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Inducing transitions in mesoscopic brain dynamics

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Book cover Modeling Phase Transitions in the Brain

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 4))

Abstract

Mesoscopic brain dynamics, typically studied with electro- and magnetoencephalography (EEG and MEG), display a rich complexity of oscillatory and chaotic-like states, including many different frequencies, amplitudes and phases. Presumably, these different dynamical states correspond to different mental states and functions; studying transitions between such states could provide valuable insights into brain—mind relations that should also be of clinical interest. We use computational methods to investigate these transitions, with the objective of finding relations between structure, dynamics, and function. In particular, we have developed models of paleo- and neocortical structures, in order to study their mesoscopic neurodynamics, as a link between the microscopic neuronal and macroscopic mental events and processes. In this chapter, we describe several types of models that emphasize network connectivity and structure, but we also include molecular and cellular properties at varying detail, depending on the particular problem and experimental data available. We use these models to study how phase transitions can be induced in the mesoscopic neurodynamics of cortical networks by internal (natural) and external (artificial) factors. We discuss the models, and relate the simulation results to macroscopic phenomena, such as arousal, attention, anesthesia, learning, and mental disorders.

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References

  1. Altar, C.A., Laeng, P., Jurata, L.W., Brockman, J.A., Lemire, A., Bullard, J., Bukhman, Y.V., Young, T.A., Charles, V., Palfreyman, M.G.: Electroconvulsive seizures regulate gene expression of distinct neurotrophic signaling pathways. J. Neurosci. 24, 2667–2677 (2004), doi:10.1523/jneurosci.5377-03.2004

    Article  CAS  PubMed  Google Scholar 

  2. Anishchenko, V.S., Neiman, A.B., Safanova, M.A.: Stochastic resonance in chaotic systems. J. Stat. Phys. 70, 183–196 (1993), doi:10.1007/bf01053962

    Article  Google Scholar 

  3. Arbib, M.A. (ed.): The Handbook of Brain Theory and Neural Networks. MIT Press, Cambridge, Mass. (1995)

    Google Scholar 

  4. Arbib, M.A., Érdi, P., Szentágothai, J.: Neural Organization Structure, Function and Dynamics. MIT Press, Cambridge, Mass. (1998)

    Google Scholar 

  5. Århem, P., Blomberg, C., Liljenström, H. (eds.): Disorder Versus Order in Brain Function. World Scientific, London (2000)

    Book  Google Scholar 

  6. Århem, P., Braun, H., Huber, M., Liljenström, H.: Nonlinear state transitions in neural systems: From ion channels to networks. In: H. Liljenström, U. Svedin (eds.), Micro - Meso - Macro: Addressing Complex Systems Couplings, pp. 37–72, World Scientific, London (2005)

    Chapter  Google Scholar 

  7. Århem, P., Johansson, S.: Spontaneous signalling in small central neurons: Mechanisms and roles of spike-amplitude and spike-interval fluctuations. Int. J. Neural Syst. 7, 369–376 (1996), doi:10.1142/s0129065796000336

    Article  PubMed  Google Scholar 

  8. Århem, P., Klement, G., Blomberg, C.: Channel density regulation of firing patterns in a cortical neuron model. Biophys. J. 90, 4392–4404 (2006)

    Article  PubMed  Google Scholar 

  9. Århem, P., Klement, G., Nilsson, J.: Mechanisms of anesthesia: Towards integrating network, cellular and molecular modeling. Neuropsycopharmacology 28, S40–S47 (2003), doi:10.1038/sj.npp.1300142

    Article  Google Scholar 

  10. Århem, P., Liljenström, H.: Fluctuations in neural systems: From subcellular to network levels. In: F. Moss, S. Gielen (eds.), Handbook of Biological Physics, vol. 4, pp. 83–129, Elsevier, Amsterdam (2001)

