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Generalized seizures in a neural field model with bursting dynamics

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Abstract

The mechanisms underlying generalized seizures are explored with neural field theory. A corticothalamic neural field model that has accounted for multiple brain activity phenomena and states is used to explore changes leading to pathological seizure states. It is found that absence seizures arise from instabilities in the system and replicate experimental studies in numerous animal models and clinical studies.

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References

  • Abeysuriya, R., Rennie, C., & Robinson, P. (2014). Prediction and verification of nonlinear sleep spindle harmonic oscillations. Journal of Theoretical Biology, 344, 70–77.

    Article  CAS  PubMed  Google Scholar 

  • Avanzini, G, de Curtis, M., Marescaux, C., Panzica, F., & Spreafico, R. (1992). Role of the thalamic reticular nucleus in the generation of rhythmic thalamo-cortical activities subserving spike and waves. In Focus on GABA-B Receptors, Generalized Non-Convulsive Epilepsy (pp. 85–95): Springer.

  • Avoli, M., & Gloor, P. (1981). The effects of transient functional depression of the thalamus on spindles and on bilateral synchronous epileptic discharges of feline generalized penicillin epilepsy. Epilepsia, 22, 443–452.

    Article  CAS  PubMed  Google Scholar 

  • Avoli, M., Gloor, P., Kostopoulos, G., & Gotman, J. (1983). An analysis of penicillin-induced generalized spike and wave discharges using simultaneous recordings of cortical and thalamic single neurons. Journal of Neuropsychology, 50, 819–837.

    CAS  Google Scholar 

  • Bazhenov, M., Timofeev, I., Steriade, M., & Sejnowski, T. J. (2002). Model of thalamocortical slow-wave sleep oscillations and transitions to activated states. The Journal of Neuroscience, 22, 8691–8704.

    CAS  PubMed  Google Scholar 

  • Blumenfeld, H., & McCormick, D.A. (2000). Corticothalamic inputs control the pattern of activity generated in thalamocortical networks. The Journal of Neuroscience, 20, 5153–5162.

    CAS  PubMed  Google Scholar 

  • Braitenberg, V., & Schüz, A. (1998). Cortical architectonics. In Cortex: Statistics and Geometry of Neuronal Connectivity (pp. 135–137): Springer.

  • Breakspear, M., Roberts, J.A., Terry, J.R., Rodrigues, S., Mahant, N., & Robinson, P.A. (2006). A unified explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cerebral Cortex, 16, 1296–1313.

    Article  CAS  PubMed  Google Scholar 

  • Browne, T.R., & Holmes, G.L. (2000). Handbook of epilepsy. Philadelphia: Williams and Wilkins.

    Google Scholar 

  • Buckwar, E., & Winkler, R. (2007). Multi-step Maruyama methods for stochastic delay differential equations. Stochastic Analysis and Applications, 25, 933–959.

    Article  Google Scholar 

  • Crunelli, V., Cope, D.W., & Terry, J.R. (2011). Transition to absence seizures and the role of GABA A receptors. Epilepsy Research, 97, 283–289.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Crunelli, V., & Leresche, N. (2002). Childhood absence epilepsy: genes, channels, neurons and networks. Nature Reviews. Neuroscience, 3(5), 371–382.

    Article  CAS  PubMed  Google Scholar 

  • Destexhe, A. (1998). Spike-and-wave oscillations based on the properties of GABA B receptors. The Journal of Neuroscience, 18, 9099–9111.

    CAS  PubMed  Google Scholar 

  • Destexhe, A. (1999). Can GABA A conductances explain the fast oscillation frequency of absence seizures in rodents. The European Journal of Neuroscience, 11, 2175–2181.

    Article  CAS  PubMed  Google Scholar 

  • Destexhe, A., Bal, T., McCormick, D.A., & Sejnowski, T.J. (1996). Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices. Journal of Neurophysiology, 76, 2049–2070.

    CAS  PubMed  Google Scholar 

  • Destexhe, A., McCormick, D.A., & Sejnowski, T.J. (1993). A model for 8–10 Hz spindling in interconnected thalamic relay and reticularis neurons. Biophysical Journal, 65, 2473–2477.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Dulac, O. (2001). Epileptic encephalopathy. Epilepsia, 42, 23–26.

