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Methods for Functional Connectivity Analysis

Part of the Biological and Medical Physics, Biomedical Engineering book series (BIOMEDICAL)

Abstract

The purpose of this chapter is to provide comprehensive and useful guidelines for the methods of the functional connectivity analysis (FCA) for electroencephalogram (EEG) and its application. After presenting the detailed procedure for the FCA, we described various methods for quantifying functional connectivity. The problem of volume conduction and the means to diminish its confounding effects on the FCA was thoroughly reviewed. As a useful preprocessing for the FCA, spatial filtering of the time-series measured on the scalp or transformation to current densities on cortical surface were described. We also reviewed ongoing efforts toward developing FC measures which are inherently robust to the volume conduction problem. Finally, we illustrated the procedures for determining significance of the FC among specific pair of regions, which exploit surrogate data generation or the characteristics of event-related data.

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References

  1. A.R. Anwar, M. Muthalib, S. Perrey et al., Effective connectivity of cortical sensorimotor networks during finger movement tasks: a simultaneous fNIRS, fMRI, EEG study. Brain Topogr. 29, 645–660 (2016)

    CrossRef  Google Scholar 

  2. F. Babiloni, F. Cincotti, C. Babiloni et al., Estimation of the cortical functional connectivity with the multimodal integration of high-resolution EEG and fMRI data by directed transfer function. Neuroimage 24, 118–131 (2004)

    CrossRef  Google Scholar 

  3. L.A. Baccalá, K. Sameshima, Partial directed coherence: a new concept in neural structure determination. Biol. Cybern. (2001). https://doi.org/10.1007/PL00007990

    CrossRef  MATH  Google Scholar 

  4. S. Baillet, J.C. Mosher, R.M. Leahy, Electromagnetic brain mapping. IEEE Signal Process. Mag. 18, 14–30 (2001). https://doi.org/10.1109/79.962275

    CrossRef  ADS  Google Scholar 

  5. E. Barzegaran, M.G. Knyazeva, Functional connectivity analysis in EEG source space: the choice of method. PLoS ONE 12, e0181105 (2017). https://doi.org/10.1371/journal.pone.0181105

    CrossRef  Google Scholar 

  6. A.M. Bastos, J.-M. Schoffelen, A tutorial review of functional connectivity analysis methods and their interpretational pitfalls. Front. Syst. Neurosci. 9, 175 (2016). https://doi.org/10.3389/fnsys.2015.00175

    CrossRef  Google Scholar 

  7. R.L. Buckner, F.M. Krienen, B.T.T. Yeo, Opportunities and limitations of intrinsic functional connectivity MRI. Nat. Neurosci. 16, 832–837 (2013). https://doi.org/10.1038/nn.3423

    CrossRef  Google Scholar 

  8. E. Bullmore, O. Sporns, Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198 (2009). https://doi.org/10.1038/nrn2575

    CrossRef  Google Scholar 

  9. G. Buzsáki, A. Draguhn, Neuronal oscillations in cortical networks. Science 304, 1926–1929 (2004)

    Google Scholar 

  10. R.T. Canolty, R.T. Knight, The functional role of cross-frequency coupling. Trends Cogn. Sci. 14, 506–515 (2010). https://doi.org/10.1016/j.tics.2010.09.001

    CrossRef  Google Scholar 

  11. L. Canuet, R. Ishii, R.D. Pascual-Marqui et al., Resting-state EEG source localization and functional connectivity in schizophrenia-like psychosis of epilepsy. PLoS ONE 6. https://doi.org/10.1371/journal.pone.0027863

  12. J.W. Choi, K.S. Cha, J.D. Choi et al., Difficulty-related changes in inter-regional neural synchrony are dissociated between target and non-target processing. Brain Res. 1603, 114–123 (2015). https://doi.org/10.1016/j.brainres.2015.01.031

    CrossRef  Google Scholar 

  13. J.W. Choi, K.M. Jang, K.Y. Jung et al., Reduced theta-band power and phase synchrony during explicit verbal memory tasks in female, non-clinical individuals with schizotypal traits. PLoS ONE 11, 1–18 (2016). https://doi.org/10.1371/journal.pone.0148272