    Google Scholar 

  11. Århem, P., Liljenström, H.: Beyond cognition - on consciousness transitions. In: H. Liljenström, P. Århem (eds.), Consciousness Transitions - Phylogenetic, Ontogenetic and Physiological Aspects, pp. 1–25, Elsevier, Amsterdam (2007)

    Google Scholar 

  12. Århem, P., Lindahl, B.I.B.: Neuroscience and the problem of consciousness: Theoretical and empirical approaches - an introduction. Theor. Med. 14, 77–88 (1993), doi:10.1007/bf00997268

    Article  PubMed  Google Scholar 

  13. Aronsson, P., Liljenström, H.: Non-synaptic modulation of cortical network dynamics. Neurocomputing 32-33, 285–290 (2000), doi:10.1016/s0925-2312(00)00176-4

    Article  Google Scholar 

  14. Aronsson, P., Liljenström, H.: Effects of non-synaptic neuronal interaction in cortex on synchronization and learning. Biosystems 63, 43–56 (2001), doi:10.1016/s0303-2647(01)00146-0

    Article  CAS  PubMed  Google Scholar 

  15. Basu, S., Liljenström, H.: Spontaneously active cells induce state transitions in a model of olfactory cortex. Biosystems 63, 57–69 (2001)

    Article  CAS  PubMed  Google Scholar 

  16. Berger, H.: Über das elektroenkephalogramm des menschen. Arch. Psychiatr. Nervenkrankh. 87, 527–570 (1929)

    Article  Google Scholar 

  17. Beyer, J.L., Weiner, R.D., Glenn, M.D.: Electroconvulsive Therapy. American Psychiatric Press, London (1998)

    Google Scholar 

  18. Biedenbach, M.A.: Effects of anesthetics and cholinergic drugs on prepyriform electrical activity in cats. Exp. Neurol. 16, 464–479 (1966), doi:10.1016/0014-4886(66)90110-5

    CAS  Google Scholar 

  19. Börgers, C., Epstein, S., Kopell, N.J.: Background gamma rhythmicity and attention in cortical local circuits: A computational study. Proc. Natl. Acad. Sci. USA 102(19), 7002–7007 (2005), doi:10.1073/pnas.0502366102

    Article  PubMed  Google Scholar 

  20. Bulsara, A., Jacobs, E.W., Zhou, T., Moss, F., Kiss, L.: Stochastic resonance in a single neuron model: Theory and analog simulation. J. Theor. Biol. 152, 531–555 (1991), doi:10.1016/s0022-5193(05)80396-0

    Article  CAS  PubMed  Google Scholar 

  21. Cobb, S.R., Buhl, E.H., Halasy, K., Paulsen, O., Somogyi, P.: Synchronization of neuronal activity in hippocampus by individual gabaergic interneurons. Nature 378, 75–78 (1995), doi:10.1038/378075a0

    Article  CAS  PubMed  Google Scholar 

  22. Corchs, S., Deco, G.: Large-scale neural model for visual attention: Integration of experimental single-cell and fmri data. Cerebr. Cortex 12, 339–348 (2002)

    Article  Google Scholar 

  23. Crick, F., Koch, C.: Towards a neurobiological theory of consciousness. Semin. Neurosci. 2, 263–275 (1990)

    Google Scholar 

  24. Eckhorn, R., Bauer, R., Jordon, W., Brosch, M., Kruse, W., Monk, M., Reitboeck, H.J.: Coherent oscillations: A mechanism of feature linking in the in the visual cortex? Biol. Cybern. 60, 121–130 (1988), doi:10.1007/bf00202899

    Article  CAS  Google Scholar 

  25. FitzHugh, R.: Mathematical models of threshold phenomena in the nerve membrane. Bull. Math. Biophys. 17, 257–278 (1955), doi:10.1007/bf02477753

    Article  Google Scholar 

  26. Freeman, W.J.: Distribution in time and space of prepyriform electrical activity. J. Neurophysiol. 22, 644–665 (1959)