    Article  PubMed  Google Scholar 

  • Freestone, D., Aram, P., Dewar, M., Scerri, K., Grayden, D.B., & Kadirkamanathan, V. (2011). A data-driven framework for neural field modeling. NeuroImage, 56(3), 1043–1058.

    Article  CAS  PubMed  Google Scholar 

  • Freestone, D.R., Nesic, D., Jafarian, A., Cook, M.J., & Grayden, D.B. (2013). A neural mass model of spontaneous burst suppression and epileptic seizures. In 2013 35th Annual International Conference of the IEEE, Engineering in Medicine and Biology Society (EMBC) (pp. 5942–5945): IEEE.

  • Gloor, P., & Fariello, R. (1988). Generalized epilepsy: some of its cellular mechanisms differ from those of focal epilepsy. Trends in Neurosciences, 11, 63–68.

    Article  CAS  PubMed  Google Scholar 

  • Gloor, P., Quesney, L., & Zumstein, H. (1977). Pathophysiology of generalized penicillin epilepsy in the cat: the role of cortical and subcortical structures. II. topical application of penicillin to the cerebral cortex and to subcortical structures. Electroencephalography and Clinical Neurophysiology, 43, 79–94.

    Article  CAS  PubMed  Google Scholar 

  • Gören, M.Z., & Onat, F. (2007). Ethosuximide: from bench to bedside. CNS Drug Reviews, 13, 224–239.

    Article  PubMed  Google Scholar 

  • Higham, D.J. (2001). An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM review, 43, 525–546.

    Article  Google Scholar 

  • Huguenard, J., & Prince, D. (1994). Clonazepam suppresses GABA B-mediated inhibition in thalamic relay neurons through effects in nucleus reticularis. Journal of Neurophysiology, 71, 2576–2581.

    CAS  PubMed  Google Scholar 

  • Izhikevich, E., & Edelman, G. (2008). Large-scale model of mammalian thalamocortical systems. Proceedings of the National Academy of Sciences of the United States of America, 105, 3593–3598.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Jasper, H., & Kershman, J. (1941). Electroencephalographic classification of the epilepsies. Archives of Neurology and Psychology, 45, 903.

    Article  Google Scholar 

  • Katzung, B.G., Masters, S.B., Trevor, A.J., & et al. (2004). Basic & clinical pharmacology. New York: McGraw Hill Medical.

  • Kim, J.W., & Robinson, P.A. (2007). Compact dynamical model of brain activity. Physical Review E, 031907, 75.

    Google Scholar 

  • Kloeden, P.E., & Platen, E. (1992). Numerical solution of stochastic differential equations, Vol. 23, Springer Science & Business Media.

  • Koch, C. (2004). Biophysics of Computation: Information Processing in Single Neurons: Information Processing in Single Neurons. New York: Oxford University Press.

    Google Scholar 

  • Kostopoulos, G., Gloor, P., Pellegrini, A., & Gotman, J. (1981a). A study of the transition from spindles to spike and wave discharge in feline generalized penicillin epilepsy: microphysiological features. Experimental Neurology, 73, 55–77.

    Article  CAS  PubMed  Google Scholar 

  • Kostopoulos, G., Gloor, P., Pellegrini, A., & Siatitsas, I. (1981b). A study of the transition from spindles to spike and wave discharge in feline generalized penicillin epilepsy: EEG features. Experimental Neurology, 73, 43–54.

    Article  CAS  PubMed  Google Scholar 

  • Liley, D.T., & Bojak, I. (2005). Understanding the transition to seizure by modeling the epileptiform activity of general anesthetic agents. Journal of Clinical Neurophysiology, 22, 300–313.

    CAS  PubMed  Google Scholar 

  • Liu, Z., Vergnes, M., Depaulis, A., & Marescaux, C. (1992). Involvement of intrathalamic GABA B neurotransmission in the control of absence seizures in the rat. Neuroscience, 48, 87–93.

    Article  CAS  PubMed  Google Scholar 

  • Loddenkemper, T., Fernández, I.S., & Peters, J.M. (2011). Continuous spike and waves during sleep and electrical status epilepticus in sleep. Journal of Clinical Neurophysiology, 28, 154–164.

