Skip to main content

Part of the book series: Understanding Complex Systems ((UCS))

Summary

This chapter presents an introductory course to the biophysics of neurons, comprising a discussion of ion channels, active and passive membranes, action potentials and postsynaptic potentials. It reviews several conductance-based and reduced neuron models, neural networks and neural .eld theories. Finally, the basic principles of the neuroelectrodynamics of mass potentials, i.e. dendritic .elds, local .eld potentials, and the electroencephalogram are elucidated and their putative functional role as a mean .eld is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. von Neumann. The Computer and the Brain. Yale University Press, New Haven (CT), 1958. Partly reprinted in J. A. Anderson and E. Rosenfeld (1988), p. 83ff.

    MATH  Google Scholar 

  2. Z. W. Pylyshyn. Computation and Cognition: Toward a Foundation for Cognitive Science. MIT Press, Cambrigde (MA), 1986.

    Google Scholar 

  3. J. R. Anderson. Cognitive Psychology and its Implications. W. H. Freeman and Company, New York (NY), 4th edition, 1995.

    Google Scholar 

  4. M. Kutas and A. Dale. Electrical and magnetic readings of mental functions. In M. Rugg, editor, Cognitive Neuroscience, pp. 197–242. Psychology Press, Hove East Sussex, 1997.

    Google Scholar 

  5. R. C. O’Reilly and Y. Munakata. Computational Explorations in Cognitive Neuroscience. Understanding the Mind by Simulating the Brain. MIT Press, Cambridge (MA), 2000.

    Google Scholar 

  6. M. S. Gazzaniga, R. B. Ivry, and G. R. Mangun, editors. Cognitive Neuroscience. The Biology of the Mind. W. W. Norton, New York (NY), 2nd edition, 2002.

    Google Scholar 

  7. J. A. Anderson and E. Rosenfeld, editors. Neurocomputing. Foundations of Research, Vol.1. MIT Press, Cambridge (MA), 1988.

    Google Scholar 

  8. J. A. Anderson, A. Pellionisz, and E. Rosenfeld, editors. Neurocomputing. Directions for Research, Vol. 2. MIT Press, Cambridge (MA), 1990.

    Google Scholar 

  9. P. S. Churchland and T. J. Sejnowski. The Computational Brain. MIT Press, Cambridge (MA), 1994.

    Google Scholar 

  10. F. Riecke, D. Warland, R. de Ruyter van Steveninck, and W. Bialek. Spikes: Exploring the Neural Code. Computational Neurosciences. MIT Press, Cambridge (MA), 1997.

    Google Scholar 

  11. M. A. Arbib, editor. The Handbook of Brain Theory and Neural Networks. MIT Press, Cambridge (MA), 1998.

    Google Scholar 

  12. C. Koch and I. Segev, editors. Methods in Neuronal Modelling. From Ions to Networks. Computational Neuroscience. MIT Press, Cambridge (MA), 1998.

    Google Scholar 

  13. C. Koch. Biophysics of Computation. Information Processing in Single Neurons. Computational Neuroscience. Oxford University Press, New York (NY), 1999.

    Google Scholar 

  14. H. R. Wilson. Spikes, Decisions and Actions. Dynamical Foundations of Neuroscience. Oxford University Press, New York (NY), 1999.

    Google Scholar 

  15. P. Dayan and L. F. Abbott. Theoretical Neuroscience. Computational Neuroscience. MIT Press, Cambridge (MA), 2001.

    MATH  Google Scholar 

  16. T. P. Trappenberg. Fundamentals of Computational Neuroscience. Oxford University Press, Oxford (GB), 2002.

    MATH  Google Scholar 

  17. R. P. N. Rao, B. A. Olshausen, and M. S. Lewicky, editors. Probabilistic Models of the Brain: Perception and Neural Function. MIT Press, Cambridge (MA), 2002.

    Google Scholar 

  18. W. Gerstner and W. Kistler. Spiking Neuron Models. Single Neurons, Populations, Plasticity. Cambridge University Press, Cambridge (UK), 2002.

    MATH  Google Scholar 

  19. E. R. Kandel, J. H. Schwartz, and T. M. Jessel, editors. Principles of Neural Science. Appleton & Lange, East Norwalk, Connecticut, 1991.

    Google Scholar 

  20. E. R. Kandel, J. H. Schwartz, and T. M. Jessel, editors. Essentials of Neural Science and Behavior. Appleton & Lange, East Norwalk, Connecticut, 1995.

