Functional and Effective Connectivity: A Review

Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.

[1]  Daniele Marinazzo,et al.  Functional and effective connectivity in EEG alpha and beta bands during intermittent flash stimulation in migraine with and without aura , 2013, Cephalalgia : an international journal of headache.

[2]  H. White,et al.  Granger Causality and Dynamic Structural Systems , 2010 .

[3]  Larry A. Kramer,et al.  Interhemispheric Effective and Functional Cortical Connectivity Signatures of Spina Bifida Are Consistent with Callosal Anomaly , 2012, Brain Connect..

[4]  D. Alexander A general framework for experiment design in diffusion MRI and its application in measuring direct tissue‐microstructure features , 2008, Magnetic resonance in medicine.

[5]  Mark W. Woolrich,et al.  Biophysical network models and the human connectome , 2013, NeuroImage.

[6]  Wei Liao,et al.  Mapping the Voxel-Wise Effective Connectome in Resting State fMRI , 2013, PloS one.

[7]  D. Mantini,et al.  Functional connectivity and oscillatory neuronal activity in the resting human brain , 2013, Neuroscience.

[8]  Philip G. F. Browning,et al.  Causal effect of disconnection lesions on interhemispheric functional connectivity in rhesus monkeys , 2013, Proceedings of the National Academy of Sciences.

[9]  P. Goldman-Rakic,et al.  Preface: Cerebral Cortex Has Come of Age , 1991 .

[10]  Clemens Brunner,et al.  Single-trial connectivity estimation for classification of motor imagery data , 2013, Journal of neural engineering.

[11]  Joachim M. Buhmann,et al.  Generative Embedding for Model-Based Classification of fMRI Data , 2011, PLoS Comput. Biol..

[12]  Hartwig R. Siebner,et al.  Effects of Cortical Stimulation on Cortical Functional Connectivity: Imaging Studies , 2012 .

[13]  Jonathan D. Power,et al.  Multi-task connectivity reveals flexible hubs for adaptive task control , 2013, Nature Neuroscience.

[14]  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.

[15]  J. Cowan,et al.  Statistical mechanics of the neocortex. , 2009, Progress in biophysics and molecular biology.

[16]  T. Soderling,et al.  Regulation of spine and synapse formation by activity-dependent intracellular signaling pathways , 2010, Current Opinion in Neurobiology.

[17]  G. Curio,et al.  Functional and effective connectivity in subthalamic local field potential recordings of patients with Parkinson’s disease , 2013, Neuroscience.

[18]  Karl J. Friston,et al.  The functional anatomy of the MMN: A DCM study of the roving paradigm , 2008, NeuroImage.

[19]  Bin He,et al.  A weighted small world network measure for assessing functional connectivity , 2013, Journal of Neuroscience Methods.

[20]  Karl J. Friston,et al.  Forward and backward connections in the brain: A DCM study of functional asymmetries , 2009, NeuroImage.

[21]  S. Bressler,et al.  Operational principles of neurocognitive networks. , 2006, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[22]  Patric Hagmann,et al.  Comparing connectomes across subjects and populations at different scales , 2013, NeuroImage.

[23]  Xiao-Jing Wang Neurophysiological and computational principles of cortical rhythms in cognition. , 2010, Physiological reviews.

[24]  P A Robinson,et al.  Discrete-network versus modal representations of brain activity: why a sparse regions-of-interest approach can work for analysis of continuous dynamics. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Ivan Toni,et al.  Parieto-Frontal Connectivity during Visually Guided Grasping , 2007, The Journal of Neuroscience.

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

[27]  Karl J. Friston,et al.  Network discovery with large DCMs , 2013, NeuroImage.

[28]  K. Cheng Theory of Superconductivity , 1948, Nature.

[29]  F. Bartolomei,et al.  Imaging structural and functional connectivity: towards a unified definition of human brain organization? , 2008, Current opinion in neurology.

