Journal of Computational Neuroscience

, Volume 16, Issue 1, pp 49–68 | Cite as

A Novel Method for the Topographic Analysis of Neural Activity Reveals Formation and Dissolution of ‘Dynamic Cell Assemblies’

  • Michael Breakspear
  • Leanne M. Williams
  • Cornelis J. Stam


The study of synchronous oscillations in neural systems is a very active area of research. However, cognitive function may depend more crucially upon a dynamic alternation between synchronous and desynchronous activity rather than synchronous behaviour per se. The principle aim of this study is to develop and validate a novel method of quantifying this complex process. The method permits a direct mapping of phase synchronous dynamics and desynchronizing bursts in the spatial and temporal domains. Two data sets are analyzed: Numeric data from a model of a sparsely coupled neural cell assembly and experimental data consisting of scalp-recorded EEG from 40 human subjects. In the numeric data, the approach enables the demonstration of complex relationships between cluster size and temporal duration that cannot be detected with other methods. Dynamic patterns of phase-clustering and desynchronization are also demonstrated in the experimental data. It is further shown that in a significant proportion of the recordings, the pattern of dynamics exhibits nonlinear structure. We argue that this procedure provides a ‘natural partitioning’ of ongoing brain dynamics into topographically distinct synchronous epochs which may be integral to the brain's adaptive function. In particular, the character of transitions between consecutive synchronous epochs may reflect important aspects of information processing and cognitive flexibility.

