problem
Partial out third input?
Granger causality?

16. Common source problem/
Volume conduction/field spread
Current source density?
Imanigary coherence?
Source localization?

17. Back to graph analysis

18. Back to graph analysis
Your suggestions?

19. References
• Bastos, André M., and Jan-Mathijs Schoffelen. “A Tutorial Review of Functional Connectivity Analysis Methods and Their Interpretational Pitfalls.” Frontiers in
Systems Neuroscience, 2016, 175. doi:10.3389/fnsys.2015.00175.
• Durand, Dominique M., Eun-Hyoung Park, and Alicia L. Jensen. “Potassium Diffusive Coupling in Neural Networks.” Philosophical Transactions of the Royal
Society of London B: Biological Sciences 365, no. 1551 (August 12, 2010): 2347–62. doi:10.1098/rstb.2010.0050.
• Finn, Emily S., Xilin Shen, Dustin Scheinost, Monica D. Rosenberg, Jessica Huang, Marvin M. Chun, Xenophon Papademetris, and R. Todd Constable.
“Functional Connectome Fingerprinting: Identifying Individuals Using Patterns of Brain Connectivity.” Nature Neuroscience 18, no. 11 (November 2015):
1664–71. doi:10.1038/nn.4135.
• Fraga González, G., M. J. W. Van der Molen, G. Žarić, M. Bonte, J. Tijms, L. Blomert, C. J. Stam, and M. W. Van der Molen. “Graph Analysis of EEG Resting
State Functional Networks in Dyslexic Readers.” Clinical Neurophysiology. Accessed July 15, 2016. doi:10.1016/j.clinph.2016.06.023.
• Hardmeier, Martin, Florian Hatz, Habib Bousleiman, Christian Schindler, Cornelis Jan Stam, and Peter Fuhr. “Reproducibility of Functional Connectivity and
Graph Measures Based on the Phase Lag Index (PLI) and Weighted Phase Lag Index (wPLI) Derived from High Resolution EEG.” PloS One 9, no. 10
(2014): e108648. doi:10.1371/journal.pone.0108648.
• Lachaux, J. P., E. Rodriguez, J. Martinerie, and F. J. Varela. “Measuring Phase Synchrony in Brain Signals.” Human Brain Mapping 8, no. 4 (1999): 194–208.
• Neubauer, Aljoscha C., and Andreas Fink. “Intelligence and Neural Efficiency: Measures of Brain Activation versus Measures of Functional Connectivity in
the Brain.” Intelligence, Intelligence and the Brain, 37, no. 2 (March 2009): 223–29. doi:10.1016/j.intell.2008.10.008.
• Nolte, Guido, Andreas Ziehe, Vadim V. Nikulin, Alois Schlögl, Nicole Krämer, Tom Brismar, and Klaus-Robert Müller. “Robustly Estimating the Flow Direction
of Information in Complex Physical Systems.” Physical Review Letters 100, no. 23 (June 10, 2008): 234101. doi:10.1103/PhysRevLett.100.234101.
• Rashid, Barnaly, Mohammad R. Arbabshirani, Eswar Damaraju, Mustafa S. Cetin, Robyn Miller, Godfrey D. Pearlson, and Vince D. Calhoun. “Classification
of Schizophrenia and Bipolar Patients Using Static and Dynamic Resting-State fMRI Brain Connectivity.” NeuroImage 134 (July 1, 2016): 645–57. doi:
10.1016/j.neuroimage.2016.04.051.
• Stam, Cornelis J., Guido Nolte, and Andreas Daffertshofer. “Phase Lag Index: Assessment of Functional Connectivity from Multi Channel EEG and MEG with
Diminished Bias from Common Sources.” Human Brain Mapping 28, no. 11 (November 1, 2007): 1178–93. doi:10.1002/hbm.20346.
• Termenon, M., A. Jaillard, C. Delon-Martin, and S. Achard. “Reliability of Graph Analysis of Resting State fMRI Using Test-Retest Dataset from the Human
Connectome Project.” NeuroImage. Accessed June 18, 2016. doi:10.1016/j.neuroimage.2016.05.062.
• Trongnetrpunya, Amy, Bijurika Nandi, Daesung Kang, Bernat Kocsis, Charles E. Schroeder, and Mingzhou Ding. “Assessing Granger Causality in
Electrophysiological Data: Removing the Adverse Effects of Common Signals via Bipolar Derivations.” Frontiers in Systems Neuroscience, 2016, 189. doi:
10.3389/fnsys.2015.00189.
• Vinck, Martin, Marijn van Wingerden, Thilo Womelsdorf, Pascal Fries, and Cyriel M. A. Pennartz. “The Pairwise Phase Consistency: A Bias-Free Measure of
Rhythmic Neuronal Synchronization.” NeuroImage 51, no. 1 (May 15, 2010): 112–22. doi:10.1016/j.neuroimage.2010.01.073.
• Wang, Xiangpeng, Ting Wang, Zhencai Chen, Glenn Hitchman, Yijun Liu, and Antao Chen. “Functional Connectivity Patterns Reflect Individual Differences
in Conflict Adaptation.” Neuropsychologia 70 (April 2015): 177–84. doi:10.1016/j.neuropsychologia.2015.02.031.
• Ding, M., Chen, Y., & Bressler, S. L. (2006). 17 Granger causality: basic theory and application to neuroscience. Handbook of time series analysis: recent
theoretical developments and applications, 437.

20. Thanks for your attention!
We are always ready to
cooperate!
iliazaharov@gmail.com