[30]  Karl J. Friston,et al.  Psychophysiological and Modulatory Interactions in Neuroimaging , 1997, NeuroImage.

[31]  Daniele Marinazzo,et al.  Mapping the epileptic brain with EEG dynamical connectivity: Established methods and novel approaches , 2012 .

[32]  Lourens J. Waldorp,et al.  Matching Structural, Effective, and Functional Connectivity: A Comparison Between Structural Equation Modeling and Ancestral Graphs , 2013, Brain Connect..

[33]  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.

[34]  Michael Breakspear,et al.  Graph analysis of the human connectome: Promise, progress, and pitfalls , 2013, NeuroImage.

[35]  G. Ermentrout,et al.  Symmetry and phaselocking in chains of weakly coupled oscillators , 1986 .

[36]  Michael Breakspear,et al.  Dynamics of a neural system with a multiscale architecture , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[37]  H. Haken,et al.  Field Theory of Electromagnetic Brain Activity. , 1996, Physical review letters.

[38]  Viktor K. Jirsa,et al.  A theoretical model of phase transitions in the human brain , 1994, Biological Cybernetics.

[39]  Leslie G. Ungerleider,et al.  Network analysis of cortical visual pathways mapped with PET , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[40]  J. A. Scott Kelso,et al.  Brain coordination dynamics: True and false faces of phase synchrony and metastability , 2009, Progress in Neurobiology.

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

[42]  Vesa Kiviniemi,et al.  A Sliding Time-Window ICA Reveals Spatial Variability of the Default Mode Network in Time , 2011, Brain Connect..

[43]  E. Bullmore,et al.  Imaging structural co-variance between human brain regions , 2013, Nature Reviews Neuroscience.

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

[45]  Andreas Kleinschmidt,et al.  Ongoing Activity Fluctuations in hMT+ Bias the Perception of Coherent Visual Motion , 2008, The Journal of Neuroscience.

[46]  J D Pickard,et al.  Altered functional connectivity in the motor network after traumatic brain injury , 2010, Neurology.

[47]  E. Bullmore,et al.  Human brain networks in health and disease , 2009, Current opinion in neurology.

[48]  Yong He,et al.  Assessment of system dysfunction in the brain through MRI-based connectomics , 2013, The Lancet Neurology.

[49]  Jeffrey S. Anderson,et al.  BOLD Granger Causality Reflects Vascular Anatomy , 2013, PloS one.

[50]  Hui Zhang,et al.  Axon diameter mapping in the presence of orientation dispersion with diffusion MRI , 2011, NeuroImage.

[51]  Julien Cohen-Adad,et al.  Visualizing integrative functioning in the human brainstem and spinal cord with spinal functional magnetic resonance imaging. , 2013, Neurosurgery.

[52]  M Staum,et al.  Physiognomy and phrenology at the Paris Athénée. , 1995, Journal of the history of ideas.

[53]  Raymond J. Dolan,et al.  Network reconfiguration and working memory impairment in mesial temporal lobe epilepsy , 2013, NeuroImage.

[54]  Rajan S. Patel,et al.  A Bayesian approach to determining connectivity of the human brain , 2006, Human brain mapping.

[55]  Karl J. Friston,et al.  Network discovery with DCM , 2011, NeuroImage.

[56]  Hermann Haken,et al.  Synergetics: An Introduction , 1983 .

[57]  Katsunori Kitano,et al.  Impact of network topology on inference of synaptic connectivity from multi-neuronal spike data simulated by a large-scale cortical network model , 2013, Journal of Computational Neuroscience.

[58]  Philip K. McGuire,et al.  Fronto-temporal Interactions during Overt Verbal Initiation and Suppression , 2008, Journal of Cognitive Neuroscience.

[59]  Andrew Zalesky,et al.  Dynamic Changes in Brain Functional Connectivity during Concurrent Dual-Task Performance , 2011, PloS one.

[60]  Karl J. Friston,et al.  Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization , 2006, NeuroImage.