    CrossRef  Google Scholar 

  14. J.W. Choi, D. Ko, G.T. Lee et al., Reduced neural synchrony in patients with restless legs syndrome during a visual oddball task. PLoS ONE 7, 1–9 (2012). https://doi.org/10.1371/journal.pone.0042312

    CrossRef  Google Scholar 

  15. M.X. Cohen, Analyzing Neural Time Series Data: Theory and Practice (The MIT Press, Cambridge, Massachusetts, 2014)

    Google Scholar 

  16. P.W. Diaconia, D. Freedman, Consistency of Bayes estimates for nonparametric regression: normal theory. Bernoulli 4, 411–444 (1998)

    CrossRef  MathSciNet  Google Scholar 

  17. K.J. Friston, Functional and effective connectivity: a review. Brain Connect 1, 13–36 (2011). https://doi.org/10.1089/brain.2011.0008

    CrossRef  Google Scholar 

  18. G. Gómez-Herrero, M. Atienza, K. Egiazarian, J.L. Cantero, Measuring directional coupling between EEG sources. Neuroimage 43, 497–508 (2008). https://doi.org/10.1016/j.neuroimage.2008.07.032

    CrossRef  Google Scholar 

  19. C.W.J. Granger, Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969)

    CrossRef  Google Scholar 

  20. M. Hassan, O. Dufor, I. Merlet et al., EEG source connectivity analysis: from dense array recordings to brain networks. PLoS ONE 9, (2014). https://doi.org/10.5281/zenodo.10498

  21. S. Haufe, Towards EEG Source Connectivity Analysis (Berlin Institute of Technology, Berlin, Germany, 2012)

    Google Scholar 

  22. S. Haufe, V.V. Nikulin, K.-R. Müller, G. Nolte, A critical assessment of connectivity measures for EEG data: a simulation study. Neuroimage 64, 120–133 (2013). https://doi.org/10.1016/j.neuroimage.2012.09.036

    CrossRef  Google Scholar 

  23. C.S. Herrmann, M.H.J. Munk, A.K. Engel, Cognitive functions of gamma-band activity: memory match and utilization. Trends Cogn. Sci. 8, 347–355 (2004). https://doi.org/10.1016/j.tics.2004.06.006

    CrossRef  Google Scholar 

  24. A.-S. Hincapié, J. Kujala, J. Mattout et al., The impact of MEG source reconstruction method on source-space connectivity estimation: a comparison between minimum-norm solution and beamforming. Neuroimage 156, 29–42 (2017). https://doi.org/10.1016/j.neuroimage.2017.04.038

    CrossRef  Google Scholar 

  25. J.F. Hipp, D.J. Hawellek, M. Corbetta et al., Large-scale cortical correlation structure of spontaneous oscillatory activity. Nat. Neurosci. (2012). https://doi.org/10.1038/nn.3101

    CrossRef  Google Scholar 

  26. R.M. Hutchison, T. Womelsdorf, E.A. Allen et al., Dynamic functional connectivity: promise, issues, and interpretations. Neuroimage 80, 360–378 (2013). https://doi.org/10.1016/j.neuroimage.2013.05.079

    CrossRef  Google Scholar 

  27. M.J. Kaminski, K.J. Blinowska, A new method of the description of the information flow in the brain structures. Biol. Cybern. 65, 203–210 (1991)

    CrossRef  Google Scholar 

  28. J. Kayser, C.E. Tenke, Principal components analysis of Laplacian waveforms as a generic method for identifying ERP generator patterns: II. Adequacy of low-density estimates. Clin. Neurophysiol. 117, 369–380 (2006). https://doi.org/10.1016/j.clinph.2005.08.033

    CrossRef  Google Scholar 

  29. S. Khan, A. Gramfort, N.R. Shetty et al., Local and long-range functional connectivity is reduced in concert in autism spectrum disorders. Proc. Natl. Acad. Sci. U S A. 110, 3107–3112 (2013). https://doi.org/10.1073/pnas.1214533110

    CrossRef  ADS  Google Scholar 

  30. J.-P. Lachaux, E. Rodriguez, J. Martinerie, F.J. Varela, Measuring phase synchrony in brain signals. Hum. Brain Mapp. 8, 194–208 (1999)

    CrossRef  Google Scholar 

  31. Y.-Y. Lee, S. Hsieh, Classifying different emotional states by means of EEG-based functional connectivity patterns. PLoS ONE 9, (2014). https://doi.org/10.1371/journal.pone.0095415

  32. L. Marzetti, C. Del Gratta, G. Nolte, Understanding brain connectivity from EEG data by identifying systems composed of interacting sources. Neuroimage 42, 87–98 (2008). https://doi.org/10.1016/j.neuroimage.2008.04.250

    CrossRef  Google Scholar 

  33. C.M. Michel, M.M. Murray, G. Lantz et al., EEG source imaging. Clin. Neurophysiol. 115, 2195–2222 (2004). https://doi.org/10.1016/j.clinph.2004.06.001

    CrossRef  Google Scholar 

  34. T. Mima, T. Matsuoka, M. Hallett, Functional coupling of human right and left cortical motor areas demonstrated with partial coherence analysis. Neurosci. Lett. 287, 93–96 (2000)

    CrossRef  Google Scholar 

  35. W. Mumtaz, S. Saad, A. Ali et al., A machine learning framework involving EEG-based functional connectivity to diagnose major depressive disorder (MDD). Med. Biol. Eng. Comput. (2017). https://doi.org/10.1007/s11517-017-1685-z

    CrossRef  Google Scholar 

  36. G. Nolte, O. Bai, L. Wheaton et al., Identifying true brain interaction from EEG data using the imaginary part of coherency. Clin. Neurophysiol. 115, 2292–2307 (2004). https://doi.org/10.1016/j.clinph.2004.04.029

    CrossRef  Google Scholar 

  37. G. Nolte, A. Ziehe, V.V. Nikulin et al., Robustly Estimating the Flow Direction of Information in Complex Physical Systems. (2007). https://doi.org/10.1103/physrevlett.100.234101

  38. P.L. Nunez, R. Srinivasan, A.F. Westdorp et al., EEG coherency I: statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales. Electroencephalogr. Clin. Neurophysiol. 103, 499–515 (1997)

    CrossRef  Google Scholar 

  39. S. Palva, J.M. Palva, The role of local and large-scale neuronal synchronization in human cognition, in Multimodal Oscillation-Based Connectivity Theory, ed. by S. Palva (Springer International Publishing Switzerland, 2016), pp. 51–67

    Google Scholar 

  40. R.D. Pascual-Marqui, Review of methods for solving the EEG inverse problem. Int. J. Bioelectromagn. Print Issue ISSN 1:75–86 (1999)

    Google Scholar 

  41. R.D. Pascual-Marqui, C.M. Michel, D. Lehmann, Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. Int. J. Psychophysiol. 18, 49–65 (1994)

    CrossRef  Google Scholar 

  42. E. Pereda, R. Quian Quiroga, J. Bhattacharya, Nonlinear multivariate analysis of neurophysiological signals. Prog. Neurobiol. 77, 1–37 (2005). https://doi.org/10.1016/j.pneurobio.2005.10.003

    CrossRef  Google Scholar 

  43. F. Perrin, J. Pernier, O. Bertrand, J.F. Echallier, Spherical splines for scalp potential and current density mapping. Electroencephalogr. Clin. Neurophysiol. 72, 184–187 (1989). https://doi.org/10.1016/0013-4694(89)90180-6

    CrossRef  Google Scholar 

  44. V. Sakkalis, Review of advanced techniques for the estimation of brain connectivity measured with EEG/MEG. Comput. Biol. Med. 41, 1110–1117 (2011). https://doi.org/10.1016/j.compbiomed.2011.06.020

    CrossRef  Google Scholar 

  45. P. Sauseng, W. Klimesch, W.R. Gruber, N. Birbaumer, Cross-frequency phase synchronization: a brain mechanism of memory matching and attention. Neuroimage 40, 308–317 (2008). https://doi.org/10.1016/j.neuroimage.2007.11.032

