Journal of Computational Neuroscience

, Volume 31, Issue 3, pp 679–684 | Cite as

A spatially extended model for macroscopic spike-wave discharges

  • Peter Neal TaylorEmail author
  • Gerold Baier


Spike-wave discharges are a distinctive feature of epileptic seizures. So far, they have not been reported in spatially extended neural field models. We study a space-independent version of the Amari neural field model with two competing inhibitory populations. We show that this competition leads to robust spike-wave dynamics if the inhibitory populations operate on different time-scales. The spike-wave oscillations present a fold/homoclinic type bursting. From this result we predict parameters of the extended Amari system where spike-wave oscillations produce a spatially homogeneous pattern. We propose this mechanism as a prototype of macroscopic epileptic spike-wave discharges. To our knowledge this is the first example of robust spike-wave patterns in a spatially extended neural field model.


Epilepsy EEG Mathematical modelling Spike-wave Bursting 



We thank H. Muhle, M. Siniatchkin and U. Stephani, Kiel, for clinical EEG data. We acknowledge financial support form EPSRC and BBSRC. We thank Kaspar Schindler, John Terry, Marc Goodfellow, Yujiang Wang and David Broomhead for discussion.

Supplementary material

10827_2011_332_MOESM1_ESM.pdf (19 kb)
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  1. Aicardi, J. (1988). Epileptic syndromes in childhood. Epilepsia, 29(Suppl 3), S1–5.CrossRefGoogle Scholar
  2. Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27(2), 77–87.PubMedCrossRefGoogle Scholar
  3. Amor, F., Rudrauf, D., Navarro, V., N’diaye, K., Garnero, L., Martinerie, J., et al. (2005). Imaging brain synchrony at high spatio-temporal resolution: Application to MEG signals during absence seizures. Signal Processing, 85(11), 2101–2111.CrossRefGoogle Scholar
  4. Asconapé, J., & Penry, J. K. (1984). Some clinical and eeg aspects of benign juvenile myoclonic epilepsy. Epilepsia, 25(1), 108–114.PubMedCrossRefGoogle Scholar
  5. Bai, X., Vestal, M., Berman, R., Negishi, M., Spann, M., Vega, C., et al. (2010). Dynamic time course of typical childhood absence seizures: Eeg, behavior, and functional magnetic resonance imaging. Journal of Neuroscience, 30(17), 5884–5893.PubMedCrossRefGoogle Scholar
  6. Bazhenov, M., Timofeev, I., Fröhlich, F., & Sejnowski, T. J. (2008). Cellular and network mechanisms of electrographic seizures. Drug Discovery Today. Disease models, 5(1), 45–57.PubMedCrossRefGoogle Scholar
  7. Blumenfeld, H. (2005). Cellular and network mechanisms of spike-wave seizures. Epilepsia, 46(Suppl 9), 21–33.PubMedCrossRefGoogle Scholar
  8. Borisyuk, R. M., & Kirillov, A. B. (1992). Bifurcation analysis of a neural network model. Biological Cybernetics, 66(4), 319–325.PubMedCrossRefGoogle Scholar
  9. Breakspear, M., Roberts, J. A., Terry, J. R., Rodrigues, S., Mahant, N., & Robinson, P. A. A. (2006). Unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cerebral Cortex, 16, 1296–1313.PubMedCrossRefGoogle Scholar
  10. David, O., Bastin, J., Chabardes, S., Minotti, L., & Kahane, P. (2010). Studying network mechanisms using intracranial stimulation in epileptic patients. Frontiers in Systems Neuroscience, 4, 12.CrossRefGoogle Scholar
  11. Destexhe, A. (1998). Spike-and-wave oscillations based on the properties of GABAB receptors. Journal of Neuroscience, 18(21), 9099.PubMedGoogle Scholar
  12. Destexhe, A., & Sejnowski, T. J. (2001). Thalamocortical assemblies. Oxford: Oxford University Press.Google Scholar
  13. da Silva, F. L., Blanes, W., Kalitzin, S. N., Parra, J., Suffczynski, P., & Velis, D. (2003). Epilepsies as dynamical diseases of brain systems: Basic models of the transition between normal and epileptic activity. Epilepsia, 44, 72–83.CrossRefGoogle Scholar
  14. Goodfellow, M., Schindler, K., & Baier, G. (2011). Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model. NeuroImage, 55(3), 920–932.PubMedCrossRefGoogle Scholar
  15. Hagmann, P., Kurant, M., Gigandet, X., Thiran, P., Wedeen, V. J., Meuli, R., et al. (2007). Mapping human whole-brain structural networks with diffusion MRI. PloS ONE, 2(7), e597.CrossRefGoogle Scholar
  16. Holmes, M. D. (2008). Dense array EEG: Methodology and new hypothesis on epilepsy syndromes. Epilepsia, 49(Suppl 3), 3–14.PubMedCrossRefGoogle Scholar
  17. Holmes, M. D., Brown, M., & Tucker, D. M. (2004). Are “generalized” seizures truly generalized? Evidence of localized mesial frontal and frontopolar discharges in absence. Epilepsia, 45(12), 1568–1579.PubMedCrossRefGoogle Scholar
