Nonlinear connectivity by Granger causality

NeuroImage

Volumn 58, Issue 2, 2011, Pages 330-338

  Marinazzo, Daniele ^a   Liao, Wei ^b   Chen, Huafu ^b   Stramaglia, Sebastiano ^c,d  

^a CNRS   (France)

^b UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c INFN SEZIONE DI BARI   (Italy)

^d UNIVERSITY OF BARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BRAIN FUNCTION; BRAIN REGION; CAUSAL MODELING; DYNAMIC CAUSAL MODELING; ELECTROENCEPHALOGRAM; ELECTROMAGNETIC FIELD; FUNCTIONAL MAGNETIC RESONANCE IMAGING; GRANGER CAUSALITY ANALYSIS; HUMAN; INFORMATION PROCESSING; KERNEL METHOD; MOTOR PERFORMANCE; NERVE CELL NETWORK; NEUROIMAGING; NONLINEAR SYSTEM; NOTE; PRIORITY JOURNAL; SIGNAL DETECTION; STATISTICAL ANALYSIS; VISUAL SYSTEM;

ALGORITHMS; BRAIN; CAUSALITY; ELECTROENCEPHALOGRAPHY; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; MAGNETOENCEPHALOGRAPHY; MODELS, NEUROLOGICAL; NEURAL PATHWAYS; NONLINEAR DYNAMICS; SYNAPTIC TRANSMISSION;

EID: 77956079564     PISSN: 10538119     EISSN: 10959572     Source Type: Journal    
DOI: 10.1016/j.neuroimage.2010.01.099     Document Type: Note

References (84)