    CAS  Google Scholar 

  27. Freeman, W.J.: Linear models of impulse inputs and linear basis functions for measuring impulse responses. Exp. Neurol. 10, 475–492 (1964), doi:10.1016/0014-4886(64)90046-9

    Article  CAS  PubMed  Google Scholar 

  28. Freeman, W.J.: Nonlinear gain mediating cortical stimulus-response relations. Biol. Cybern. 33, 237–247 (1979), doi:10.1007/bf00337412

    Article  CAS  PubMed  Google Scholar 

  29. Freeman, W.J.: Societies of Brains - A Study in the Neuroscience of Love and Hate. Lawrence Erlbaum, Hillsdale, NJ (1995)

    Google Scholar 

  30. Freeman, W.J.: Neurodynamics: An Exploration in Mesoscopic Brain Dynamics. Springer, Berlin (2000)

    Google Scholar 

  31. Freeman, W.J.: The necessity for mesoscopic organization to connect neural function to brain function. In: H. Liljenström, U. Svedin (eds.), Micro - Meso - Macro: Addressing Complex Systems Couplings, pp. 25–36, World Scientific, London (2005)

    Chapter  Google Scholar 

  32. Freeman, W.: Mass Action in the Nervous System. Academic Press, New York (1975)

    Google Scholar 

  33. Friedrich, P., Urban, B.W.: Interaction of intravenous anesthetics with human neuronal potassium currents in relation to clinical concentrations. Anesthesiology 91, 1853–1860 (1999)

    Article  Google Scholar 

  34. Fries, P., Reynolds, J.H., Rorie, A.E., Desimone, R.: Modulation of oscillatory neuronal synchronization by selective visual attention. Science 291, 1560–1563 (2001), doi:10.1126/science.1055465

    Article  CAS  PubMed  Google Scholar 

  35. Giannakopoulos, F., Bihler, U., Hauptmann, C., Luhmann, H.: Epileptiform activity in a neo-cortical network: a mathematical model. Biol. Cybern. 85, 257–268 (2001), doi:10.1007/s004220100257

    Article  CAS  PubMed  Google Scholar 

  36. Gordon, E. (ed.): Integrative Neuroscience: Bringing Together Biological Psychological and Clinical Models of the Human Brain. Harwood Academic Press, New York (2000)

    Google Scholar 

  37. Gray, C.M., Konig, P., Engel, A.K., Singer, W.: Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338, 334–337 (1989), doi:10.1038/338334a0

    Article  CAS  PubMed  Google Scholar 

  38. Gray, C.M., Singer, W.: Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Natl. Acad. Sci. USA 86, 1698–1702 (1989)

    Article  CAS  PubMed  Google Scholar 

  39. Gu, Y., Halnes, G., Liljenström, H., von Rosen, D., Wahlund, B., Liang, H.: Modelling ect effects by connectivity changes in cortical neural networks. Neurocomputing 69, 1341–1347 (2006), doi:10.1016/j.neucom.2005.12.104

    Article  Google Scholar 

  40. Gu, Y., Halnes, G., Liljenström, H., Wahlund, B.: A cortical network model for clinical EEG data analysis. Neurocomputing 58-60, 1187–1196 (2004), doi:10.1016/j.neucom.2004.01.184

    Article  Google Scholar 

  41. Gu, Y., Liljenström, H.: A neural network model of attention-modulated neurodynamics. Cognitive Neurodynamics 1, 275–285 (2007), doi:10.1007/s11571-007-9028-7

    Article  PubMed  Google Scholar 

  42. Gu, Y., Wahlund, B., Liljenström, H., von Rosen, D., Liang, H.: Analysis of phase shifts in clinical EEG evoked by ect. Neurocomputing 65, 475–483 (2005), doi:10.1016/j.neucom.2004.11.004

    Article  Google Scholar 

  43. Haken, H.: Synergetics: An Introduction. Springer-Verlag, Berlin (1983)

    Google Scholar 

  44. Haken, H.: Principles of Brain Functioning. Springer, Berlin (1996)

    Google Scholar 

  45. Halnes, G., Liljenström, H., Århem, P.: Density dependent neurodynamics. Biosystems 89, 126–134 (2007), doi:10.1016/j.biosystems.2006.06.010