  18. Izhikhevich, E. (2000). Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos, 10(6), 1171–1266.CrossRefGoogle Scholar
  19. Jansen, B. H., & Rit, V. G. (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics, 73, 357–366.PubMedCrossRefGoogle Scholar
  20. Kilpatrick, Z. P., & Bressloff, P. C. (2010). Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression. Journal of Computational Neuroscience, 28(2):193–209.PubMedCrossRefGoogle Scholar
  21. Marten, F., Rodrigues, S., Benjamin, O., Richardson, M. P., & Terry, J. R. (2009a). Onset of polyspike complexes in a mean-field model of human electroencephalography and its application to absence epilepsy. Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences, 367(1891), 1145–1161.CrossRefGoogle Scholar
  22. Marten, F., Rodrigues, S., Suffczynski, P., Richardson P. M., & Terry, J. R. (2009b). Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 79(2), 21911.CrossRefGoogle Scholar
  23. McCormick, D. A., & Contreras, D. (2001). On the cellular and network bases of epileptic seizures. Annual Review of Physiology, 63, 815–846.PubMedCrossRefGoogle Scholar
  24. Meeren, H. K. M., Pijn, J. P. M., Van Luijtelaar, E. L. J. M., Coenen, A. M. L., & Lopes da Silva, F. H. (2002). Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats. Journal of Neuroscience, 22(4), 1480–1495.PubMedGoogle Scholar
  25. Moeller, F., Siebner, H. R., Wolff, S., Muhle, H., Granert, O., Jansen, O., et al. (2008). Simultaneous EEG-fMRI in drug-naive children with newly diagnosed absence epilepsy. Epilepsia, 49(9), 1510–1519.PubMedCrossRefGoogle Scholar
  26. Otis, T. S., & De Koninck, Y. (1993). Characterization of synaptically elicited GABAB responses using patch-clamp recordings in rat hippocampal slices. Journal of Physiology, 463, 391–407.PubMedGoogle Scholar
  27. Robinson, P. A., Rennie, C. J., & Rowe, D. L. (2002). Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Physical Review E, 65(4), 41924.CrossRefGoogle Scholar
  28. Rodin, E., & Ancheta, O. (1987). Cerebral electrical fields during petit mal absences. Electroencephalography and Clinical Neurophysiology, 66(6), 457–466.PubMedCrossRefGoogle Scholar
  29. Rodrigues, S., Barton, D., Marten, F., Kibuuka, M., Alarcon, G., Richardson, M. P., et al. (2010). A method for detecting false bifurcations in dynamical systems: Application to neural-field models. Biological Cybernetics, 102(2), 145–154.PubMedCrossRefGoogle Scholar
  30. Rodrigues, S., Terry, J. R., & Breakspear, M. (2006). On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics. Physics Letters A, 355(4–5), 352–357.CrossRefGoogle Scholar
  31. Sadleir, L. G., Farrell, K., Smith, S., Connolly, M. B., & Scheffer, I. E. (2006). Electroclinical features of absence seizures in childhood absence epilepsy. Neurology, 67(3), 413–418.PubMedCrossRefGoogle Scholar
  32. Stead, M., Bower, M., Brinkmann, B. H., Lee, K., Marsh, W. R., Meyer, F. B., et al. (2010). Microseizures and the spatiotemporal scales of human partial epilepsy. Brain, 133(9), 2789–2797.PubMedCrossRefGoogle Scholar
  33. Stern, J. M., & Engel, J. (2005). Atlas of EEG patterns. Philadelphia: Lippincott Williams & Wilkins.Google Scholar
  34. Suffczynski, P., Kalitzin, S., & Lopes Da Silva, F. H. (2004). Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience, 126(2), 467–484.PubMedCrossRefGoogle Scholar
  35. Thomson, A. M., & Deuchars, J. (1997). Synaptic interactions in neocortical local circuits: Dual intracellular recordings in vitro. Cerebral Cortex, 7(6), 510–522.PubMedCrossRefGoogle Scholar
  36. van Luijtelaar, G., & Sitnikova, E. (2006). Global and focal aspects of absence epilepsy: The contribution of genetic models. Neuroscience and Biobehavioral Reviews, 30(7), 983–1003.PubMedCrossRefGoogle Scholar
  37. Wendling, F., Bartolomei, F., Bellanger, 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.PubMedCrossRefGoogle Scholar
  38. Westmijse, I., Ossenblok, P., Gunning, B., & van Luijtelaar, G. (2009). Onset and propagation of spike and slow wave discharges in human absence epilepsy: A MEG study. Epilepsia, 50(12), 2538–2548.PubMedCrossRefGoogle Scholar
  39. Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12(1), 1–24.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Manchester Interdisciplinary BiocentreThe University of ManchesterManchesterUK

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