[61]  Russell A. Poldrack,et al.  Six problems for causal inference from fMRI , 2010, NeuroImage.

[62]  M. Boly,et al.  Granger Causality Analysis of Steady-State Electroencephalographic Signals during Propofol-Induced Anaesthesia , 2012, PloS one.

[63]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[64]  Steffen L. Lauritzen,et al.  Graphical models in R , 1996 .

[65]  Ali Yener Mutlu,et al.  A Signal-Processing-Based Approach to Time-Varying Graph Analysis for Dynamic Brain Network Identification , 2012, Comput. Math. Methods Medicine.

[66]  R Cameron Craddock,et al.  Disease state prediction from resting state functional connectivity , 2009, Magnetic resonance in medicine.

[67]  Amir Shmuel,et al.  Evaluation and calibration of functional network modeling methods based on known anatomical connections , 2012 .

[68]  Karl J. Friston,et al.  Repetition suppression and plasticity in the human brain , 2009, NeuroImage.

[69]  K. Kaplan H. Haken, Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry, and Biology (2nd Edition). XI + 355 S., 152 Abb. Berlin—Heidelberg—New York 1978. Springer-Verlag. DM 66,00 , 1980 .

[70]  Jeff H. Duyn,et al.  Modulation of spontaneous fMRI activity in human visual cortex by behavioral state , 2009, NeuroImage.

[71]  Karl J. Friston,et al.  Nonlinear Dynamic Causal Models for Fmri Nonlinear Dynamic Causal Models for Fmri Nonlinear Dynamic Causal Models for Fmri , 2022 .

[72]  Stefan Rotter,et al.  Correlations and Population Dynamics in Cortical Networks , 2008, Neural Computation.

[73]  Catie Chang,et al.  Mapping and correction of vascular hemodynamic latency in the BOLD signal , 2008, NeuroImage.

[74]  R. Näätänen Mismatch negativity: clinical research and possible applications. , 2003, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[75]  C. Bédard,et al.  Model of low-pass filtering of local field potentials in brain tissue. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  Scott T. Grafton,et al.  Structural foundations of resting-state and task-based functional connectivity in the human brain , 2013, Proceedings of the National Academy of Sciences.

[77]  Hae-Jeong Park,et al.  A System for Concurrent TMS-fMRI and Evaluation of Imaging Effects , 2013 .

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

[79]  Stefan Golaszewski,et al.  Mechanical flutter stimulation induces a lasting response in the sensorimotor cortex as revealed with BOLD fMRI , 2013, Human brain mapping.

[80]  Gian Luca Romani,et al.  Long-range functional interactions of anterior insula and medial frontal cortex are differently modulated by visuospatial and inductive reasoning tasks , 2013, NeuroImage.

[81]  George A Mashour,et al.  Interfaces of sleep and anesthesia. , 2012, Anesthesiology clinics.

[82]  John C Gore,et al.  Functional MRI and multivariate autoregressive models. , 2010, Magnetic resonance imaging.

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

[84]  A. McIntosh,et al.  Structural modeling of functional neural pathways mapped with 2-deoxyglucose: effects of acoustic startle habituation on the auditory system , 1991, Brain Research.

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

[86]  P. Spirtes,et al.  Causation, prediction, and search , 1993 .

[87]  Olaf Sporns,et al.  Brain connectivity , 2007, Scholarpedia.

[88]  R. Buxton The physics of functional magnetic resonance imaging (fMRI) , 2013, Reports on progress in physics. Physical Society.

[89]  D Marinazzo,et al.  Recovering directed networks in neuroimaging datasets using partially conditioned Granger causality , 2013, BMC Neuroscience.

[90]  G. Deco,et al.  Emerging concepts for the dynamical organization of resting-state activity in the brain , 2010, Nature Reviews Neuroscience.