    Article  PubMed  Google Scholar 

  46. Hamker, F.H.: A dynamic model of how feature cues guide spatial attention. Vision Res. 44, 501–521 (2004), doi:10.1016/j.visres.2003.09.033

    Article  PubMed  Google Scholar 

  47. Harris, T., Shahidullah, M., Ellingson, J., Covarrubias, M.: General anesthetic action at an internal protein site involving the S4-S5 cytoplasmic loop of a neuronal K+ channel. J. Biol. Chem. 275, 4928–4936 (2000)

    Article  CAS  PubMed  Google Scholar 

  48. Hille, B.: Ion Channels of Excitable Membranes. Sinauer, Sunderland, Mass., 3rd edn. (2001)

    Google Scholar 

  49. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)

    CAS  PubMed  Google Scholar 

  50. Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)

    Article  CAS  PubMed  Google Scholar 

  51. Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA 81, 3088–3092 (1984)

    Article  CAS  PubMed  Google Scholar 

  52. Huber, M.T., Braun, H.A., Krieg, J.C.: Consequences of deterministic and random dynamics for the course of affective disorders. Biol. Psychiatr. 46, 256–262 (1999), doi:10.1016/s0006-3223(98)00311-4

    Article  CAS  Google Scholar 

  53. Huber, M.T., Braun, H.A., Krieg, J.C.: Effects of noise on different disease states of recurrent affective disorders. Biol. Psychiatr. 47, 634–642 (2000), doi:10.1016/s0006-3223(99)00174-2

    Article  CAS  Google Scholar 

  54. Johansson, S., Århem, P.: Single-channel currents trigger action potentials in small cultured hippocampal neurons. Proc. Natl. Acad. Sci. USA 91, 1761–1765 (1994)

    Article  CAS  PubMed  Google Scholar 

  55. John, E.R., Prichep, L.S.: The anesthetic cascade: A theory of how anesthesia suppresses consciousness. Anesthesiology 102, 447–471 (2005)

    Article  PubMed  Google Scholar 

  56. Kelso, S.: Fluctuations in the coordination dynamics of brain and behaviour. In: P. Arhem, C. Blomberg, H. Liljenström (eds.), Disorder versus Order in Brain Function, pp. 185–204, World Scientific, London (2000)

    Chapter  Google Scholar 

  57. Koch, C.: Biophysics of Computation: Information Processing in Single Neurons. Oxford University Press, New York (1999)

    Google Scholar 

  58. Korchounov, A., Ilic, T., Schwinge, T., Ziemann, U.: Modification of motor cortical excitability by an acetylcholinesterase inhibitor. Exp. Brain Res. 164, 399–405 (2005), doi:10.1007/s00221-005-2326-6

    Article  CAS  PubMed  Google Scholar 

  59. Kuczewski, N., Aztiria, E., Gautam, D., Wess, J., Domenici, L.: Acetylcholine modulates cortical synaptic transmission via different muscarinic receptors, as studied with receptor knockout mice. J. Physiol. 566(3), 907–919 (2005), doi:10.1113/jphysiol.2005.089987

    Article  CAS  PubMed  Google Scholar 

  60. Liljenström, H.: Modeling the dynamics of olfactory cortex using simplified network units and realistic architecture. Int. J. Neural Syst. 2, 1–15 (1991), doi:10.1142/S0129065791000029

    Article  Google Scholar 

  61. Liljenström, H.: Autonomous learning with complex dynamics. Int. J. Intell. Syst. 10, 119–153 (1995), doi:10.1002/int.4550100109

    Article  Google Scholar 

  62. Liljenström, H.: Global effects of fluctuations in neural information processing. Int. J. Neural Syst. 7, 497–505 (1996), doi:10.1142/S0129065796000488