1. Ancona N., Stramaglia S. An invariance property of predictors in kernel-induced hypothesis spaces. Neural Comput. 2006, 18:749.
2. Angelini L., Pellicoro M., Stramaglia S. Granger causality for circular variables. Phys. Lett. A 2009, 373:2460-2470.
3. Angelini, L., Tommaso, M.d., Marinazzo, D., Nitti, L., Pellicoro, M., Stramaglia, S., 2009b. Redundant variables and Granger causality. Submitted (arXiv:0909.5117).
4. Astolfi L., Cincotti F., Mattia D., Marciani M.G., Baccala L.A., de Vico Fallani F., Salinari S., Ursino M., Zavaglia M., Babiloni F. Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data. IEEE Trans. Biomed. Eng. 2006, 53:1802-1812.
5. Baccala L.A., Sameshima K. Partial directed coherence: a new concept in neural structure determination. Biol. Cybern. 2001, 84:463-474.
6. Barnett L., Barrett A.B., Seth A.K. Granger causality and transfer entropy are equivalent for Gaussian variables. Phys. Rev. Lett. 2009, 103:238701.
7. Bell D., Kay J., Malley J. A non-parametric approach to non-linear causality testing. Econom. Lett. 1996, 51:7-18.
8. Bezruchko B.P., Ponomarenko V.I., Prokhorov M.D., Smirnov D.A., Tass P.A. Modeling nonlinear oscillatory systems and diagnostics of coupling between them using chaotic time series analysis: applications in neurophysiology. Physics-Uspekhi 2008, 51:304-310.
9. Blinowska K.J., Kus R., Kaminski M. Granger causality and information flow in multivariate processes. Phys. Rev., E Stat. Nonlinear Soft Matter Phys. 2004, 70:050902.
10. Boynton G.M., Engel S.A., Glover G.H., Heeger D.J. Linear systems analysis of functional magnetic resonance imaging in human V1. J. Neurosci. 1996, 16:4207-4221.
11. Boynton G.M., Demb J.B., Glover G.H., Heeger D.J. Neuronal basis of contrast discrimination. Vision Res. 1999, 39:257-269.
12. Breakspear M. "Dynamic" connectivity in neural systems: theoretical and empirical considerations. Neuroinformatics 2004, 2:205-226.
13. Bressler S.E., Seth A.K. Wiener-Granger Causality: A Well-Established Methodology. Neuroimage. 2011, 58:323-329. (this issue).
14. Brovelli A., Ding M., Ledberg A., Chen Y., Nakamura R., Bressler S.L. Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality. Proc. Natl. Acad. Sci. U. S. A. 2004, 101:9849-9854.
15. Buxton R.B., Uludag K., Dubowitz D.J., Liu T.T. Modeling the hemodynamic response to brain activation. NeuroImage 2004, 23(Suppl. 1):S220-S233.
16. Chavez M., Martinerie J., Le Van Quyen M. Statistical assessment of nonlinear causality: application to epileptic EEG signals. J. Neurosci. Methods 2003, 124:113-128.
17. Chen Y., Bressler S.L., Ding M. Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data. J. Neurosci. Methods 2006, 150:228-237.
18. Chen H., Yang Q., Liao W., Gong Q., Shen S. Evaluation of the effective connectivity of supplementary motor areas during motor imagery using Granger causality mapping. NeuroImage 2009, 47:1844-1853.
19. Cherkassky V., Ma Y. Comparison of model selection for regression. Neural Comput. 2003, 15:1691-1714.
20. Daunizeau J., David O., Stephan K.E. Dynamic causal modelling: A critical review of the biophysical and statistical foundations. Neuroimage. 2011, 58:312-322. (this issue).
21. David O., Guillemain I., Saillet S., Reyt S., Deransart C., Segebarth C., Depaulis A. Identifying neural drivers with functional MRI: an electrophysiological validation. PLoS Biol. 2008, 6:2683-2697.
22. Davidson R., MacKinnon J.G. Econometric Theory and Methods 2004, Oxford Univ. Press, New York.
23. Delorme A., 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. Deshpande G., LaConte S., James G.A., Peltier S., Hu X. Multivariate Granger causality analysis of fMRI data. Hum. Brain Mapp. 2009, 30:1361-1373.
25. Dhamala M., Rangarajan G., Ding M. Estimating Granger causality from Fourier and wavelet transforms of time series data. Phys. Rev. Lett. 2008, 100:018701.
26. Freiwald W.A., Valdes P., Bosch J., Biscay R., Jimenez J.C., Rodriguez L.M., Rodriguez V., Kreiter A.K., Singer W. Testing non-linearity and directedness of interactions between neural groups in the macaque inferotemporal cortex. J. Neurosci. Methods 1999, 94:105-119.
27. Friston K.J. Functional and effective connectivity in neuroimaging: a synthesis. Hum. Brain Mapp. 1994, 2:56-78.
28. Friston K.J. Dynamic causal modeling and Granger causality Comments on: The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution. Neuroimage. 2011, 58:303-305. (this issue).
