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Limited spreading: How hierarchical networks prevent the transition to the epileptic state

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Modeling Phase Transitions in the Brain

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

Abstract

An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable network activations within a limited critical range. In this range, the activity of neural populations in the network persists between the extremes of quickly dying out, or activating the whole network. The latter case of large-scale activation is visible in the transition to the epileptic state. After describing the shift to large-scale synchronization we study the role of network topology on this transition. Whereas standard explanations for balanced activity involve populations of inhibitory neurons for limiting activity, we observe how network topology limits activity spreading. A random or small-world topology results in low or high levels of activation. In contrast, a cluster hierarchy based on neuroanatomical knowledge—from cortical clusters such as the visual cortex at the highest level, to individual columns at the lowest level—enables sustained activity in neural systems and prevents large-scale activation as observed during epileptic seizures. The containment of activation critically depends on the ratio of inter-cluster connections. Such topological inhibition by means of a modular hierarchy, in addition to neuronal inhibition, might help to maintain healthy levels of neural activity.

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Notes

  1. 1.

    The work described here was undertaken at the University of Florida as part of the “Evolution into Epilepsy” NIH/NHS joint research project (grant no. 1R01EB004752).

References

  1. Achard, S., Salvador, R., Whitcher, B., Suckling, J., Bullmore, E.: A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J. Neurosci. 26, 63–72 (2006), doi:10.1523/jneurosci.3874-05.2006

    Article  CAS  PubMed  Google Scholar 

  2. Albert, R., Jeong, H., Barabási, A.L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000), doi:10.1038/35019019

    Article  CAS  PubMed  Google Scholar 

  3. Avoli, M., D’Antuono, M., Louvel, J., KÖhling, R.: Network and pharmacological mechanisms leading to epileptiform synchronization in the limbic system. Prog. Neurobiol. 68, 167–207 (2002), doi:10.1016/S0301-0082(02)00077-1

    CAS  Google Scholar 

  4. Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality. Phys. Rev. A 38, 364–374 (1988), doi:10.1103/PhysRevA.38.364

    Article  Google Scholar 

  5. Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987), doi:10.1103/PhysRevLett.59.381

    Article  PubMed  Google Scholar 

  6. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999), doi:10.1126/science.286.5439.509

    Article  PubMed  Google Scholar 

  7. Beggs, J.M., Plenz, D.: Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003)

    CAS  PubMed  Google Scholar 

  8. Binzegger, T., Douglas, R.J., Martin, K.A.C.: A quantitative map of the circuit of cat primary visual cortex. J. Neurosci. 24, 8441–8453 (2004), doi:10.1523/jneurosci.1400-04.200

    Article  CAS  PubMed  Google Scholar 

  9. Cranstoun, S., Worrell, G., Echauz, J., Litt, B.: Self-organized criticality in the epileptic brain. Proc. Joint EMBS/BMES Conf. 2002 1, 232–233 (2002)

    Google Scholar 

  10. Dezso, Z., Barabási, A.L.: Halting viruses in scale-free networks. Phys. Rev. E 65, 055103 (2002), doi:10.1103/PhysRevE.65.055103

    Google Scholar 

  11. Dyhrfjeld-Johnsen, J., Santhakumar, V., Morgan, R.J., Huerta, R., Tsimring, L., Soltesz, I.: Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data. J. Neurophysiol. 97, 1566–1587 (2007), doi:10.1152/jn.00950.2006

    Article  PubMed  Google Scholar 

  12. Engel, J.: Surgical Treatment of the Epilepsies. Lippincott Williams & Wilkins (1993)

    Google Scholar 

  13. Erdös, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)

    Google Scholar 

  14. Erice workshop on Complexity, Metastability and Nonextensivity: Networks as Renormalized Models for Emergent Behavior in Physical Systems (2004), doi:10.1142/9789812701558_0042

    Google Scholar 

  15. Gevins, A., Rémond, A.: Methods of Analysis of Brain Electrical and Magnetic Signals. Elsevier (1987)

    Google Scholar 

  16. Gómez-Gardeñes, J., Moreno, Y., Arenas, A.: Synchronizability determined by coupling strengths and topology on complex networks. Phys. Rev. E 75, 066106 (2007), doi:10.1103/PhysRevE.75.066106

    Google Scholar 

  17. Gotman, J.: Measurement of small time differences between EEG channels: Method and application to epileptic seizure propagation. Electroenceph. Clin. Neurophysiol. 56(5), 501–14 (1983), doi:10.1016/0013-4694(83)90235-3

    Google Scholar 

  18. Haider, B., Duque, A., Hasenstaub, A.R., McCormick, D.A.: Neocortical network activity in vivo is generated through a dynamic balance of excitation and inhibition. J. Neurosci. 26(17), 4535–4545 (2006), doi:10.1523/jneurosci.5297-05.2006

