Analyzing the connectivity between regions of interest: An approach based on cluster Granger causality for fMRI data analysis

The identification, modeling, and analysis of interactions between nodes of neural systems in the human brain have become the aim of interest of many studies in neuroscience. The complex neural network structure and its correlations with brain functions have played a role in all areas of neuroscience, including the comprehension of cognitive and emotional processing. Indeed, understanding how information is stored, retrieved, processed, and transmitted is one of the ultimate challenges in brain research. In this context, in functional neuroimaging, connectivity analysis is a major tool for the exploration and characterization of the information flow between specialized brain regions. In most functional magnetic resonance imaging (fMRI) studies, connectivity analysis is carried out by first selecting regions of interest (ROI) and then calculating an average BOLD time series (across the voxels in each cluster). Some studies have shown that the average may not be a good choice and have suggested, as an alternative, the use of principal component analysis (PCA) to extract the principal eigen-time series from the ROI(s). In this paper, we introduce a novel approach called cluster Granger analysis (CGA) to study connectivity between ROIs. The main aim of this method was to employ multiple eigen-time series in each ROI to avoid temporal information loss during identification of Granger causality. Such information loss is inherent in averaging (e.g., to yield a single "representative" time series per ROI). This, in turn, may lead to a lack of power in detecting connections. The proposed approach is based on multivariate statistical analysis and integrates PCA and partial canonical correlation in a framework of Granger causality for clusters (sets) of time series. We also describe an algorithm for statistical significance testing based on bootstrapping. By using Monte Carlo simulations, we show that the proposed approach outperforms conventional Granger causality analysis (i.e., using representative time series extracted by signal averaging or first principal components estimation from ROIs). The usefulness of the CGA approach in real fMRI data is illustrated in an experiment using human faces expressing emotions. With this data set, the proposed approach suggested the presence of significantly more connections between the ROIs than were detected using a single representative time series in each ROI.

[1]  João Ricardo Sato,et al.  Intervention Models in Functional Connectivity Identification Applied to fMRI , 2006, Int. J. Biomed. Imaging.

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

[3]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[4]  G. Dunteman Principal Components Analysis , 1989 .

[5]  S C Williams,et al.  Generic brain activation mapping in functional magnetic resonance imaging: a nonparametric approach. , 1997, Magnetic resonance imaging.

[6]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .

[7]  Mingzhou Ding,et al.  Detecting directional influence in fMRI connectivity analysis using PCA based Granger causality , 2009, Brain Research.

[8]  Rainer Goebel,et al.  Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. , 2003, Magnetic resonance imaging.

[9]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[10]  Xue Wang,et al.  Granger Causality between Multiple Interdependent Neurobiological Time Series: Blockwise versus Pairwise Methods , 2007, Int. J. Neural Syst..

[11]  J. Elsner Evidence in support of the climate change–Atlantic hurricane hypothesis , 2006 .

[12]  João Ricardo Sato,et al.  Modeling Nonlinear Gene Regulatory Networks from Time Series Gene Expression Data , 2008, J. Bioinform. Comput. Biol..

[13]  D. Tank,et al.  Brain magnetic resonance imaging with contrast dependent on blood oxygenation. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Craig Hiemstra,et al.  Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation , 1994 .

[15]  Wayne H. Joerding Economic growth and defense spending: Granger Causality , 1986 .

[16]  João Ricardo Sato,et al.  GEDI: a user-friendly toolbox for analysis of large-scale gene expression data , 2007, BMC Bioinformatics.

[17]  Lee Friedman,et al.  Report on a multicenter fMRI quality assurance protocol , 2006, Journal of magnetic resonance imaging : JMRI.

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

[19]  D. Kupfer,et al.  Elevated striatal and decreased dorsolateral prefrontal cortical activity in response to emotional stimuli in euthymic bipolar disorder: no associations with psychotropic medication load. , 2008, Bipolar disorders.