    Google Scholar 

  21. J. G. Nicholls, A. R-Martin, B. G. Wallace, and P. A. Fuchs. From Neuron to Brain. Sinauer, Sunderland (MA), 2001.

    Google Scholar 

  22. H. C. Tuckwell. Introduction to Theoretical Neurobiology, Vol. 1. Cambridge University Press, Cambridge (UK), 1988.

    MATH  Google Scholar 

  23. H. C. Tuckwell. Introduction to Theoretical Neurobiology, Vol. 2. Cambridge University Press, Cambridge (UK), 1988.

    Google Scholar 

  24. D. Johnston and S. M.-S. Wu. Foundations of Cellular Neurophysiology. MIT Press, Cambridge (MA), 1997.

    Google Scholar 

  25. B. Hille. Ion Channels of Excitable Membranes. Sinauer, Sunderland, 2001.

    Google Scholar 

  26. A. Einstein. Eine neue Bestimmung der Moleküldimensionen. Annalen der Physik, 19:289–306, 1906.

    Google Scholar 

  27. S. B. Laughlin, R. R. de Ruyter van Steveninck, and J. C. Anderson. The metabolic cost of neural information. Nature Neuroscience, 1(1): 36–41, 1998.

    Google Scholar 

  28. W. W. Orrison Jr., J. D. Lewine, J. A. Sanders, and M. F. Hartshorne. Functional Brain Imaging. Mosby, St. Louis, 1995.

    Google Scholar 

  29. N. K. Logothetis, J. Pauls, M. Augath, T. Trinath, and A. Oeltermann. Neurophysiological investigation of the basis of the fMRI signal. Nature, 412: 150–157, 2001.

    Article  ADS  Google Scholar 

  30. H. Haken. Synergetics. An Introduction, Vol. 1 of Springer Series in Synergetics. Springer, Berlin, 1983.

    Google Scholar 

  31. N. G. van Kampen. Stochastic Processes in Physics and Chemistry. Elsevier, Amsterdam, 1992.

    Google Scholar 

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

    Google Scholar 

  33. I. Swameye, T. G. Müller, J. Timmer, O. Sandra, and U. Klingmüller. Identification of nucleocytoplasmatic cycling as a remote sensor in cellular signaling by databased modeling. Proceedings of the National Academy of Sciences of the U.S.A., 100(3): 1028–1033, 2003.

    Article  ADS  Google Scholar 

  34. J. M. Bower and D. Beeman. The Book of GENESIS. Exploring Realistic Neural Models with the GEneral NEural SImulation System. Springer, New York (NY), 1998.

    Google Scholar 

  35. J. W. Moore and M. L Hines. Simulations with NEURON. Duke and Yale University, 1994.

    Google Scholar 

  36. A. Destexhe, D. Contreras, and M. Steriade. Cortically-induced coherence of a thalamic-generated oscillation. Neuroscience, 92(2): 427–443, 1999.

    Article  Google Scholar 

  37. C. Bèdard, H. Kröger, and A. Destexhe. Modeling extracellular field potentials and the frequency-filtering properties of extracellular space. Biophys. J., 86(3): 1829–1842, 2004.

    Article  Google Scholar 

  38. O. Creutzfeld and J. Houchin. Neuronal basis of EEG-waves. In Handbook of Electroencephalography and Clinical Neurophysiology, Vol. 2, Part C, pp. 2C-5–2C-55. Elsevier, Amsterdam, 1974.

    Google Scholar 

  39. W. J. Freeman. Mass Action in the Nervous System. Academic Press, New York (NY), 1975.

    Google Scholar 

  40. D. T. J. Liley, D. M. Alexander, J. J. Wright, and M. D. Aldous. Alpha rhythm emerges from large-scale networks of realistically coupled multicompartmental model cortical neurons. Network: Comput. Neural Syst., 10: 79–92, 1999.

    Article  MATH  Google Scholar 

  41. A. J. Trevelyan and O. Watkinson. Does inhibition balance excitation in neocortex? Prog. Biophys. Mol. Biol.,, 87: 109–143, 2005.

    Article  Google Scholar 

  42. P. L. Nunez and R. Srinivasan. Electric Fields of the Brain: The Neurophysics of EEG. Oxford University Press, New York, 2006.