    Article  PubMed  Google Scholar 

  63. Liljenström, H.: Cognition and the efficiency of neural processes. In: P. Århem, H. Liljenström, U. Svedin (eds.), Matter Matters? On the Material Basis of the Cognitive Aspects of Mind, pp. 177–213, Springer, Heidelberg (1997)

    Google Scholar 

  64. Liljenström, H.: Neural stability and flexibility - a computational approach. Neuropsychopharmacology 28, S64–S73 (2003), doi:10.1038/sj.npp.1300137

    Article  PubMed  Google Scholar 

  65. Liljenström, H., Århem, P.: Investigating amplifying and controlling mechanisms for random events in neural systems. In: J.M. Bower (ed.), Computational Neuroscience, pp. 711–716, Plenum Press, New York (1997)

    Google Scholar 

  66. Liljenström, H., Halnes, G.: Noise in neural networks– in terms of relations. Fluct. Noise Lett. 4(1), L97–L106 (2004), doi:10.1142/S0219477504001707

    Article  Google Scholar 

  67. Liljenström, H., Hasselmo, M.E.: Cholinergic modulation of cortical oscillatory dynamics. J. Neurophysiol. 74, 288–297 (1995)

    PubMed  Google Scholar 

  68. Liljenström, H., Svedin, U. (eds.): Micro-Meso-Macro: Addressing Complex Systems Couplings. World Scientific, London (2005)

    Book  Google Scholar 

  69. Liljenström, H., Wu, X.: Noise-enhanced performance in a cortical associative memory model. Int. J. Neural Systems 6, 19–29 (1995), doi:10.1142/S0129065795000032

    Article  Google Scholar 

  70. Lindahl, B.I.B., Århem, P.: Mind as a force field: Comments on a new interactionistic hypothesis. J. Theor. Biol. 171, 111–122 (1994), doi:10.1006/jtbi.1994.1217

    Article  CAS  PubMed  Google Scholar 

  71. Mandell, A., Selz, K.: Brain stem neuronal noise and neocortical resonance. J. Stat. Phys. 70, 355–373 (1993), doi:10.1007/bf01053973

    Article  Google Scholar 

  72. McAdams, C., Maunsell, J.: Effects of attention on orientation-tuning functions of single neurons in macaque cortical are v4. J. Neurosci. 19, 431–441 (1999)

    CAS  PubMed  Google Scholar 

  73. Moss, F., Gielen, S. (eds.): Neuro-Informatics and Neural Modelling, vol. 4 of Handbook of Biological Physics. Elsevier, Amsterdam (2001)

    Google Scholar 

  74. Robinson, P.A., Rennie, C.J., Rowe, D.L., O’Connor, S.C., Wright, J.J., Gordon, E.: Neurophysical modeling of brain dynamics. Neuropsychopharmacology 28, S74–S79 (2003), doi:10.1038/sj.npp.1300143

    Article  PubMed  Google Scholar 

  75. Shepherd, G.M.: The Synaptic Organization of the Brain. Oxford University Press, Oxford (1998)

    Google Scholar 

  76. Siegel, M., Körding, K., König, P.: Integrating top-down and bottom-up sensory processing by somato-dendritic interactions. J. Comput. Neurosci. 8, 161–173 (2000), doi:10.1023/a:1008973215925

    Article  CAS  PubMed  Google Scholar 

  77. Sirosh, J., Miikkulainen, R.: Self-organizing feature maps with lateral connections: Modeling ocular dominance. In: M.C. Mozer, P. Smolensky, D.S. Touretzky, J.L. Elman, A.S. Weigend (eds.), Proceedings of the 1993 Connectionist Models Summer School, pp. 31–38, CMSS-93, Boulder, Colorado (1994)

    Google Scholar 

  78. Skarda, C.A., Freeman, W.J.: How brains make chaos in order to make sense of the world. Behav. Brain Sci. 10, 161–195 (1987)

