Quantifying the Effect of Demixing Approaches on Directed Connectivity Estimated Between Reconstructed EEG Sources

  • Alessandra Anzolin
  • Paolo Presti
  • Frederik Van De Steen
  • Laura Astolfi
  • Stefan Haufe
  • Daniele MarinazzoEmail author
Original Paper


Electrical activity recorded on the scalp using electroencephalography (EEG) results from the mixing of signals originating from different regions of the brain as well as from artifactual sources. In order to investigate the role of distinct brain areas in a given experiment, the signal recorded on the sensors is typically projected back into the brain (source reconstruction) using algorithms that address the so-called EEG “inverse problem”. Once the activity of sources located inside of the brain has been reconstructed, it is often desirable to study the statistical dependencies among them, in particular to quantify directional dynamical interactions between brain areas. Unfortunately, even when performing source reconstruction, the superposition of signals that is due to the propagation of activity from sources to sensors cannot be completely undone, resulting in potentially biased estimates of directional functional connectivity. Here we perform a set of simulations involving interacting sources to quantify source connectivity estimation performance as a function of the location of the sources, their distance to each other, the noise level, the source reconstruction algorithm, and the connectivity estimator. The generated source activity was projected onto the scalp and projected back to the cortical level using two source reconstruction algorithms, linearly constrained minimum variance beamforming and ‘Exact’ low-resolution tomography (eLORETA). In source space, directed connectivity was estimated using multi-variate Granger causality and time-reversed Granger causality, and compared with the imposed ground truth. Our results demonstrate that all considered factors significantly affect the connectivity estimation performance.


Brain connectivity Source reconstruction Granger causality Modelling 


Supplementary material

10548_2019_705_MOESM1_ESM.docx (10.3 mb)
Supplementary material 1 (DOCX 10545 KB)


