Functional and Effective Connectivity: A Review

Brain Connectivity

Volumn 1, Issue 1, 2011, Pages 13-36

  Friston, Karl J ^a  

^a WELLCOME TRUST CENTRE FOR NEUROIMAGING   (United Kingdom)

Author keywords

brain connectivity; causal modeling; effective connectivity; functional connectivity

Indexed keywords

EID: 81355137473     PISSN: 21580014     EISSN: 21580022     Source Type: Journal    
DOI: 10.1089/brain.2011.0008     Document Type: Article

References (154)

1. Abbott L.F., Varela J.A., Sen K, Nelson SB. 1997. Synaptic depression and cortical gain control. Science 275:220-224.
2. Absher J.R., Benson DF. 1993. Disconnection syndromes: an overview of Geschwind's contributions. Neurology 43:862-867.
3. Achard S, Salvador R, Whitcher B, Suckling J, Bullmore E. 2006. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J Neurosci 26:63-72.
4. Acs F, Greenlee MW. 2008. Connectivity modulation of early visual processing areas during covert and overt tracking tasks. Neuroimage 41:380-388.
5. Aertsen A, Preiãl H. 1991. Dynamics of activity and connectivity in physiological neuronal networks. In: Schuster HG (ed.) Nonlinear Dynamics and Neuronal Networks. New York: VCH publishers, Inc.; pp. 281-302.
6. Alexander DC. 2008. A general framework for experiment design in diffusion MRI and its application in measuring direct tissue-microstructure features. Magn Reson Med 60:439-448.
7. Allen P, Mechelli A, Stephan K.E., Day F, Dalton J, Williams S, McGuire PK. 2008. Fronto-temporal interactions during overt verbal initiation and suppression. J Cogn Neurosci 20:1656-1669.
8. Alstott J, Breakspear M, Hagmann P, Cammoun L, Sporns O. 2009. Modeling the impact of lesions in the human brain. PLoS Comput Biol 5:e1000408.
9. Baccalã L, Sameshima K. 2001. Partial directed coherence: a new concept in neural structure determination. Biol Cybern 84:463-474.
10. Ballard D.H., Hinton G.E., Sejnowski TJ. 1983. Parallel visual computation. Nature 306:21-26.
11. Bassett D.S., Bullmore ET. 2009. Human brain networks in health and disease. Curr Opin Neurol 22:340-347.
12. Bassett D.S., Meyer-Lindenberg A, Achard S, Duke T, Bullmore E. 2006. Adaptive reconfiguration of fractal small-world human brain functional networks. Proc Natl Acad Sci U S A 103:19518-19523.
13. Bedard C, Kroger H, Destexhe A. 2006. Model of low-pass filtering of local field potentials in brain tissue. Phys Rev E Stat Nonlin Soft Matter Phys 73(5 Pt 1):051911.
14. Behrens T.E., Johansen-Berg H. 2005. Relating connectional architecture to grey matter function using diffusion imaging. Philos Trans R Soc Lond B Biol Sci 360:903-911.
15. Bianciardi M, Fukunaga M, Van Gelderen P, Horovitz S.G., De Zwart J.A., Duyn JH. 2009. Modulation of spontaneous fMRI activity in human visual cortex by behavioral state. Neuroimage 45:160-168.
16. Biswal B, Yetkin F.Z., Haughton V.M., Hyde JS. 1995. Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn Reson Med 34:537-541.
17. Breakspear M, Stam CJ. 2005. Dynamics of a neural system with a multiscale architecture. Philos Trans R Soc Lond B Biol Sci 360:1051-1074.
18. Bressler S.L., Tognoli E. 2006. Operational principles of neurocognitive networks. Int J Psychophysiol 60:139-148.
19. Brodersen K.H., Haiss F, Ong C.S., Jung F, Tittgemeyer M, Buhmann J.M., Weber B, Stephan KE. (2011a). Model-based feature construction for multivariate decoding. Neuroimage (in press); doi:10.1016/j.neuroimage.2010.04.036.