[91]  Dimitri Van De Ville,et al.  Connectivity searchlight: A novel approach for MRI information mapping using multivariate connectivity , 2013, 2013 IEEE 10th International Symposium on Biomedical Imaging.

[92]  James J. Wright,et al.  Propagation and stability of waves of electrical activity in the cerebral cortex , 1997 .

[93]  Karl J. Friston,et al.  Multivariate Autoregressive Modelling of fMRI time series , 2003 .

[94]  Francisco del Pozo,et al.  HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity , 2013, Neuroinformatics.

[95]  Marc-Thorsten Hütt,et al.  Organization of Excitable Dynamics in Hierarchical Biological Networks , 2008, PLoS Comput. Biol..

[96]  Tongsheng Zhang,et al.  Facilitating Neuronal Connectivity Analysis of Evoked Responses by Exposing Local Activity with Principal Component Analysis Preprocessing: Simulation of Evoked MEG , 2013, Brain Topography.

[97]  F. H. Lopes da Silva,et al.  Model of brain rhythmic activity , 1974, Kybernetik.

[98]  Tai Sing Lee,et al.  Hierarchical Bayesian inference in the visual cortex. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[99]  Matteo Colombo,et al.  Moving Forward (and Beyond) the Modularity Debate: A Network Perspective , 2013, Philosophy of Science.

[100]  Joshua Kahan,et al.  Comments and Controversies Understanding Dcm: Ten Simple Rules for the Clinician , 2022 .

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

[102]  Geoffrey E. Hinton,et al.  The Helmholtz Machine , 1995, Neural Computation.

[103]  Yilun Wang,et al.  Feature Selection via Sparse Regression for Classification of Functional Brain Networks , 2013, IScIDE.

[104]  Thomas E. Nichols,et al.  Functional connectomics from resting-state fMRI , 2013, Trends in Cognitive Sciences.

[105]  Karl J. Friston Functional and effective connectivity in neuroimaging: A synthesis , 1994 .

[106]  J. Mattingley,et al.  Dynamic cooperation and competition between brain systems during cognitive control , 2013, Trends in Cognitive Sciences.

[107]  T. Adali,et al.  Unmixing fMRI with independent component analysis , 2006, IEEE Engineering in Medicine and Biology Magazine.

[108]  Timothy E. J. Behrens,et al.  Tools of the trade: psychophysiological interactions and functional connectivity. , 2012, Social cognitive and affective neuroscience.

[109]  David Mumford,et al.  On the computational architecture of the neocortex , 2004, Biological Cybernetics.

[110]  Olaf Sporns,et al.  Network attributes for segregation and integration in the human brain , 2013, Current Opinion in Neurobiology.

[111]  R. Dolan,et al.  Task and Content Modulate Amygdala-Hippocampal Connectivity in Emotional Retrieval , 2006, Neuron.

[112]  Aaron Kucyi,et al.  Hemispheric Asymmetry in White Matter Connectivity of the Temporoparietal Junction with the Insula and Prefrontal Cortex , 2012, PloS one.

[113]  D Mumford,et al.  On the computational architecture of the neocortex. II. The role of cortico-cortical loops. , 1992, Biological cybernetics.

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

[115]  Andrea Soddu,et al.  Changes in Effective Connectivity by Propofol Sedation , 2013, PloS one.

[116]  D. Benson,et al.  Disconnection syndromes , 1993, Neurology.

[117]  Kerstin Preuschoff,et al.  Optimizing Experimental Design for Comparing Models of Brain Function , 2011, PLoS Comput. Biol..

[118]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[119]  C. Summerfield,et al.  A Neural Representation of Prior Information during Perceptual Inference , 2008, Neuron.

[120]  Karl J. Friston Modes or models: a critique on independent component analysis for fMRI , 1998, Trends in Cognitive Sciences.

[121]  Karl J. Friston,et al.  A free energy principle for the brain , 2006, Journal of Physiology-Paris.

