Brain Topography

, Volume 1, Issue 3, pp 199–215 | Cite as

Generation of human EEG by a combination of long and short range neocortical interactions

  • Paul L. Nunez


A theory of neocortical interactions is developed involving both local delays (PSP rise and decay times) and global delays due to finite velocity of action potentials in corticocortical fibers. The theory is based on plausible assumptions regarding input/output relations in neocortical columns and realistic neural parameters. The simultaneous existence of short wavelength waves propagating away from multiple epicenters and long wavelength standing waves due to global boundary conditions is predicted. Both phenomena appear to have dominant oscillation frequencies in the general range of observed EEG phenomena in humans. A mechanism by which removal of diffuse input from the reticular formation may cause an abrupt drop in EEG frequency (as in the transition from the awake to sleeping state) is postulated.

Key words

EEG theory neocortical dynamics EEG dispersion relations alpha rhythm standing waves 


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  1. Abeles, M. Local Cortical Circuits. Springer-Verlag, New York, 1982.Google Scholar
  2. Adey, W. R. Electromagnetic field interactions in the brain. In: E. Basar (Ed.), Dynamics of Sensory and Cognitive Processing by the Brain. Springer-Verlag, Berlin, 1988.Google Scholar
  3. Braitenberg, V. Cortical architectonics: general and areal. In: M.A.B. Brazier, H. Petsche (Eds.), Architechtonics of the Cerebral Cortex. Raven Press, New York, 1978.Google Scholar
  4. Cooper R., Winter, A. L., Crow, H. J. and Walter, W. G. Comparison of subcortical, cortical, and scalp activity using chronically indwelling electrodes in man. Electroencephal. Clin. Neruophysiol., 1965, 18: 217–228.Google Scholar
  5. DeLucchi, M. R., Garoutte, B. and Aird, R. B. The scalp as an electroencephalographic averager. Electroencephal. Clin. Neurophysiol., 1975, 38: 93–96.Google Scholar
  6. Freeman, W.J. Mass Action in the Nervous System. Academic Press, New York, 1975.Google Scholar
  7. Freeman, W. J. Analytic techniques used in the search for the physiological basis of the EEG. In: A. S. Gevins and A. Remond (Eds.), Handbook of Electroencephalography and Clinical Neurophysiology. Elsevier, New York, 1987.Google Scholar
  8. Gleick, J. Chaos. Viking, New York, 1987.Google Scholar
  9. Ingber, L. Statistical mechanics of neocortical interactions. Basic formulation. Physica 5D, 1982, 83–107.Google Scholar
  10. Ingber, L. Statistical mechanics of neocortical interactions. Derivation of short-term memory capacity. Phys. Rev. A., 1984, 29: 3346–3358.Google Scholar
  11. Ingber, L. Statistical mechanics of neocortical interactions: EEG dispersion relations. IEEE Trans. Biomed. Eng., 1985, 32: 91–94.PubMedGoogle Scholar
  12. Ingber, L. and Nunez, P. L. Multiple scales of statistical physics of neocortex: application to electroencephalography. Math. Comput. Modelling., 1989, in press.Google Scholar
  13. Katznelson, R.D. Normal modes of the brain: neuroanatomical basis and a physiological theoretical model. In: P.L. Nunez (Ed.), Electric Fields of the Brain: The Neurophysics of EEG. Oxford U Press, New York, 1981.Google Scholar
  14. Katznelson, R.D. Deterministic and Stochastic Field Theoretic Models in the Neurophysics of EEG. Ph.D. Dissertation, U. of Calif. at San Diego, 1982.Google Scholar
  15. Lopes da Silva, F. H., Hoeks, H., Smiths, H. and Zetterberg, H. Model of brain rhythmic activity. Kybernetik, 1974, 15: 27–37.PubMedGoogle Scholar
  16. Lopes da Silva, F.H. and Storm van Leeuwen, W. The cortical alpha rhythm in dog: the depth and surface profile of phase. In: M.A.B. Brazier and H. Petsche (Eds.), Architectonics of the Cerebral Cortex. Raven Press, New York, 1978, 319–333.Google Scholar
  17. Lopes da Silva, F. H. Dynamics of EEGs as signals of neuronal populations: models and theoretical considerations. In: E. Niedermeyer and F.H. Lopes da Silva (Eds.), Electroencephalography. Basic Principles, Clinical Applications and Related Fields. Urban and Schwarzenberg, Baltimore-Munich, 1987, 15–28.Google Scholar
  18. Moon, F. C. Chaotic Vibrations. Wiley, New York, 1987.Google Scholar