20. Brodersen K.H., Schofield T.M., Leff A.P., Ong C.S., Lomakina E.I., Buhmann J.M., Stephan KE (2011b). Generative embedding for model-based classification of fMRI data. Under review.
21. Buice M.A., Cowan JD. 2009. Statistical mechanics of the neocortex. Prog Biophys Mol Biol 99:53-86.
22. Bullmore E, Sporns O. 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10:186-198.
23. Calhoun V.D., Adali T. 2006. Unmixing fMRI with independent component analysis. IEEE Eng Med Biol Mag 25:79-90.
24. Carr J. 1981. Applications of Centre Manifold Theory. Applied Mathematical Sciences 35, Berlin-Heidelberg-New York: Springer-Verlag.
25. Chang C, Thomason M, Glover G. 2008. Mapping and correction of vascular hemodynamic latency in the BOLD signal. Neuroimage 43:90-102.
26. Chen C.C., Kiebel S.J., Friston KJ. 2008. Dynamic causal modelling of induced responses. Neuroimage 41:1293-1312.
27. Chen C.C., Henson R.N., Stephan K.E., Kilner J.M., Friston KJ. 2009. Forward and backward connections in the brain: a DCM study of functional asymmetries. Neuroimage 45:453-462.
28. Chrobak J.J., Buzsaki G. 1998. Gamma oscillations in the entorhinal cortex of the freely behaving rat. J Neurosci 18:388-398.
29. Clearwater J.M., Kerr C.C., Rennie C.J., Robinson PA. 2008. Neural mechanisms of ERP change: combining insights from electrophysiology and mathematical modeling. J Integr Neurosci 7:529-550.
30. Coombes S, Doole SH. 1996. Neuronal populations with reciprocal inhibition and rebound currents: effects of synaptic and threshold noise. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Top 54:4054-4065.
31. Craddock R.C., Holtzheimer PE 3rd, Hu X.P., Mayberg HS. 2009. Disease state prediction from resting state functional connectivity. Magn Reson Med 62:1619-1628.
32. Daunizeau J, Kiebel S.J., Friston KJ. 2009. Dynamic causal modelling of distributed electromagnetic responses. Neuroimage 47:590-601.
33. David O, Friston KJ. 2003. A neural-mass model for MEG/EEG: coupling and neuronal dynamics. Neuroimage 20:1743-1755.
34. David O, Cosmelli D, Friston KJ. 2004. Evaluation of different measures of functional connectivity using a neural-mass model. Neuroimage 21:659-673.
35. David O, Kiebel S.J., Harrison L.M., Mattout J, Kilner J.M., Friston KJ. 2006. Dynamic causal modeling of evoked responses in EEG and MEG. Neuroimage 30:1255-1272.
36. David O, Guillemain I, Saillet S, Reyt S, Deransart C, Segebarth C, Depaulis A. 2008. Identifying neural drivers with functional MRI: an electrophysiological validation. PLoS Biology 6:2683-2697.
37. Dayan P, Hinton G.E., Neal RM. 1995. The Helmholtz machine. Neural Comput 7:889-904.
38. Deco G, Jirsa V.K., Robinson P.A., Breakspear M, Friston K. 2008. The dynamic brain: from spiking neurons to neural-masses and cortical fields. PLoS Comput Biol 4:e1000092.
39. Deco G, Jirsa V, McIntosh A.R., Sporns O, Kãtter R. 2009. Key role of coupling, delay, and noise in resting brain fluctuations. Proc Natl Acad Sci U S A 106:10302-10307.
40. Deco G, Jirsa V.K., McIntosh AR. 2011. Emerging concepts for the dynamical organization of resting-state activity in the brain. Nat Rev Neurosci 12:43-56.
41. Deshpande G, Sathian K, Hu X. 2010. Assessing and compensating for zero-lag correlation effects in time-lagged Granger causality analysis of FMRI. IEEE Trans Biomed Eng 57:1446-1456.
