“Dynamic” connectivity in neural systems

The study of functional interdependences between brain regions is a rapidly growing focus of neuroscience research. This endeavor has been greatly facilitated by the appearance of a number of innovative methodologies for the examination of neurophysiological and neuroimaging data. The aim of this article is to present an overview of dynamical measures of interdependence and contrast these with statistical measures that have been more widely employed. We first review the motivation, conceptual basis, and experimental approach of dynamical measures of interdependence and their application to the study of neural systems. A consideration of boot-strap “surrogate data” techniques, which facilitate hypothesis testing of dynamical measures, is then used to clarify the difference between dynamical and statistical measures of interdependence. An overview of some of the most active research areas—such as the study of the “synchronization manifold,” dynamical interdependence in neurophysiology data and the putative role of nonlinear desynchronization—is then given. We conclude by suggesting that techniques based on dynamical interdependence—or “dynamical connectivity”—show significant potential for extracting meaningful information from functional neuroimaging data.

[1]  GOTTFRIED MAYER‐KRESS AND,et al.  Dimensionality of the Human Electroencephalogram , 1987, Annals of the New York Academy of Sciences.

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

[3]  Michael Breakspear,et al.  Perception of Odors by a Nonlinear Model of the Olfactory Bulb , 2001, Int. J. Neural Syst..

[4]  Michael Breakspear,et al.  An improved algorithm for the detection of dynamical interdependence in bivariate time-series , 2003, Biological Cybernetics.

[5]  T A Carpenter,et al.  Colored noise and computational inference in neurophysiological (fMRI) time series analysis: Resampling methods in time and wavelet domains , 2001, Human brain mapping.

[6]  David Ruelle,et al.  Deterministic chaos: the science and the fiction , 1995 .

[7]  P. Robinson,et al.  Prediction of electroencephalographic spectra from neurophysiology. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  C. Stam,et al.  Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets , 2002 .

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

[10]  E. M. Shahverdiev,et al.  Lag synchronization in time-delayed systems , 2002 .

[11]  A. McIntosh,et al.  Functional Connectivity of the Medial Temporal Lobe Relates to Learning and Awareness , 2003, The Journal of Neuroscience.

[12]  Karl J. Friston,et al.  Modulation of Excitatory Synaptic Coupling Facilitates Synchronization and Complex Dynamics in a Nonlinear Model of Neuronal Dynamics , 2002, Neurocomputing.

[13]  Olaf Sporns,et al.  Classes of network connectivity and dynamics , 2001, Complex..

[14]  J. Yorke,et al.  Differentiable generalized synchronization of chaos , 1997 .

[15]  A. Haig,et al.  Prestimulus EEG alpha phase synchronicity influences N100 amplitude and reaction time. , 1998, Psychophysiology.

[16]  Krešimir Josić,et al.  INVARIANT MANIFOLDS AND SYNCHRONIZATION OF COUPLED DYNAMICAL SYSTEMS , 1998 .

[17]  A. Babloyantz,et al.  Predictability of human EEG: a dynamical approach , 1991, Biological Cybernetics.

[18]  Robert A. M. Gregson,et al.  Comparisons of the nonlinear dynamics of electroencephalograms under various task loading conditions: A preliminary report , 1990, Biological Psychology.

[19]  N. Rulkov,et al.  Robustness of Synchronized Chaotic Oscillations , 1997 .

[20]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[21]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[22]  J. V. Haxby,et al.  Spatial Pattern Analysis of Functional Brain Images Using Partial Least Squares , 1996, NeuroImage.

[23]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  T. Collura Neocortical Dynamics and Human EEG Rhythms , 1996 .

[25]  A. J. Hermans,et al.  A model of the spatial-temporal characteristics of the alpha rhythm , 1982 .

[26]  H. Witte,et al.  Time-variant non-linear phase-coupling analysis of EEG burst patterns in sedated patients during electroencephalic burst suppression period , 2001, Clinical Neurophysiology.

[27]  A. Soong,et al.  Evidence of chaotic dynamics underlying the human alpha-rhythm electroencephalogram , 1989, Biological Cybernetics.

[28]  Karl J. Friston,et al.  Functional topography: multidimensional scaling and functional connectivity in the brain. , 1996, Cerebral cortex.

[29]  A. Babloyantz,et al.  Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle , 1985 .

[30]  Michael Breakspear,et al.  A Novel Method for the Topographic Analysis of Neural Activity Reveals Formation and Dissolution of ‘Dynamic Cell Assemblies’ , 2004, Journal of Computational Neuroscience.

[31]  I. Stewart,et al.  Bubbling of attractors and synchronisation of chaotic oscillators , 1994 .

[32]  Carroll,et al.  Desynchronization by periodic orbits. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  John Suckling,et al.  Colored noise and computational inference in fMRI time series analysis: resampling methods in time and wavelet domains , 2001, NeuroImage.