neural synchronization cognition nonlinear desynchronization EEG coherence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arnhold J, Grassberger P, Lehnertz K, Elger C (1999) A robust method for detecting interdependencies: Application to intracranially recorded EEG. Physica D 134: 419-430.Google Scholar
  2. Ashwin P, Covas E, Tavakol R (1999) Transverse instability for nonnormal parameters. Nonlinearity 12: 563-577.Google Scholar
  3. Bak P (1996) How Nature Works: The Science of Self-Organized Criticality. Oxford University Press, New York.Google Scholar
  4. Basar E, Basar-Eroglu C, Karakas S, Schurmann S (2001) Gamma, alpha, delta and theta oscillations govern cognitive processes. Int. J. Psychophysiol. 39: 241-248.Google Scholar
  5. Bertrand O, Tallon-Baudry C (2000) Oscillatory gamma activity in humans: A possible role for object representation. Int. J. Psychophysiol. 38: 211-223.Google Scholar
  6. Bullmore ET, Fadili J, Breakspear M, Salvador R, Suckling J, Brammer MJ (2003) Wavelets and statistical analysis of functional magnetic resonance images of the human brain. Statistical Methods in Medical Research 12: 375-399.Google Scholar
  7. Burgess AP, Ali L (2002) Functional connectivity of gamma EEG activity is modulated at low frequency during conscious recollection. Int. J. Psychophysiol. 46: 91-100.Google Scholar
  8. Breakspear M (2002) Nonlinear phase desynchronization in human EEG data. Human Brain Mapping 15: 175-198.Google Scholar
  9. Breakspear M, Terry J (2002a) Nonlinear interdependence in neural systems: Motivation, theory and relevance. Int. J. Neurosci. 112: 1263-1284.Google Scholar
  10. Breakspear M, Terry J (2002b) Detection and description of nonlinear interdependence in normal multichannel human EEG. Clin. Neurophysiol. 113: 635-753.Google Scholar
  11. Breakspear M, Terry J (2002c) Topographic organisation of nonlinear interdependence in multichannel human EEG. Neuroimage 16: 822-825.Google Scholar
  12. Breakspear M, Terry J, Friston K (2003a) Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a nonlinear model of neuronal dynamics. Network: Comput. Neural Syst. 14: 703-732.Google Scholar
  13. Breakspear M, Terry J, Friston K, Williams L, Brown K, Brennan J, Gordon E (2003b) A disturbance of nonlinear interdependence in scalp EEG of subjects with first episode schizophrenia. NeuroImage 20: 466-478.Google Scholar
  14. Ebeling W (1995) Dynamic entropies and predictability of evolutionary processes. In: Nonlinear Dynamics, Chaotic and Complex Systems, E Infeld, R Zelazny, A Galkowski, eds. Cambridge University Press, Cambridge.Google Scholar
  15. Freeman WJ, Rogers LJ (2002) Fine temporal resolution of analytic phase reveals episodic synchronization by state transitions in gamma EEGs. J. Neurophysiol. 87: 937-945.Google Scholar
  16. Freund J, Rateitschak K (1998) Entropy analysis of noise contaminated sequences. International Journal of Bifurcations and Chaos 8: 933-940.Google Scholar
  17. Friston KJ, Tononi G, Sporns O, Edleman G (1995) Characterising the complexity of neuronal interactions. Human Brain Mapping 3: 302-314.Google Scholar
  18. Friston KJ (1997) Another neural code? NeuroImage 5: 213-220.Google Scholar
  19. Friston KJ (2000) The labile brain. II. Transients, complexity and selection. Philosophical Transactions of the Royal Society of London, 355B: 237-252.Google Scholar
  20. Gatlin L (1972) Information Theory and the Living System. Columbia University Press, New York.Google Scholar
  21. Gratton G, Coles M, Donchin E (1983) A new method for off-line removal of ocular artifact. Electroencephalogr. Clin. Neurophysiol. 55: 468-484.Google Scholar
  22. Haig A, Gordon E (1998) Prestimulus EEG alpha phase synchronicity influences N100 amplitude and reaction time. Psychophysiology 35: 591-595.Google Scholar
  23. Haig A, Gordon E, Wright JJ, Meares R, Bahramali H (2000) Synchronous gamma-band activity in task-relevant cognition. Neuroreport 11: 1-7.Google Scholar
  24. Hebb D (1949) The first stage of perception. Reprinted in: G Shaw, G Palm, eds. Brain Function, World Scientific, Singapore.Google Scholar
  25. Kaneko K (1997) Dominance of Milnor attractors and noise-induced selection in a multiattractor system. Phys. Rev. Lett. 78: 2736-2739.Google Scholar
  26. Kelso J, Bressler S, Buchanan S, DeGuzman G, Ding M, Fuchs A, Holroyd T (1992) A phase transition in human brain and behaviour. Physics Letters A 169: 134-144.Google Scholar
  27. Lachaux JP, Rodriguez E, Martinerie J, Varela F (1999) Measuring phase synchrony in brain signals. Human Brain Mapping 8: 194-208.Google Scholar
  28. Larter R, Speelman B (1999) A coupled ordinary differential equation lattice model for the simulation of epileptic seizures. Chaos 9: 795-804.Google Scholar
  29. Le Van Quyen M, Martinerie J, Adam C, Varela F (1999) Nonlinear analyses of interictal EEG map the interdependencies in human focal epilepsy. Physica D 127:250-266.Google Scholar
  30. Lee KH, Williams LM, Breakspear M, Gordon E (2002) Synchronous Gamma activity: A review and contribution to an integrative neuroscience model of schizophrenia. Brain Res. Rev. 41: 57-78.Google Scholar
  31. Maistrenko Y, Maistrenko V, Popovich A, Mosekilde E (1998) Transverse instability and riddled basins in a system of two coupled logistic maps. Physical Review E 57: 2713-2724.Google Scholar