42. Felleman D.J., Van Essen DC. 1991. Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1-47.
43. Fox M, Zhang D, Snyder A, Raichle M. 2009. The global signal and observed anticorrelated resting state brain networks. J Neurophysiol 101:3270-3283.
44. Freeman WJ. 1994. Characterization of state transitions in spatially distributed, chaotic, nonlinear, dynamical systems in cerebral cortex. Integr Physiol Behav Sci 29:294-306.
45. Freeman WJ. 2005. A field-theoretic approach to understanding scale-free neocortical dynamics. Biol Cybern 92:350-359.
46. Freyer F, Aquino K, Robinson P.A., Ritter P, Breakspear M. 2009. Non-Gaussian statistics in temporal fluctuations of spontaneous cortical activity. J Neurosci 29:8512-8524.
47. Fries P. 2009. Neuronal gamma-band synchronization as a fundamental process in cortical computation. Annu Rev Neurosci 32:209-224.
48. Friston K, Kilner J, Harrison L. 2006. A free-energy principle for the brain. J Physiol Paris 100:70-87.
49. Friston KJ. 1995. Functional and effective connectivity in neuroimaging: a synthesis. Hum Brain Mapp 2:56-78.
50. Friston KJ. 1998. Modes or models: a critique on independent component analysis for fMRI. Trends Cogn Sci 2:373-375.
51. Friston K.J., Dolan RJ. 2010. Computational and dynamic models in neuroimaging. Neuroimage 52:752-765.
52. Friston K.J., Frith C.D., Liddle P.F., Frackowiak RS. 1993. Functional connectivity: the principal-component analysis of large (PET) data sets. J Cereb Blood Flow Metab 13:5-14.
53. Friston K.J., Ungerleider L.G., Jezzard P, Turner R. 1995. Characterizing modulatory interactions between areas V1 and V2 in human cortex: a new treatment of functional MRI data. Hum Brain Mapp 2:211-224.
54. Friston K.J., Büchel C, Fink G.R., Morris J, Rolls E, Dolan RJ. 1997. Psychophysiological and modulatory interactions in neuroimaging. Neuroimage 6:218-229.
55. Friston K.J., Harrison L, Penny W. 2003. Dynamic causal modelling. Neuroimage 19:1273-1302.
56. Friston K.J., Trujillo-Barreto N, Daunizeau J. 2008. DEM: a variational treatment of dynamic systems. Neuroimage 41:849-885.
57. Friston K.J., Li B, Daunizeau J, Stephan KE. 2010. Network discovery with DCM. Neuroimage 56:1202-1221.
58. Garrido M.I., Kilner J.M., Kiebel S.J., Friston KJ. 2007a. Evoked brain responses are generated by feedback loops. Proc Natl Acad Sci U S A 104:20961-20966.
59. Garrido M.I., Kilner J.M., Kiebel S.J., Stephan K.E., Friston KJ. 2007b. Dynamic causal modelling of evoked potentials: a reproducibility study. Neuroimage 36:571-580.
60. Garrido M.I., Friston K.J., Kiebel S.J., Stephan K.E., Baldeweg T, Kilner JM. 2008. The functional anatomy of the MMN: a DCM study of the roving paradigm. Neuroimage 42:936-944.
61. Garrido M.I., Kilner J.M., Kiebel S.J., Stephan K.E., Baldeweg T, Friston KJ. 2009. Repetition suppression and plasticity in the human brain. Neuroimage 48:269-279.
62. Gerstein G.L., Perkel DH. 1969. Simultaneously recorded trains of action potentials: analysis and functional interpretation. Science 164:828-830.
63. Geweke JF. 1984. Measures of conditional linear dependence and feedback between time series. J Am Stat Assoc 79:907-915.
64. Ghosh A, Rho Y, McIntosh A.R., Kãtter R, Jirsa VK. 2008. Cortical network dynamics with time delays reveals functional connectivity in the resting brain. Cogn Neurodyn 2:115-120.