    Article  Google Scholar 

  79. Steyn-Ross, D.A., Steyn-Ross, M.L., Sleigh, J.W., Wilson, M.T., Gillies, I.P., Wright, J.J.: The sleep cycle modelled as a cortical phase transition. J. Biol. Phys. 31, 547–569 (2005), doi:10.1007/s10867-005-1285-2

    Article  Google Scholar 

  80. Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W.: Modelling general anaesthesia as a first-order phase transition in the cortex. Progr. Biophys. Mol. Biol. 85, 369–385 (2004), doi:10.1016/j.pbiomolbio.2004.02.001

    Article  CAS  Google Scholar 

  81. Szentagothai, J.: Local neuron circuits of the neocortex. In: F. Schmitt, F. Worden (eds.), The Neurosciences 4th Study Program, pp. 399–415, MIT Press, Cambridge, Mass. (1979)

    Google Scholar 

  82. Tass, P.A.: Desynchronizing double-pulse phase resetting and application to deep brain stimulation. Biol. Cybern. 85(5), 343–354 (2001), doi:10.1007/s004220100268

    Article  CAS  PubMed  Google Scholar 

  83. Tharyan, P., Adams, C.E.: Electroconvulsive therapy for schizophrenia. Cochrane Db. Syst. Rev. 2, CD000076 (2005), doi:10.1002/14651858.cd000076

    Google Scholar 

  84. von Stein, A., Chiang, C., König, P.: Top-down processing mediated by interareal synchronization. Proc. Natl. Acad. Sci. USA 97(26), 14748–14753 (2000)

    Article  Google Scholar 

  85. Wahlund, B., Piazza, P., von Rosen, D., Liberg, B., Liljenström, H.: Seizure (ictal)-EEG characteristics subgroup depressive disorder in patients receiving ECT– A preliminary study and multivariate approach. Comput. Intell. Neurosci. (2009), [In press]

    Google Scholar 

  86. Wahlund, B., von Rosen, D.: ECT of major depressed patients in relation to biological and clinical variables: A brief overview. Neuropsychopharmacology 28, S21–S26 (2003), doi:10.1038/sj.npp.1300135

    Article  CAS  PubMed  Google Scholar 

  87. Wright, J.J., Bourke, P.D., Chapman, C.L.: Synchronous oscillation in the cerebral cortex and object coherence: Simulation of basic electrophysiological findings. Biol. Cybern. 83, 341–353 (2000), doi:10.1007/s004220000155

    Article  CAS  PubMed  Google Scholar 

  88. Wright, J.J., Liley, D.T.J.: Dynamics of the brain at global and microscopic scales. Neural networks and the EEG. Behav. Brain Sci. 19, 285–320 (1996)

    Article  Google Scholar 

  89. Wright, J.J., Rennie, C.J., Lees, G.J., Robinson, P.A., Bourke, P.D., Chapman, C.L., Gordon, E., Rowe, D.L.: Simulated electrocortical activity at microscopic, mesoscopic, and global scales. Neuropsychopharmacology 28, S80 –S93 (2003), doi:10.1038/sj.npp.1300138

    Article  PubMed  Google Scholar 

  90. Wu, X., Liljenström, H.: Regulating the nonlinear dynamics of olfactory cortex. Netw. Comput. Neural Syst. 5, 47–60 (1994), doi:10.1088/0954-898x/5/1/003

    Article  Google Scholar 

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Acknowledgments

I would like to thank my co-workers, Peter Århem, Per Aronsson, Soumalee Basu, Yuqiao Gu, Geir Halnes, Björn Wahlund, and Xiangbao Wu. I also appreciate valuable discussions with Hans Braun, Walter Freeman, Hermann Haken, and Frank Moss. Grants from Vinnova and the Swedish Research Council are gratefully acknowledged.

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Liljenström, H. (2010). Inducing transitions in mesoscopic brain dynamics. In: Steyn-Ross, D., Steyn-Ross, M. (eds) Modeling Phase Transitions in the Brain. Springer Series in Computational Neuroscience, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0796-7_7

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