  32. Miltner WHR, Braun C, Arnold M, Witte M, Taub E (1999) Coherence of gamma-band EEG activity as a basis for associative learning. Nature 397: 434-436.Google Scholar
  33. Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35: 193-213.Google Scholar
  34. Netoff TI, Schiff SJ (2002) Decreased neuronal synchronization during experimental seizures. J. Neurosci. 22: 7297-7307.Google Scholar
  35. Nunez PL, Srinivasan R, Westdorp A, Wijesinghe RS, Tucker DM, Silberstein RB, Cadusch PJ (1997) EEG coherency I: Statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales. Electroencephalogr. Clin. Neurophysiol. 103: 499-515.Google Scholar
  36. Nunez P, Silberstein R, Shi Z, Carpenter M, Srinivasan R, Tucker D, Doran S, Cadusch P, Wijesinghe R (1999) EEG coherency II: Experimental comparisons of multiple measures. Clin. Neurophysiol. 110: 469-486.Google Scholar
  37. Osborne A, Provencale A (1989) Finite correlation dimension for stochastic systems with power-law spectra. Physica 35D: 357-381.Google Scholar
  38. Pfurtscheller G (1977) Graphical display and statistical evaluation of event-related desynchronization. Electroenceph Clin. Neurophysiol. 43: 757-760.Google Scholar
  39. Pikovsky A, Grassberger P (1991) Symmetry breaking bifurcation for coupled chaotic attractors. J. Phys. A 24: 4587-4597.Google Scholar
  40. Prichard W, Theiler J (1994) Generating surrogate data for time series with several simultaneously measured variables. Phys. Rev. Lett. 73: 951-954.Google Scholar
  41. Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL (2001) Prediction of electroencephalographic spectra from neurophysiology. Phys. Rev. E 63: 021903.Google Scholar
  42. Rodriguez E, George N, Lachaux F, Martinerie J, Renault B, Varela F (1999) Perception's shadow: Long-distance synchronization of human brain activity. Nature 397: 430-433.Google Scholar
  43. Rosenblum M, Pikovsky A, Kurths J (1996) Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76: 1804-1807.Google Scholar
  44. Ruelle D (1990) Deterministic chaos: The science and the fiction. Proceedings of the Royal Society of London 427A: 241-248.Google Scholar
  45. Rulkov N, Sushchik M (1997) Robustness of synchronized chaotic oscillations. Int J Bifurcation and Chaos 7: 625-643.Google Scholar
  46. Schreiber T, Schmitz A (2000) Surrogate time series. Physica 142D: 346-382.Google Scholar
  47. Sergeant J, Geuze R, Van Winsum W (1987) Event-related desynchronization and p300. Psychophysiology 24: 272-277.Google Scholar
  48. Singer W (1995) Putative functions of temporal correlations in neocortical processing. In: C Koch, J Davis, eds. Large-Scale Neuronal Theories of the Brain, MIT Press, London.Google Scholar
  49. Stam CJ, Pijn J, Suffczynski P, Lopes da Silva (1999) Dynamics of the alpha rhythm: evidence for non-linearity? Clin. Neurophysiol. 110: 1801-1813.Google Scholar
  50. Stam CJ, van Dijk BW (2002) Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets. Physica 163D: 236-251.Google Scholar
  51. Stam CJ, van der Made Y, Pijnenburg YAL, Scheltens Ph (2002a) EEG synchronization in mild cognitive impairment and Alzheimer's disease. Acta Neurol. Scand. 106: 1-7.Google Scholar
  52. Stam CJ, van Cappellen van Walsum AM, Pijnenburg YAL, Berendse HW, de Munck JC, Scheltens Ph, van Dijk BW (2002b) Generalized synchronization of MEG recordings in Alzheimer's disease: Evidence for involvement of the gamma band. J. Clin. Neurophysiol 19: 562-574.Google Scholar
  53. Stam CJ, van Cappellen van Walsum AM, Micheloyannis S (2002) Variability of EEG synchronization during a working memory task in healthy subjects. Int. J. Psychopysiol. 46: 53-66.Google Scholar
  54. Stam CJ, Breakspear M, van Cappellen van Walsum AM, van Dijk BW (2003) Nonlinear synchronization in EEG and whole-head MEG recordings of healthy subjects. Human Brain Mapping 19: 63-78.Google Scholar
  55. Tallon-Baudry C, Betrand O, Fischer C (2001) Oscillatory synchrony between human extrastriate areas during visual short-term memory maintenance. J. Neurosci. 21: 1-5.Google Scholar
  56. Tass P, Rosenblum M, Weule J, Kurths J, Pikovsky A, Volkmann J, Schnitzler A, Freund H (1998) Detection of n:m phase locking from noisy data: Application to magnetoencephalography. Phys. Rev. Lett. 81: 3291-3294.Google Scholar
  57. Tononi G, Sporns O, Edelman GM (1994) A measure for brain complexity: Relating functional segregation and integration in the nervous system. Proc. Nati. Acad. Sci. USA 91: 5033-5037.Google Scholar
  58. Van Putten MJAM, Stam CJ (2001) Application of a neural complexity measure to multichannel EEG. Physics Letters A 281: 131-141.Google Scholar
  59. Van Putten MJAM (2002) Proposed links rates in the human brain. Clin. Neurophysiol. 113 (Suppl. 1) S110: 17-01.Google Scholar
  60. Van Winsum W, Sergeant J, Geuze R (1984) The functional significance of event-related desynchronization of alpha rhythm in attentional and activating tasks. Electroenceph Clin. Neurophysiol. 58: 519-524.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Michael Breakspear
    • 1
    • 2
  • Leanne M. Williams
    • 1
  • Cornelis J. Stam
    • 3
  1. 1.Brain Dynamics CentreWestmead HospitalWestmeadAustralia
  2. 2.School of PsychologyUniversity of SydneyAustralia.
  3. 3.Department of Clinical NeurophysiologyVU University Medical CentreAmsterdamThe Netherlands

Personalised recommendations