    Google Scholar 

  43. R. FitzHugh. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J., 1: 445–466, 1961.

    Google Scholar 

  44. T. Pavlidis. A new model for simple neural nets and its application in the design of a neural oscillator. Bull. Math. Biol., 27: 215–229, 1965.

    Google Scholar 

  45. R. B. Stein, K. V. Leung, M. N. Oğuztöreli, and D. W. Williams. Properties of small neural networks. Kybernetik, 14:223–230, 1974.

    Google Scholar 

  46. R. B. Stein, K. V. Leung, D. Mangeron, and M. N. Oğuztöreli. Improved neuronal models for studying neural networks. Kybernetik, 15: 1–9, 1974.

    Article  Google Scholar 

  47. J. L. Hindmarsh and R. M. Rose. A model of neuronal bursting using three coupled first-order differential equations. Proceedings of the Royal Society London, B221:87–102, 1984.

    Article  ADS  Google Scholar 

  48. N. F. Rulkov. Modeling of spiking-bursting neural behavior using two-dimensional map. Phys. Rev. E, 65: 041922, 2002.

    Article  ADS  MathSciNet  Google Scholar 

  49. E. M. Izhikevich. Simple model of spiking neurons. IEEE Trans. Neural Networks, 14(6): 1569–1572, 2003.

    Article  MathSciNet  Google Scholar 

  50. E. M. Izhikevich. Which model to use for cortical spiking neurons? IEEE Trans. Neural Networks, 15(5): 1063–1070, 2004.

    Article  Google Scholar 

  51. W. S. McCulloch and W. Pitts. A logical calculus of ideas immanent in nervous activity. Bull. Math. Biophys., 5:115–133, 1943. Reprinted in J. A. Anderson and E. Rosenfeld (1988) AndersonRosenfeld88, p. 83ff.

    Article  MATH  MathSciNet  Google Scholar 

  52. S. Amari. A method of statistical neurodynamics. Kybernetik, 14: 201–215, 1974.

    MathSciNet  Google Scholar 

  53. D. J. Amit. Modeling Brain Function. The World of Attractor Neural Networks. Cambridge University Press, Cambridge (MA), 1989.

    MATH  Google Scholar 

  54. A. Kuhn, A. Aertsen, and S. Rotter. Neuronal integration of synaptic input in the fluctuation-driven regime. J. Neurosci., 24(10): 2345–2356, 2004.

    Google Scholar 

  55. J. S. Griffith. A field theory of neural nets: I. derivation of field equations. Bull. Math. Biophys., 25:111–120, 1963.

    Article  MATH  MathSciNet  Google Scholar 

  56. J. S. Griffith. A field theory of neural nets: II. properties of the field equations. Bull. Math. Biophys., 27: 187–195, 1965.

    Article  MATH  MathSciNet  Google Scholar 

  57. H. R. Wilson and J. D. Cowan. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13: 55–80, 1973.

    Article  Google Scholar 

  58. P. L. Nunez, editor. Neocortical Dynamics and Human EEG Rhythms. Oxford University Press, New York (NY), 1995.

    Google Scholar 

  59. V. K. Jirsa and H. Haken. Field theory of electromagnetic brain activity. Phys. Rev. Lett., 77(5): 960–963, 1996.

    Article  ADS  Google Scholar 

  60. V. K. Jirsa and H. Haken. A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics. Physica D, 99: 503–526, 1997.

    Google Scholar 

  61. J. J. Wright and D. T. J. Liley. Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behavioral and Brain Sciences, 19:285–320, 1996.

    Article  Google Scholar 

  62. D. T. J. Liley, P. J. Cadusch, and J. J. Wright. A continuum theory of electro-cortical activity. Neurocomputing, 26–27: 795–800, 1999.

    Article  Google Scholar 

  63. P. A. Robinson, C. J. Rennie, J. J. Wright, H. Bahramali, E. Gordon, and D. L. Rowe. Prediction of electroencephalic spectra from neurophysiology. Phys. Rev. E, 63, 2001. 021903.

    Article  ADS  Google Scholar 

  64. C. J. Rennie, P. A. Robinson, and J. J. Wright. Effects of local feedback on dispersion of electrical waves in the cerebral cortex. Phys. Rev. E., 59(3): 3320–3329, 1999.

    Google Scholar 

  65. P. A. Robinson, C. J. Rennie, J. J. Wright, and P. D. Bourke. Steady states and global dynamics of electrical activity in the cerebral cortex. Phys. Rev. E., 58(3): 3557–3571, 1998.

