GMAC: A Matlab toolbox for spectral Granger causality analysis of fMRI data

Investigation of causal interactions within brain networks using Granger causality analysis (GCA) is a key challenge in studying neural activity on the basis of functional magnetic resonance imaging (fMRI). The article describes an open-source software toolbox GMAC (Granger multivariate autoregressive connectivity) implementing multivariate spectral GCA. Available features are: fMRI data importing/exporting, network nodes definition, time series preprocessing, multivariate autoregressive modeling, spectral Granger causality indexes estimation, statistical significance assessment using surrogate data, network analysis and visualization of connectivity results. All functions have been integrated into a user-friendly graphical interface developed in the Matlab environment, easily accessible to both technical and clinical users.

[1]  S.C. Strother,et al.  Evaluating fMRI preprocessing pipelines , 2006, IEEE Engineering in Medicine and Biology Magazine.

[2]  Rainer Goebel,et al.  The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution , 2011, NeuroImage.

[3]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[4]  Mark W. Woolrich,et al.  Network modelling methods for FMRI , 2011, NeuroImage.

[5]  J. Rajapakse,et al.  Human Brain Mapping 6:283–300(1998) � Modeling Hemodynamic Response for Analysis of Functional MRI Time-Series , 2022 .

[6]  Xiaoping Hu,et al.  Neural processing underlying tactile microspatial discrimination in the blind: a functional magnetic resonance imaging study. , 2008, Journal of vision.

[7]  H. Benali,et al.  Exploring large-scale brain networks in functional MRI , 2006, Journal of Physiology-Paris.

[8]  João Ricardo Sato,et al.  A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality , 2006, NeuroImage.

[9]  Karl J. Friston,et al.  Dynamic causal modeling , 2010, Scholarpedia.

[10]  Erik J. Peterson,et al.  Dissociating hippocampal and basal ganglia contributions to category learning using stimulus novelty and subjective judgments , 2011, NeuroImage.

[11]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[12]  F Kruggel,et al.  Modeling the hemodynamic response in single‐trial functional MRI experiments , 1999, Magnetic resonance in medicine.

[13]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[14]  Vince D. Calhoun,et al.  Dynamic Granger causality based on Kalman filter for evaluation of functional network connectivity in fMRI data , 2010, NeuroImage.

[15]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[16]  Anil K. Seth,et al.  A MATLAB toolbox for Granger causal connectivity analysis , 2010, Journal of Neuroscience Methods.

[17]  Rainer Goebel,et al.  Mapping directed influence over the brain using Granger causality and fMRI , 2005, NeuroImage.

[18]  Luiz A Baccalá,et al.  Frequency domain connectivity identification: An application of partial directed coherence in fMRI , 2009, Human brain mapping.

[19]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[20]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[21]  Edward T. Bullmore,et al.  Whole-brain anatomical networks: Does the choice of nodes matter? , 2010, NeuroImage.

[22]  L. Fahrmeir,et al.  Bayesian Modeling of the Hemodynamic Response Function in BOLD fMRI , 2001, NeuroImage.

[23]  Xiaoping Hu,et al.  Effect of hemodynamic variability on Granger causality analysis of fMRI , 2010, NeuroImage.

[24]  R. Goebel,et al.  Investigating directed influences between activated brain areas in a motor-response task using fMRI. , 2006, Magnetic resonance imaging.

[25]  M. D’Esposito,et al.  The variability of human BOLD hemodynamic responses , 1998, NeuroImage.

[26]  Yihong Yang,et al.  Evaluating the effective connectivity of resting state networks using conditional Granger causality , 2010, Biological Cybernetics.

[27]  Olivier David,et al.  fMRI connectivity, meaning and empiricism Comments on: Roebroeck et al. The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution , 2011, NeuroImage.

[28]  Steven L. Bressler,et al.  Wiener–Granger Causality: A well established methodology , 2011, NeuroImage.

[29]  Qiang Xu,et al.  Small-world directed networks in the human brain: Multivariate Granger causality analysis of resting-state fMRI , 2011, NeuroImage.

[30]  M. Kaminski,et al.  Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method , 2003, Journal of Neuroscience Methods.

[31]  Carlos E. Thomaz,et al.  Analyzing the connectivity between regions of interest: An approach based on cluster Granger causality for fMRI data analysis , 2010, NeuroImage.

[32]  M. D’Esposito,et al.  The Variability of Human, BOLD Hemodynamic Responses , 1998, NeuroImage.

[33]  M. Ding,et al.  Granger causal influence predicts BOLD activity levels in the default mode network , 2011, Human brain mapping.

