Kernel Granger Causality Mapping Effective Connectivity on fMRI Data

Although it is accepted that linear Granger causality can reveal effective connectivity in functional magnetic resonance imaging (fMRI), the issue of detecting nonlinear connectivity has hitherto not been considered. In this paper, we address kernel Granger causality (KGC) to describe effective connectivity in simulation studies and real fMRI data of a motor imagery task. Based on the theory of reproducing kernel Hilbert spaces, KGC performs linear Granger causality in the feature space of suitable kernel functions, assuming an arbitrary degree of nonlinearity. Our results demonstrate that KGC captures effective couplings not revealed by the linear case. In addition, effective connectivity networks between the supplementary motor area (SMA) as the seed and other brain areas are obtained from KGC.

[1]  C. Büchel,et al.  Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. , 1997, Cerebral cortex.

[2]  Xiaoping Hu,et al.  Connectivity Analysis of Human Functional MRI Data: From Linear to Nonlinear and Static to Dynamic , 2006, MIAR.

[3]  H. Lüders,et al.  Functional connectivity in human cortical motor system: a cortico-cortical evoked potential study. , 2006, Brain : a journal of neurology.

[4]  Wlodzimierz Klonowski,et al.  From conformons to human brains: an informal overview of nonlinear dynamics and its applications in biomedicine , 2007, Nonlinear biomedical physics.

[5]  Kristen A. Lindgren,et al.  Effective and Structural Connectivity in the Human Auditory Cortex , 2008, The Journal of Neuroscience.

[6]  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.

[7]  Silke Dodel,et al.  Functional connectivity: studying nonlinear, delayed interactions between BOLD signals , 2003, NeuroImage.

[8]  K. Kendrick,et al.  Partial Granger causality—Eliminating exogenous inputs and latent variables , 2008, Journal of Neuroscience Methods.

[9]  S. Bressler,et al.  Granger Causality: Basic Theory and Application to Neuroscience , 2006, q-bio/0608035.

[10]  Karl J. Friston.  Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging , 2009, PLoS biology.

[11]  Xue Wang,et al.  Estimating Granger causality after stimulus onset: A cautionary note , 2008, NeuroImage.

[12]  Qiyong Gong,et al.  Evaluation of the effective connectivity of the dominant primary motor cortex during bimanual movement using Granger causality , 2008, Neuroscience Letters.

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

[14]  Thomas E. Nichols,et al.  Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate , 2002, NeuroImage.

[15]  Iven M. Y. Mareels,et al.  Nonlinear estimation of the BOLD signal , 2008, NeuroImage.

[16]  Karl J. Friston,et al.  Time‐dependent changes in effective connectivity measured with PET , 1993 .

[17]  R. Buxton,et al.  Modeling the hemodynamic response to brain activation , 2004, NeuroImage.

[18]  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.

[19]  J B Poline,et al.  Partially overlapping neural networks for real and imagined hand movements. , 2000, Cerebral cortex.

[20]  D. Heeger,et al.  Linear Systems Analysis of Functional Magnetic Resonance Imaging in Human V1 , 1996, The Journal of Neuroscience.

[21]  Mingzhou Ding,et al.  Estimating Granger causality from fourier and wavelet transforms of time series data. , 2007, Physical review letters.

[22]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[23]  P. Matthews,et al.  Changing brain networks for visuomotor control with increased movement automaticity. , 2004, Journal of neurophysiology.

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

[25]  S. Small,et al.  Fine modulation in network activation during motor execution and motor imagery. , 2004, Cerebral cortex.

[26]  S. Bressler,et al.  Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[28]  Daniele Marinazzo,et al.  Kernel-Granger causality and the analysis of dynamical networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  A. McQuarrie,et al.  Regression and Time Series Model Selection , 1998 .

[30]  Karl J. Friston,et al.  Attentional modulation of effective connectivity from V2 to V5/MT in humans. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[31]  J. Geweke,et al.  Measures of Conditional Linear Dependence and Feedback between Time Series , 1984 .

[32]  D. Heeger,et al.  Neuronal basis of contrast discrimination , 1999, Vision Research.

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

[34]  Nikos K Logothetis,et al.  Interpreting the BOLD signal. , 2004, Annual review of physiology.

[35]  Litvak,et al.  164 Dynamic Causal Modeling 6 . 1 , 2010 .

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

[37]  John D Carew,et al.  Hemispheric asymmetry in supplementary motor area connectivity during unilateral finger movements , 2004, NeuroImage.

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

[39]  G. Rizzolatti,et al.  The organization of the cortical motor system: new concepts. , 1998, Electroencephalography and clinical neurophysiology.

[40]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .

[41]  M. Hallett,et al.  Functional properties of brain areas associated with motor execution and imagery. , 2003, Journal of neurophysiology.

[42]  K. Hlavácková-Schindler,et al.  Causality detection based on information-theoretic approaches in time series analysis , 2007 .

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

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

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

[46]  Daniele Marinazzo,et al.  Kernel method for nonlinear granger causality. , 2007, Physical review letters.