Document Type : Full Research Paper


1 PHD Candidate of Biomedical Engineering Group, The Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, College of Engineering, University of Tehran

2 Associate Professor of Biomedical Engineering Group, The Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, College of Engineering, University of Tehran. School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM),



Exploring the causal (delayed) brain relations is an important topic in the Neuroscience. The traditional estimators of brain causal (delayed) relations are mainly model-based and put restrictive assumptions on the brain dynamics. In the recent years, some nonparametric measures have been introduced to solve this problem. Among them, the most important one is Transfer Entropy (TE) which is based on the information theory and Conditional Mutual Information concept. However, in the presence of significant instantaneous relations that are observed extensively in the brain functional datasets, TE may estimate the causal (delayed) relations inaccurately. In this paper, two information theoretic based measures called Instantaneous Interaction (II) and Modified Transfer entropy (MTE) are introduced to estimate the instantaneous and causal (delayed) brain relations, respectively. MTE is used instead of TE whenever II is significant. These measures are evaluated on 3 simulated models and eyes-closed resting state EEG data. The simulation results show high ability of II to estimate the linear and nonlinear instantaneous relations. Also, based on the simulation results MTE outperforms TE to estimate causal (delayed) relations in presence of significant instantaneous relations (significant II). For the real EEG data, II detects a significant instantaneous relation between Posterior and Frontal EEG channels. Also MTE detects the information flow from Posterior EEG channels to Frontal ones more significantly than TE does. So in presence of significant instantaneous relations in the real EEG data, MTE outperforms TE.