[122]  Walter J. Freeman,et al.  A field-theoretic approach to understanding scale-free neocortical dynamics , 2005, Biological Cybernetics.

[123]  Olaf Sporns,et al.  Network structure of cerebral cortex shapes functional connectivity on multiple time scales , 2007, Proceedings of the National Academy of Sciences.

[124]  G. Rangarajan,et al.  Mitigating the effects of measurement noise on Granger causality. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[125]  C. Spearman The proof and measurement of association between two things. , 2015, International journal of epidemiology.

[126]  Wei Liao,et al.  Nonlinear connectivity by Granger causality , 2011, NeuroImage.

[127]  Karl J. Friston,et al.  Dynamic causal modelling of distributed electromagnetic responses , 2009, NeuroImage.

[128]  Emeran A. Mayer,et al.  Alterations in Prefrontal-Limbic Functional Activation and Connectivity in Chronic Stress-Induced Visceral Hyperalgesia , 2013, PloS one.

[129]  Olaf Sporns,et al.  Making sense of brain network data , 2013, Nature Methods.

[130]  Robert D. Nowak,et al.  Cross Validation for Selection of Cortical Interaction Models From Scalp EEG or MEG , 2012, IEEE Transactions on Biomedical Engineering.

[131]  Karl J. Friston,et al.  Effective connectivity: Influence, causality and biophysical modeling , 2011, NeuroImage.

[132]  Karl J. Friston,et al.  Characterizing modulatory interactions between areas V1 and V2 in human cortex: A new treatment of functional MRI data , 1994 .

[133]  Raymond J. Dolan,et al.  Dynamic causal models of steady-state responses , 2009, NeuroImage.

[134]  Gabriele Lohmann,et al.  "More Is Different" in Functional Magnetic Resonance Imaging: A Review of Recent Data Analysis Techniques , 2013, Brain Connect..

[135]  Oguz Dikenelli,et al.  Mimicking human neuronal pathways in silico: an emergent model on the effective connectivity , 2013, Journal of Computational Neuroscience.

[136]  Gordana Derado,et al.  BSMac: A MATLAB toolbox implementing a Bayesian spatial model for brain activation and connectivity , 2012, Journal of Neuroscience Methods.

[137]  J. Carr Applications of Centre Manifold Theory , 1981 .

[138]  Xiaoping Hu,et al.  Assessing and Compensating for Zero-Lag Correlation Effects in Time-Lagged Granger Causality Analysis of fMRI , 2010, IEEE Transactions on Biomedical Engineering.

[139]  P. Games Correlation and Causation: A Logical Snafu , 1990 .

[140]  Karl J. Friston,et al.  Bayesian estimation of synaptic physiology from the spectral responses of neural masses , 2008, NeuroImage.

[141]  C. Rondinoni,et al.  Effect of scanner acoustic background noise on strict resting-state fMRI , 2013, Brazilian journal of medical and biological research = Revista brasileira de pesquisas medicas e biologicas.

[142]  Karl J. Friston,et al.  The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields , 2008, PLoS Comput. Biol..

[143]  H. Haken,et al.  Intentionality in non-equilibrium systems? The functional aspects of self-organized pattern formation , 2007 .

[144]  Bernhard Hemmer,et al.  Simultaneous Electroencephalographic and Functional Magnetic Resonance Imaging Indicate Impaired Cortical Top–Down Processing in Association with Anesthetic-induced Unconsciousness , 2013, Anesthesiology.

[145]  I. Tsuda Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. , 2001, The Behavioral and brain sciences.

[146]  A. Borst Seeing smells: imaging olfactory learning in bees , 1999, Nature Neuroscience.

[147]  Karl J. Friston,et al.  A neural mass model for MEG/EEG: coupling and neuronal dynamics , 2003, NeuroImage.

[148]  Karl J. Friston,et al.  Evoked brain responses are generated by feedback loops , 2007, Proceedings of the National Academy of Sciences.