29. Friston K.J. Causal modelling and brain connectivity in functional magnetic resonance imaging. PLoS Biol. 2009, 7:e33.
30. Friston K.J., Buchel C. Attentional modulation of effective connectivity from V2 to V5/MT in humans. Proc. Natl. Acad. Sci. U. S. A. 2000, 97:7591-7596.
31. Friston K.J., Frith C.D., Fletcher P., Liddle P.F., Frackowiak R.S. Functional topography: multidimensional scaling and functional connectivity in the brain. Cereb. Cortex 1996, 6:156-164.
32. Friston K.J., Harrison L., Penny W. Dynamic causal modelling. NeuroImage 2003, 19:1273-1302.
33. Fujita A., Sato J.R., Garay-Malpartida H.M., Morettin P.A., Sogayar M.C., Ferreira C.E. Time-varying modeling of gene expression regulatory networks using the wavelet dynamic vector autoregressive method. Bioinformatics 2007, 23:1623-1630.
34. Gao Q., Chen H., Gong Q. Evaluation of the effective connectivity of the dominant primary motor cortex during bimanual movement using Granger causality. Neurosci. Lett. 2008, 443:1-6.
35. Ge T., Kendrick K.M., Feng J. A novel extended Granger causal model approach demonstrates brain hemispheric differences during face recognition learning. PLoS Comput. Biol. 2009, 5:e1000570.
36. Geweke J.F. Measures of conditional linear dependence and feedback between time series. J. Am. Stat. Assoc. 1984, 79:709-715.
37. Goebel R., Roebroeck A., Kim D.S., Formisano E. Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn. Reson. Imaging 2003, 21:1251-1261.
38. Gourevitch B., Bouquin-Jeannes R.L., Faucon G. Linear and nonlinear causality between signals: methods, examples and neurophysiological applications. Biol. Cybern. 2006, 95:349-369.
39. Granger C.W.J. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 1969, 37:424-438.
40. Granger C.W.J. Testing for causality: a personal viewpoint. J. Econ. Dyn. Control 1980, 2:1477-1491.
41. Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D 1983, 9:189-208.
42. Guo S., Seth A.K., Kendrick K.M., Zhou C., Feng J. Partial Granger causality-eliminating exogenous inputs and latent variables. J. Neurosci. Methods 2008, 172:79-93.
43. Haufe S., Müller K.R., Nolte G., Krämer N. Sparse causal discovery in multivariate time series. Proceedings or the NIPS'08 Workshop on Causality 2008, 1-16.
44. Hesse W., Moller E., Arnold M., Schack B. The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies. J. Neurosci. Methods 2003, 124:27-44.
45. Hiemstra C., Jones J.D. Testing for linear and nonlinear Granger causality in the stock price-volume relation. J. Finance 1994, 49:1639-1664.
46. Johnston L.A., Duff E., Mareels I., Egan G.F. Nonlinear estimation of the BOLD signal. NeuroImage 2008, 40:504-514.
47. Kaminski M.J., Blinowska K.J. A new method of the description of the information flow in the brain structures. Biol. Cybern. 1991, 65:203-210.
48. Kaminski M., Ding M., Truccolo W.A., Bressler S.L. Evaluating causal relations in neural systems: granger causality, directed transfer function and statistical assessment of significance. Biol. Cybern. 2001, 85:145-157.
49. Kantz H., Schreiber T. Nonlinear Time Series Analysis 1997, Cambridge Univ. Press, Cambridge.
50. Korzeniewska A., Manczak M., Kaminski M., Blinowska K.J., Kasicki S. Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method. J. Neurosci. Methods 2003, 125:195-207.
51. Lahaye P.J., Poline J.B., Flandin G., Dodel S., Garnero L. Functional connectivity: studying nonlinear, delayed interactions between BOLD signals. NeuroImage 2003, 20:962-974.
52. Liao W., Mantini D., Zhang Z., Pan Z., Ding J., Gong G., Yang Y., Chen H. Evaluating the effective connectivity of resting state networks using conditional Granger causality. Biol. Cybern. 2009, 102:57-69.
53. Liao W., Marinazzo D., Pan Z., Gong Q., Chen H. Kernel Granger causality mapping effective connectivity on fMRI data. IEEE. Trans Med. Imaging 2009, 28:1825-1835.
54. Li X., Marrelec G., Hess R.F., Benali H. A nonlinear identification method to study effective connectivity in functional MRI. Med. Image. Anal. 2010, 14:30-38.
55. Logothetis N.K., Pauls J., Augath M., Trinath T., Oeltermann A. Neurophysiological investigation of the basis of the fMRI signal. Nature 2001, 412:150-157.
