Multistability in the corticothalamic system.

Neural field theory of the corticothalamic system is used to analyze the properties of its steady-state solutions, including their linear stability, in the parameter space of synaptic couplings for physiological parameter ranges representing normal arousal waking states in adult humans. The independent connections of the corticothalamic model define an eight-dimensional parameter space, while specific combinations of these connections parameterize intracortical, corticothalamic, and intrathalamic loops. Multistable regions are systematically identified and the existence of up to five steady-state solutions is confirmed, up to three of which are linearly stable. A key determinant for the existence of five steady states is found to be the number of nonzero connections. This finding had not been previously proposed as the determining factor of high multiplicities of multistability in mesoscopic models of the brain. In the corticothalamic model presented here, multistability occurs when the intrathalamic loop is present (i.e., the reticular nucleus inhibits the relay nuclei), and when the net synaptic effect of the intracortical loop is inhibitory. The signature of these additional waking states is an overall increased level of thalamic activity. It is argued that the additional steady states found may represent hyperarousal states which occur when the corticothalamic projections do not attenuate the activity of the cortex.

[1]  J. Sleigh,et al.  Theoretical predictions for spatial covariance of the electroencephalographic signal during the anesthetic-induced phase transition: Increased correlation length and emergence of spatial self-organization. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Donald L Rowe,et al.  Estimation of neurophysiological parameters from the waking EEG using a biophysical model of brain dynamics. , 2004, Journal of theoretical biology.

[3]  Peter N. Robinson,et al.  STEADY STATES AND GLOBAL DYNAMICS OF ELECTRICAL ACTIVITY IN THE CEREBRAL CORTEX , 1998 .

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

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

[6]  Arnaud Delorme,et al.  Occipital gamma activation during Vipassana meditation , 2009, Cognitive Processing.

[7]  P. Robinson,et al.  Neurophysical theory of coherence and correlations of electroencephalographic and electrocorticographic signals. , 2003, Journal of theoretical biology.

[8]  Janne Grønli,et al.  Beta EEG reflects sensory processing in active wakefulness and homeostatic sleep drive in quiet wakefulness , 2016, Journal of sleep research.

[9]  D A Steyn-Ross,et al.  Toward a theory of the general-anesthetic-induced phase transition of the cerebral cortex. I. A thermodynamics analogy. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  P. Robinson,et al.  Prediction and verification of nonlinear sleep spindle harmonic oscillations. , 2014, Journal of theoretical biology.

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

[12]  S. Smalley,et al.  Mindfulness Meditation Training in Adults and Adolescents With ADHD , 2008, Journal of attention disorders.

[13]  Viktor K. Jirsa,et al.  Systematic approximations of neural fields through networks of neural masses in the virtual brain , 2013, NeuroImage.

[14]  P. Robinson,et al.  Physiologically based arousal state estimation and dynamics , 2015, Journal of Neuroscience Methods.

[15]  Anne Hauswald,et al.  What it means to be Zen: Marked modulations of local and interareal synchronization during open monitoring meditation , 2015, NeuroImage.

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

[17]  J. Sleigh,et al.  Toward a theory of the general-anesthetic-induced phase transition of the cerebral cortex. II. Numerical simulations, spectral entropy, and correlation times. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  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.

[19]  D. Liley,et al.  Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: evidence for a general anesthetic-induced phase transition. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Prof. Dr. Dr. Valentino Braitenberg,et al.  Cortex: Statistics and Geometry of Neuronal Connectivity , 1998, Springer Berlin Heidelberg.

[21]  D. Liley,et al.  Computer simulation of electrocortical activity at millimetric scale. , 1994, Electroencephalography and clinical neurophysiology.

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

[23]  P. Robinson,et al.  Spatially uniform and nonuniform analyses of electroencephalographic dynamics,with application to the topography of the alpha rhythm. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[25]  Naresh K. Sinha,et al.  Modern Control Systems , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[26]  Narayanan Srinivasan,et al.  Theta activity and meditative states: spectral changes during concentrative meditation , 2010, Cognitive Processing.

[27]  Russell Anderson,et al.  A Multiscale “Working Brain” Model , 2015 .

[28]  P A Robinson,et al.  Corticothalamic dynamics: structure of parameter space, spectra, instabilities, and reduced model. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[30]  A. Lutz,et al.  Long-term meditators self-induce high-amplitude gamma synchrony during mental practice. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

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

[32]  Gustavo Deco,et al.  Functional connectivity dynamics: Modeling the switching behavior of the resting state , 2015, NeuroImage.

[33]  Marcus T. Wilson,et al.  EEG slow-wave coherence changes in propofol-induced general anesthesia: experiment and theory , 2014, Front. Syst. Neurosci..

[34]  Risto Miikkulainen,et al.  Mean-field thalamocortical modeling of longitudinal EEG acquired during intensive meditation training , 2015, NeuroImage.

[35]  Ben D. Fulcher,et al.  Quantitative modelling of sleep dynamics , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[36]  P. Nunez,et al.  Neocortical Dynamics and Human EEG Rhythms , 1995 .

[37]  B. Roth,et al.  The clinical and theoretical importance of EEG rhythms corresponding to states of lowered vigilance. , 1961, Electroencephalography and clinical neurophysiology.

[38]  J. Polich,et al.  Meditation states and traits: EEG, ERP, and neuroimaging studies. , 2013 .

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

[40]  Julie Carrier,et al.  Sleep EEG power spectra, insomnia, and chronic use of benzodiazepines. , 2003, Sleep.

[41]  Viktor K. Jirsa,et al.  Mathematical framework for large-scale brain network modeling in The Virtual Brain , 2015, NeuroImage.

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