Journal of Computational Neuroscience

, Volume 41, Issue 1, pp 15–28 | Cite as

Modeling the effect of sleep regulation on a neural mass model

  • Michael Schellenberger Costa
  • Jan Born
  • Jens Christian Claussen
  • Thomas Martinetz
Article

Abstract

In mammals, sleep is categorized by two main sleep stages, rapid eye movement (REM) and non-REM (NREM) sleep that are known to fulfill different functional roles, the most notable being the consolidation of memory. While REM sleep is characterized by brain activity similar to wakefulness, the EEG activity changes drastically with the emergence of K-complexes, sleep spindles and slow oscillations during NREM sleep. These changes are regulated by circadian and ultradian rhythms, which emerge from an intricate interplay between multiple neuronal populations in the brainstem, forebrain and hypothalamus and the resulting varying levels of neuromodulators. Recently, there has been progress in the understanding of those rhythms both from a physiological as well as theoretical perspective. However, how these neuromodulators affect the generation of the different EEG patterns and their temporal dynamics is poorly understood. Here, we build upon previous work on a neural mass model of the sleeping cortex and investigate the effect of those neuromodulators on the dynamics of the cortex and the corresponding transition between wakefulness and the different sleep stages. We show that our simplified model is sufficient to generate the essential features of human EEG over a full day. This approach builds a bridge between sleep regulatory networks and EEG generating neural mass models and provides a valuable tool for model validation.

