The K-complex and slow oscillation in terms of a mean-field cortical model

We use a mean-field macrocolumn model of the cerebral cortex to offer an interpretation of the K-complex of the electroencephalogram to complement those of more detailed neuron-by-neuron models. We interpret the K-complex as a momentary excursion of the cortex from a stable low-firing state to an unstable high-firing state, and hypothesize that the related slow oscillation can be considered as the periodic oscillation between two meta-stable solutions of the mean-field model. By incorporating a Hebbian-style learning rule that links the growth in synapse strength to fluctuations in soma potential, we demonstrate a self-organization behaviour that draws the modelled cortex close to the edge of stability of the low-firing state. Furthermore, a very slow oscillation can occur in the excitability of the cortex that has similarities with the infra-slow oscillation of sleep.

[1]  J. Born,et al.  Spindle and slow wave rhythms at slow wave sleep transitions are linked to strong shifts in the cortical direct current potential , 2003, Neuroscience.

[2]  J. Mäkelä,et al.  Distributions and sources of magnetoencephalographic K-complexes. , 1996, Electroencephalography and clinical neurophysiology.

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

[4]  Sean L. Hill,et al.  The Sleep Slow Oscillation as a Traveling Wave , 2004, The Journal of Neuroscience.

[5]  Y. Amitai,et al.  Propagating neuronal discharges in neocortical slices: computational and experimental study. , 1997, Journal of neurophysiology.

[6]  David T. J. Liley,et al.  A continuum theory of electro-cortical activity , 1999, Neurocomputing.

[7]  P. Robinson,et al.  Mechanisms of cortical electrical activity and emergence of gamma rhythm. , 2000, Journal of theoretical biology.

[8]  T. Sejnowski,et al.  Model of Thalamocortical Slow-Wave Sleep Oscillations and Transitions to Activated States , 2002, The Journal of Neuroscience.

[9]  Peter A. Robinson,et al.  Synchronous oscillations in the cerebral cortex , 1998 .

[10]  J. Lacaille,et al.  Cell‐type specific GABA synaptic transmission and activity‐dependent plasticity in rat hippocampal stratum radiatum interneurons , 2005, The European journal of neuroscience.

[11]  Florin Amzica,et al.  The functional significance of K-complexes. , 2002, Sleep medicine reviews.

[12]  Ian M Colrain,et al.  The K-complex: a 7-decade history. , 2005, Sleep.

[13]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of rhythmic recurrent activity in neocortex , 2000, Nature Neuroscience.

[14]  M. Steriade,et al.  Natural waking and sleep states: a view from inside neocortical neurons. , 2001, Journal of neurophysiology.

[15]  W. Freeman.  Predictions on Neocortical Dynamics Derived from Studies in Paleocortex , 1992 .

[16]  M. Kramer,et al.  Pathological pattern formation and cortical propagation of epileptic seizures , 2005, Journal of The Royal Society Interface.

[17]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of slow oscillatory activity (<1 Hz) and wave propagations in a cortical network model. , 2003, Journal of neurophysiology.

[18]  D. Contreras,et al.  Spatiotemporal Analysis of Local Field Potentials and Unit Discharges in Cat Cerebral Cortex during Natural Wake and Sleep States , 1999, The Journal of Neuroscience.

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

[20]  T. Sejnowski,et al.  Spatiotemporal Patterns of Spindle Oscillations in Cortex and Thalamus , 1997, The Journal of Neuroscience.

[21]  D. Liley,et al.  Modeling the effects of anesthesia on the electroencephalogram. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Moira L Steyn-Ross,et al.  Proposed mechanism for learning and memory erasure in a white-noise-driven sleeping cortex. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[24]  Daniel Lehmann,et al.  Regulated Criticality in the Brain? , 1998, Adv. Complex Syst..

[25]  D A Steyn-Ross,et al.  Predictions and simulations of cortical dynamics during natural sleep using a continuum approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Giulio Tononi,et al.  Modeling sleep and wakefulness in the thalamocortical system. , 2005, Journal of neurophysiology.

[27]  J. Hobson,et al.  The Neurobiology of Sleep: Genetics, cellular physiology and subcortical networks , 2002, Nature Reviews Neuroscience.

[28]  E. Bienenstock,et al.  Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

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

[30]  J. Sleigh,et al.  Modelling general anaesthesia as a first-order phase transition in the cortex. , 2004, Progress in biophysics and molecular biology.

[31]  M. Steriade,et al.  A novel slow (< 1 Hz) oscillation of neocortical neurons in vivo: depolarizing and hyperpolarizing components , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[32]  J. Sleigh,et al.  The Sleep Cycle Modelled as a Cortical Phase Transition , 2005, Journal of biological physics.

[33]  J. Palva,et al.  Infraslow oscillations modulate excitability and interictal epileptic activity in the human cortex during sleep. , 2004, Proceedings of the National Academy of Sciences of the United States of America.