65. Ginzburg V.L., Landau LD. 1950. On the theory of superconductivity. Zh Eksp Teor Fiz 20:1064.
66. Goebel R, Roebroeck A, Kim D-S, Formisano E. 2003. Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn Reson Imaging 21:1251-1261.
67. Goltz F. 1881. In: MacCormac W (ed.) Transactions of the 7th International Medical Congress. Vol. I. London: JW Kolkmann; pp. 218-228.
68. Granger CWJ. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424-438.
69. Greicius M.D., Supekar K, Menon V, Dougherty RF. 2009. Resting-state functional connectivity reflects structural connectivity in the default mode network. Cereb Cortex 19:72-78.
70. Grol M.Y., Majdandzic J, Stephan K.E., Verhagen L, Dijkerman H.C., Bekkering H, Verstraten F.A., Toni I. 2007. Parieto-frontal connectivity during visually guided grasping. J Neurosci 27:11877-11887.
71. Guye M, Bartolomei F, Ranjeva JP. 2008. Imaging structural and functional connectivity: towards a unified definition of human brain organization? Curr Opin Neurol 21:393-403.
72. Haken H. 1983. Synergetics: An Introduction. Non-Equilibrium Phase Transition and Self-Organisation in Physics, Chemistry and Biology. 3rd Edition. Berlin-Heidelberg-New York: Springer-Verlag.
73. Harrison L.M., Penny W, Friston KJ. 2003. Multivariate autoregressive modeling of fMRI time series. Neuroimage 19:1477-1491.
74. Havlicek M, Jan J, Brazdil M, Calhoun VD. 2010. Dynamic Granger causality based on Kalman filter for evaluation of functional network connectivity in fMRI data. Neuroimage 53:65-77.
75. Heim S, Eickhoff S.B., Ischebeck A.K., Friederici A.D., Stephan K.E., Amunts K. 2009. Effective connectivity of the left BA 44, BA 45, and inferior temporal gyrus during lexical and phonological decisions identified with DCM. Hum Brain Mapp 30:392-402.
76. Hesselmann G, Kell C.A., Kleinschmidt A. 2008. Ongoing activity fluctuations in hMT+ bias the perception of coherent visual motion. J Neurosci 28:14481-14485.
77. Honey C.J., Kãtter R, Breakspear M, Sporns O. 2007. Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc Natl Acad Sci U S A 104:10240-10245.
78. Honey C.J., Sporns O, Cammoun L, Gigandet X, Thiran J.P., Meuli R, Hagmann P. 2009. Predicting human resting-state functional connectivity from structural connectivity. Proc Natl Acad Sci U S A 106:2035-2040.
79. Jansen B.H., Rit VG. 1995. Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol Cybern 73:357-366.
80. Jirsa V.K., Haken H. 1996. Field theory of electromagnetic brain activity. Phys Rev Lett 77:960-963.
81. Jirsa V.K., Kelso JA. 2000. Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 62(6 Pt B):8462-8465.
82. Jirsa V.K., Friedrich R, Haken H, Kelso JA. 1994. A theoretical model of phase transitions in the human brain. Biol Cybern 71:27-35.
83. Kasahara M, Menon D.K., Salmond C.H., Outtrim J.G., Taylor Tavares J.V., Carpenter T.A., Pickard J.D., Sahakian B.J., Stamatakis EA. 2010. Altered functional connectivity in the motor network after traumatic brain injury. Neurology 75:168-176.
84. Kass R.E., Raftery AE. 1995. Bayes factors. J Am Stat Assoc 90:773-795.
85. Kiebel S.J., David O, Friston KJ. 2006. Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization. Neuroimage 30:1273-1284.
86. Kiebel S.J., Garrido M.I., Friston KJ. 2007. Dynamic causal modelling of evoked responses: the role of intrinsic connections. Neuroimage 36:332-345.
87. Kitzbichler M.G., Smith M.L., Christensen S.R., Bullmore E. 2009. Broadband criticality of human brain network synchronization. PLoS Comput Biol 5:e1000314.