[34]  Jean-Baptiste Poline,et al.  A supervised clustering approach for extracting predictive information from brain activation images , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Workshops.

[35]  Moriah E. Thomason,et al.  Vector autoregression, structural equation modeling, and their synthesis in neuroimaging data analysis , 2011, Comput. Biol. Medicine.

[36]  C. Segebarth,et al.  Identifying Neural Drivers with Functional MRI: An Electrophysiological Validation , 2008, PLoS biology.

[37]  D. Dickey,et al.  Testing for unit roots in autoregressive-moving average models of unknown order , 1984 .

[38]  Jean-Baptiste Poline,et al.  Dealing with the shortcomings of spatial normalization: Multi‐subject parcellation of fMRI datasets , 2006, Human brain mapping.

[39]  G. Glover.  Deconvolution of Impulse Response in Event-Related BOLD fMRI1 , 1999, NeuroImage.

[40]  Qing Gao,et al.  Evaluation of effective connectivity of motor areas during motor imagery and execution using conditional Granger causality , 2011, NeuroImage.

[41]  J C Mazziotta,et al.  Creation and use of a Talairach‐compatible atlas for accurate, automated, nonlinear intersubject registration, and analysis of functional imaging data , 1999, Human brain mapping.

[42]  Vangelis Sakkalis,et al.  Review of advanced techniques for the estimation of brain connectivity measured with EEG/MEG , 2011, Comput. Biol. Medicine.

[43]  Qin Yang,et al.  Evaluation of the effective connectivity of supplementary motor areas during motor imagery using Granger causality mapping , 2009, NeuroImage.

[44]  Alberto Leal,et al.  Parcel-Based Connectivity Analysis of fMRI Data for the Study of Epileptic Seizure Propagation , 2012, Brain Topography.

[45]  Jie Cui,et al.  2008 Special Issue: BSMART: A Matlab/C toolbox for analysis of multichannel neural time series , 2008 .

[46]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[47]  P. Hluštík,et al.  Effects of spatial smoothing on fMRI group inferences. , 2008, Magnetic resonance imaging.

[48]  René van den Brink,et al.  The Outflow Ranking Method for Weighted Directed Graphs , 2006, Eur. J. Oper. Res..

[49]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[50]  Mingzhou Ding,et al.  Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance , 2001, Biological Cybernetics.

[51]  Xiaoping Hu,et al.  Effective connectivity during haptic perception: A study using Granger causality analysis of functional magnetic resonance imaging data , 2008, NeuroImage.

[52]  Bertrand Thirion,et al.  A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI , 2008, NeuroImage.

[53]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[54]  Karl J. Friston,et al.  Functional Connectivity: The Principal-Component Analysis of Large (PET) Data Sets , 1993, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[55]  Maurizio Corbetta,et al.  The human brain is intrinsically organized into dynamic, anticorrelated functional networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[56]  Christian Keysers,et al.  Mapping the flow of information within the putative mirror neuron system during gesture observation , 2011, NeuroImage.

[57]  Karl J. Friston,et al.  Movement‐Related effects in fMRI time‐series , 1996, Magnetic resonance in medicine.

[58]  Xiaoping Hu,et al.  Multivariate Granger causality analysis of fMRI data , 2009, Human brain mapping.

[59]  Jaime S. Ide,et al.  A cerebellar thalamic cortical circuit for error-related cognitive control , 2011, NeuroImage.

[60]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[61]  Scott Peltier,et al.  Connectivity exploration with structural equation modeling: an fMRI study of bimanual motor coordination , 2005, NeuroImage.

[62]  Klaas E. Stephan,et al.  A short history of causal modeling of fMRI data , 2012, NeuroImage.

[63]  Liang Wang,et al.  Parcellation‐dependent small‐world brain functional networks: A resting‐state fMRI study , 2009, Human brain mapping.

[64]  P. Ciuciu,et al.  Spatially adaptive mixture modeling for analysis of fMRI time series , 2009, NeuroImage.

[65]  Vince D. Calhoun,et al.  Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls , 2009, NeuroImage.

[66]  Xiaoping Hu,et al.  Posteromedial Parietal Cortical Activity and Inputs Predict Tactile Spatial Acuity , 2007, The Journal of Neuroscience.

[67]  Katarzyna J. Blinowska,et al.  Determination of EEG activity propagation: pair-wise versus multichannel estimate , 2004, IEEE Transactions on Biomedical Engineering.

[68]  H. Akaike.  A new look at the statistical model identification , 1974 .

[69]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.