  1. Astolfi L, Cincotti F, Mattia D, Salinari S, Babiloni C, Basilisco A, Rossini PM, Ding L, Ni Y, He B, Marciani MG, Babiloni F (2004) Estimation of the effective and functional human cortical connectivity with structural equation modeling and directed transfer function applied to high-resolution EEG. Magn Reson Imaging 22(10):1457–1470CrossRefGoogle Scholar
  2. Babiloni F, Cincotti F, Babiloni C, Carducci F, Mattia D, Astolfi L, Basilisco A, Rossini PM, Ding L, Ni Y, Cheng J, Christine K, Sweeney J, He B (2005) Estimation of the cortical functional connectivity with the multimodal integration of high-resolution EEG and fMRI data by directed transfer function. NeuroImage 24(1):118–131CrossRefGoogle Scholar
  3. Barnett L, Seth AK (2014) The MVGC multivariate granger causality toolbox: a new approach to granger-causal inference. J Neurosci Methods 223:50–68CrossRefGoogle Scholar
  4. Bell JB (1978) Review of solutions of Ill-posed problems. Math Comput 32(144):1320–1322CrossRefGoogle Scholar
  5. Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57(1):289–300Google Scholar
  6. Biscay RJ, Bosch-Bayard JF, Pascual-Marqui RD (2018) Unmixing EEG inverse solutions based on brain segmentation. Front Neurosci 12:325CrossRefGoogle Scholar
  7. Blinowska KJ (2011) Review of the methods of determination of directed connectivity from multichannel data. Med Biol Eng Comput 49(5):521–529CrossRefGoogle Scholar
  8. Brookes MJ, Woolrich MW, Barnes GR (2012) Measuring functional connectivity in MEG: a multivariate approach insensitive to linear source leakage. NeuroImage 63(2):910–920CrossRefGoogle Scholar
  9. Brunner C, Billinger M, Seeber M, Mullen TR, Makeig S (2016) Volume conduction influences scalp-based connectivity estimates. Front Comput Neurosci 10:121CrossRefGoogle Scholar
  10. Cheung BLP, Riedner BA, Tononi G, Van Veen BD (2010) Estimation of cortical connectivity from EEG using state-space models. IEEE Trans Biomed Eng 57(9):2122–2134CrossRefGoogle Scholar
  11. Colclough GL, Brookes MJ, Smith SM, Woolrich MW (2015) A symmetric multivariate leakage correction for MEG connectomes. NeuroImage 117:439–448CrossRefGoogle Scholar
  12. de Steen FD, Faes L, Karahan E, Songsiri J, Valdes-Sosa PA, Marinazzo D (2016) Critical comments on EEG sensor space dynamical connectivity analysis. Brain Topogr. Google Scholar
  13. Faes L, Stramaglia S, Marinazzo D (2017) On the interpretability and computational reliability of frequency-domain Granger causality. F1000Research 6:1710CrossRefGoogle Scholar
  14. Farahibozorg S-R, Henson RN, Hauk O (2018) Adaptive cortical parcellations for source reconstructed EEG/MEG connectomes. NeuroImage 169:23–45CrossRefGoogle Scholar
  15. Fonov V, Evans AC, Botteron K, Almli CR, McKinstry RC, Collins DL (2011) Unbiased average age-appropriate atlases for pediatric studies. NeuroImage 54(1):313–327CrossRefGoogle Scholar
  16. Friston KJ (1994) Functional and effective connectivity in neuroimaging: a synthesis. Hum Brain Mapp 2(1–2):56–78CrossRefGoogle Scholar
  17. Geweke JF (1984) Measures of conditional linear dependence and feedback between time series. J Am Stat Assoc 79(388):907–915CrossRefGoogle Scholar
  18. Gómez-Herrero G, Atienza M, Egiazarian K, Cantero JL (2008) Measuring directional coupling between EEG sources. NeuroImage 43(3):497–508CrossRefGoogle Scholar
  19. Gonzalez-Moreira E. Paz-Linares D, Martinez-Montes E, Valdes-Hernandez P, Bosch-Bayard J, Bringas-Vega ML, Valdes-Sosa P (2018) Populational super-resolution sparse M/EEG sources and connectivity estimation. bioRxiv. Google Scholar
  20. Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37(3):424–438CrossRefGoogle Scholar
  21. Grech R, Cassar T, Muscat J, Camilleri KP, Fabri SG, Zervakis M, Xanthopoulos P, Sakkalis V, Vanrumste B (2008) Review on solving the inverse problem in EEG source analysis. J Neuroeng Rehabil 5:25CrossRefGoogle Scholar
  22. Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143(1):29–36CrossRefGoogle Scholar
  23. Haufe S, Ewald A (2016) A simulation framework for benchmarking EEG-based brain connectivity estimation methodologies. Brain Topogr. Google Scholar
  24. Haufe S, Tomioka R, Nolte G, Müller KR, Kawanabe M (2010) Modeling sparse connectivity between underlying brain sources for EEG/MEG. IEEE Trans Biomed Eng 57(8):1954–1963CrossRefGoogle Scholar
  25. Haufe S, Nikulin VV, Nolte G (2012) Alleviating the influence of weak data asymmetries on granger-causal analyses. In: Theis F, Cichocki A, Yeredor A, Zibulevsky M (eds) Latent variable analysis and signal separation. Springer, Berlin, pp 25–33CrossRefGoogle Scholar
  26. Haufe S, Nikulin VV, Müller KR, Nolte G (2013) A critical assessment of connectivity measures for EEG data: a simulation study. NeuroImage 64:120–133CrossRefGoogle Scholar
  27. Hedrich T, Pellegrino G, Kobayashi E, Lina JM, Grova C (2017) Comparison of the spatial resolution of source imaging techniques in high-density EEG and MEG. NeuroImage 157:531–544CrossRefGoogle Scholar