[149]  P A Robinson,et al.  Neural mechanisms of ERP change: combining insights from electrophysiology and mathematical modeling. , 2008, Journal of integrative neuroscience.

[150]  Mark W. Greenlee,et al.  Connectivity modulation of early visual processing areas during covert and overt tracking tasks , 2008, NeuroImage.

[151]  Jeffrey G. Ojemann,et al.  Power-Law Scaling in the Brain Surface Electric Potential , 2009, PLoS Comput. Biol..

[152]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[153]  O. Sporns,et al.  Key role of coupling, delay, and noise in resting brain fluctuations , 2009, Proceedings of the National Academy of Sciences.

[154]  Habib Benali,et al.  Partial correlation for functional brain interactivity investigation in functional MRI , 2006, NeuroImage.

[155]  Jürgen Popp,et al.  Accumulating advantages, reducing limitations: Multimodal nonlinear imaging in biomedical sciences – The synergy of multiple contrast mechanisms , 2013, Journal of biophotonics.

[156]  G. C. Tiao,et al.  Effect of temporal aggregation on the dynamic relationship of two time series variables , 1976 .

[157]  Karl J. Friston,et al.  Population dynamics under the Laplace assumption , 2009, NeuroImage.

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

[159]  Olaf Sporns,et al.  Modeling the Impact of Lesions in the Human Brain , 2009, PLoS Comput. Biol..

[160]  K. Linkenkaer-Hansen,et al.  Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations , 2001, The Journal of Neuroscience.

[161]  M. Emri,et al.  Remission of benign epilepsy with rolandic spikes: An EEG-based connectivity study at the onset of the disease and at remission , 2013, Epilepsy Research.

[162]  Karl J. Friston,et al.  Evaluation of different measures of functional connectivity using a neural mass model , 2004, NeuroImage.

[163]  H Preißl,et al.  Dynamics of activity and connectivity in physiological neuronal networks , 1991 .

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

[165]  R. Kötter,et al.  Cortical network dynamics with time delays reveals functional connectivity in the resting brain , 2008, Cognitive Neurodynamics.

[166]  Tianzi Jiang,et al.  A review of functional magnetic resonance imaging for Brainnetome , 2012, Neuroscience Bulletin.

[167]  Zenas C. Chao,et al.  Large-Scale Information Flow in Conscious and Unconscious States: an ECoG Study in Monkeys , 2013, PloS one.

[168]  Karl J. Friston,et al.  Comparing dynamic causal models , 2004, NeuroImage.

[169]  Seth R. Jones,et al.  Resting‐state functional connectivity of the rat brain , 2008, Magnetic resonance in medicine.

[170]  P. Fries Neuronal gamma-band synchronization as a fundamental process in cortical computation. , 2009, Annual review of neuroscience.

[171]  Timothy Edward John Behrens,et al.  Relating connectional architecture to grey matter function using diffusion imaging , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[172]  C. Stam,et al.  Scale‐free dynamics of global functional connectivity in the human brain , 2004, Human brain mapping.

[173]  Jane E. Huggins,et al.  Altered cortical communication in amyotrophic lateral sclerosis , 2013, Neuroscience Letters.

[174]  Mark W. Woolrich,et al.  Resting-state fMRI in the Human Connectome Project , 2013, NeuroImage.

[175]  J. Touboul,et al.  Can Power-Law Scaling and Neuronal Avalanches Arise from Stochastic Dynamics? , 2009, PloS one.

[176]  Annette Witt,et al.  Dynamic Effective Connectivity of Inter-Areal Brain Circuits , 2011, PLoS Comput. Biol..

[177]  Bernard Ng,et al.  Overlapping Replicator Dynamics for Functional Subnetwork Identification , 2013, MICCAI.

[178]  Kathleen M. Gates,et al.  Inferring functional connectivity in MRI using Bayesian network structure learning with a modified PC algorithm , 2013, NeuroImage.