Keywords

Neural mass EEG Sleep regulation Neuromodulators Sleep Sleep rhythms 

References

  1. Atay, F.M., & Hutt, A. (2006). Neural fields with distributed transmission speeds and long range feedback delays. SIAM Journal on Applied Dynamical Systems, 5(4), 670–698. doi:10.1137/050629367.CrossRefGoogle Scholar
  2. Barkai, E., & Hasselmo, M.E. (1994). Modulation of the input/output function of rat piriform cortex pyramidal cells. Journal of Neurophysiology, 72(2), 644–658.PubMedGoogle Scholar
  3. Benita, J.M., Guillamon, A., Deco, G., & Sanchez-Vives, M.V. (2012). Synaptic depression and slow oscillatory activity in a biophysical network model of the cerebral cortex. Frontiers in computational neuroscience, 6 (64). doi:10.3389/fncom.2012.00064.
  4. Benoıt, E., Callot, J.L., Diener, F., & Diener, M. (1981). Chasse au canard. Collectanea Mathematica, 31-32(1-3), 37–119.Google Scholar
  5. Booth, V., & Diniz Behn, C.G. (2014). Physiologically-based modeling of sleep-wake regulatory networks. Mathematical Biosciences, 250(1), 54–68. doi:10.1016/j.mbs.2014.01.012.CrossRefPubMedGoogle Scholar
  6. Borbély, A.A. (1982). A two process model of sleep regulation Human neurobiology.Google Scholar
  7. Brown, R.E., McKenna, J.T., Winston, S., Basheer, R., Yanagawa, Y., Thakkar, M.M., & McCarley, R.W. (2008). Characterization of GABAergic neurons in rapid-eye-movement sleep controlling regions of the brainstem reticular formation in GAD67-green fluorescent protein knock-in mice. European Journal of Neuroscience, 27(2), 352–363. doi:10.1111/j.1460-9568.2008.06024.x.CrossRefPubMedPubMedCentralGoogle Scholar
  8. Colino, A., & Halliwell, J.V. (1987). Differential modulation of three separate K-conductances in hippocampal CA1 neurons by serotonin. Nature, 328(6125), 73–7. doi:10.1038/328073a0.CrossRefPubMedGoogle Scholar
  9. Compte, A., Sanchez-Vives, M. V., McCormick, D. A., & Wang, X. J. (2003). Cellular and network mechanisms of slow oscillatory activity (<1Hz) and wave propagations in a cortical network model. Journal of Neurophysiology, 89 (5), 2707–25. doi:10.1152/jn.00845.2002.CrossRefPubMedGoogle Scholar
  10. Coombes, S. (2005). Waves, bumps, and patterns in neural field theories. Biological Cybernetics, 93(2), 91–108. doi:10.1007/s00422-005-0574-y.CrossRefPubMedGoogle Scholar
  11. Daan, S., Beersma, D.G.M., & Borbély, A.A. (1984). Timing of human sleep: recovery process gated by a circadian pacemaker. The American Journal of Physiology, 246(2 Pt 2), 161– 183.Google Scholar
  12. Datta, S., & MacLean, R.R. (2007). Neurobiological Mechanisms for the Regulation of Mammalian Sleep-Wake Behavior: Reinterpretation of Historical Evidence and Inclusion of Contemporary Cellular and Molecular Evidence. Neuroscience Biobehavior Reviews, 31(5), 775–824. doi:10.1016/j.biotechadv.2011.08.021.Secreted.CrossRefGoogle Scholar
  13. David, O., & Friston, K. J. (2003). A neural mass model for MEG/EEG: coupling and neuronal dynamics. NeuroImage, 20(3), 1743–1755. doi:10.1016/j.neuroimage.2003.07.015.CrossRefPubMedGoogle Scholar
  14. Davies, M.F., Deisz, R.A., Prince, D.A., & Peroutka, S.J. (1987). Two distinct effects of 5-hydroxytryptamine on single cortical neurons. Brain Research, 423(1-2), 347–52. doi:10.1016/0006-8993(87)90861-4 10.1016/0006-.CrossRefPubMedGoogle Scholar
  15. Deco, G., Jirsa, V.K., Robinson, P.A., Breakspear, M., & Friston, K.J. (2008). The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Computational Biology, 4(8), e1000,092. doi:10.1371/journal.pcbi.1000092.CrossRefGoogle Scholar
  16. Deco, G., Martí, D., & Ledberg, A. (2009). Effective reduced diffusion-models: a data driven approach to the analysis of neuronal dynamics. PLoS Computational Biology, 5(12), e1000,587. doi:10.1371/journal.pcbi.1000587.CrossRefGoogle Scholar
  17. Diniz Behn, C. G., & Booth, V. (2010). Simulating microinjection experiments in a novel model of the rat sleep-wake regulatory network. Journal of Neurophysiology, 103(4), 1937–1953. doi:10.1152/jn.00795.2009.CrossRefPubMedGoogle Scholar