88. Kiviniemi V, Kantola J-H, Jauhiainen J, Hyvãrinen A, Tervonen O. 2003. Independent component analysis of nondeterministic fMRI signal sources. Neuroimage 19:253-260.
89. Kopell N, Ermentrout GB. 1986. Symmetry and phase-locking in chains of weakly coupled oscillators. Comm Pure Appl Math 39:623-660.
90. Kriener B, Tetzlaff T, Aertsen A, Diesmann M, Rotter S. 2008. Correlations and population dynamics in cortical networks. Neural Comput 20:2185-2226.
91. Lauritzen S. 1996. Graphical Models. Oxford University Press: Oxford, UK.
92. Lee T.S., Mumford D. 2003. Hierarchical Bayesian inference in the visual cortex. J Opt Soc Am Opt Image Sci Vis 20:1434-1448.
93. Linkenkaer-Hansen K, Nikouline V.V., Palva J.M., Ilmoniemi RJ. 2001. Long-range temporal correlations and scaling behavior in human brain oscillations. J Neurosci 21:1370-1377.
94. Lopes da Silva F.H., Hoeks A, Smits H, Zetterberg LH. 1974. Model of brain rhythmic activity. The alpha-rhythm of the thalamus. Kybernetik 15:27-37.
95. Marinazzo D, Liao W, Chen H. Stramaglia S. 2010. Nonlinear connectivity by Granger causality. Neuroimage. [Epub ahead of print].
96. Marreiros A.C., Kiebel S.J., Daunizeau J, Harrison L.M., Friston KJ. 2009. Population dynamics under the Laplace assumption. Neuroimage 44:701-714.
97. Marrelec G, Krainik A, Duffau H, Pãlãgrini-Issac M, Lehãricy S, Doyon J, Benali H. 2006. Partial correlation for functional brain interactivity investigation in functional MRI. Neuroimage 32:228-237.
98. McIntosh A.R., Gonzalez-Lima F. 1991. Structural modeling of functional neural pathways mapped with 2-deoxyglucose: effects of acoustic startle habituation on the auditory system. Brain Res 547:295-302.
99. McIntosh A.R., Grady C.L., Ungerleider L.G., Haxby J.V., Rapoport S.I., Horwitz B. 1994. Network analysis of cortical visual pathways mapped with PET. J Neurosci 14:655-666.
100. McKeown M.J., Makeig S, Brown G.G., Jung T.P., Kindermann S.S., Bell A.J., Sejnowski TJ. 1998. Analysis of fMRI data by blind separation into independent spatial components. Hum Brain Mapp 6:160-188.
101. Miller K.J., Sorensen L.B., Ojemann J.G., den Nijs M. 2009. ECoG observations of power-law scaling in the human cortex. PLoS Comput Biol 5:e1000609.
102. Moran R.J., Kiebel S.J., Stephan K.E., Reilly R.B., Daunizeau J, Friston KJ. 2007. A neural-mass model of spectral responses in electrophysiology. Neuroimage 37:706-720.
103. Moran R.J., Stephan K.E., Kiebel S.J., Rombach N, O'Connor W.T., Murphy K.J., Reilly R.B., Friston KJ. 2008. Bayesian estimation of synaptic physiology from the spectral responses of neural-masses. Neuroimage 42:272-284.
104. Moran R.J., Stephan K.E., Seidenbecher T, Pape H.C., Dolan R.J., Friston KJ. 2009. Dynamic causal models of steady-state responses. NeuroImage 44:796-811.
105. Morris C, Lecar H. 1981. Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193-213.
106. Müller-Linow M, Hilgetag C.C., Hütt M-T. 2008. Organization of excitable dynamics in hierarchical biological networks. PLoS Comput Biol 4:e1000190.
107. Mumford D. 1992. On the computational architecture of the neocortex. II. The role of cortico-cortical loops. Biol Cybern 66:241-251.