[20]  Lutz Kilian,et al.  NEW INTRODUCTION TO MULTIPLE TIME SERIES ANALYSIS, by Helmut Lütkepohl, Springer, 2005 , 2006, Econometric Theory.

[21]  G. Duncan,et al.  Multivariate Analysis: With Applications in Education and Psychology. , 1977 .

[22]  Filip Deleus,et al.  A Connectivity-Based Method for Defining Regions-of-Interest in fMRI Data , 2009, IEEE Transactions on Image Processing.

[23]  João Ricardo Sato,et al.  Wavelet based time-varying vector autoregressive modelling , 2007, Comput. Stat. Data Anal..

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

[25]  H. Hotelling The most predictable criterion. , 1935 .

[26]  A. McIntosh,et al.  Understanding Neural Interactions in Learning and Memory Using Functional Neuroimaging , 1998, Annals of the New York Academy of Sciences.

[27]  Michael Eichler,et al.  Abstract Journal of Neuroscience Methods xxx (2005) xxx–xxx Testing for directed influences among neural signals using partial directed coherence , 2005 .

[28]  B. Biswal,et al.  Cocaine administration decreases functional connectivity in human primary visual and motor cortex as detected by functional MRI , 2000, Magnetic resonance in medicine.

[29]  Lester Melie-García,et al.  Estimating brain functional connectivity with sparse multivariate autoregression , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[30]  Koichi Sameshima,et al.  Using partial directed coherence to describe neuronal ensemble interactions , 1999, Journal of Neuroscience Methods.

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

[32]  J. A. López del Val,et al.  Principal Components Analysis , 2018, Applied Univariate, Bivariate, and Multivariate Statistics Using Python.

[33]  H. Hotelling Relations Between Two Sets of Variates , 1936 .

[34]  N. Logothetis,et al.  Neurophysiological investigation of the basis of the fMRI signal , 2001, Nature.

[35]  S. Lahiri Resampling Methods for Dependent Data , 2003 .

[36]  S. Rauch,et al.  Neurobiology of emotion perception I: the neural basis of normal emotion perception , 2003, Biological Psychiatry.

[37]  Sik-Yum Lee Generalizations of the partial, part and bipartial canonical correlation analysis , 1978 .

[38]  Ranga B. Myneni,et al.  The effect of growing season and summer greenness on northern forests , 2004 .

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

[40]  Jorge Moll,et al.  Social attachment and aversion in human moral cognition , 2009, Neuroscience & Biobehavioral Reviews.

[41]  M. Eichler,et al.  Assessing the strength of directed influences among neural signals using renormalized partial directed coherence , 2009, Journal of Neuroscience Methods.

[42]  Gerald M. Edelman,et al.  The Remembered Present; A Biological Theory of Consciousness. , 1994 .

[43]  João Ricardo Sato,et al.  Depression in Parkinson's disease: Convergence from voxel-based morphometry and functional magnetic resonance imaging in the limbic thalamus , 2009, NeuroImage.

[44]  B. R. Rao Partial canonical correlations , 1969 .

[45]  B. Biswal,et al.  Functional connectivity in the motor cortex of resting human brain using echo‐planar mri , 1995, Magnetic resonance in medicine.

[46]  Felipe Fregni,et al.  rTMS treatment for depression in Parkinson's disease increases BOLD responses in the left prefrontal cortex. , 2008, The international journal of neuropsychopharmacology.

[47]  Otto W. Witte,et al.  Modelling and analysis of time-variant directed interrelations between brain regions based on BOLD-signals , 2009, NeuroImage.

[48]  W. Singer,et al.  Testing non-linearity and directedness of interactions between neural groups in the macaque inferotemporal cortex , 1999, Journal of Neuroscience Methods.

[49]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[50]  Robert D. McPhee,et al.  Commonality Analysis: A Method for Decomposing Explained Variance in Multiple Regression Analyses. , 1979 .

[51]  Peter Bandettini,et al.  Functional MRI today. , 2007, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

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