  18. Diniz Behn, C.G., & Booth, V. (2012). A fast-slow analysis of the dynamics of REM sleep. SIAM Journal on Applied Dynamical Systems, 11(1), 212–242. doi:10.1137/110832823.CrossRefGoogle Scholar
  19. Diniz Behn, C.G., Brown, E.N., Scammell, T.E., & Kopell, N.J. (2007). Mathematical model of network dynamics governing mouse sleep wake behavior. Journal of Neurophysiology, 97, 3828–3840. doi:10.1152/jn.01184.2006.CrossRefGoogle Scholar
  20. Disney, A.A., Aoki, C., & Hawken, M.J. (2007). Gain modulation by nicotine in macaque v1. Neuron, 56, 701–713. doi:10.1016/j.neuron.2007.09.034.CrossRefPubMedPubMedCentralGoogle Scholar
  21. Fleshner, M., Booth, V., Forger, D.B., & Diniz Behn, C.G. (2011). Circadian regulation of sleep-wake behaviour in nocturnal rats requires multiple signals from suprachiasmatic nucleus. Philosophical Transactions of the Royal Society A: Mathematical, physical, and engineering sciences, 369(1952), 3855–3883. doi:10.1098/rsta.2011.0085.CrossRefGoogle Scholar
  22. Forger, D.B., Jewett, M.E., & Kronauer, R.E. (1999). A simpler model of the human circadian pacemaker. Journal of Biological Rhythms, 14(6), 532–537. doi:10.1177/074873099129000867.CrossRefPubMedGoogle Scholar
  23. Fuller, P.M., Saper, C.B., & Lu, J. (2007). The pontine REM switch: past and present. The Journal of physiology, 584(Pt 3), 735–741. doi:10.1113/jphysiol.2007.140160.CrossRefPubMedPubMedCentralGoogle Scholar
  24. Gage, P.W. (1992). Activation and modulation of neuronal K+ channels by GABA. Trends in neurosciences, 15(2), 46–51. doi:10.1016/0166-2236(92)90025-4.CrossRefPubMedGoogle Scholar
  25. Gleit, R.D., Diniz Behn, C.G., & Booth, V. (2013). Modeling interindividual differences in spontaneous internal desynchrony patterns. Journal of Biological Rhythms, 28(5), 339–55. doi:10.1177/0748730413504277.CrossRefPubMedGoogle Scholar
  26. Gulledge, A.T., Bucci, D.J., Zhang, S.S., Matsui, M., & Yeh, H.H. (2009). M1 receptors mediate cholinergic modulation of excitability in neocortical pyramidal neurons. The Journal of Neuroscience, 29(31), 9888–9902. doi:10.1523/JNEUROSCI.1366-09.2009.CrossRefPubMedPubMedCentralGoogle Scholar
  27. Hasselmo, M.E. (1995). Neuromodulation and cortical function: modeling the physiological basis of behavior. Behavioural Brain Research, 67(1), 1–27.CrossRefPubMedGoogle Scholar
  28. Iber, C., Ancoli-Israel, S., Chesson Jr., A.L., & Quan, S.F. (2007). The AASM Manual for the Scoring of Sleep and Associated Events: Rules Terminology and Technical Specifications 1st ed.Google Scholar
  29. Jansen, B.H., Zouridakis, G., & Brandt, M.E. (1993). A neurophysiologically-based mathematical model of flash visual evoked potentials. Electrical Engineering, 283, 275–283.Google Scholar
  30. Kales, A., & Rechtschaffen, A. (1968). Rechtschaffen, A.: A manual of standardized terminology, techniques and scoring system for sleep stages of human subjects. U. S. National Institute of Neurological Diseases and Blindness, Neurological Information Network.Google Scholar
  31. Kiebel, S.J., Garrido, M.I., Moran, R.J., & Friston, K.J. (2008). Dynamic causal modelling for EEG and MEG. Cognitive Neurodynamics, 2(2), 121–136. doi:10.1007/s11571-008-9038-0.CrossRefPubMedPubMedCentralGoogle Scholar
  32. Kumar, R., Bose, A., & Mallick, B.N. (2012). A mathematical model towards understanding the mechanism of neuronal regulation of wake-NREMS-REMS states. PLoS One, 7(8), 1–17. doi:10.1371/journal.pone.0042059.CrossRefGoogle Scholar
  33. Léna, I., Parrot, S., Deschaux, O., Muffat-Joly, S., Sauvinet, V., Renaud, B., Suaud-Chagny, M.F., & Gottesmann, C. (2005). 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. Journal of Neuroscience Research, 81(6), 891–899. doi:10.1002/jnr.20602.CrossRefPubMedGoogle Scholar
  34. Liljenström, N., & Hasselmo, M.E. (1995). Cholinergic modulation of cortical oscillatory dynamics. Journal of Neurophysiology, 74(1), 288–297.PubMedGoogle Scholar