    Article  PubMed  Google Scholar 

  • Lytton, W.W., Contreras, D., Destexhe, A., & Steriade, M. (1997). Dynamic interactions determine partial thalamic quiescence in a computer network model of spike-and-wave seizures. Journal of Neurophysiology, 77, 1679–1696.

    CAS  PubMed  Google Scholar 

  • Marten, F., Rodrigues, S., Benjamin, O., Richardson, M.P., & Terry, J.R. (2009). Onset of polyspike complexes in a mean-field model of human electroencephalography and its application to absence epilepsy. Philosophical Transactions of the Royal Society A, 367(1891), 1145–1161.

    Article  Google Scholar 

  • McCormick, D., & Hashemiyoon, R. (1998). Thalamocortical neurons actively participate in the generation of spike-and-wave seizures in rodents. Society for Neuroscience Abstracts, 24, 129.

    Google Scholar 

  • McLachlan, R.S., Avoli, M., & Gloor, P. (1984). Transition from spindles to generalized spike and wave discharges in the cat: simultaneous single-cell recordings in cortex and thalamus. Experimental Neurology, 85, 413–425.

    Article  CAS  PubMed  Google Scholar 

  • Nelson, M., Todorovic, S., & Perez-Reyes, E. (2006). The role of T-type calcium channels in epilepsy and pain. Current Pharmaceutical Design, 12, 2189–2197.

    Article  CAS  PubMed  Google Scholar 

  • Nevado-Holgado, A.J., Marten, F., Richardson, M.P., & Terry, J.R. (2012). Characterising the dynamics of EEG waveforms as the path through parameter space of a neural mass model: application to epilepsy seizure evolution. Neuroimage, 59, 2374–2392.

    Article  PubMed  Google Scholar 

  • Nunez, P.L. (1995). Neocortical Dynamics and Human EEG Rhythms. Oxford: Oxford University Press.

    Google Scholar 

  • OConnor, S., & Robinson, P. (2003). Wave-number spectrum of electrocorticographic signals. Physical Review E, 051912, 67.

    Google Scholar 

  • OConnor, S., Robinson, P., & Chiang, A. (2002). Wave-number spectrum of electroencephalographic signals. Physical Review E, 061905, 66.

    Google Scholar 

  • Panayiotopoulos, C.P. (2008). Typical absence seizures and related epileptic syndromes: assessment of current state and directions for future research. Epilepsia, 49, 2131–2139.

    Article  PubMed  Google Scholar 

  • Pellegrini, A., Musgrave, J., & Gloor, P. (1979). Role of afferent input of subcortical origin in the genesis of bilaterally synchronous epileptic discharges of feline generalized penicillin epilepsy. Experimental Neurology, 64, 155–173.

    Article  CAS  PubMed  Google Scholar 

  • Pinault, D., Leresche, N., Charpier, S., Deniau, J.-M., Marescaux, C., Vergnes, M., & Crunelli, V. (1998). Intracellular recordings in thalamic neurones during spontaneous spike and wave discharges in rats with absence epilepsy. The Journal of Physiology, 509, 449–456.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Prevett, M., Duncan, J., Jones, T., Fish, D., & Brooks, D. (1995). Demonstration of thalamic activation during typical absence seizures using H\(_{2}^{15}\)O and PET. Neurology, 45, 1396–1402.

    Article  CAS  PubMed  Google Scholar 

  • Rennie, C., Robinson, P., & Wright, J. (2002). Unified neurophysical model of EEG spectra and evoked potentials. Biological Cybernetics, 86, 457–471.

    Article  CAS  PubMed  Google Scholar 

  • Roberts, J.A., & Robinson, P.A. (2008). Modeling absence seizure dynamics: implications for basic mechanisms and measurement of thalamocortical and corticothalamic latencies. Journal of Thermal Biology, 253, 189–201.

    Article  Google Scholar 

  • Roberts, J.A., & Robinson, P.A. (2012). Corticothalamic dynamics: Structure of parameter space, spectra, instabilities, and reduced model. Physical Review E, 011910, 85.

    Google Scholar 

  • Robinson, P.A. (2006). Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations. Physical Review E, 041904, 73.

    Google Scholar 

  • 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, 041924, 64.

    Google Scholar 

  • Robinson, P.A., Rennie, C.J., Rowe, D.L., & O’Connor, S.C. (2004). Estimation of multiscale neurophysiologic parameters by electroencephalographic means. Human Brain Mapping, 23, 53–72.

