Time-Varying Effective Connectivity for Investigating the Neurophysiological Basis of Cognitive Processes

  • Jlenia Toppi
  • Manuela Petti
  • Donatella Mattia
  • Fabio Babiloni
  • Laura Astolfi
Part of the Neuromethods book series (NM, volume 91)


This chapter describes the methodological advancements developed during the last 20 years in the field of effective connectivity based on Granger causality and linear autoregressive modeling. At first we introduce the concept of Granger causality and its application to the connectivity field. Then, a detailed description of both stationary and time-varying versions of Partial Directed Coherence (PDC) estimator for effective connectivity will be given. The General Linear Kalman Filter (GLKF) approach is described an algorithm, recently introduced for estimating the temporal evolution of the parameters of adaptive multivariate model, able to overcome the limits of existing time-varying approaches. Then a detailed description of the graph theory approach and of possible indexes which could be defined is given. At the end, the potentiality of the described methodologies is demonstrated in an application aiming at investigating the neurophysiological basis of motor imagery processes.


Electroencephalography (EEG) Effective connectivity Non-stationarity Graph theory Statistical assessment Multiple comparisons Motor imagery 



This work was partly supported by the European ICT Program FP7-ICT-2009-4 Grant Agreement 287320 CONTRAST and by the grant provided by the Minister of Foreign Affair, “Direzione Generale Sistema Paese”.


