Spike-rate adaptation and neuronal bursting in a mean-field model of brain activity

Spike-rate adaptation is investigated within a mean-field model of brain activity. Two different mechanisms of negative feedback are considered; one involving modulation of the mean firing threshold, and the other, modulation of the mean synaptic strength. Adaptation to a constant stimulus is shown to take place for both mechanisms, and limit-cycle oscillations in the firing rate corresponding to bursts of neuronal activity are investigated. These oscillations are found to result from a Hopf bifurcation when the equilibrium lies between the local maximum and local minimum of a given nullcline. Oscillations with amplitudes significantly below the maximum firing rate are found over a narrow range of possible equilibriums.

[1]  P. Nunez.  The brain wave equation: a model for the EEG , 1974 .

[2]  James J. Wright,et al.  Effects of local feedback on dispersion of electrical waves in the cerebral cortex , 1999 .

[3]  R. Whitehouse,et al.  Neurophysical Modeling of Brain Dynamics , 2003, Neuropsychopharmacology.

[4]  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.

[5]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[6]  J. Cowan,et al.  A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue , 1973, Kybernetik.

[7]  Peter A. Robinson,et al.  Unified neurophysical model of EEG spectra and evoked potentials , 2002, Biological Cybernetics.

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

[9]  A. Herz,et al.  Input-Driven Components of Spike-Frequency Adaptation Can Be Unmasked In Vivo , 2004, The Journal of Neuroscience.

[10]  Christof Koch,et al.  Biophysics of Computation: Information Processing in Single Neurons (Computational Neuroscience Series) , 1998 .

[11]  P. Robinson,et al.  Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Maria V. Sanchez-Vives,et al.  Cellular Mechanisms of Long-Lasting Adaptation in Visual Cortical Neurons In Vitro , 2000, The Journal of Neuroscience.

[13]  H. Wilson.  Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience , 1999 .

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

[15]  Andreas V. M. Herz,et al.  A Universal Model for Spike-Frequency Adaptation , 2003, Neural Computation.

[16]  Hugh R. Wilson,et al.  Dynamics of perceptual oscillations in form vision , 2000, Nature Neuroscience.

[17]  Paul C Bressloff,et al.  Bloch waves, periodic feature maps, and cortical pattern formation. , 2002, Physical review letters.

[18]  L. Maler,et al.  Spike-Frequency Adaptation Separates Transient Communication Signals from Background Oscillations , 2005, The Journal of Neuroscience.

[19]  Joel L. Davis,et al.  Large-Scale Neuronal Theories of the Brain , 1994 .

[20]  S. R. Lehky.  An Astable Multivibrator Model of Binocular Rivalry , 1988, Perception.

[21]  James J. Wright,et al.  Dynamics of the brain at global and microscopic scales: Neural networks and the EEG , 1996, Behavioral and Brain Sciences.

[22]  P. Robinson,et al.  Multiscale brain modelling , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

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

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

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

[26]  R. Foehring,et al.  Relationship between repetitive firing and afterhyperpolarizations in human neocortical neurons. , 1992, Journal of neurophysiology.

[27]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[28]  Maria V. Sanchez-Vives,et al.  Membrane Mechanisms Underlying Contrast Adaptation in Cat Area 17In Vivo , 2000, The Journal of Neuroscience.

[29]  H. Wilson,et al.  Dynamics of travelling waves in visual perception , 2001, Nature.