[34]  J. Martinerie,et al.  Nonlinear analyses of interictal EEG map the brain interdependences in human focal epilepsy , 1999 .

[35]  Evelyn Sander,et al.  The geometry of chaos synchronization. , 2003, Chaos.

[36]  Kunihiko Kaneko,et al.  On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection , 1998, chao-dyn/9802016.

[37]  R. Eckhorn,et al.  Phase correlation among rhythms present at different frequencies: spectral methods, application to microelectrode recordings from visual cortex and functional implications. , 1997, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[38]  W. Pritchard,et al.  Dimensional analysis of no-task human EEG using the Grassberger-Procaccia method. , 1992, Psychophysiology.

[39]  Werner Lutzenberger,et al.  Dimensional analysis of the human EEG and intelligence , 1992, Neuroscience Letters.

[40]  Philippe Faure,et al.  Is there chaos in the brain? II. Experimental evidence and related models. , 2003, Comptes rendus biologies.

[41]  T. Sejnowski,et al.  Thalamocortical Assemblies: How Ion Channels, Single Neurons and Large-Scale Networks Organize Sleep Oscillations , 2001 .

[42]  Peter A. Tass,et al.  Desynchronization of brain rhythms with soft phase-resetting techniques , 2002, Biological Cybernetics.

[43]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[44]  G. Edelman,et al.  A measure for brain complexity: relating functional segregation and integration in the nervous system. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[45]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[46]  H. Berendse,et al.  Generalized Synchronization of MEG Recordings in Alzheimer’s Disease: Evidence for Involvement of the Gamma Band , 2002, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[47]  P. Grassberger,et al.  A robust method for detecting interdependences: application to intracranially recorded EEG , 1999, chao-dyn/9907013.

[48]  A. Peled Multiple constraint organization in the brain: A theory for schizophrenia , 1999, Brain Research Bulletin.

[49]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[50]  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.

[51]  Karl J. Friston,et al.  Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics , 2003 .

[52]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[53]  R. Burke,et al.  Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[54]  A. J. Hermans,et al.  A model of the spatial-temporal characteristics of the alpha rhythm. , 1982, Bulletin of mathematical biology.

[55]  C. Stam,et al.  Nonlinear synchronization in EEG and whole‐head MEG recordings of healthy subjects , 2003, Human brain mapping.

[56]  P. Rapp,et al.  Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. , 1996, Electroencephalography and clinical neurophysiology.

[57]  P. Grassberger,et al.  Symmetry breaking bifurcation for coupled chaotic attractors , 1991 .

[58]  M. Breakspear Nonlinear phase desynchronization in human electroencephalographic data , 2002, Human brain mapping.

[59]  J. Milnor On the concept of attractor , 1985 .

[60]  Michael Breakspear,et al.  Anisotropic properties of riddled basins , 2001 .

[61]  John R. Terry,et al.  Topographic Organization of Nonlinear Interdependence in Multichannel Human EEG , 2002, NeuroImage.

[62]  Karl J. Friston,et al.  Schizophrenia: a disconnection syndrome? , 1995, Clinical neuroscience.

[63]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals , 1995 .

[64]  M. Carpenter The cerebral cortex , 1976 .

[65]  L. Pecora Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems , 1998 .

[66]  Karl J. Friston Another Neural Code? , 1997, NeuroImage.

[67]  F. Takens Detecting strange attractors in turbulence , 1981 .

[68]  John R. Terry,et al.  Detection and description of non-linear interdependence in normal multichannel human EEG data , 2002, Clinical Neurophysiology.

[69]  J. Szentágothai The modular architectonic principle of neural centers. , 1983, Reviews of physiology, biochemistry and pharmacology.

[70]  L Pecora,et al.  Early Seizure Detection , 2001, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[71]  Jürgen Fell,et al.  Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep , 1993, Biological Cybernetics.

[72]  P. Ashwin,et al.  On riddling and weak attractors , 2000 .

[73]  P. Agostino Accardo,et al.  Use of the fractal dimension for the analysis of electroencephalographic time series , 1997, Biological Cybernetics.

[74]  S. Schiff,et al.  Decreased Neuronal Synchronization during Experimental Seizures , 2002, The Journal of Neuroscience.

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

[76]  W. Pritchard,et al.  Dimensional analysis of resting human EEG. II: Surrogate-data testing indicates nonlinearity but not low-dimensional chaos. , 1995, Psychophysiology.

[77]  W. Freeman,et al.  Fine temporal resolution of analytic phase reveals episodic synchronization by state transitions in gamma EEGs. , 2002, Journal of neurophysiology.

[78]  Parlitz,et al.  Experimental observation of phase synchronization. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[79]  J. J. Wright,et al.  State-changes in the brain viewed as linear steady-states and non-linear transitions between steady-states , 2004, Biological Cybernetics.

