Biophysical Mechanisms of Multistability in Resting-State Cortical Rhythms

The human alpha (8–12 Hz) rhythm is one of the most prominent, robust, and widely studied attributes of ongoing cortical activity. Contrary to the prevalent notion that it simply “waxes and wanes,” spontaneous alpha activity bursts erratically between two distinct modes of activity. We now establish a mechanism for this multistable phenomenon in resting-state cortical recordings by characterizing the complex dynamics of a biophysical model of macroscopic corticothalamic activity. This is achieved by studying the predicted activity of cortical and thalamic neuronal populations in this model as a function of its dynamic stability and the role of nonspecific synaptic noise. We hence find that fluctuating noisy inputs into thalamic neurons elicit spontaneous bursts between low- and high-amplitude alpha oscillations when the system is near a particular type of dynamical instability, namely a subcritical Hopf bifurcation. When the postsynaptic potentials associated with these noisy inputs are modulated by cortical feedback, the SD of power within each of these modes scale in proportion to their mean, showing remarkable concordance with empirical data. Our state-dependent corticothalamic model hence exhibits multistability and scale-invariant fluctuations—key features of resting-state cortical activity and indeed, of human perception, cognition, and behavior—thus providing a unified account of these apparently divergent phenomena.

[1]  L. Pinneo On noise in the nervous system. , 1966, Psychological review.

[2]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[3]  R. Mazo On the theory of brownian motion , 1973 .

[4]  F. D. da Silva,et al.  Organization of thalamic and cortical alpha rhythms: spectra and coherences. , 1973, Electroencephalography and clinical neurophysiology.

[5]  W. Freeman Mass action in the nervous system : examination of the neurophysiological basis of adaptive behavior through the EEG , 1975 .

[6]  J A Kelso,et al.  Dynamic pattern generation in behavioral and neural systems. , 1988, Science.

[7]  D. McCormick Neurotransmitter actions in the thalamus and cerebral cortex and their role in neuromodulation of thalamocortical activity , 1992, Progress in Neurobiology.

[8]  W. J. Nowack Neocortical Dynamics and Human EEG Rhythms , 1995, Neurology.

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

[10]  A. Singh Exponential Distribution: Theory, Methods and Applications , 1996 .

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

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

[13]  F. H. Lopes da Silva,et al.  Alpha rhythms: noise, dynamics and models. , 1997, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[14]  Karl J. Friston Transients, Metastability, and Neuronal Dynamics , 1997, NeuroImage.

[15]  Daniel M. Wolpert,et al.  Signal-dependent noise determines motor planning , 1998, Nature.

[16]  G. Rees,et al.  Neural correlates of perceptual rivalry in the human brain. , 1998, Science.

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

[18]  Juan C. Jiménez,et al.  Nonlinear EEG analysis based on a neural mass model , 1999, Biological Cybernetics.

[19]  P. Ashwin,et al.  Heteroclinic Networks in Coupled Cell Systems , 1999 .

[20]  P. Nunez Toward a quantitative description of large-scale neocortical dynamic function and EEG , 2000, Behavioral and Brain Sciences.

[21]  Christensen,et al.  Universal fluctuations in correlated systems , 1999, Physical review letters.

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

[23]  P. Robinson,et al.  Modal analysis of corticothalamic dynamics, electroencephalographic spectra, and evoked potentials. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Dirk Roose,et al.  Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL , 2002, TOMS.

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

[26]  Xiao-Jing Wang,et al.  Probabilistic Decision Making by Slow Reverberation in Cortical Circuits , 2002, Neuron.

[27]  Riccardo Mannella,et al.  Integration Of Stochastic Differential Equations On A Computer , 2002 .

[28]  Mathew P. Dafilis,et al.  A spatially continuous mean field theory of electrocortical activity , 2002, Network.

[29]  G. Zaslavsky Chaos, fractional kinetics, and anomalous transport , 2002 .

[30]  P. Robinson,et al.  Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  J. Parra,et al.  Epilepsies as Dynamical Diseases of Brain Systems: Basic Models of the Transition Between Normal and Epileptic Activity , 2003, Epilepsia.

[32]  Andrea Hasenstaub,et al.  Barrages of Synaptic Activity Control the Gain and Sensitivity of Cortical Neurons , 2003, The Journal of Neuroscience.

[33]  H. Haken,et al.  Oscillations in the perception of ambiguous patterns a model based on synergetics , 1989, Biological Cybernetics.

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

[35]  P A Robinson,et al.  Estimation of multiscale neurophysiologic parameters by electroencephalographic means , 2004, Human brain mapping.

[36]  F. L. D. Silva,et al.  Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network , 2004, Neuroscience.

[37]  R. Deichmann,et al.  Eye-specific effects of binocular rivalry in the human lateral geniculate nucleus , 2005, Nature.

[38]  Karl J. Friston,et al.  A theory of cortical responses , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[39]  John R. Terry,et al.  A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. , 2006, Cerebral cortex.

[40]  Constantino Tsallis Occupancy of phase space, extensivity of Sq, and q-generalized central limit theorem , 2006 .

[41]  E. Rolls,et al.  Decision‐making and Weber's law: a neurophysiological model , 2006, The European journal of neuroscience.

[42]  R. Romo,et al.  Perceptual detection as a dynamical bistability phenomenon: A neurocomputational correlate of sensation , 2007, Proceedings of the National Academy of Sciences.

[43]  Zbigniew R Struzik,et al.  Universal scaling law in human behavioral organization. , 2007, Physical review letters.

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

[45]  Viktor K. Jirsa,et al.  Noise during Rest Enables the Exploration of the Brain's Dynamic Repertoire , 2008, PLoS Comput. Biol..

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

[47]  Karl J. Friston,et al.  Population dynamics: Variance and the sigmoid activation function , 2008, NeuroImage.

[48]  Gustavo Deco,et al.  Stochastic dynamics as a principle of brain function , 2009, Progress in Neurobiology.

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

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

[51]  W. Maass,et al.  State-dependent computations: spatiotemporal processing in cortical networks , 2009, Nature Reviews Neuroscience.

[52]  Jochen Braun,et al.  Attractors and noise: Twin drivers of decisions and multistability , 2010, NeuroImage.

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