A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation

Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12–15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols.

[1]  J. Born,et al.  About sleep's role in memory. , 2013, Physiological reviews.

[2]  P. Golshani,et al.  Cellular mechanisms of brain-state-dependent gain modulation in visual cortex , 2013, Nature Neuroscience.

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

[4]  Manuel Salto-Tellez,et al.  Gelsolin Induces Colorectal Tumor Cell Invasion via Modulation of the Urokinase-Type Plasminogen Activator Cascade , 2012, PloS one.

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

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

[7]  Thomas Martinetz,et al.  Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model , 2014, PLoS Comput. Biol..

[8]  Andrey Shilnikov,et al.  Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. , 2005, Physical review letters.

[9]  Olivier D. Faugeras,et al.  Neural Mass Activity, Bifurcations, and Epilepsy , 2011, Neural Computation.

[10]  Nelson J. Trujillo-Barreto,et al.  Biophysical model for integrating neuronal activity, EEG, fMRI and metabolism , 2008, NeuroImage.

[11]  D. Contreras,et al.  Cellular basis of EEG slow rhythms: a study of dynamic corticothalamic relationships , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  Thomas Martinetz,et al.  Modeling the effect of sleep regulation on a neural mass model , 2016, Journal of Computational Neuroscience.

[13]  Stephen Coombes,et al.  Waves, bumps, and patterns in neural field theories , 2005, Biological Cybernetics.

[14]  Maxime Bonjean,et al.  Corticothalamic Feedback Controls Sleep Spindle Duration In Vivo , 2011, The Journal of Neuroscience.

[15]  D. McCormick,et al.  Periodicity of Thalamic Synchronized Oscillations: the Role of Ca2+-Mediated Upregulation of Ih , 1998, Neuron.

[16]  Jaroslaw Zygierewicz,et al.  A model of sleep spindles generation , 2001, Neurocomputing.

[17]  T J Sejnowski,et al.  In vivo, in vitro, and computational analysis of dendritic calcium currents in thalamic reticular neurons , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

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

[19]  J. Born,et al.  Hippocampal sharp wave-ripples linked to slow oscillations in rat slow-wave sleep. , 2006, Journal of neurophysiology.

[20]  Hamid Reza Mohseni,et al.  How delays matter in an oscillatory whole-brain spiking-neuron network model for MEG alpha-rhythms at rest , 2014, NeuroImage.

[21]  Michel J. A. M. van Putten,et al.  A neural mass model based on single cell dynamics to model pathophysiology , 2014, Journal of Computational Neuroscience.

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

[23]  Peter A. Robinson,et al.  Physiology-based modeling of cortical auditory evoked potentials , 2008, Biological Cybernetics.

[24]  David Terman,et al.  A mathematical model of the sleep/wake cycle , 2010, Journal of mathematical biology.

[25]  Vincenzo Crunelli,et al.  Cellular Mechanisms of the Slow (<1 Hz) Oscillation in Thalamocortical Neurons In Vitro , 2002, Neuron.

[26]  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.

[27]  I. Timofeev,et al.  Chapter 1 MECHANISMS AND BIOLOGICAL ROLE OF THALAMOCORTICAL OSCILLATIONS , 2005 .

[28]  Maxim Volgushev,et al.  Properties of Slow Oscillation during Slow-Wave Sleep and Anesthesia in Cats , 2011, The Journal of Neuroscience.

[29]  T. Tsumoto,et al.  Change of conduction velocity by regional myelination yields constant latency irrespective of distance between thalamus and cortex , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Amitabha Bose,et al.  A Mathematical Model towards Understanding the Mechanism of Neuronal Regulation of Wake-NREMS-REMS States , 2012, PloS one.

[31]  J. Born,et al.  Grouping of Spindle Activity during Slow Oscillations in Human Non-Rapid Eye Movement Sleep , 2002, The Journal of Neuroscience.

[32]  Muscarinic Inhibition of Persistent Na / Current in Rat Neocortical Pyramidal Neurons , 1998 .

