nach oben

Journal of Computational Neuroscience

Erschienen in:

01.12.2009

Transitions to spike-wave oscillations and epileptic dynamics in a human cortico-thalamic mean-field model

verfasst von: Serafim Rodrigues, David Barton, Robert Szalai, Oscar Benjamin, Mark P. Richardson, John R. Terry

Erschienen in: Journal of Computational Neuroscience | Ausgabe 3/2009

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper we present a detailed theoretical analysis of the onset of spike-wave activity in a model of human electroencephalogram (EEG) activity, relating this to clinical recordings from patients with absence seizures. We present a complete explanation of the transition from inter-ictal activity to spike and wave using a combination of bifurcation theory, numerical continuation and techniques for detecting the occurrence of inflection points in systems of delay differential equations (DDEs). We demonstrate that the initial transition to oscillatory behaviour occurs as a result of a Hopf bifurcation, whereas the addition of spikes arises as a result of an inflection point of the vector field. Strikingly these findings are consistent with EEG data recorded from patients with absence seizures and we present a discussion of the clinical significance of these results, suggesting potential new techniques for detection and anticipation of seizures.

Vorheriger Artikel Self-sustained asynchronous irregular states and Up–Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons

Nächster Artikel Variability of bursting patterns in a neuron model in the presence of noise

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Amari, S. I. (1972). Characteristics of randomly connected threshold-element networks and network systems. Proceedings of the IEEE, 59, 35–47.CrossRef

Amari, S. I. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27, 77–87.CrossRefPubMed

Arndt, H. (1984). Numerical solution of retarded initial value problems: Local and global error and stepsize control. Numerical Mathematics, 43, 343–360.CrossRef

Baker, C. T. H., Paul, C. A. H., & Willé, D. R. (1995). A bibliography on the numerical solution of delay differential equations. Technical Report 269, University of Manchester.

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

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

Danober, L., Deransart, C., Depaulis, A., Vergnes, M., & Marescaux, C. (1998). Pathophysiological mechanisms of genetic absence epilepsy in the rat. Progress in Neurobiology, 55, 27–57.CrossRefPubMed

Destexhe, A., & Sejnowski, T. J. (2001). Thalamocortical assemblies. How ion channels, single neurons and large-scale networks organize sleep oscillations. Oxford: Oxford University Press.

Engelborghs, K., Luzyanina, T., & Samaey, G. (2001a). DDE-BIFTOOL v.200 user manual: A M atlab package for bifurcation analysis of delay differential equations. Technical Report tw-330, Department of Computer Science, K. U. Leuven, Leuven, Belgium.

Engelborghs, K., Luzyanina, Hout, K. J., & Roose, D. (2001b). Collocation methods for the computation of periodic solutions of differential equations. SIAM Journal on Scientific Computation, 22(5), 1593–1609.CrossRef

Freeman, W. J. (1975). Mass action in the nervous system. Examination of the neurophysiological basis of adaptive behavior through the EEG. New York: Academic.

Friston, K. J., Jezzard, P., & Turner, R. (1994). Analysis of functional mri time-series. Human Brain Mapping, 1, 153–171.CrossRef

Friedrich, R., & Uhl, C. (1996). Spatio-temporal analysis of human electroencephalograms: Petit-mal epilepsy. Physica. D, 98, 171–182.CrossRef

Geman, S. (1982). Almost sure stable oscillations in a large system of randomly coupled equations. SIAM Journal on Applied Mathematics, 42, 695–703.CrossRef

Hairer, E., Norsett, S. P., & Wanner, G. (1993). Solving ordinary differential equations I, nonstiff problems. In Springer series computational mathematics (2nd rev. ed.). New York: Springer.

Hairer, E., & Wanner, G. (1996). Solving ordinary differential equations II, stiff and differential algebraic problems. In Springer series computational mathematics (2nd rev. ed.). New York: Springer.

Hernández, J. L., Valdés, P. A., & Vila, P. (1996). EEG spike and wave modelled by a stochastic limit cycle. Neuroreport, 7, 2246–2248.CrossRefPubMed

Hirschberg, P., & Knobloch, E. (1993). Šilnikov-hopf bifurcation. Physica D, 62, 202–216.CrossRef

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, 1568–1579.CrossRefPubMed

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.CrossRefPubMed

Jirsa, V. K., & Haken, H. (1996). Field theory of electromagnetic brain activity. Physical Review Letters, 77, 960–963.CrossRefPubMed

Kim, A. V., & Pimenov, V. G. (1997). Numerical methods for time-delay systems on the basis of i-smooth analysis. Computational Mathematics, 1, 193–196.

Kuznetsov, Y., Kuznetsov, L., & Marsde, J. (1998). Elements of applied bifurcation theory. New York: Springer.

Lopes da Silva, F. H., Hoeks, A., Smits, H., & Zetterberg, L. H. (1974). Model of brain rhythmic activity. The alpha-rhythm of the thalamus. Kybernetik, 15, 27–37.CrossRefPubMed

Lopes da Silva, F. H., & Pijn, J. P. (1999). Epilepsy as a dynamic disease of brain systems. Advances in Neurology, 81, 97–104.