  19. Nunez, P.L. The brain wave equation: a model for the EEG. Amer. EEG Soc. Meeting Houston, 1972, and Math Biosciences, 1974a, 21: 279–297.Google Scholar
  20. Nunez, P.L. Wave-like properties of the alpha rhythm. IEEE Trans. Biomed. Eng., 1974b, 21: 473–482.Google Scholar
  21. Nunez, P.L., Reid, L. and Bickford, R.G. The relationship of head size to alpha frequency with implications to a brain wave model. Electroencephal. Clin. Neurophysiol., 1977, 44: 344- 352.Google Scholar
  22. Nunez, P.L. Electric Fields of the Brain: The Neurophysics of EEG. Oxford U. Press, New York, 1981a.Google Scholar
  23. Nunez, P.L. A study of origins of the time dependencies of scalp EEG: I. Theoretical basis. IEEE Trans. Biomed. Eng., 1981b, 28: 271–280.PubMedGoogle Scholar
  24. Nunez, P.L. A study of the origins of the time dependencies of scalp EEG: II. Experimental support of theory. IEEE Trans. Biomed. Eng., 1981c, 28: 281–288.PubMedGoogle Scholar
  25. Nunez, P. L. Spatial filtering and experimental strategies in EEG. In: D. Samson-Dollfus (Ed.), Statistics and Topography in Quantitative EEG. Elsevier, Paris, 1988a.Google Scholar
  26. Nunez, P.L. Global contributions to cortical dynamics: theoretical and experimental evidence for standing wave phenomena. In: E. Basar (Ed.), Dynamics of Sensory and Cognitive Processing by the Brain. Springer-Verlag, New York, 1988b.Google Scholar
  27. Nunez, P. L. Towards a physics of neocortex. In: V.Z. Marmarelis (Ed.), Advanced Methods of Physiological Systems Modeling, vol.2, 1989, in press.Google Scholar
  28. Petsche, H., Pockberger, H. and Rappelsberger, P. On the search for the sources of the electroencephalogram. Neuroscience, 1984, 11: 10–27.Google Scholar
  29. Pfurtscheller, G. and Cooper, R. Frequency dependence of the transmission of the EEG from cortex to scalp. Electroencephal. Clin. Neurophysiol., 1975, 38: 93–96.Google Scholar
  30. Plonsey, R. Bioelectric Phenomena. McGraw-Hill, New York, 1969.Google Scholar
  31. Rall, W.A. A statistical theory of monosynaptic input—output relations, J. Cell. Comp. Physiol., 1955, 46: 373–411.Google Scholar
  32. Rall, W.A. Experimental monosynaptic input—output relations in mammalian spinal cord. J. Cell. Comp. Physiol., 1955, 46: 413–437.Google Scholar
  33. Sholl, D.A. The Organization of the Cerebral Cortex. Wiley, London, 1956.Google Scholar
  34. Szentagothai, J. The neural network of the cerebral cortex: a functional interpretation. Proc. Roy. Soc. Lond., 1978a, 201: 219–248.Google Scholar
  35. Szentagothai, J. Specificity versus (quasi) randomness in cortical connectivity. In: M.A.B. Brazier and H. Petsche (Eds.), Architectonics of the Cerebral Cortex. Raven Press, New York, 1978b, 77–97.Google Scholar
  36. Taylor, C. P., and Dudek, F. E. Excitation of hippocampal pyramidal cells by an electrical field effect. J. Neurophysiol., 1984a, 52: 126–142.PubMedGoogle Scholar
  37. Taylor, C. P. and Dudek, F. E. Synchronization without active chemical synapses during hippocampal afterdischarges. J. Neurophysiol., 1984b, 52: 143–155.PubMedGoogle Scholar
  38. Thatcher, R.W., Krouse, P.J. and Hrybyk, M. Cortico-cortical associations and EEG coherence: a two compartmental model. Electroencephal. Clin. Neurophysiol., 1986, 64: 123–143.Google Scholar
  39. van Rotterdam, A., Lopes da Silva, F.H., van der Ende, J., Viergever, M.A. and Hermans, A.J. A model of the spatialtemporal characteristics of the alpha rhythm. Bull. Math. Biology., 1982, 44: 283–305.Google Scholar
  40. Walter, D.O., Rhodes, J.M., Brown, D. and Adey, W.R. Comprehensive spectral analysis of human EEG generators in posterior cerebral regions. Electroencephal. Clin. Neurophysiol., 1966, 20: 224–237.Google Scholar
  41. Wilson, H. R. and Cowan, J. D. Excitatory and inhibitory interactions in localized populations of model neurons. Biophysics, 12: 1–12.Google Scholar
  42. Wilson, H.R. and Cowan, J.D. A mathematical theory of the functional dynamics of cortical and thalmic nervous tissue. Kybernetik, 1973, 13: 55–80.PubMedGoogle Scholar
  43. Zhadin, M.N. Rhythmic processes in the cerebral cortex. J. Theor. Biol., 1984, 108: 565–595.PubMedGoogle Scholar

Copyright information

© Human Sciences Press, Inc 1989

Authors and Affiliations

  • Paul L. Nunez
    • 1
  1. 1.Department of Biomedical EngineeringTulane UniversityNew OrleansUSA

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