108. Murray S.O., Kersten D, Olshausen B.A., Schrater P, Woods DL. 2002. Shape perception reduces activity in human primary visual cortex. Proc Natl Acad Sci U S A 99:15164-15169.
109. Nããtãnen R. 2003. Mismatch negativity: clinical research and possible applications. Int J Psychophysiol 48:179-188.
110. Nalatore H, Ding M, Rangarajan G. 2007. Mitigating the effects of measurement noise on Granger causality. Phys Rev E 75:31123.1-31123.10.
111. Nolte G, Ziehe A, Nikulin V, Schlãgl A, Krãmer N, Brismar T, Müller K. 2008. Robustly estimating the flow direction of information in complex physical systems. Phys Rev Lett 100:234101.1-234101.4.
112. Patel R, Bowman F, Rilling J. 2006. A Bayesian approach to determining connectivity of the human brain. Hum Brain Mapp 27:267-276.
113. Pawela C.P., Biswal B.B., Cho Y.R., Kao D.S., Li R, Jones S.R., Schulte M.L., Matloub H.S., Hudetz A.G., Hyde JS. 2008. Resting-state functional connectivity of the rat brain. Magn Reson Med 59:1021-1029.
114. Pearl J. 2000. Causality: Models, Reasoning and Inference. Cambridge University Press: Cambridge, UK.
115. Penny W.D., Stephan K.E., Mechelli A, Friston KJ. 2004. Comparing dynamic causal models. Neuroimage 22:1157-1172.
116. Phillips C.G., Zeki S, Barlow HB. 1984. Localisation of function in the cerebral cortex past present and future. Brain 107:327-361.
117. Protzner A.B., McIntosh AR. 2006. Testing effective connectivity changes with structural equation modeling: what does a bad model tell us? Hum Brain Mapp 27:935-947.
118. Raichle M.E., MacLeod A.M., Snyder A.Z., Powers W.J., Gusnard D.A., Shulman GL. 2001. A default mode of brain function. Proc Natl Acad Sci U S A 98:676-682.
119. Ramsey J.D., Hanson S.J., Hanson C, Halchenko Y.O., Poldrack R.A., Glymour C. 2010. Six problems for causal inference from fMRI. Neuroimage 49:1545-1558.
120. Rao R.P., Ballard DH. 1998. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive field effects. Nat Neurosci 2:79-87.
121. Robinson P.A., Rennie C.J., Wright JJ. 1997. Propagation and stability of waves of electrical activity in the cerebral cortex. Phys Rev E 56:826-840.
122. Roebroeck A, Formisano E, Goebel R. 2005. Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 25:230-242.
123. Roebroeck A, Formisano E, Goebel R. 2009. The identification of interacting networks in the brain using fMRI: model selection, causality and deconvolution. Neuroimage Sep 25. [Epub ahead of print].
124. Rogers B.P., Katwal S.B., Morgan V.L., Asplund C.L., Gore JC. 2010. Functional MRI and multivariate autoregressive models. Magn Reson Imaging 28:1058-1065.
125. Roopun A.K., Kramer M.A., Carracedo L.M., Kaiser M, Davies C.H., Traub R.D., Kopell N.J., Whittington MA. 2008. Period concatenation underlies interactions between gamma and beta rhythms in neocortex. Front Cell Neurosci 2:1.
126. Rubinov M, Sporns O, van Leeuwen C, Breakspear M. 2009. Symbiotic relationship between brain structure and dynamics. BMC Neurosci 10:55.
127. Saneyoshi T, Fortin D.A., Soderling TR. 2010. Regulation of spine and synapse formation by activity-dependent intracellular signaling pathways. Curr Opin Neurobiol 20:108-115.
128. Scherg M, Von Cramon D. 1985. Two bilateral sources of the late AEP as identified by a spatio-temporal dipole model. Electroencephalogr Clin Neurophysiol 62:32-44.
129. Smith A.P., Stephan K.E., Rugg M.D., Dolan RJ. 2006. Task and content modulate amygdala-hippocampal connectivity in emotional retrieval. Neuron 49:631-638.