[80]  F. Gonzalez-Lima,et al.  Structural equation modeling and its application to network analysis in functional brain imaging , 1994 .

[81]  E. Bullmore,et al.  Functional Magnetic Resonance Image Analysis of a Large-Scale Neurocognitive Network , 1996, NeuroImage.

[82]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[83]  W. Freeman,et al.  Aperiodic phase re‐setting in scalp EEG of beta–gamma oscillations by state transitions at alpha–theta rates , 2003, Human brain mapping.

[84]  Theiler,et al.  Generating surrogate data for time series with several simultaneously measured variables. , 1994, Physical review letters.

[85]  Karl J. Friston,et al.  A disturbance of nonlinear interdependence in scalp EEG of subjects with first episode schizophrenia , 2003, NeuroImage.

[86]  R. Abraham,et al.  Dynamics--the geometry of behavior , 1983 .

[87]  F. L. D. Silva,et al.  Dynamics of the human alpha rhythm: evidence for non-linearity? , 1999, Clinical Neurophysiology.

[88]  Barry Horwitz,et al.  The elusive concept of brain connectivity , 2003, NeuroImage.

[89]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals; dependence on state and brain site. , 1991, Electroencephalography and clinical neurophysiology.

[90]  R. Larter,et al.  A coupled ordinary differential equation lattice model for the simulation of epileptic seizures. , 1999, Chaos.

[91]  Kestutis Pyragas SYNCHRONIZATION OF COUPLED TIME-DELAY SYSTEMS : ANALYTICAL ESTIMATIONS , 1998 .

[92]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[93]  Kurths,et al.  Synchronization of chaotic structurally nonequivalent systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[94]  Karl J. Friston The labile brain. II. Transients, complexity and selection. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[95]  Michael Breakspear,et al.  Spatiotemporal wavelet resampling for functional neuroimaging data , 2004, Human brain mapping.

[96]  E. Mosekilde,et al.  TRANSVERSE INSTABILITY AND RIDDLED BASINS IN A SYSTEM OF TWO COUPLED LOGISTIC MAPS , 1998 .

[97]  M. Breakspear,et al.  Construction of multivariate surrogate sets from nonlinear data using the wavelet transform , 2003 .

[98]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[99]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.

[100]  Karl J. Friston,et al.  Characterising the complexity of neuronal interactions , 1995 .

[101]  John R. Terry,et al.  NONLINEAR INTERDEPENDENCE IN NEURAL SYSTEMS: MOTIVATION, THEORY, AND RELEVANCE , 2002, The International journal of neuroscience.

[102]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[103]  C. Stam,et al.  Variability of EEG synchronization during a working memory task in healthy subjects. , 2002, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[104]  D. Ruelle,et al.  The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fiction , 1990, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[105]  M. Rabinovich,et al.  Stochastic synchronization of oscillation in dissipative systems , 1986 .

[106]  Karl J. Friston The labile brain. I. Neuronal transients and nonlinear coupling. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[107]  Lila L. Gatlin,et al.  Information theory and the living system , 1972 .

[108]  Milan Palus,et al.  Nonlinearity in normal human EEG: cycles, temporal asymmetry, nonstationarity and randomness, not chaos , 1996, Biological Cybernetics.

[109]  Agnessa Babloyantz,et al.  A comparative study of the experimental quantification of deterministic chaos , 1988 .

[110]  U Parlitz,et al.  Robust synchronization of chaotic systems. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[111]  K. Kaneko Dominance of Milnor Attractors and Noise-Induced Selection in a Multiattractor System , 1997 .

[112]  Blending chaotic attractors using the synchronization of chaos. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[113]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[114]  J. Röschke,et al.  The dimensionality of human's electroencephalogram during sleep , 1991, Biological Cybernetics.

[115]  Thomas Schreiber,et al.  Constrained Randomization of Time Series Data , 1998, chao-dyn/9909042.

[116]  E. Ott,et al.  Blowout bifurcations: the occurrence of riddled basins and on-off intermittency , 1994 .

[117]  H. Haken,et al.  Towards a comprehensive theory of brain activity: coupled oscillator systems under external forces , 2000 .

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

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

[120]  C. J. Stam,et al.  Investigation of nonlinear structure in multichannel EEG , 1995 .

[121]  Donald O. Walter,et al.  Mass action in the nervous system , 1975 .

[122]  R. Eckhorn,et al.  Phase correlation of cortical rhythms at different frequencies: higher-order spectral analysis of multiple-microelectrode recordings from cat and monkey visual cortex , 1997 .

[123]  I. Stewart,et al.  From attractor to chaotic saddle: a tale of transverse instability , 1996 .

[124]  V. Mountcastle Perceptual Neuroscience: The Cerebral Cortex , 1998 .