    Article  CAS  PubMed  Google Scholar 

  19. Hilgetag, C.C., Burns, G.A.P.C., O’Neill, M.A., Scannell, J.W., Young, M.P.: Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Phil. Trans. R. Soc. Lond. B 355, 91–110 (2000), doi:10.1098/rstb.2000.0551

    Article  CAS  Google Scholar 

  20. Hilgetag, C.C., Kaiser, M.: Clustered organisation of cortical connectivity. Neuroinf. 2, 353–360 (2004), doi:10.1385/NI:2:3:353

    Article  Google Scholar 

  21. Hufnagel, L., Brockmann, D., Geisel, T.: Forecast and control of epidemics in a globalized world. Proc. Natl. Acad. Sci. USA 101, 15124–15129 (2004), doi:10.1073/pnas.0308344101

    Article  CAS  PubMed  Google Scholar 

  22. Izhikevich, E.M., Gally, J.A., Edelman, G.M.: Spike-timing dynamics of neuronal groups. Cereb. Cortex 14, 933–944 (2004), doi:10.1093/cercor/bhh053

    Article  PubMed  Google Scholar 

  23. Jenkins, G.M., Watts, D.G.: Spectral Analysis and Its Applications. Holden-Day (1968)

    Google Scholar 

  24. Jung, P., Milton, J.: Epilepsy as a Dynamic Disease. Biological and Medical Physics Series, Springer (2003)

    Google Scholar 

  25. Kaiser, M., Goerner, M., Hilgetag, C.C.: Criticality of spreading dynamics in hierarchical cluster networks without inhibition. New J. Phys. 9, 110 (2007), doi:10.1088/1367-2630/9/5/110

    Google Scholar 

  26. Kaiser, M., Hilgetag, C.C.: Edge vulnerability in neural and metabolic networks. Biol. Cybern. 90, 311–317 (2004), doi:10.1007/s00422-004-0479-1

    Article  PubMed  Google Scholar 

  27. Kaiser, M., Hilgetag, C.C.: Spatial growth of real-world networks. Phys. Rev. E 69, 036103 (2004), doi:10.1103/PhysRevE.69.036103

    Google Scholar 

  28. Kaiser, M., Hilgetag, C.C.: Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. e95 (2006), doi:10.1371/journal.pcbi.0020095

    Google Scholar 

  29. Kaiser, M., Hilgetag, C.C.: Development of multi-cluster cortical networks by time windows for spatial growth. Neurocomputing 70(10–12), 1829–1832 (2007), doi:10.1016/j.neucom.2006.10.060

    Article  Google Scholar 

  30. Kaiser, M., Martin, R., Andras, P., Young, M.P.: Simulation of robustness against lesions of cortical networks. European J. Neurosci. 25, 3185–3192 (2007), doi:10.1111/j.1460-9568.2007.05574.x

    Google Scholar 

  31. Khalilov, I., Quyen, M.L.V., Gozlan, H., Ben-Ari, Y.: Epileptogenic actions of GABA and fast oscillations in the developing hippocampus. Neuron 48, 787–796 (2005), doi:10.1016/j.neuron.2005.09.026

    Article  CAS  PubMed  Google Scholar 

  32. Koch, C., Laurent, G.: Complexity and the nervous system. Science 284, 96–98 (1999), doi:10.1126/science.284.5411.96

    Article  CAS  PubMed  Google Scholar 

  33. Kötter, R., Sommer, F.T.: Global relationship between anatomical connectivity and activity propagation in the cerebral cortex. Philos. Trans. R. Soc. Lond. B 355, 127–134 (2000), doi:10.1098/rstb.2000.0553

    Article  Google Scholar 

  34. Latham, P.E., Nirenberg, S.: Computing and stability in cortical networks. Neural Comput. 16, 1385–1412 (2004), doi:10.1162/08997660432305743

    Article  PubMed  Google Scholar 

  35. Lothman, E.W., Bertram, E.H., Bekenstein, J.W., Perlin, J.B.: Self-sustaining limbic status epilepticus induced by ‘continuous’ hippocampal stimulation: Electrographic and behavioral characteristics. Epilepsy Res. 3(2), 107–19 (1989)

    Article  Google Scholar 

  36. Lothman, E.W., Bertram, E.H., Kapur, J., Stringer, J.L.: Recurrent spontaneous hippocampal seizures in the rat as a chronic sequela to limbic status epilepticus. Epilepsy Res. 6(2), 110–8 (1990), doi:10.1016/0920-1211(90)90085-A

    Article  Google Scholar 

  37. Masuda, N., Aihara, K.: Global and local synchrony of coupled neurons in small-world networks. Biol. Cybern. 90, 302–309 (2004), doi:10.1007/s00422-004-0471-9

