Seizure dynamics of coupled oscillators with epileptor field model. (English) Zbl 1388.34053


34C60 Qualitative investigation and simulation of ordinary differential equation models
34A36 Discontinuous ordinary differential equations
92C20 Neural biology
34D06 Synchronization of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
Full Text: DOI


[1] Amzica, F.; Massimini, M.; Manfridi, A., Spatial buffering during slow and paroxysmal sleep oscillations in cortical networks of glial cells in vivo, J. Neurosci., 22, 1042-1053, (2002)
[2] Anja, S.; Gustavo, D.; Astrid, B.; Werner, X. S., Neurons and the synaptic basis of the fMRI signal associated with cognitive flexibility, NeuroImage, 26, 454-470, (2005)
[3] Avoli, M.; De Curtis, M.; Gnatkovsky, V.; Gotman, J.; Kohling, R.; Levesque, M.; Manseau, F.; Shiri, Z.; Williams, S., Specific imbalance of excitatory/inhibitory signaling establishes seizure onset pattern in temporal lobe epilepsy, J. Neurophysiol., 115, 3229-3237, (2016)
[4] Boucetta, S.; Chauvette, S.; Bazhenov, M.; Timofeev, I., Focal generation of paroxysmal fast runs during electrographic seizures, Epilepsia, 49, 1925-1940, (2008)
[5] Chen, M.; Guo, D.; Wang, T.; Jing, W.; Xia, Y.; Xu, P.; Luo, C.; Valdes-Sosa, P. A.; Yao, D., Bidirectional control of absence seizures by the basal ganglia: A computational evidence, PLoS Comput. Biol., 10, e1003495, (2014)
[6] Chen, M.; Guo, D.; Li, M.; Ma, T.; Wu, S., Critical roles of the direct gabaergic pallido-cortical pathway in controlling absence seizures, PLoS Comput. Biol., 11, e1004539, (2015)
[7] Chen, M.; Guo, D.; Yang, X.; Yao, D., Control of absence seizures by the thalamic feed-forward inhibition, Front. Comput. Neurosci., 11, 31, (2017)
[8] Cosandier-Rimele, D.; Bartolomei, F.; Merlet, I.; Chauvel, P.; Wendling, F., Recording of fast activity at the onset of partial seizures: depth EEG vs. scalp EEG, NeuroImage, 59, 3474-3487, (2012)
[9] Cressman, J.; Ullah, G.; Ziburkus, J.; Schiff, S. J.; Barreto, E., The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics, J. Comput. Neurosci., 26, 159-170, (2009)
[10] Destexhe, A.; Mainen, Z. F.; Sejnowski, T. J., An efficient method for computing synaptic conductances based on a kinetic model of receptor binding, Neural Comput., 6, 14-18, (1994)
[11] Destexhe, A., Spike-and-wave oscillations based on the properties of GABAB receptors, J. Neurosci., 18, 9099-9111, (1998)
[12] Durand, D. M.; Park, E. H.; Jensen, A. L., Potassium diffusive coupling in neural networks, Philos. Trans. Roy. Soc. London Ser. B — Biol. Sci., 65, 2347-2362, (2010)
[13] 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)
[14] Fan, D.; Wang, Q., Synchronization and bursting transition of the coupled hindmarsh-rose systems with asymmetrical time-delays, Sci. China Technol. Sci., 60, 1-13, (2017)
[15] Fan, D.; Liao, F.; Wang, Q., The pacemaker role of thalamic reticular nucleus in controlling spike-wave discharges and spindles, Chaos, 27, 331-343, (2017)
[16] Frohlich, F.; Bazhenov, M.; Sejnowski, T. J., Pathological effect of homeostatic synaptic scaling on network dynamics in diseases of the cortex, J. Neurosci., 28, 1709-1720, (2008)
[17] Goodfellow, M.; Taylor, P. N.; Wang, Y.; Garry, D. J.; Baier, G., Modelling the role of tissue heterogeneity in epileptic rhythms, Eur. J. Neurosci., 36, 2178-2187, (2012)
[18] Guo, S.; Tang, J.; Ma, J.; Wang, C., Autaptic modulation of electrical activity in a network of neuron-coupled astrocyte, Complexity, 2017, 4631602, (2017)
[19] Guo, D.; Xia, C.; Wu, S., Stochastic fluctuations of permittivity coupling regulate seizure dynamics in partial epilepsy, Sci. China Technol. Sci., 60, 995, (2017)