  1. 1.
    Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. J Econ 37(3):424–438Google Scholar
  2. 2.
    Wiener N (1956) The theory of prediction. In: Beckenbach EF (ed) Modern mathematics for engineers, vol 1. McGraw-Hill, New YorkGoogle Scholar
  3. 3.
    Horwitz B (2003) The elusive concept of brain connectivity. Neuroimage 19(2):466–470PubMedCrossRefGoogle Scholar
  4. 4.
    Lee L, Harrison LM, Mechelli A (2003) A report of the functional connectivity workshop. Neuroimage 19(2):457–465PubMedCrossRefGoogle Scholar
  5. 5.
    Aertsen A, Preissl H (1991) Dynamics of activity and connectivity in physiological neuronal networks. In: Schuster HG (ed) Non linear dynamics and neuronal networks. VCH, New York, NY, 281–302 pGoogle Scholar
  6. 6.
    Blinowska KJ, Kaminski M, Kaminski J, Brzezicka A (2010) Information processing in brain and dynamic patterns of transmission during working memory task by the SDTF function. Conf Proc IEEE Eng Med Biol Soc 2010:1722–1725PubMedGoogle Scholar
  7. 7.
    Sameshima K, Baccalá LA (1999) Using partial directed coherence to describe neuronal ensemble interactions. J Neurosci Methods 94(1):93–103PubMedCrossRefGoogle Scholar
  8. 8.
    Kaminski MJ, Blinowska KJ (1991) A new method of the description of the information flow in the brain structures. Biol Cybern 65(3):203–210PubMedCrossRefGoogle Scholar
  9. 9.
    Turbes CC, Schneider GT, Morgan RJ (1983) Partial coherence estimates of brain rhythms. Biomed Sci Instrum 19:97–102PubMedGoogle Scholar
  10. 10.
    Baccalá LA, Sameshima K (2001) Partial directed coherence: a new concept in neural structure determination. Biol Cybern 84:463–474PubMedCrossRefGoogle Scholar
  11. 11.
    Kus R, Kaminski M, Blinowska KJ (2004) Determination of EEG activity propagation: pair-wise versus multichannel estimate. IEEE Trans Biomed Eng 51(9):1501–1510PubMedCrossRefGoogle Scholar
  12. 12.
    Blinowska KJ, Kuś R, Kamiński M (2004) Granger causality and information flow in multivariate processes. Phys Rev E Stat Nonlin Soft Matter Phys 70(5 Pt 1):050902PubMedCrossRefGoogle Scholar
  13. 13.
    David O, Cosmelli D, Friston KJ (2004) Evaluation of different measures of functional connectivity using a neural mass model. Neuroimage 21(2):659–673PubMedCrossRefGoogle Scholar
  14. 14.
    Astolfi L, Cincotti F, Mattia D, Marciani MG, Baccala LA, de Vico Fallani F et al (2007) Comparison of different cortical connectivity estimators for high-resolution EEG recordings. Hum Brain Mapp 28(2):143–157PubMedCrossRefGoogle Scholar
  15. 15.
    Blinowska KJ (2011) Review of the methods of determination of directed connectivity from multichannel data. Med Biol Eng Comput 49(5):521–529PubMedCentralPubMedCrossRefGoogle Scholar
  16. 16.
    Ding M, Bressler SL, Yang W, Liang H (2000) Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment. Biol Cybern 83(1):35–45PubMedCrossRefGoogle Scholar
  17. 17.
    Astolfi L, Cincotti F, Mattia D, De Vico Fallani F, Tocci A, Colosimo A et al (2008) Tracking the time-varying cortical connectivity patterns by adaptive multivariate estimators. IEEE Trans Biomed Eng 55(3):902–913PubMedCrossRefGoogle Scholar
  18. 18.
    Möller E, Schack B, Arnold M, Witte H (2001) Instantaneous multivariate EEG coherence analysis by means of adaptive high-dimensional autoregressive models. J Neurosci Methods 105(2):143–158PubMedCrossRefGoogle Scholar
  19. 19.
    Milde T, Leistritz L, Astolfi L, Miltner WHR, Weiss T, Babiloni F et al (2010) A new Kalman filter approach for the estimation of high-dimensional time-variant multivariate AR models and its application in analysis of laser-evoked brain potentials. Neuroimage 50(3):960–969PubMedCrossRefGoogle Scholar
  20. 20.
    Weiss T, Hesse W, Ungureanu M, Hecht H, Leistritz L, Witte H et al (2008) How do brain areas communicate during the processing of noxious stimuli? An analysis of laser-evoked event-related potentials using the Granger causality index. J Neurophysiol 99(5):2220–2231PubMedCrossRefGoogle Scholar
  21. 21.
    Zhu C, Guo X, Jin Z, Sun J, Qiu Y, Zhu Y et al (2011) Influences of brain development and ageing on cortical interactive networks. Clin Neurophysiol 122(2):278–283PubMedCrossRefGoogle Scholar
  22. 22.
    Toppi J, Babiloni F, Vecchiato G, De Vico Fallani F, Mattia D, Salinari S et al (2012) Towards the time varying estimation of complex brain connectivity networks by means of a general linear Kalman filter approach. Conf Proc IEEE Eng Med Biol Soc 2012:6192–6195PubMedGoogle Scholar
  23. 23.
    Akaike H (1974) A new look at statistical model identification. IEEE Trans Autom Control 19:716–723CrossRefGoogle Scholar
  24. 24.
    Baccalá LA (2001) On the efficient computation of partial coherence from multivariate autoregressive model. Biol Cybern 84:463–474PubMedCrossRefGoogle Scholar
  25. 25.
    Astolfi L, Cincotti F, Mattia D, Marciani MG, Baccalà LA, de Vico Fallani F et al (2006) Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data. IEEE Trans Biomed Eng 53(9):1802–1812PubMedCrossRefGoogle Scholar
  26. 26.
    Nichols T, Hayasaka S (2003) Controlling the familywise error rate in functional neuroimaging: a comparative review. Stat Methods Med Res 12(5):419–446PubMedCrossRefGoogle Scholar
  27. 27.
    Bonferroni C (1936) Teoria statistica delle classi e calcolo delle probabilità, vol 8. Libreria Internazionale Seeber, FlorenceGoogle Scholar
  28. 28.
    Zar JH (2010) Biostatistical analysis. Prentice Hall, Upper Saddle River, 964 pGoogle Scholar
  29. 29.