    Article  CAS  PubMed  Google Scholar 

  • Robinson, P.A., Rennie, C.J., Rowe, D.L., O’Connor, S.C., Wright, J.J., Gordon, E., Whitehouse, R.W., & et al. (2003). Neurophysical modeling of brain dynamics. Neuropharmacology, 28, S74.

    Google Scholar 

  • Robinson, P.A., Rennie, C.J., Wright, J., & Bourke, P. (1998). Steady states and global dynamics of electrical activity in the cerebral cortex. Physical Review E, 58, 3557.

    Article  CAS  Google Scholar 

  • Robinson, P.A., Rennie, C.J., & Wright, J.J. (1997). Propagation and stability of waves of electrical activity in the cerebral cortex. Physical Review E, 56, 826–840.

    Article  CAS  Google Scholar 

  • Robinson, P.A., Rennie, C.J., Wright, J.J., Bahramali, H., Gordon, E., & Rowe, D.L. (2001). Prediction of electroencephalographic spectra from neurophysiology. Physical Review E, 021903, 63.

    Google Scholar 

  • Robinson, P.A., Wu, H., & Kim, J.W. (2008). Neural rate equations for bursting dynamics derived from conductance-based equations. Journal of Thermal Biology, 250, 663–672.

    Article  CAS  Google Scholar 

  • Sadleir, L.G., Scheffer, I.E., Smith, S., Carstensen, B., Farrell, K., & Connolly, M.B. (2009). Eeg features of absence seizures in idiopathic generalized epilepsy: impact of syndrome, age, and state. Epilepsia, 50, 1572–1578.

    Article  PubMed  Google Scholar 

  • Schiff, S.J., & Sauer, T. (2008). Kalman filter control of a model of spatiotemporal cortical dynamics. BMC Neuroscience, 9(Suppl 1), O1.

    Article  Google Scholar 

  • Schiff, S.J., Sauer, T., Kumar, R., & Weinstein, S.L. (2005). Neuronal spatiotemporal pattern discrimination: The dynamical evolution of seizures. NeuroImage, 28, 1043.

    Article  PubMed Central  PubMed  Google Scholar 

  • Seidenbecher, T., Staak, R., & Pape, H.-C. (1998). Relations between cortical and thalamic cellular activities during absence seizures in rats. The European Journal of Neuroscience, 10, 1103–1112.

    Article  CAS  PubMed  Google Scholar 

  • Shorvon, S.D. (2010). Handbook of epilepsy treatment. New York: Wiley.

    Book  Google Scholar 

  • Srinivasan, R., Nunez, P.L., & Silberstein, R.B. (1998). Spatial filtering and neocortical dynamics: estimates of EEG coherence. IEEE Transactions on Biomedical Engineering, 45, 814–826.

    Article  CAS  PubMed  Google Scholar 

  • Steriade, M. (1974). Interneuronal epileptic discharges related to spike-and-wave cortical seizures in behaving monkeys. Electroencephalography and Clinical Neurophysiology, 37, 247–263.

    Article  CAS  PubMed  Google Scholar 

  • Steriade, M., Amzica, F., Neckelmann, D., & Timofeev, I. (1998). Spike-wave complexes and fast components of cortically generated seizures. ii. extra-and intracellular patterns. Journal of Neurophysiology, 80, 1456–1479.

    CAS  PubMed  Google Scholar 

  • Steriade, M., & Contreras, D. (1995). Relations between cortical and thalamic cellular events during transition from sleep patterns to paroxysmal activity. The Journal of Neuroscience, 15, 623–642.

    CAS  PubMed  Google Scholar 

  • Steriade, M., & Contreras, D. (1998). Spike-wave complexes and fast components of cortically generated seizures. I. Role of neocortex and thalamus. Journal of Neurophysiology, 80, 1439–1455.

    CAS  PubMed  Google Scholar 

  • Steriade, M., & Deschenes, M. (1984). The thalamus as a neuronal oscillator. Brain Research Reviews, 8, 1–63.

    Article  Google Scholar 

  • Steriade, M., Gloor, P., Llinas, R.R., da Silva, F.H.L., & Mesulam, M.-M. (1990). Report of IFCN committee on basic mechanisms. Basic mechanisms of cerebral rhythmic activities. Electroencephalography and Clinical Neurophysiology, 76, 481–508.