  35. Lopes da Silva, F.H., Hoeks, A., Smits, H., & Zetterberg, L.H. (1974). Model of brain rhythmic activity. The alpha-rhythm of the thalamus. Kybernetik, 15(1), 27–37.CrossRefPubMedGoogle Scholar
  36. Lu, J., Sherman, D., Devor, M., & Saper, C.B. (2006). A putative flip-flop switch for control of REM sleep. Nature, 441(7093), 589–594. doi:10.1038/nature04767.CrossRefPubMedGoogle Scholar
  37. Luppi, P.H., Gervasoni, D., Verret, L., Goutagny, R., Peyron, C., Salvert, D., Leger, L., & Fort, P. (2006). Paradoxical (REM) sleep genesis: The switch from an aminergic-cholinergic to a GABAergic-glutamatergic hypothesis. Journal of Physiology Paris, 100(5-6), 271–283. doi:10.1016/j.jphysparis.2007.05.006.CrossRefGoogle Scholar
  38. Lydic, R., & Baghdoyan, H.A. (2005). Sleep, anesthesiology, and the neurobiology of arousal state control. Anesthesiology, 103(6), 1268–1295. doi:10.1097/00000542-200512010-00024.CrossRefPubMedGoogle Scholar
  39. Madison, D.V., & Nicoll, R.A. (1982). Noradrenaline blocks accommodation of pyramidal cell discharge in the hippocampus. Nature, 299, 636–638. doi:10.1038/299636a0.CrossRefPubMedGoogle Scholar
  40. Madison, D.V., & Nicoll, R.A. (1986). Actions of noradrenaline recorded intracellularly in rat hippocampal CA1 pyramidal neurons, in vitro. The Journal of Physiology, 372, 221– 244.CrossRefPubMedPubMedCentralGoogle Scholar
  41. Madison, D. V., Lancaster, B., & Nicoll, R.A. (1987). Voltage clamp analysis of cholinergic action in the hippocampus. The Journal of Neuroscience, 7(3), 733–741.PubMedGoogle Scholar
  42. Marreiros, A.C., Daunizeau, J., Kiebel, S.J., & Friston, K.J. (2008). Population dynamics: Variance and the sigmoid activation function. NeuroImage, 42, 147–157. doi:10.1016/j.neuroimage.2008.04.239.CrossRefPubMedGoogle Scholar
  43. McCarley, R.W., & Hobson, J.A. (1975). Neuronal excitability modulation over the sleep cycle: a structural and mathematical model. Science, 189(4196), 58–60. doi:10.1126/science.1135627.CrossRefPubMedGoogle Scholar
  44. McCormick, D.A. (1989). Cholinergic and noradrenergic modulation of thalamocortical processing. Trends in Neurosciences, 12(6), 215–221. doi:10.1016/0166-2236(89)90125-2.CrossRefPubMedGoogle Scholar
  45. McCormick, D.A., & Huguenard, J.R. (1992). A model of the electrophysiological properties of thalamocortical relay neurons. Journal of Neurophysiology, 68(4), 1384–400.PubMedGoogle Scholar
  46. Moruzzi, G. (1972). The sleep-waking cycle. Ergebnisse der Physiologie, biologischen Chemie und experimentellen Pharmakologie, 64, 1–165.PubMedGoogle Scholar
  47. Nicoll, R.A., Malenka, R.C., & Kauer, J.A. (1990). Functional comparison of neurotransmitter receptor subtypes in mamMalian central nervous system. Physiological Reviews, 70(2), 513– 565.PubMedGoogle Scholar
  48. Patel, A.J., Honoré, E., Lesage, F., Fink, M., Romey, G., & Lazdunski, M. (1999). Inhalational anesthetics activate two-pore-domain background K+ channels. Nature Neuroscience, 2(5), 422–426. doi:10.1038/8084.CrossRefPubMedGoogle Scholar
  49. Peyron, C., Tighe, D.K., Van den Pol, A.N., de Lecea, L., Heller, H.C., Sutcliffe, J.G., & Kilduff, T.S. (1998). Neurons containing hypocretin (orexin) project to multiple neuronal systems. The Journal of Neuroscience, 015(23), 9996–10.Google Scholar
  50. Phillips, A.J.K., & Robinson, P.A. (2007). A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system. Journal of Biological Rhythms, 22(2), 167–179. doi:10.1177/0748730406297512.CrossRefPubMedGoogle Scholar
  51. Rasch, B., & Born, J. (2013). About sleep’s role in memory. Physiological Reviews, 93(2), 681–766. doi:10.1152/physrev.00032.2012.CrossRefPubMedPubMedCentralGoogle Scholar
  52. Rempe, M.J., Best, J., & Terman, D.H. (2009). A mathematical model of the sleep/wake cycle. Journal of Mathematical Biology, 60(5), 615–644. doi:10.1007/s00285-009-0276-5.CrossRefPubMedGoogle Scholar
  53. Rößler, A. (2010). Runge-Kutta methods for the strong approximation of solutions of stochastic differential equations. SIAM Journal on Numerical Analysis, 48(3), 922–952 . doi:10.1137/09076636X.CrossRefGoogle Scholar