    Article  PubMed  Google Scholar 

  38. Medvedev, A.V.: Epileptiform spikes desynchronize and diminish fast (gamma) activity of the brain: An ‘anti-binding’ mechanism? Brain Res. Bull. 58(1), 0115–28 (2002), doi:10.1016/S0361-9230(02)00768-2

    Google Scholar 

  39. Milgram, S.: The small-world problem. Psychol. Today 1, 60–67 (1967)

    Google Scholar 

  40. Netoff, T.I., Clewley, R., Arno, S., Keck, T., White, J.A.: Epilepsy in small-world networks. J. Neurosci. 24, 8075–8083 (2004), doi:10.1523/jneurosci.1509-04.200

    Article  CAS  PubMed  Google Scholar 

  41. Newman, M.E.J.: Power laws, pareto distributions and Zipf’s law. Contemp. Phys. 46, 323–351 (2005), doi:10.1080/0010751050005244

    Article  Google Scholar 

  42. Nisbach, F., Kaiser, M.: Developmental time windows for spatial growth generate multiple-cluster small-world networks. European Phys. J. B 58, 185–191 (2007), doi:10.1140/epjb/e2007-00214-

    Article  CAS  Google Scholar 

  43. Otnes, R.K., Enochson, L.: Digital Time Series Analysis. John Wiley and Sons (1972)

    Google Scholar 

  44. Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200 (2001), doi:10.1103/PhysRevLett.86.3200

    Google Scholar 

  45. Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N., Barabáasi, A.L.: Hierarchical organization of modularity in metabolic networks. Science 297, 1551–1555 (2002), doi:10.1126/science.107337

    Article  CAS  PubMed  Google Scholar 

  46. Salvador, R., Suckling, J., Coleman, M.R., Pickard, J.D., Menon, D., Bullmore, E.: Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb. Cortex 15(9), 1332–1342 (2005), doi:10.1093/cercor/bhi016

    Article  PubMed  Google Scholar 

  47. Sauer, T., Yorke, J., Casdagli, M.: Embedology. J. Stat. Phys. 65, 579–616 (1991), doi:10.1007/BF01053745

    Article  Google Scholar 

  48. Scannell, J.W., Burns, G.A., Hilgetag, C.C., OÒNeil, M.A., Young, M.P.: The connectional organization of the cortico-thalamic system of the cat. Cereb. Cortex 9(3), 277–299 (1999), doi:10.1093/cercor/9.3.277

    Article  CAS  PubMed  Google Scholar 

  49. Scannell, J., Blakemore, C., Young, M.: Analysis of connectivity in the cat cerebral cortex. J. Neurosci. 15(2), 1463–1483 (1995)

    CAS  PubMed  Google Scholar 

  50. Sporns, O., Chialvo, D.R., Kaiser, M., Hilgetag, C.C.: Organization, development and function of complex brain networks. Trends Cogn. Sci. 8, 418–425 (2004), doi:10.1016/j.tics.2004.07.008

    Article  PubMed  Google Scholar 

  51. Taken, F.: Detecting strange attractors in turbulence. Lecture Notes in Mathematics 898, 366–381 (1981), doi:10.1007/BFb009192

    Article  Google Scholar 

  52. Turcotte, D.: Fractals and Chaos in Geology and Geophysics. Cambridge University Press (1997)

    Google Scholar 

  53. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998), doi:10.1038/30918

    Article  CAS  PubMed  Google Scholar 

  54. Young, M.P.: The architecture of visual cortex and inferential processes in vision. Spat. Vis. 13(2–3), 137–146 (2000), doi:10.1163/156856800741162

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

We thank Claus Hilgetag, Matthias Görner and Bernhard Kramer for helpful comments on this chapter. We also thank Tadas Jucikas for performing control simulations with integrate-and-fire networks. Financial support from the German National Merit Foundation, EPSRC (EP/E002331/1), and Royal Society (RG/2006/R2) is gratefully acknowledged.

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Authors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle-upon-Tyne, Newcastle, NE1 7RU, UK

    M. Kaiser

  2. Institute of Neuroscience, Newcastle University, Newcastle-upon-Tyne, Newcastle, NE2 4HH, UK

    J. Simonotto

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Correspondence to M. Kaiser or J. Simonotto .

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Editors and Affiliations

  1. Dept. Engineering, University of Waikato, Hillcrest Road, Hamilton, 3240, New Zealand

    D. Alistair Steyn-Ross

  2. Dept. Engineering, University of Waikato, Hillcrest Road, Hamilton, 3240, New Zealand

    Moira Steyn-Ross

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Kaiser, M., Simonotto, J. (2010). Limited spreading: How hierarchical networks prevent the transition to the epileptic state. 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_5

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