    Toppi J, Babiloni F, Vecchiato G, Cincotti F, De Vico Fallani F, Mattia D et al (2011) Testing the asymptotic statistic for the assessment of the significance of partial directed coherence connectivity patterns. Conf Proc IEEE Eng Med Biol Soc 2011:5016–5019PubMedGoogle Scholar
  30. 30.
    Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc 57(1):289–300Google Scholar
  31. 31.
    Benjamini Y, Yekutieli D (2001) The control of the false discovery rate in multiple testing under dependency. Ann Stat 29(4):1165–1188CrossRefGoogle Scholar
  32. 32.
    Toppi J, De Vico Fallani F, Vecchiato G, Maglione AG, Cincotti F, Mattia D et al (2012) How the statistical validation of functional connectivity patterns can prevent erroneous definition of small-world properties of a brain connectivity network. Comput Math Methods Med 2012:130985PubMedCentralPubMedCrossRefGoogle Scholar
  33. 33.
    Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 87(19):198701PubMedCrossRefGoogle Scholar
  34. 34.
    Sporns O, Chialvo DR, Kaiser M, Hilgetag CC (2004) Organization, development and function of complex brain networks. Trends Cogn Sci 8(9):418–425PubMedCrossRefGoogle Scholar
  35. 35.
    Watts DJ, Strogatz SH (1998) Collective dynamics of “small-world” networks. Nature 393(6684):440–442PubMedCrossRefGoogle Scholar
  36. 36.
    Fagiolo G (2007) Clustering in complex directed networks. Phys Rev E Stat Nonlin Soft Matter Phys 76(2 Pt 2):026107PubMedCrossRefGoogle Scholar
  37. 37.
    Humphries MD, Gurney K (2008) Network “small-world-ness”: a quantitative method for determining canonical network equivalence. PLoS ONE 3(4):e0002051PubMedCrossRefGoogle Scholar
  38. 38.
    Toppi J, Petti M, De Vico Fallani F, Vecchiato G, Maglione AG, Cincotti F et al (2012) Describing relevant indices from the resting state electrophysiological networks. Conf Proc IEEE Eng Med Biol Soc 2012:2547–2550PubMedGoogle Scholar
  39. 39.
    Hoffmann S, Falkenstein M (2008) The correction of eye blink artefacts in the EEG: a comparison of two prominent methods. PLoS ONE 3(8):e3004PubMedCentralPubMedCrossRefGoogle Scholar
  40. 40.
    Klimesch W (1999) EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis. Brain Res Brain Res Rev 29(2–3):169–195PubMedCrossRefGoogle Scholar
  41. 41.
    De Vico Fallani F, Astolfi L, Cincotti F, Mattia D, Tocci A, Salinari S et al (2008) Brain network analysis from high-resolution EEG recordings by the application of theoretical graph indexes. IEEE Trans Neural Syst Rehabil Eng 16(5):442–452PubMedCrossRefGoogle Scholar
  42. 42.
    Takahashi DY, Baccalà LA, Sameshima K (2007) Connectivity inference between neural structures via partial directed coherence. J Appl Stat 34(10):1259–1273CrossRefGoogle Scholar
  43. 43.
    Pfurtscheller G, Aranibar A (1979) Evaluation of event-related desynchronization (ERD) preceding and following voluntary self-paced movement. Electroencephalogr Clin Neurophysiol 46(2):138–146PubMedCrossRefGoogle Scholar
  44. 44.
    Pfurtscheller G, Berghold A (1989) Patterns of cortical activation during planning of voluntary movement. Electroencephalogr Clin Neurophysiol 72(3):250–258PubMedCrossRefGoogle Scholar
  45. 45.
    Pfurtscheller G, Lopes da Silva FH (1999) Event-related EEG/MEG synchronization and desynchronization: basic principles. Clin Neurophysiol 110(11):1842–1857PubMedCrossRefGoogle Scholar
  46. 46.
    Porro CA, Francescato MP, Cettolo V, Diamond ME, Baraldi P, Zuiani C et al (1996) Primary motor and sensory cortex activation during motor performance and motor imagery: a functional magnetic resonance imaging study. J Neurosci 16(23):7688–7698PubMedGoogle Scholar
  47. 47.
    Schnitzler A, Salenius S, Salmelin R, Jousmäki V, Hari R (1997) Involvement of primary motor cortex in motor imagery: a neuromagnetic study. Neuroimage 6(3):201–208PubMedCrossRefGoogle Scholar
  48. 48.
    Crone NE, Miglioretti DL, Gordon B, Sieracki JM, Wilson MT, Uematsu S et al (1998) Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. I. Alpha and beta event-related desynchronization. Brain 121(Pt 12):2271–2299PubMedCrossRefGoogle Scholar
  49. 49.
    Cochin S, Barthelemy C, Roux S, Martineau J (1999) Observation and execution of movement: similarities demonstrated by quantified electroencephalography. Eur J Neurosci 11(5):1839–1842PubMedCrossRefGoogle Scholar
  50. 50.
    Jeannerod M, Frak V (1999) Mental imaging of motor activity in humans. Curr Opin Neurobiol 9(6):735–739PubMedCrossRefGoogle Scholar
  51. 51.
    Miller KJ, Schalk G, Fetz EE, den Nijs M, Ojemann JG, Rao RPN (2010) Cortical activity during motor execution, motor imagery, and imagery-based online feedback. Proc Natl Acad Sci U S A 107(9):4430–4435PubMedCentralPubMedCrossRefGoogle Scholar
  52. 52.
    Zapparoli L, Invernizzi P, Gandola M, Verardi M, Berlingeri M, Sberna M et al (2012) Mental images across the adult lifespan: a behavioural and fMRI investigation of motor execution and motor imagery. Exp Brain Res 224(4):519–540PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jlenia Toppi
    • 1
    • 2
  • Manuela Petti
    • 1
    • 2
  • Donatella Mattia
    • 2
  • Fabio Babiloni
    • 3
  • Laura Astolfi
    • 1
    • 2
  1. 1.Department of Computer, Control, and Management Engineering Antonio RubertiSapienza UniversityRomeItaly
  2. 2.Neuroelectrical Imaging and BCI LabIRCCS Fondazione Santa LuciaRomeItaly
  3. 3.Department of Physiology and PharmacologySapienza UniversityRomeItaly

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