  54. Saint, D.A., Thomas, T., & Gage, P.W. (1990). GABAB agonists modulate a transient potassium current in cultured mammalian hippocampal neurons. Neuroscience Letters, 118(1), 9–13. doi:10.1016/0304-3940(90)90236-3.CrossRefPubMedGoogle Scholar
  55. Sanchez-Vives, M.V., & McCormick, D.A. (2000). Cellular and network mechanisms of rhythmic recurrent activity in neocortex. Nature Neuroscience, 3(10), 1027–34. doi:10.1038/79848.CrossRefPubMedGoogle Scholar
  56. Saper, C.B., Chou, T.C., & Scammell, T.E. (2001). The sleep switch: Hypothalamic control of sleep and wakefulness. Trends in Neurosciences, 24(12), 726–731. doi:10.1016/S0166-2236(00)02002-6.CrossRefPubMedGoogle Scholar
  57. Saper, C.B., Scammell, T.E., & Lu, J. (2005). Hypothalamic regulation of sleep and circadian rhythms. Nature, 437(7063), 1257–1263. doi:10.1038/nature04284.CrossRefPubMedGoogle Scholar
  58. Sapin, E., Lapray, D., Bérod, A., Goutagny, R., Léger, L., Ravassard, P., Clément, O., Hanriot, L., Fort, P., & Luppi, P.H. (2009). Localization of the brainstem GABAergic neurons controlling Paradoxical (REM) sleep. PLoS One, 4(1). doi:10.1371/journal.pone.0004272.
  59. Schellenberger Costa, M. (2006a). Simulation routine of the model. https://github.com/miscco/NM_Cortex_SR.
  60. Soma, S., & Shimegi, S. (2016). Cholinergic modulation of response gain in the primary visual cortex of the macaque. Journal of Neurophysiology, 107, 283–291. doi:10.1152/jn.00330.2011.
  61. Steyn-Ross, D.A., Steyn-Ross, M.L., Sleigh, J.W., Wilson, M.T., Gillies, I.P., & Wright, J.J. (2005). The sleep cycle modelled as a cortical phase transition. Journal of Biological Physics, 31(3-4), 547–569. doi:10.1007/s10867-005-1285-2.CrossRefPubMedPubMedCentralGoogle Scholar
  62. Talley, E.M., & Bayliss, D.A. (2002). Modulation of TASK-1 (Kcnk3) and TASK-3 (Kcnk9) potassium channels volatile anesthetics and neurotransmitters share a molecular site of action. Journal of Biological Chemistry, 277(20), 17,733–17,742. doi:10.1074/jbc.M200502200.CrossRefGoogle Scholar
  63. Tamakawa, Y., Karashima, A., Koyama, Y., Katayama, N., & Nakao, M. (2006). A quartet neural system model orchestrating sleep and wakefulness mechanisms. Journal of Neurophysiology, 95(4), 2055–2069. doi:10.1152/jn.00575.2005.CrossRefPubMedGoogle Scholar
  64. Timmons, D., Geisert, E., Stewart, E., Lorenzon, M., & Foehring, R. C. (2004). Alpha 2-Adrenergic receptor-mediated modulation of calcium current in neocortical pyramidal neurons. Brain Research, 1014, 184–196. doi:10.1016/j.brainres.2004.04.025.CrossRefPubMedGoogle Scholar
  65. Weigenand, A., Schellenberger Costa, M., Ngo, H.V.V., Claussen, J.C., & Martinetz, T. (2014). Characterization of K-complexes and slow wave activity in a neural mass model. PLoS Computational Biology, 10, e1003,923. doi:10.1371/journal.pcbi.1003923.CrossRefGoogle Scholar
  66. Wendling, F., Bartolomei, F., Bellanger, J.J.J., & Chauvel, P. (2002). Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. European Journal of Neuroscience, 15(9), 1499–1508. doi:10.1046/j.1460-9568.2002.01985.x.CrossRefPubMedGoogle Scholar
  67. Wilson, H.R., & Cowan, J.D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13(2), 55–80.CrossRefPubMedGoogle Scholar
  68. Zhang, Z.W., & Arsenault, D. (2005). Gain modulation by serotonin in pyramidal neurones of the rat prefrontal cortex. The Journal of Physiology, 2, 379–394. doi:10.1113/jphysiol.2005.086066.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Michael Schellenberger Costa
    • 1
  • Jan Born
    • 2
  • Jens Christian Claussen
    • 3
  • Thomas Martinetz
    • 1
  1. 1.Institute for Neuro and BioinformaticsUniversity of LübeckLübeckGermany
  2. 2.Institute for Medical Psychology and Behavioural NeurobiologyUniversity of TübingenTübingenGermany
  3. 3.Life Sciences, ChemistryJacobs University BremenBremenGermany

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