Using granger-geweke causality model to evaluate the effective connectivity of primary motor cortex, supplementary motor area and cerebellum

Le Zhang, Guangjin Zhong, Yukun Wu, Mark G. Vangel, Beini Jiang, Jian Kong

.

DOI: 10.4236/jbise.2010.39115                

Abstract

Currently, Granger-Geweke causality models have been widely applied to investigate the dynamic direction relationships among brain regions. In a previous study, we have found that the right hand finger-tapping task can produce relatively reliable brain response. As an extension of our previous study, we developed an algorithm based on the classical Granger- Geweke causality model to further investigate the effective connectivity of three brain regions (left primary motor cortex (M1), supplementary motor area (SMA) and right cerebellum) that showed the most robust brain activations. Our computational results not only confirm the strong linear feedback among SMA, M1 and right cerebellum, but also demonstrate that M1 is the hub of these three regions indicated by the anatomy research. Moreover, the model predicts the high intermediate node density existing in the area between SMA and M1, which will stimulate the imaging experimentalists to carry out new experiments to validate this postulation.

Keywords

Granger-Geweke Causality Model; Time Series; Computational Neuroscience; fMRI; Finger-tapping; Hand Movement; Math Modeling

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Astolfi, L., Cincotti, F., Mattia, D., Salinari, S., Babiloni, C. and Basilisco, A., et al. (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), 1457-1470.
[2]	Brovelli, A., Ding, M.Z., Ledberg, A., Chen, Y.H., Nakamura, R. and Bressler, S.L. (2004) Beta oscillations in a large- scale sensorimotor cortical network: Directional influences revealed by Granger causality. Proceedings of the National Academy of Sciences of the United States of America, 101(26), 9849-9854.
[3]	Eichler, M. (2005) A graphical approach for evaluating effective connectivity in neural systems. Philos Trans R Soc Lond B Biol Sci, 360(1457), 953-967.
[4]	Sato, J.R., Amaro, E.D. Takahashi, Y., Felix, M.D., Brammer, M.J. and Morettin, P.A. (2006) A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality. Neuroimage, 31(1), 187- 196.
[5]	Smith, J.F., Pillai, A., Chen, K. and Horwitz, B. (2009) Identification and validation of effective connectivity ne- tworks in functional magnetic resonance imaging using switching linear dynamic systems. Neuroimage, 52(3), 1027-1040.
[6]	Chen, H.F., Yang, Q., Liao, W., Gong, Q. Y. and Shen, S. (2009) Evaluation of the effective connectivity of supple- mentary motor areas during motor imagery using Gra- nger causality mapping. Neuroimage, 47(4), 1844-1853.
[7]	Geweke, J. (1982) The measurement of Linear dependence and feedback between multiple Time-Series rejoinder. Journal of the American Statistical Association, 77 (378), 323-324.
[8]	Gow, Jr, D.W., Segawa, J.A., Ahlfors, S.P. and Lin, F.H. (2008) Lexical influences on speech perception: A Granger causality analysis of MEG and EEG source estimates. Neuroimage, 43(3), 614-623.
[9]	Liao, W., Mantini, D., Zhang, Z., Pan, Z., Ding J. and Gong, Q. et al. (2010) Evaluating the effective connectivity of resting state networks using conditional Granger causality. Biological. Cybernetics, 102(1), 57-69.
[10]	Liao, W., Marinazzo, D., Pan, Z., Gong, Q. and Chen, H. Kernel Granger causality mapping effective connectivity on FMRI data. IEEE Trans Med Imaging, 28(11), 1825- 1835.
[11]	Lin, F.H., Hara, K., Solo, V., Vangel, M., Belliveau, J.W. and Stufflebeam, S.M., et al. (2009) Dynamic Granger- Geweke Causality Modeling With Application to Interictal Spike Propagation. Human Brain Mapping, 30(6), 1877-1886.
[12]	Marinazzo, D., Liao, W., Chen, H. and Stramaglia, S. (2010) Nonlinear connectivity by Granger causality. Ne- uroimage.
[13]	Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994) Time series analysis: Forecasting and control, Prentice Hall, New Jersey.
[14]	Chatfield, C. (2001) Time-series forecasting. Chapman & Hall/CRC.
[15]	Londei, A., D’Ausilio, A., Basso, D. and Belardinelli, M. O. (2006) A new method for detecting causality in fMRI data of cognitive processing. Cogn Process, 7(1), 42-52.
[16]	Nedungadi, A.G., Rangarajan, G., Jain, N. and Ding, M. Z. (2009) Analyzing multiple spike trains with nonparametric granger causality. Journal of Computational Neu- roscience, 27(1), 55-64.
[17]	Roebroeck, A., Formisano, E. and Goebel, R. (2005) Ma- pping directed influence over the brain using Granger causality and fMRI. Neuroimage, 25(1), 230-242.
[18]	Zhang, Y., Chen, Y., Bressler, S.L. and Ding, M. (2008) Response preparation and inhibition: The role of the cortical sensorimotor beta rhythm. Neuroscience, 156(1), 238-246.
[19]	Kong, J., Gollub, R.L., Webb, J.M., Kong, J.T., Vangel, M.G. and Kwong, K. (2007) Test-retest study of fMRI signal change evoked by electroacupuncture stimulation. Neuroimage, 34(3), 1171-1181.
[20]	Greene, W.H., (2003) Econometric analysis. Prentice Ha- ll, New Jersey.
[21]	Yaffee, R.A. and McGee, M. (2000) Introduction to time series analysis and forecasting: With applications in SAS and SPSS. Academic Press,USA.
[22]	Dickey, D.A. and Fuller, W.A. (1979) Distribution of the Estimators for Autoregressive Time-Series with a Unit Root. Journal of the American Statistical Association, 74(366), 427-431.
[23]	Neumaier, A. and Schneider, T. (2001) Estimation of parameters and eigenmodes of multivariate autoregressive models. Acm Transactions on Mathematical Software, 27(1), 27-57.
[24]	Notle, J. (1999) The Human Brain: An Introduction to its functional anatomy. Mosby Inc., Louis.
[25]	Friston, K.J., Ashburner, J.T., Kiebel, S.J., Nichols, T.E. and Penny, W.D. (2007) Statistical parametric mapping. Elsevier. Academic Press, USA.
[26]	Priestley, M.B. (1981) Spectral analysis and time series. Academic Press, USA.
[27]	Priestley, M.B. (1988) Non-linear and non-stationary time series analysis. Academic, USA.
[28]	Wei, W. (2006) Time Series Analysis. Perrson Education, inc., Chichester.
[29]	Pearl, J. (2000) Causality: Models, reasoning, and inference. Cambridge University Press, UK.
[30]	Brooks, C. (2008) Introductory econometrics for finance. Cambridge University Press, UK.
[31]	Baum, C.F. (2006) An introduction to modern econometrics using Stata. Stata Press, Texas.
[32]	Warner, R.M. (1998) Spectral analysis of time-series data. Guilford Press, New York.
[33]	Mills, T.C. (1990) Time series techniques for economists, Cambridge University Press, UK.
[34]	Clements, P. and Hendry, D.F. (1999) Forecasting non- stationary economic time series. MIT Press, Cambridge.
[35]	Storch, H.V. and Zwiers, F.W. (1999) Statistical analysis in climate research. Cambridge University Press, UK.
[36]	Kirchg?ssner, G. and Wolters, J. (2007) Introduction to modern time series analysis. Springer, New York.
[37]	Hochberg, Y. (1988) A Sharper Bonferroni Procedure for Multiple Tests of Significance. Biometrika, 75(4), 800- 802.