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.
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
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
Albert, R., Jeong, H., Barabási, A.L.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000), doi:10.1038/35019019
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
Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality. Phys. Rev. A 38, 364–374 (1988), doi:10.1103/PhysRevA.38.364
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
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999), doi:10.1126/science.286.5439.509
Beggs, J.M., Plenz, D.: Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003)
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
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)
Dezso, Z., Barabási, A.L.: Halting viruses in scale-free networks. Phys. Rev. E 65, 055103 (2002), doi:10.1103/PhysRevE.65.055103
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
Engel, J.: Surgical Treatment of the Epilepsies. Lippincott Williams & Wilkins (1993)
Erdös, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)
Erice workshop on Complexity, Metastability and Nonextensivity: Networks as Renormalized Models for Emergent Behavior in Physical Systems (2004), doi:10.1142/9789812701558_0042
Gevins, A., Rémond, A.: Methods of Analysis of Brain Electrical and Magnetic Signals. Elsevier (1987)
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
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
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
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
Hilgetag, C.C., Kaiser, M.: Clustered organisation of cortical connectivity. Neuroinf. 2, 353–360 (2004), doi:10.1385/NI:2:3:353
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
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
Jenkins, G.M., Watts, D.G.: Spectral Analysis and Its Applications. Holden-Day (1968)
Jung, P., Milton, J.: Epilepsy as a Dynamic Disease. Biological and Medical Physics Series, Springer (2003)
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
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
Kaiser, M., Hilgetag, C.C.: Spatial growth of real-world networks. Phys. Rev. E 69, 036103 (2004), doi:10.1103/PhysRevE.69.036103
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
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
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
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
Koch, C., Laurent, G.: Complexity and the nervous system. Science 284, 96–98 (1999), doi:10.1126/science.284.5411.96
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
Latham, P.E., Nirenberg, S.: Computing and stability in cortical networks. Neural Comput. 16, 1385–1412 (2004), doi:10.1162/08997660432305743
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)
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
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
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
Milgram, S.: The small-world problem. Psychol. Today 1, 60–67 (1967)
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
Newman, M.E.J.: Power laws, pareto distributions and Zipf’s law. Contemp. Phys. 46, 323–351 (2005), doi:10.1080/0010751050005244
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-
Otnes, R.K., Enochson, L.: Digital Time Series Analysis. John Wiley and Sons (1972)
Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200 (2001), doi:10.1103/PhysRevLett.86.3200
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
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
Sauer, T., Yorke, J., Casdagli, M.: Embedology. J. Stat. Phys. 65, 579–616 (1991), doi:10.1007/BF01053745
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
Scannell, J., Blakemore, C., Young, M.: Analysis of connectivity in the cat cerebral cortex. J. Neurosci. 15(2), 1463–1483 (1995)
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
Taken, F.: Detecting strange attractors in turbulence. Lecture Notes in Mathematics 898, 366–381 (1981), doi:10.1007/BFb009192
Turcotte, D.: Fractals and Chaos in Geology and Geophysics. Cambridge University Press (1997)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998), doi:10.1038/30918
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
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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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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