  28. Hipp JF, Hawellek DJ, Corbetta M, Siegel M, Engel AK (2012) Large-scale cortical correlation structure of spontaneous oscillatory activity. Nat Neurosci 15(6):884–890CrossRefGoogle Scholar
  29. Horwitz B (2003) The elusive concept of brain connectivity. NeuroImage 19(2):466–470CrossRefGoogle Scholar
  30. Huang Y, Parra LC, Haufe S (2016) The New York Head—A precise standardized volume conductor model for EEG source localization and tES targeting. NeuroImage 140:150–162CrossRefGoogle Scholar
  31. Lachaux JP, Rodriguez E, Martinerie J, Varela FJ (1999) Measuring phase synchrony in brain signals. Hum Brain Mapp 8(4):194–208CrossRefGoogle Scholar
  32. Mahjoory K, Nikulin VV, Botrel L, Linkenkaer-Hansen K, Fato MM, Haufe S (2017) Consistency of EEG source localization and connectivity estimates. NeuroImage 152:590–601CrossRefGoogle Scholar
  33. Nolte G, Bai O, Wheaton L, Mari Z, Vorbach S, Hallett M (2004) Identifying true brain interaction from EEG data using the imaginary part of coherency. Clin Neurophysiol 115(10):2292–2307CrossRefGoogle Scholar
  34. Nolte G, Ziehe A, Nikulin VV, Schlögl A, Krämer N, Brismar T, Müller KR (2008) Robustly estimating the flow direction of information in complex physical systems. Phys Rev Lett 100(23):234101CrossRefGoogle Scholar
  35. Nolte G, Ziehe A, Krämer N, Popescu F, Müller K-R (2010) Comparison of granger causality and phase slope index. In: Proceedings of workshop on causality: objectives and assessment at NIPS 2008. PMLR 6:267–276Google Scholar
  36. Nunez PL, Srinivasan R (2006) Electric fields of the brain: the Neurophysics of EEG. Oxford University Press, OxfordCrossRefGoogle Scholar
  37. Nunez PL, Srinivasan R, Westdorp AF, Wijesinghe RS, Tucker DM, Silberstein RB, Cadusch PJ (1997) EEG coherency: I: statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales. Electroencephalogr Clin Neurophysiol 103(5):499–515CrossRefGoogle Scholar
  38. Palva JM, Wang SH, Palva S, Zhigalov A, Monto S, Brookes MJ, Schoffelen JM, Jerbi K (2018) Ghost interactions in MEG/EEG source space: a note of caution on inter-areal coupling measures. NeuroImage 173:632–643CrossRefGoogle Scholar
  39. Pascual-Marqui RD (2007) Discrete, 3D distributed, linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization. ArXiv07103341 Math-Ph Physicsphysics Q-Bio, Oct. 2007Google Scholar
  40. Pascual-Marqui RD et al (2011) Assessing interactions in the brain with exact low-resolution electromagnetic tomography. Philos Transact A 369(1952):3768–3784CrossRefGoogle Scholar
  41. Pascual-Marqui R, Biscay RJ, Bosch-Bayard J, Faber PL, Kinoshita T, Kochi K, Milz P, Nishida K, Yoshimura M (2017) Innovations orthogonalization: a solution to the major pitfalls of EEG/MEG ‘leakage correction. bioRxiv. Google Scholar
  42. Tikhonov AN, Arsenin VI (1977) Solutions of ill-posed problems. Winston, New YorkGoogle Scholar
  43. van Veen BD, van Drongelen W, Yuchtman M, Suzuki A (1997) Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 44(9):867–880CrossRefGoogle Scholar
  44. Vinck M, Oostenveld R, van Wingerden M, Battaglia F, Pennartz CMA (2011) An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. NeuroImage 55(4):1548–1565CrossRefGoogle Scholar
  45. Vinck M, Huurdeman L, Bosman CA, Fries P, Battaglia FP, Pennartz CM, Tiesinga PH (2015) How to detect the Granger-causal flow direction in the presence of additive noise? NeuroImage 108(Supplement C):301–318CrossRefGoogle Scholar
  46. Wang SH, Lobier M, Siebenhuhner F, Puolivali T, Palva S, Palva JM (2017) Hyperedge bundling: a practical solution to spurious interactions in MEG/EEG source connectivity analyses. NeuroImage 173:610–622CrossRefGoogle Scholar
  47. Whittingstall K, Stroink G, Gates L, Connolly J, Finley A (2003) Effects of dipole position, orientation and noise on the accuracy of EEG source localization. Biomed Eng Online 2:14CrossRefGoogle Scholar
  48. Wilks SS (1938) The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann Math Stat 9(1):60–62CrossRefGoogle Scholar
  49. Winkler I, Panknin D, Bartz D, Müller KR, Haufe S (2016) Validity of time reversal for testing granger causality. IEEE Trans Signal Process 64(11):2746–2760CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer, Control and Management EngineeringSapienza University of RomeRomeItaly
  2. 2.Neuroelectrical Imaging and Brain-Computer Interface LaboratoryFondazione Santa Lucia IRCCSRomeItaly
  3. 3.Department of Data Analysis, Faculty of Psychology and Educational SciencesUniversity of GhentGhentBelgium
  4. 4.Institute of Software Engineering and Theoretical Computer ScienceTechnische Universität BerlinBerlinGermany
  5. 5.MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science InstituteUniversity of Electronic Science and Technology of ChinaChengduChina

Personalised recommendations