[179]  Stephen M. Smith,et al.  The future of FMRI connectivity , 2012, NeuroImage.

[180]  Andrea B Protzner,et al.  Testing effective connectivity changes with structural equation modeling: What does a bad model tell us? , 2006, Human brain mapping.

[181]  Heidi Johansen-Berg,et al.  Tractography: Where Do We Go from Here? , 2011, Brain Connect..

[182]  M. Greicius,et al.  Resting-state functional connectivity reflects structural connectivity in the default mode network. , 2009, Cerebral cortex.

[183]  S. Coombes,et al.  Neuronal populations with reciprocal inhibition and rebound currents: Effects of synaptic and threshold noise. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[184]  S Makeig,et al.  Analysis of fMRI data by blind separation into independent spatial components , 1998, Human brain mapping.

[185]  G L Shulman,et al.  INAUGURAL ARTICLE by a Recently Elected Academy Member:A default mode of brain function , 2001 .

[186]  Karl J. Friston,et al.  Tractography-based priors for dynamic causal models , 2009, NeuroImage.

[187]  William W. S. Wei,et al.  The effect of temporal aggregation on parameter estimation in distributed lag model , 1978 .

[188]  Lucy M. Carracedo,et al.  Period Concatenation Underlies Interactions between Gamma and Beta Rhythms in Neocortex , 2008, Frontiers in cellular neuroscience.

[189]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[190]  Raymond J. Dolan,et al.  Computational and dynamic models in neuroimaging , 2010, NeuroImage.

[191]  Aiping Liu,et al.  A Computationally Efficient, Exploratory Approach to Brain Connectivity Incorporating False Discovery Rate Control, A Priori Knowledge, and Group Inference , 2012, Comput. Math. Methods Medicine.

[192]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[193]  Anil K. Seth,et al.  Granger causality analysis of fMRI BOLD signals is invariant to hemodynamic convolution but not downsampling , 2013, NeuroImage.

[194]  Michael J Frank,et al.  Freezing of gait in Parkinson's disease is associated with functional decoupling between the cognitive control network and the basal ganglia. , 2013, Brain : a journal of neurology.

[195]  L. Shah,et al.  Functional magnetic resonance imaging. , 2010, Seminars in roentgenology.

[196]  Karl J. Friston,et al.  a K.E. Stephan, a R.B. Reilly, , 2007 .

[197]  Ying Liu,et al.  Quantification of Effective Connectivity in the Brain Using a Measure of Directed Information , 2012, Comput. Math. Methods Medicine.

[198]  Luca Faes,et al.  Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis , 2012, Comput. Math. Methods Medicine.

[199]  M. Breakspear,et al.  Bistability and Non-Gaussian Fluctuations in Spontaneous Cortical Activity , 2009, The Journal of Neuroscience.

[200]  Karl J. Friston,et al.  Dynamic causal modeling of evoked responses in EEG and MEG , 2006, NeuroImage.

[201]  Aapo Hyvärinen,et al.  Independent component analysis of nondeterministic fMRI signal sources , 2003, NeuroImage.

[202]  L. Abbott,et al.  Synaptic Depression and Cortical Gain Control , 1997, Science.

[203]  P A Robinson,et al.  Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[204]  W J Freeman,et al.  Characterization of state transitions in spatially distributed, chaotic, nonlinear, dynamical systems in cerebral cortex , 1994, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[205]  K. Müller,et al.  Robustly estimating the flow direction of information in complex physical systems. , 2007, Physical review letters.

[206]  G. Buzsáki,et al.  Gamma Oscillations in the Entorhinal Cortex of the Freely Behaving Rat , 1998, The Journal of Neuroscience.

[207]  Karl J. Friston,et al.  DEM: A variational treatment of dynamic systems , 2008, NeuroImage.

[208]  Karl J. Friston,et al.  Comparing hemodynamic models with DCM , 2007, NeuroImage.

[209]  J. Pearl Causality: Models, Reasoning and Inference , 2000 .