56. Londei A., D'Ausilio A., Basso D., Sestieri C., Del Gratta C., Romani G.L., Olivetti Belardinelli M. Brain network for passive word listening as evaluated with ICA and Granger causality. Brain Res. Bull. 2007, 72:284-292.
57. Lütkepohl, H., 2005. New Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin.
58. Mak B.K., Lai T., Tsang I.W., Kwok J.T. Maximum penalized likelihood kernel regression for fast adaptation. Trans. Audio, Speech Lang. Proc. 2009, 17(7):1372.
59. Marinazzo D., Pellicoro M., Stramaglia S. Kernel method for nonlinear granger causality. Phys. Rev. Lett. 2008, 100:144103.
60. Marinazzo D., Pellicoro M., Stramaglia S. Kernel-Granger causality and the analysis of dynamical networks. Phys. Rev. E. Stat. Nonlin. Soft. Matter. Phys. 2008, 77:056215.
61. McQuarrie A.D.R., Tsai C.L. Regression and Time Series Model Selection 1998, World Scientific, Singapore.
62. Napoletani D., Sauer T.D. Reconstructing the topology of sparsely connected dynamical networks. Phys. Rev. E Stat. Nonlin. Soft. Matter. Phys. 2008, 77:026103.
63. Palus M., Vejmelka M. Directionality of coupling from bivariate time series: how to avoid false causalities and missed connections. Phys. Rev. E Stat. Nonlin. Soft. Matter. Phys. 2007, 75:056211.
64. Papoulis A. Probability, Random Variables and Stochastic Processes 1985, McGraw-Hill, New York.
65. Pereda E., Quiroga R.Q., Bhattacharya J. Nonlinear multivariate analysis of neurophysiological signals. Prog. Neurobiol. 2005, 77:1-37.
66. Roebroeck A., Formisano E., Goebel R. Mapping directed influence over the brain using Granger causality and fMRI. NeuroImage 2005, 25:230-242.
67. Roebroeck A., Formisano E., Goebel R. The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution. Neuroimage. 2011, 58:296-302. (this issue).
68. Sato J.R., Junior E.A., Takahashi D.Y., de Maria Felix M., Brammer M.J., Morettin P.A. A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality. NeuroImage 2006, 31:187-196.
69. Schneidman E., Bialek W., Berry M.J. Synergy, redundancy, and independence in population codes. J. Neurosci. 2003, 23:11539-11553.
70. Seth A.K. Causal connectivity of evolved neural networks during behavior. Network 2005, 16:35-54.
71. Shawe-Taylor J., Cristianini N. Kernel Methods for Pattern Analysis 2004, Cambridge Univ. Press.
72. Sridharan D., Levitin D.J., Menon V. A critical role for the right fronto-insular cortex in switching between central-executive and default-mode networks. Proc. Natl. Acad. Sci. U. S. A. 2008, 105:12569-12574.
73. Stephan K.E., Kasper L., Harrison L.M., Daunizeau J., den Ouden H.E., Breakspear M., Friston K.J. Nonlinear dynamic causal models for fMRI. NeuroImage 2008, 42:649-662.
74. Teräsvirta T. Modeling economic relationships with smooth transition regressions. Handbook of Applied Economic Statistics 1998, 507-552. Marcel Dekker, New York. A. Ullah, D.E.A. Giles (Eds.).
75. Uddin L.Q., Clare Kelly A.M., Biswal B.B., Xavier Castellanos F., Milham M.P. Functional connectivity of default mode network components: correlation, anticorrelation, and causality. Hum. Brain. Mapp. 2009, 30:625-637.
76. Upadhyay J., Silver A., Knaus T.A., Lindgren K.A., Ducros M., Kim D.S., Tager- Flusberg H. Effective and structural connectivity in the human auditory cortex. J. Neurosci. 2008, 28:3341-3349.
77. Valdes P.A., Jimenez J.C., Riera J., Biscay R., Ozaki T. Nonlinear EEG analysis based on a neural mass model. Biol. Cybern. 1999, 81:415-424.
78. Vapnik V. Statistical Learning Theory 1998, John Wiley & Sons, New York.
79. Wang X., Chen Y., Ding M. Estimating Granger causality after stimulus onset: a cautionary note. NeuroImage 2008, 41:767-776.
80. Warne A. Causality and regime inference in a Markow switching VAR. Sveriges Riksbank, Stockholm 2000, 118:1-41.
81. Wiener N. The theory of predicition. Modern Mathematics for Engineers 1956, McGraw-Hill, New York. E.F. Berkenbach (Ed.).
82. Wilke M., Lidzba K., Krageloh-Mann I. Combined functional and causal connectivity analyses of language networks in children: a feasibility study. Brain Lang. 2009, 108:22-29.
83. Zhou Z., Chen Y., Ding M., Wright P., Lu Z., Liu Y. Analyzing brain networks with PCA and conditional Granger causality. Hum. Brain Mapp. 2009, 30:2197-2206.
84. Zhou Z., Ding M., Chen Y., Wright P., Lu Z., Liu Y. Detecting directional influence in fMRI connectivity analysis using PCA based Granger causality. Brain Res. 2009, 1289:22-29.