    Article  ADS  Google Scholar 

  66. J. J. Wright, C. J. Rennie, G. J. Lees, P. A. Robinson, P. D. Bourke, C. L. Chapman, E. Gordon, and D. L. Rowe. Simulated electrocortical activity at microscopic, mesoscopic, and global scales. Neuropsychopharmacology, 28: S80–S93, 2003.

    Article  Google Scholar 

  67. V. K. Jirsa. Information processing in brain and behavior displayed in large-scale scalp topographies such as EEG and MEG. Int. J. Bifurcation and Chaos, 14(2): 679–692, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  68. J. J. Wright, C. J. Rennie, G. J. Lees, P. A. Robinson, P. D. Bourke, C. L. Chapman, E. Gordon, and D. L. Rowe. Simulated electrocortical activity at microscopic, mesoscopic and global scales. Int. J. Bifurcation and Chaos, 14(2): 853–872, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  69. J. J. Wright, P. A. Robinson, C. J. Rennie, E. Gordon, P. D. Burke, C. L. Chapman, N. Hawthorn, G. J. Lees, and D. Alexander. Toward an integrated continuum model of cerebral dynamics: the cerebral rhythms, synchronous oscillation and cortical stability. Biosystems, 63: 71–88, 2001.

    Article  Google Scholar 

  70. V. K. Jirsa and J. A. S. Kelso. Spatiotemporal pattern formation in neural systems with heterogeneous connection toplogies. Phys. Rev. E., 62(6): 8462–8465, 2000.

    Article  ADS  Google Scholar 

  71. H. R. Wilson and J. D. Cowan. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J., 12: 1–24, 1972.

    Article  ADS  Google Scholar 

  72. F. H. Lopes da Silva, A. Hoecks, H. Smits, and L. H. Zetterberg. Model of brain rhythmic activity: The alpha-rhythm of the thalamus. Kybernetik, 15: 27–37, 1974.

    Article  Google Scholar 

  73. F. H. Lopes da Silva, A. van Rotterdam, P. Bartels, E. van Heusden, and W. Burr. Models of neuronal populations: The basic mechanisms of rhythmicity. In M. A. Corner and D. F. Swaab, editors, Perspectives of Brain Research, Vol. 45 of Prog. Brain Res., pp. 281–308. 1976.

    Google Scholar 

  74. W. J. Freeman. Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biol. Cybern., 56: 139–150, 1987.

    Google Scholar 

  75. B. H. Jansen, G. Zouridakis, and M. E. Brandt. A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol. Cybern., 68: 275–283, 1993.

    Article  Google Scholar 

  76. B. H. Jansen and V. G. Rit. Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol. Cybern., 73: 357–366, 1995.

    Article  MATH  Google Scholar 

  77. F. Wendling, J. J. Bellanger, F. Bartolomei, and P. Chauvel. Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol. Cybern., 83: 367–378, 2000.

    Article  Google Scholar 

  78. F. Wendling, F. Bartolomei, J. J. Bellanger, and P. Chauvel. Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur. J. Neurosci., 15: 1499–1508, 2002.

    Article  Google Scholar 

  79. O. David and K. J. Friston. A neural mass model for MEG/EEG: coupling and neuronal dynamics. Neuroimage, 20: 1743–1755, 2003.

    Article  Google Scholar 

  80. O. David, D. Cosmelli, and K. J. Friston. Evaluation of different measures of functional connectivity using a neural mass model. Neuroimage, 21: 659–673, 2004.

    Article  Google Scholar 

  81. O. David, L. Harrison, and K. J. Friston. Modelling event-related respones in the brain. Neuroimage, 25: 756–770, 2005.

    Article  Google Scholar 

  82. P. beim Graben. Symbolische Dynamik Ereigniskorrelierter Potentiale in der Sprachverarbeitung. Berichte aus der Biophysik. Shaker Verlag, Aachen, 2001.

    Google Scholar 

  83. C. Baumgartner. Clinical applications of source localisation techniques — the human somatosensory cortex. In F. Angelieri, S. Butler, S. Giaquinto, and J. Majkowski, editors, Analysis of the Electrical Activity of the Brain, pp. 271–308. Wiley & Sons, Chichester, 1997.