Main Subjects

[1]     Jirsa V., and McIntosh A. R., Handbook of brain connectivity; Springer, 2007.
[2]     Wiener N., The theory of prediction; Modern Mathematics for Engineers, ed. Beckenbach E. F., McGraw-Hill, New York, 1956.
[3]     Granger C. W. J, Investigating causal relations by econometric models and cross-spectral methods; Econometrica, 1969; 37:424–438.
[4]     Kaminski M., and Liang H., Causal influence: Advances in neurosignal analysis; Crit. Rev. Biomed. Eng., 2005; 33:347–430.
[5]     Marinazzo D., Liao W., Chen H. and Stramaglia S., Nonlinear connectivity by Granger causality; Neuroimage, 2011; 58(2):330-338.
[6]     Schreiber T., Measuring information transfer; Phys. Rev. Lett., 2000; 85:461– 464.
[7]     Faes L., Erla S. and Nollo G., Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis; Comput. Math. Methods Med., 2012; 2012:1-18.
[8]     Faes L., and Nollo G., Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions; Biol. Cybern., 2010; 103:387–400.
[9]     Erlaa S., Faes L., Tranquillinic E., Orricoc D., and Nollo G., Multivariate autoregressive model with instantaneous effects to improve brain connectivity estimation; Int. J. Bioelectromagnetism, 2009; 11(2):74-79.
[10] Hyvarinen A., Shimizu Sh., and Hoyer P. O., Causal modelling combining instantaneous and lagged effects: an identifiable model based on non-gaussianity; Proceedings of the 25’th International Conference on Machine Learning, Helsinki, Finland, 2008:424-431.
[11] Hyvarinen A., Zhang K., Shimizu Sh., and Hoyer P. O., Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity; J. Machine Learning Research, 2010; 11:1709-1731.
[12] Pipa G., Vicente R., Gollo L. L., Mirasso C., and Fischer I., A mechanism for achieving zero-lag long-range synchronization of neural activity; BMC Neuroscience, 2009; 10(1):240.
[13] Deshpande G., Sathian K. and Hu X., Assessing and compensating for zero-lag correlation effects in time-lagged granger causality analysis of fMRI; IEEE Trans. Biomed. Eng., 2010; 57(6):1446-1456.
[14] Deshpande G., Santhanam P. and Hu X., Instantaneous and causal connectivity in resting state brain networks derived from functional MRI data; NeuroImage, 2011; 54:1043–1052.
[15] Schoffelen J. M., and Gross J., Source connectivity analysis with MEG and MEG; Hum. Brain Mapp., 2009; 30:1857–1865.
[16] Schiff S. J., Dangerous phase; Neuroinformatics, 2005; 3(4):315–318.
[17] Gollo L. L., Mirasso C., and Villa A. E., Dynamic control for synchronization of separated cortical areas through thalamic relay; NeuroImage, 2010; 52(3):947-955.
[18]  Gollo L. L., Mirasso C., Atienza M., Crespo-Garcia M., and Cantero J. L., Theta band zero-lag long-range synchronization via hippocampal dynamical relaying; PLoS One. 2011; 6(3):e17756
[19] Cover T. M. and Thomas J. M., Elements of information theory; Second edition, John Wiley & Sons, 2006.
[20] Vicente R., Wibral M., Lindner M., and Pipa G., Transfer entropy—a model-free measure of effective connectivity for the neurosciences; J. Comput. Neurosci., 2011; 30(1):45-67.
[21] Jin S. H., Lin P., and Hallett M., Linear and nonlinear information flow based on time-delayed mutual information method and its application to corticomuscular interaction; Clin. Neurophysiol., 2010; 121:392–401.
[22] David O., Cosmelli D. and Friston K. J., Evaluation of different measures of functional connectivity using a neural mass model; NeuroImage, 2004; 21:659–673.
[23] Delorme A. and Makeig S., EEGLAB: an open source toolbox for analysis of single trial EEG dynamics including independent component analysis; J. Neurosci. Methods, 2004; 134(1):9–21.
[24] EEGLAB freeware,  Available online:
[25] Lee T. W., Girolami M., Bell A. J. and Sejnowski T. J., A unifying information theoretic framework for independent component analysis; Comput. Math. Appl., 2000; 31:1–21.
[26] Rutanen K., TIM C++ library, Available online:
[27] Gomez-Herrero G., Brain connectivity analysis with EEG; PHD Dissertation, Tamper university of technology, 2010.
[28] Kus R., Kaminski M., and Blinowska K. J., Determination of EEG activity propagation: pair-wise versus multichannel estimate; IEEE Trans. Biomed. Eng., 2004; 51:1501-1510.
[29] Faes L., Porta A. and Nollo G., Testing frequency-domain causality in multivariate time series; IEEE Trans. Biomed. Eng., 2010; 57(8):1897-1906.
[30] Faes L., Nollo G. and Porta A., Information-based detection of nonlinear Granger causality in multivariate processes via a non uniform embedding technique; Phys. Rev. E., 2011; 83(5):051112.
[31] Kaminski M., Blinowska K. and Szelenberger W., Investigation of coherence structure and EEG activity propagation during sleep; Acta Neurobiol. Exp., 1995; 55:213–219.
[32] Kaminski M., Blinowska K. and Szelenberger W., Topographic analysis of coherence and propagation of EEG activity during sleep and wakefulness; Electroencephalogr. Clin. Neurophysiol., 1997; 102:216–227.
[33] Babiloni C., Binetti G., Cassarino A., Dal Forno G., Del Percio C., Ferreri F., Ferri R., Frisoni G., Galderisi S., Hirata K., Lanuzza B., Miniussi C., Mucci A., Nobili F., Rodriguez G., Luca Romani G. and Rossini P. M., Sources of cortical rhythms in adults during physiological aging: a multicentric EEG study; Hum. Brain Mapp., 2006; 27:162-172.
[34] Kraskov A., Stögbauer H. and Grassberger P.,  Estimating mutual information; Phys. Rev. E, 2004; 69(6): 066138.
[35]  Vakorin V. A., Krakovsk O. A., and McIntosh A. R., Confounding effects of indirect connections on causality estimation; Neuroscience Methods, 2009; 184:152–160.