[20] Gustavo, D.; Edmund, T. R.; Ranulfo, R., Synaptic dynamics and decision making, Proc. Natl. Acad. Sci. USA, 107, 7545-7549, (2010)
[21] Hall, D.; Kuhlmann, L., Mechanisms of seizure propagation in 2-dimensional centre-surround recurrent networks, PLoS One, 8, e71369, (2013)
[22] Heinemann, U.; Konnerth, A.; Pumain, R.; Wadman, W. J., Extracellular calcium and potassium concentration changes in chronic epileptic brain tissue, Adv. Neurother., 44, 641-661, (1986)
[23] Houssaini, K. E.; Ivanov, A.; Bernard, C.; Jirsa, V. K., Seizures, refractory status epilepticus, and depolarization block as endogenous brain activities, Phys. Rev. E, Statist. Nonlin. Soft Matter Phys., 91, 010701, (2015)
[24] Ikeda, A.; Taki, W.; Kunieda, T.; Terada, K.; Mikuni, N.; Nagamine, T.; Yazawa, S.; Ohara, S.; Hori, T.; Kaji, R.; Kimura, J.; Shibasaki, H., Focal ictal direct current shifts in human epilepsy as studied by subdural and scalp recording, Brain, 122, 827-838, (1999)
[25] Isomura, Y.; Fujiwara-Tsukamoto, Y.; Takada, M., A network mechanism underlying hippocampal seizure like synchronous oscillations, Neurosci. Res., 61, 227-233, (2008)
[26] Izhikevich, E. M., Neural excitability, spiking and bursting, Int. J. Bifurcation and Chaos, 10, 1171-1266, (2000) · Zbl 1090.92505
[27] Jirsa, V. K.; Stacey, W. C.; Quilichini, P. P.; Ivanov, A. I.; Bernard, C., On the nature of seizure dynamics, Brain, 137, 2210-2230, (2014)
[28] Jiruska, P.; de Curtis, M.; Jefferys, J. G.; Schevon, C. A.; Schiff, S. J.; Schindler, K., Synchronization and desynchronization in epilepsy: controversies and hypotheses, J. Physiol., 591, 787-797, (2003)
[29] Jiruska, P.; de Curtis, M.; Jefferys, J. G., Modern concepts of focal epileptic networks, Int. Rev. Neurol., 114, 5-8, (2014)
[30] Kager, H.; Wadman, W. J.; Somjen, G. G., Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations, J. Neurophysiol., 84, 495-512, (2000)
[31] Krishnan, G. P.; Bazhenov, M., Ionic dynamics mediate spontaneous termination of seizures and postictal depression state, J. Neurosci., 31, 8870-8882, (2011)
[32] Liu, S.; Wang, Q., Transition dynamics of generalized multiple epileptic seizures associated with thalamic reticular nucleus excitability: A computational study, Commun. Nonlin. Sci. Numer. Simul., 52, 203-213, (2017)
[33] Mao, X.; Wang, Z., Stability, bifurcation, and synchronization of delay-coupled ring neural networks, Nonlin. Dyn., 84, 1063-1078, (2016) · Zbl 1354.93133
[34] Mao, X., Complicated dynamics of a ring of nonidentical Fitzhugh-Nagumo neurons with delayed couplings, Nonlin. Dyn., 87, 2395-2406, (2017) · Zbl 1373.34112
[35] Meeren, H. K.; Pijn, J. P.; Van Luijtelaar, E. L.; Coenen, A. M.; Lopes da Silva, F. H., Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats, J. Neurosci., 22, 1480-1495, (2002)
[36] Molaee-Ardekani, B.; Benquet, P.; Bartolomei, F.; Wendling, F., Computational modeling of high-frequency oscillations at the onset of neocortical partial seizures: from ‘altered structure’ to ‘dysfunction’, Neuroimage, 52, 1109-1122, (2010)
[37] Naze, S.; Bernard, C.; Jirsa, V., Computational modeling of seizure dynamics using coupled neuronal networks: factors shaping epileptiform activity, PLoS Comput. Biol., 11, e1004209, (2015)
[38] Netoff, T. I.; Clewley, R.; Arno, S.; Keck, T.; White, J. A., Epilepsy in small-world networks, J. Neurosci., 24, 8075-8083, (2004)
[39] Proix, T.; Bartolomei, F.; Chauvel, P.; Bernard, C.; Jirsa, J. K., Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy, J. Neurosci., 34, 15009-15021, (2014)
[40] Proix, T.; Bartolomei, B.; Guy, M.; Jirsa, V. K., Individual brain structure and modeling predict seizure propagation, Brain, 140, 641-654, (2017)
[41] Proix, T.; Jirsa, V. K.; Bartolomei, F.; Guye, M.; