Applications of Granger Causality Model to Connectivity Network Based on fMRI Time Series

  • Xiao-Tong Wen
  • Xiao-Jie Zhao
  • Li Yao
  • Xia Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4221)


The connectivity network with direction of brain is a significant work to reveal interaction and coordination between different brain areas. Because Granger causality model can explore causal relationship between time series, the direction of the network can be specified when the model is applied to connectivity network of brain. Although the model has been used in EEG time sires more and more, it was seldom used in fMRI time series because of lower time resolution of fMRI time series. In this paper, we introduced a pre-processing method to fMRI time series in order to alleviate the magnetic disturbance, and then expand the time series to fit the requirement of time-variant algorism. We applied recursive least square (RLS) algorithm to estimate time-variant parameters of Granger model, and introduced a time-variant index to describe the directional connectivity network in a typical finger tapping fMRI experiment. The results showed there were strong directional connectivity between the activated motor areas and gave a possibility to explain them.


Connectivity Network Granger Causality Surrogate Data Recursive Less Square Recursive Less Square Algorithm 
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  1. 1.
    Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969)CrossRefGoogle Scholar
  2. 2.
    Kaminski, M.J., Ding, M., Truccolo, W.A., Bressler, S.L.: Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol. Cybern. 85, 145–157 (2001)MATHCrossRefGoogle Scholar
  3. 3.
    Goebel, R., Roebroeck, A., Kim, D.S., Formisano, E.: Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn. Reson. Imaging 21, 1251–1261 (2003)CrossRefGoogle Scholar
  4. 4.
    Moller, E., Schack, B., Arnold, M., Witte, H.: Instantaneous multivariate EEG coherence analysis by means of adaptive high-dimensional autoregressive models. J. Neurosci. Methods 105, 143–158 (2001)CrossRefGoogle Scholar
  5. 5.
    Ding, M., Bressler, S.L., Yang, W., Liang, H.: Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modelling: data preprocessing, model validation, and variability assessment. Biol. Cybern. 83, 35–45 (2000)MATHCrossRefGoogle Scholar
  6. 6.
    van de Ven, V.G., Formisano, E., Prvulovic, D., et al.: Functional Connectivity as Revealed by Spatial Independent Component Analysis of fMRI Measurements During Rest. Hum. Brain Mapp. 22, 165–178 (2004)CrossRefGoogle Scholar
  7. 7.
    Astolfi, L., Cincotti, F., Mattia, D., et al.: Estimation of the effective and functional human cortical connectivity with structural quation modeling and directed transfer function applied to high-resolution EEG. Magn. Reson. Imaging 22, 1457–1470 (2004)CrossRefGoogle Scholar
  8. 8.
    Geweke, J.: Measurement of linear dependence and feedback between multiple time series. J. Amer. Statist. Assoc. 77, 304–324 (1982)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods, pp. 417–420. Springer, New York (1987)MATHGoogle Scholar
  10. 10.
    Haykin, S.: Adaptive Filter Theory, pp. 381–407. Prentice-Hall, Englewood Cliffs (1986)Google Scholar
  11. 11.
    Theiler, J., Eubank, Longtin, S.J., Galdrikian, B., Farmer, J.D.: Testing for nonlinearity in time series: The method of surrogate data. Phys. D 58, 77–94 (1992)CrossRefMATHGoogle Scholar
  12. 12.
    Wiley, J.: Programs for Digital Signal Processing. IEEE Press, New York (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiao-Tong Wen
    • 2
  • Xiao-Jie Zhao
    • 1
    • 2
  • Li Yao
    • 1
    • 2
  • Xia Wu
    • 2
  1. 1.School of Information Science and TechnologyBeijing Normal UniversityBeijingChina
  2. 2.State Key Laboratory of Cognitive Neuroscience and LearningBeijing Normal UniversityBeijingChina

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