[33]  D. Contreras,et al.  Mechanisms underlying the synchronizing action of corticothalamic feedback through inhibition of thalamic relay cells. , 1998, Journal of neurophysiology.

[34]  Mitsuyuki Nakao,et al.  A quartet neural system model orchestrating sleep and wakefulness mechanisms. , 2006, Journal of neurophysiology.

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

[36]  I. Fried,et al.  Sleep Spindles in Humans: Insights from Intracranial EEG and Unit Recordings , 2011, The Journal of Neuroscience.

[37]  Roy Cox,et al.  Involvement of spindles in memory consolidation is slow wave sleep-specific. , 2012, Learning & memory.

[38]  Ben H. Jansen,et al.  A neurophysiologically-based mathematical model of flash visual evoked potentials , 2004, Biological Cybernetics.

[39]  D. Ulrich,et al.  Electrophysiological characterization of synaptic connections between layer VI cortical cells and neurons of the nucleus reticularis thalami in juvenile rats , 2004, The European journal of neuroscience.

[40]  P. Achermann,et al.  Low-frequency (<1Hz) oscillations in the human sleep electroencephalogram , 1997, Neuroscience.

[41]  J. Born,et al.  Boosting slow oscillations during sleep potentiates memory , 2006, Nature.

[42]  Gustavo Deco,et al.  Synaptic depression and slow oscillatory activity in a biophysical network model of the cerebral cortex , 2012, Front. Comput. Neurosci..

[43]  Helen A. Baghdoyan,et al.  Sleep, Anesthesiology, and the Neurobiology of Arousal State Control , 2005, Anesthesiology.

[44]  Mohammad Wahid Ansari,et al.  The legal status of in vitro embryos , 2014 .

[45]  P. Robinson,et al.  A Quantitative Model of Sleep-Wake Dynamics Based on the Physiology of the Brainstem Ascending Arousal System , 2007, Journal of biological rhythms.

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

[47]  Hironobu Osaki,et al.  Cholinergic modulation of response gain in the primary visual cortex of the macaque. , 2012, Journal of neurophysiology.

[48]  E. Halgren,et al.  Spatiotemporal dynamics of neocortical excitation and inhibition during human sleep , 2012, Proceedings of the National Academy of Sciences.

[49]  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.

[50]  T J Sejnowski,et al.  Cellular and network models for intrathalamic augmenting responses during 10-Hz stimulation. , 1998, Journal of neurophysiology.

[51]  M. Steriade.  The corticothalamic system in sleep. , 2003, Frontiers in bioscience : a journal and virtual library.

[52]  J. Born,et al.  Induction of slow oscillations by rhythmic acoustic stimulation , 2013, Journal of sleep research.

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

[54]  A. Destexhe,et al.  Dendritic Low-Threshold Calcium Currents in Thalamic Relay Cells , 1998, The Journal of Neuroscience.

[55]  Andreas Rößler,et al.  Runge-Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations , 2010, SIAM J. Numer. Anal..

[56]  D. McCormick,et al.  Corticothalamic activation modulates thalamic firing through glutamate "metabotropic" receptors. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[57]  L. Sebastiani,et al.  Fragments of wake-like activity frame down-states of sleep slow oscillations in humans: new vistas for studying homeostatic processes during sleep. , 2013, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[58]  Brent Doiron,et al.  Deterministic Multiplicative Gain Control with Active Dendrites , 2005, The Journal of Neuroscience.

[59]  W. Senn,et al.  Dopamine increases the gain of the input–output response of rat prefrontal pyramidal neurons. J. Neurophysiol. (in press). doi: 10.1152/jn.01098.2007 [epub ahead of print , 2008 .

[60]  Marco Storace,et al.  Non-instantaneous synaptic transmission in spiking neuron networks and equivalence with delay distribution , 2013, BMC Neuroscience.

[61]  Dany Arsenault,et al.  Gain modulation by serotonin in pyramidal neurones of the rat prefrontal cortex , 2005, The Journal of physiology.

[62]  E. Geisert,et al.  α2-Adrenergic receptor-mediated modulation of calcium current in neocortical pyramidal neurons , 2004, Brain Research.