Lopes da Silva, F. H., Blanes, W., Kalitzin, S. N., Parra, J., Suffczynski, P., & Velis, D. N. (2003). Epilepsies as dynamical diseases of brain systems: Basic models of the transition between normal and epileptic activity. Epilepsia, 44, 72–83.CrossRefPubMed

Marescaux, C., Vergnes, M., & Depaulis, A. (1992). Genetic absence epilepsy rat from Strasbourg: A review. Journal of Neural Transmission, 35, 37–69.PubMed

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

Milton, J., & Jung, P. (2003). Epilepsy as a dynamic disease. Berlin: Springer.

Nunez, P. L. (1995). Neocortical dynamics and human EEG rhythms. Oxford: Oxford University Press.

Nunez, P. L., & Srinivasan R. (2006). Electric fields of the brain: The neurophysics of EEG (2nd ed.). Oxford: Oxford University Press.

Omurtag, A., Knight, B. W., & Sirovich, L. (2000). On the simulation of large populations of neurons. Journal of Computational Neuroscience, 8, 51–63.CrossRefPubMed

Paul, C. A. H. (1992). Developing a delay differential equation solver. Applied Numerical Mathematics, 9, 403–414.CrossRef

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.CrossRef

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

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, 041924.CrossRef

Rodrigues, S., Terry, J. R., & Breakspear, M. (2006). On the genesis of spike-wave activity in a mean-field model of human thalamic and cortico-thalamic dynamics. Physics Letters A, 355, 352–357.CrossRef

Rodrigues, S., Barton, D., Szalai, R., Benjamin, O., Richardson, M. P., & Terry, J. R. (2008). Inflection point periodic boundary value problem. http://seis.bris.ac.uk/~enxsr/code.html.

Rozonoér, L. I. (1969). Random logical nets I, II and III. Automation and Remote Control, 5, 773–781 (Translation of Avtomatika i Telemekhanika).

Schiff, N. D., Victor, J. D., Canel, A., & Labar, D. R. (1995). Characteristic nonlinearities of the 3/s ictal electroencephalogram identified by nonlinear autoregressive analysis. Biological Cybernetics, 72, 519–526.CrossRefPubMed

Sieber, J., & Krauskopf, B. (2008). Control-based bifurcation analysis for experiments. Nonlinear Dynamics, 51(3), 365–377.CrossRef

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.PubMed

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.PubMed

Suffczynski, P. (2000). Neural dynamics underlying brain thalamic oscillations investigated with computational models. Ph.D. Diss., Institute of experimental physics, Department of Physics, Warsaw University.

Suffczynski, P., Kalitzin, S., & da Silva, F. H. L. (2004). Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Journal of Neuroscience, 126, 467–484.CrossRef

Szalai, R., Stépán, G., & Hogan, S. J. (2006). Continuation of bifurcations in periodic delay-differential equations using characteristic matrices. SIAM Journal on Scientific Computing, 4, 1301–1317.CrossRef

van Luijtelaar, E. L., & Coenen, A. M. L. (1986). Two types of electrocortical paroxysms in an inbred strain of rats. Neuroscience Letters, 70, 393–397.CrossRefPubMed

van Luijtelaar, E. L. J. M., & Coenen, A. M. L. (2003). Genetic animal models for absence epilepsy: A review of the WAG/Rij strain of rats. Behavior Genetics, 33, 635–655.CrossRefPubMed

Wang, X. J., Golomb, D., & Rinzel, J. (1995). Emergent spindle oscillations and intermittent bursts firing in a thalamic model: Specific neuronal parameters. Proceedings of the National Academy of Sciences of the United States of America, 92, 5577–5581.CrossRefPubMed

Wendling, F., Bartolomei, F., Bellanger, J. J., F. B., & Chauvel, P. (2002). Epileptic fast activity can be explained by a model of impaired gabaergic dendritic inhibition. European Journal of Neuroscience, 15, 1499–1508.CrossRefPubMed

Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12, 1–24.CrossRefPubMed

Wright, J. J., & Liley, D. J. (1996). Dynamics of the brain at global and microscopic scales: Neural networks and the EEG. Behavioral Brain Science, 19, 285–320.CrossRef

Titel: Transitions to spike-wave oscillations and epileptic dynamics in a human cortico-thalamic mean-field model
verfasst von: Serafim Rodrigues
David Barton
Robert Szalai
Oscar Benjamin
Mark P. Richardson
John R. Terry
Publikationsdatum: 01.12.2009
Verlag: Springer US
Erschienen in: Journal of Computational Neuroscience / Ausgabe 3/2009
Print ISSN: 0929-5313
Elektronische ISSN: 1573-6873
DOI: https://doi.org/10.1007/s10827-009-0166-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 3/2009

Library-based numerical reduction of the Hodgkin–Huxley neuron for network simulation

Spatial and temporal jitter distort estimated functional properties of visual sensory neurons

Recurrent networks with short term synaptic depression

Crossover inhibition in the retina: circuitry that compensates for nonlinear rectifying synaptic transmission

Thermodynamic constraints on neural dimensions, firing rates, brain temperature and size

Model analyses of visual biofeedback training for EEG-based brain-computer interface