    CrossRef  Google Scholar 

  46. J.M. Schoffelen, J. Gross, Source connectivity analysis with MEG and EEG. Hum. Brain Mapp. 30, 1857–1865 (2009). https://doi.org/10.1002/hbm.20745

    CrossRef  Google Scholar 

  47. A.K. Seth, A.B. Barrett, L. Barnett, Toolbox granger causality analysis in neuroscience and neuroimaging. J. Neurosci. 35, 3293–3297 (2015). https://doi.org/10.1523/JNEUROSCI.4399-14.2015

    CrossRef  Google Scholar 

  48. C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948). https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

    CrossRef  MathSciNet  MATH  Google Scholar 

  49. M. Siegel, T.H. Donner, A.K. Engel, Spectral fingerprints of large-scale neuronal interactions. Nat. Rev. Neurosci. 13, 121–134 (2012). https://doi.org/10.1038/nrn3137

    CrossRef  Google Scholar 

  50. W. Singer, Synchronization of cortical activity and its putative role in information processing and learning. Annu. Rev. Physiol. 55, 349–374 (1993)

    CrossRef  Google Scholar 

  51. C.J. Stam, W. De Haan, A. Daffertshofer et al., Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer’s disease. Brain 132, 213–224 (2009). https://doi.org/10.1093/brain/awn262

    CrossRef  Google Scholar 

  52. C.J. Stam, G. Nolte, A. Daffertshofer, Phase lag index: assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources. Hum. Brain Mapp. 28, 1178–1193 (2007). https://doi.org/10.1002/hbm.20346

    CrossRef  Google Scholar 

  53. C.J. Stam, J.C. Reijneveld, Nonlinear biomedical physics graph theoretical analysis of complex networks in the brain. Nonlinear Biomed. Phys. 1, 1–19 (2007). https://doi.org/10.1186/1753-4631-1-3

    CrossRef  Google Scholar 

  54. J. Theilier, S. Eubank, A. Longtin et al., Testing for nonlinearity in time series: the method of surrogate data. Phys. D 58, (1992)

    Google Scholar 

  55. M.P. Van Den Heuvel, H.E. Hulshoff Pol, Exploring the brain network: a review on resting-state fMRI functional connectivity. Eur. Neuropsychopharmacol. 20, 519–534 (2010). https://doi.org/10.1016/j.euroneuro.2010.03.008

    CrossRef  Google Scholar 

  56. F. Varela, J.-P. Lachaux, E. Rodriguez, J. Martinerie, The brainweb: phase synchronization and large-scale integration. Nat. Rev. Neurosci. 2, 229–239 (2001)

    CrossRef  Google Scholar 

  57. F. Vecchio, F. Miraglia, C. Marra et al., Human brain networks in cognitive decline: a graph theoretical analysis of cortical connectivity from EEG data. J. Alzheimer’s Dis. 41, 113–127 (2014). https://doi.org/10.3233/JAD-132087

    CrossRef  Google Scholar 

  58. M. Vinck, R. Oostenveld, M. Van Wingerden et al., An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. Neuroimage 55, 1548–1565 (2011). https://doi.org/10.1016/j.neuroimage.2011.01.055

    CrossRef  Google Scholar 

  59. B. Voytek, M. D’esposito, N. Crone, R.T. Knight, A method for event-related phase/amplitude coupling. Neuroimage 64, 416–424 (2013). https://doi.org/10.1016/j.neuroimage.2012.09.023

    CrossRef  Google Scholar 

  60. L.M. Ward, Synchronous neural oscillations and cognitive processes. Trends Cogn. Sci. 7, 553–559 (2003). https://doi.org/10.1016/j.tics.2003.10.012

    CrossRef  Google Scholar 

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Choi, J.W., Kim, K.H. (2018). Methods for Functional Connectivity Analysis. In: Im, CH. (eds) Computational EEG Analysis. Biological and Medical Physics, Biomedical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-0908-3_6

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