[63]  David A. McCormick,et al.  Modulation of a pacemaker current through Ca2+-induced stimulation of cAMP production , 1999, Nature Neuroscience.

[64]  Viktor Jirsa.  Neural field dynamics with local and global connectivity and time delay , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[66]  D. McCormick.  Cholinergic and noradrenergic modulation of thalamocortical processing , 1989, Trends in Neurosciences.

[67]  Fiona E. N. LeBeau,et al.  Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. , 2005, Journal of neurophysiology.

[68]  T. Sejnowski,et al.  Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices. , 1996, Journal of neurophysiology.

[69]  Thomas Martinetz,et al.  Driving Sleep Slow Oscillations by Auditory Closed-Loop Stimulation—A Self-Limiting Process , 2015, The Journal of Neuroscience.

[70]  Mathieu S. Capcarrère,et al.  Necessary conditions for density classification by cellular automata. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[71]  J. Born,et al.  Fast and slow spindles during the sleep slow oscillation: disparate coalescence and engagement in memory processing. , 2011, Sleep.

[72]  J. Born,et al.  Auditory Closed-Loop Stimulation of the Sleep Slow Oscillation Enhances Memory , 2013, Neuron.

[73]  B. Connors,et al.  Correlation between intrinsic firing patterns and thalamocortical synaptic responses of neurons in mouse barrel cortex , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

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

[75]  M. Steriade.  Acetylcholine systems and rhythmic activities during the waking--sleep cycle. , 2004, Progress in brain research.

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

[77]  Heinz Georg Schuster,et al.  Role of inhibitory feedback for information processing in thalamocortical circuits. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[78]  J. Born,et al.  The memory function of sleep , 2010, Nature Reviews Neuroscience.

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

[80]  R. Stickgold,et al.  Sleep-Dependent Learning and Memory Consolidation , 2004, Neuron.

[81]  D. Bucci,et al.  M1 Receptors Mediate Cholinergic Modulation of Excitability in Neocortical Pyramidal Neurons , 2009, The Journal of Neuroscience.

[82]  I. Timofeev,et al.  Interneuron‐mediated inhibition synchronizes neuronal activity during slow oscillation , 2012, The Journal of physiology.

[83]  Alain Destexhe,et al.  Dendritic calcium currents in thalamic relay cells , 1998 .

[84]  Mario Rosanova,et al.  Pattern-Specific Associative Long-Term Potentiation Induced by a Sleep Spindle-Related Spike Train , 2005, The Journal of Neuroscience.

[85]  Victoria Booth,et al.  Simulating microinjection experiments in a novel model of the rat sleep-wake regulatory network. , 2010, Journal of neurophysiology.

[86]  Lisa M. Giocomo,et al.  Cholinergic modulation of cortical function , 2007, Journal of Molecular Neuroscience.

[87]  C Gottesmann,et al.  Variations in extracellular levels of dopamine, noradrenaline, glutamate, and aspartate across the sleep–wake cycle in the medial prefrontal cortex and nucleus accumbens of freely moving rats , 2005, Journal of neuroscience research.

[88]  C. Koch,et al.  The origin of extracellular fields and currents — EEG, ECoG, LFP and spikes , 2012, Nature Reviews Neuroscience.

[89]  Marcus T. Wilson,et al.  General Anesthetic-induced Seizures Can Be Explained by a Mean-field Model of Cortical Dynamics , 2006, Anesthesiology.

[90]  M. Breakspear,et al.  Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[91]  Mauro Ursino,et al.  A thalamo-cortical neural mass model for the simulation of brain rhythms during sleep , 2013, Journal of Computational Neuroscience.

[92]  Andreas Spiegler,et al.  Bifurcation Analysis of Neural Mass Models , 2010 .

[93]  M. Hawken,et al.  Gain Modulation by Nicotine in Macaque V1 , 2007, Neuron.

[94]  T. Sejnowski,et al.  Interactions between membrane conductances underlying thalamocortical slow-wave oscillations. , 2003, Physiological reviews.