[210]  Karl J. Friston,et al.  Dynamic causal modelling of evoked potentials: A reproducibility study , 2007, NeuroImage.

[211]  K. Miller,et al.  ECoG observations of power-law scaling in the human cortex , 2007, 0712.0846.

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

[213]  Ali Yener Mutlu,et al.  Subspace analysis for characterizing dynamic functional brain networks , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[214]  Paul Schrater,et al.  Shape perception reduces activity in human primary visual cortex , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[215]  Ben H. Jansen,et al.  Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns , 1995, Biological Cybernetics.

[216]  Edward T. Bullmore,et al.  Broadband Criticality of Human Brain Network Synchronization , 2009, PLoS Comput. Biol..

[217]  S. Mangiavacchi,et al.  Mechanisms by which Dopamine Receptors May Influence Synaptic Plasticity , 2003, Annals of the New York Academy of Sciences.

[218]  D. Mantini,et al.  Functional Connectivity in the Normal and Injured Brain , 2013, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[219]  E. Bullmore,et al.  Adaptive reconfiguration of fractal small-world human brain functional networks , 2006, Proceedings of the National Academy of Sciences.

[220]  Salvatore Torrisi,et al.  Advancing understanding of affect labeling with dynamic causal modeling , 2013, NeuroImage.

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

[222]  Geoffrey E. Hinton,et al.  Parallel visual computation , 1983, Nature.

[223]  J A Kelso,et al.  Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[224]  Olaf Sporns,et al.  The human connectome: Origins and challenges , 2013, NeuroImage.

[225]  Olaf Sporns,et al.  Symbiotic relationship between brain structure and dynamics , 2009, BMC Neuroscience.

[226]  Christian Kaufmann,et al.  Altered Cingulostriatal Coupling in Obsessive-Compulsive Disorder , 2012, Brain Connect..

[227]  Joachim M. Buhmann,et al.  Model-based feature construction for multivariate decoding , 2011, NeuroImage.

[228]  M. Scherg,et al.  Two bilateral sources of the late AEP as identified by a spatio-temporal dipole model. , 1985, Electroencephalography and clinical neurophysiology.

[229]  M. Fox,et al.  The global signal and observed anticorrelated resting state brain networks. , 2009, Journal of neurophysiology.

[230]  Maurizio Corbetta,et al.  Measuring Granger Causality between Cortical Regions from Voxelwise fMRI BOLD Signals with LASSO , 2012, PLoS Comput. Biol..

[231]  Karl J. Friston,et al.  Dynamic causal modelling of evoked responses: The role of intrinsic connections , 2007, NeuroImage.

[232]  C. J. Honeya,et al.  Predicting human resting-state functional connectivity from structural connectivity , 2009 .

[233]  C. G. Phillips,et al.  Localization of function in the cerebral cortex. Past, present and future. , 1984, Brain : a journal of neurology.

[234]  Archana Venkataraman,et al.  Intrinsic functional connectivity as a tool for human connectomics: theory, properties, and optimization. , 2010, Journal of neurophysiology.

[235]  P. Anderson More is different. , 1972, Science.

[236]  D. Perkel,et al.  Simultaneously Recorded Trains of Action Potentials: Analysis and Functional Interpretation , 1969, Science.

[237]  Mason A. Porter,et al.  Task-Based Core-Periphery Organization of Human Brain Dynamics , 2012, PLoS Comput. Biol..

[238]  M. Emri,et al.  Neurophysiology of juvenile myoclonic epilepsy: EEG-based network and graph analysis of the interictal and immediate preictal states , 2013, Epilepsy Research.

[239]  Karl J. Friston,et al.  Dynamic causal modelling of induced responses , 2008, NeuroImage.

[240]  K. Amunts,et al.  Effective connectivity of the left BA 44, BA 45, and inferior temporal gyrus during lexical and phonological decisions identified with DCM , 2009, Human brain mapping.