    Google Scholar 

  84. W. Lutzenberger, T. Elbert, B. Rockstroh, and N. Birbaumer. Das EEG. Springer, Berlin, 1985.

    Google Scholar 

  85. N. Birbaumer and R. F. Schmidt. Biologische Psychologie. Springer, Berlin, 1996.

    Google Scholar 

  86. S. Zschocke. Klinische Elektroenzephalographie. Springer, Berlin, 1995.

    Google Scholar 

  87. A. Wunderlin. On the slaving principle. In R. Graham and A. Wunderlin, editors, Lasers and Synergetics, pp. 140–147, Springer, Berlin, 1987.

    Google Scholar 

  88. J. Dudel, R. Menzel, and R. F. Schmidt, editors. Neurowissenschaft. Vom Molekül zur Kognition. Springer, Berlin, 1996.

    Google Scholar 

  89. W. R. Adey. Molecular aspects of cell membranes as substrates for interaction with electromagnetic fields. In E. Başar, H. Flohr, H. Haken, and A. J. Mandell, editors, Synergetics of the Brain, pp. 201–211, Springer, Berlin, 1983.

    Google Scholar 

  90. E. Bracci, M. Vreugdenhil, S. P. Hack, and J. G. R. Jefferys. On the synchronizing mechanism of tetanically induced hippocampal oscillations. J. Neurosci., 19(18): 8104–8113, 1999.

    Google Scholar 

  91. J. G. R. Jefferys. Nonsynaptic modulation of neuronal activity in the brain: Electric currents and extracellular ions. Physiol. Rev., 75: 689–723, 1995.

    Google Scholar 

  92. K. A. Richardson, S. J. Schiff, and B. J. Gluckman. Electric field control of seizure propagation: From theory to experiment. In S. Boccaletti, B. Gluckman, J. Kurths, L. M. Pecora, R. Meucci, and O. Yordanov, editors, Proceeding of the 8th Experimental Chaos Conference 2004, pp. 185–196, American Institute of Physics, Melville (NY), 2004.

    Google Scholar 

  93. K. A. Richardson, S. J. Schiff, and B. J. Gluckman. Control of traveling waves in the mammalian cortex. Phys. Rev. Lett., 94: 028103, 2005.

    Article  ADS  Google Scholar 

  94. V. Braitenberg and A. Schüz. Cortex: Statistics and Geometry of Neuronal Connectivity. Springer, Berlin, 1998.

    Google Scholar 

  95. P. beim Graben and H. Atmanspacher. Complementarity in classical dynamical systems. Found. Phys., 36(2): 291–306, 2006.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  96. D. Lind and B. Marcus. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (UK), 1995.

    Book  MATH  Google Scholar 

  97. P. beim Graben, J. D. Saddy, M. Schlesewsky, and J. Kurths. Symbolic dynamics of event–related brain potentials. Phys. Rev. E., 62(4): 5518–5541, 2000.

    Google Scholar 

  98. P. beim Graben and J. Kurths. Detecting subthreshold events in noisy data by symbolic dynamics. Phys. Rev. Let., 90(10): 100602, 2003.

    Google Scholar 

  99. H. Atmanspacher and P. beim Graben. Contextual emergence of mental states from neurodynamics. Chaos and Complexity Letters, 2(2/3), 151–168, 2007.

    Google Scholar 

  100. H. Atmanspacher. Contextual emergence from physics to cognitive neuroscience. J. of Consciousness Stud., 14(1–2): 18–36, 2007.

    Google Scholar 

  101. T. Metzinger, editor. Neural Correlates of Consciousness. MIT Press, Cambridge (MA), 2000.

    Google Scholar 

  102. D. J. Chalmers. What is a neural correlate of consciousness? In Metzinger Metzinger00, Chap. 2, pp. 17–39, 2000.

    Google Scholar 

  103. P. beim Graben. Incompatible implementations of physical symbol systems. Mind and Matter, 2(2): 29–51, 2004.

    Google Scholar 

  104. R. Dale and M. J. Spivey. From apples and oranges to symbolic dynamics: A framework for conciliating notions of cognitive representation. J. Exp. & Theor. Artific. Intell., 17(4): 317–342, 2005.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Graben, P.b. (2007). Foundations of Neurophysics. In: Graben, P.b., Zhou, C., Thiel, M., Kurths, J. (eds) Lectures in Supercomputational Neurosciences. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73159-7_1

Download citation

Publish with us

Policies and ethics