    Article  CAS  PubMed  Google Scholar 

  • Steriade, M., McCormick, D.A., & Sejnowski, T.J. (1993a). Thalamocortical oscillations in the sleeping and aroused brain. Science, 262, 679–685.

    Article  CAS  PubMed  Google Scholar 

  • Steriade, M., Nuñez, A., & Amzica, F. (1993b). Intracellular analysis of relations between the slow (<1 Hz) neocortical oscillation and other sleep rhythms of the electroencephalogram. The Journal of Neuroscience, 13, 3266–3283.

    CAS  PubMed  Google Scholar 

  • Steyn-Ross, M.L., Steyn-Ross, D.A., & Sleigh, J.W. (2012). Gap junctions modulate seizures in a mean-field model of general anesthesia for the cortex. Cognitive Neurodynamics, 6, 215–225.

    Article  PubMed Central  PubMed  Google Scholar 

  • Suffczynski, P., Kalitzin, S., & Lopes Da Silva, F. (2004). Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience, 126, 467–484.

    Article  CAS  PubMed  Google Scholar 

  • Tatum, W.O., Ho, S., & Benbadis, S.R. (2010). Polyspike ictal onset absence seizures. Journal of Clinical Neurophysiology, 27, 93–99.

    Article  PubMed  Google Scholar 

  • Tsakiridou, E., Bertollini, L., de Curtis, M., Avanzini, G., & Pape, H.-C. (1995). Selective increase in T-type calcium conductance of reticular thalamic neurons in a rat model of absence epilepsy. The Journal of Neuroscience, 15, 3110–3117.

    CAS  PubMed  Google Scholar 

  • Velazquez, J.L.P., Huo, J.Z., Dominguez, L.G., Leshchenko, Y., & Snead III, O.C. (2007). Typical versus atypical absence seizures: network mechanisms of the spread of paroxysms. Epilepsia, 48, 1585–1593.

    Article  PubMed  Google Scholar 

  • Vergnes, M., & Marescaux, C. (1992). Cortical and thalamic lesions in rats with genetic absence epilepsy. In Focus on GABA B Receptors, Generalized Non-Convulsive Epilepsy (pp. 71–83): Springer.

  • Williams, D. (1953). A study of thalamic and cortical rhythms in petit mal. Brain, 76, 50–69.

    Article  CAS  PubMed  Google Scholar 

  • Wilson, H. (1999). Spikes, Decisions and Actions: The Dynamical Foundations of Neuroscience. New York: Oxford University Press.

    Google Scholar 

  • Wright, J.J., & Liley, D.T.J. (1996). Dynamics of the brain at global and microscopic scales; neural networks and the EEG. The Behavioral and Brain Sciences, 19, 285–295.

    Article  Google Scholar 

  • Wu, H.-Y., Robinson, P.A., & Kim, J.W. (2011). Firing responses of bursting neurons with delayed feedback. Journal of Computational Neuroscience, 31, 61–71.

    Article  PubMed  Google Scholar 

  • Zhao, X., Kim, J., & Robinson, P (2015). Slow-wave oscillations in a corticothalamic model of sleep and wake. Journal of Thermal Biology.

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Acknowledgments

This work was supported by the Australian Research Council Center of Excellence for Integrative Brain Function (ARC Grant CE140100007) and by ARC Grant FL1401000225.

Conflict of Interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. School of Physics, The University of Sydney, Sydney, New South Wales, 2006, Australia

    X. Zhao & P. A. Robinson

  2. Center for Integrative Brain Function, University of Sydney, NSW, 2006, Australia

    X. Zhao & P. A. Robinson

  3. Neurosleep, 431 Glebe Point Rd, Glebe, New South Wales, 2037, Australia

    X. Zhao & P. A. Robinson

  4. Cooperative Research Center for Alertness, Safety, and Productivity, University of Sydney, NSW, 2006, Australia

    X. Zhao & P. A. Robinson

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Zhao, X., Robinson, P.A. Generalized seizures in a neural field model with bursting dynamics. J Comput Neurosci 39, 197–216 (2015). https://doi.org/10.1007/s10827-015-0571-7

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