130. Smith S.M., Miller K.L., Salimi-Khorshidi G, Webster M, Beckmann C.F., Nichols T.E., Woolrich M. 2010. Network Modelling Methods for FMRI. Neuroimage 54:875-891.
131. Spearman C. 1904. The proof and measurement of association between two things. Am J Psychol 15:72-101.
132. Spirtes P, Glymour C, Scheines R. 1993. Causation, Prediction, and Search. Berlin-Heidelberg-New York: Springer-Verlag.
133. Sporns O. 2007. Brain connectivity. Scholarpedia 2:4695.
134. Sporns O. 2010. Networks of the Brain. Boston: MIT Press. ISBN-13: 978-0-262-01469-4.
135. Sporns O, Tononi G, Kãtter R. 2005. The human connectome: a structural description of the human brain. PLoS Comput Biol 1:e42.
136. Stam C.J., de Bruin EA. 2004. Scale-free dynamics of global functional connectivity in the human brain. Hum Brain Mapp 22:97-109.
137. Staum M. 1995. Physiognomy and phrenology at the Paris Athãnãe. J Hist Ideas 56:443-462.
138. Stephan K.E., Weiskopf N, Drysdale P.M., Robinson P.A., Friston KJ. 2007. Comparing hemodynamic models with DCM. Neuroimage 38:387-401.
139. Stephan K.E., Kasper L, Harrison L.M., Daunizeau J, den Ouden H.E., Breakspear M, Friston KJ. 2008. Nonlinear dynamic causal models for fMRI. Neuroimage 42:649-662.
140. Stephan K.E., Tittgemeyer M, Knãsche T.R., Moran R.J., Friston KJ. 2009. Tractography-based priors for dynamic causal models. Neuroimage 47:1628-1638.
141. Summerfield C, Koechlin E. 2008. A neural representation of prior information during perceptual inference. Neuron 59:336-347.
142. Tiao G, Wei W. 1976. Effect of temporal aggregation on the dynamic relationship of two time series variables. Biometrika 63:513-523.
143. Tognoli E, Kelso JA. 2009. Brain coordination dynamics: true and false faces of phase synchrony and metastability. Prog Neurobiol 87:31-40.
144. Touboul J, Destexhe A. 2009. Can power-law scaling and neuronal avalanches arise from stochastic dynamics? PLoS One 5:e8982.
145. Tschacher W, Haken H. 2007. Intentionality in non-equilibrium systems? The functional aspects of self-organised pattern formation. New Ideas Psychol 25:1-15.
146. Tsuda I. 2001. Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24:793-810.
147. Valdãs-Sosa P.A., Roebroeck A, Daunizeau J, Friston K. 2011. Effective connectivity: influence, causality and biophysical modeling. Neuroimage Apr 5. [Epub a head of print].
148. Van Dijk K.R., Hedden T, Venkataraman A, Evans K.C., Lazar S.W., Buckner RL. 2010. Intrinsic functional connectivity as a tool for human connectomics: theory, properties, and optimization. J Neurophysiol 103:297-321.
149. Wang XJ. 2010. Physiological and computational principles of cortical rhythms in cognition. Physiol Rev 90:1195-1268.
150. Wei W. 1978. The effect of temporal aggregation on parameter estimation in distributed lag model. J Econometrics 8:237-246.
151. White H, Lu X. 2010. Granger causality and dynamic structural systems. J Financial Econometrics 8:193-243.
152. Wolf M.E., Mangiavacchi S, Sun X. 2003. Mechanisms by which dopamine receptors may influence synaptic plasticity. Ann N Y Acad Sci 1003:241-249.
153. Wright S. 1921. Correlation and causation. J Agric Res 20:557-585.
154. Zhang H, Alexander DC. 2010. Axon diameter mapping in the presence of orientation dispersion with diffusion MRI. Med Image Comput Comput Assist Interv 13:640-647.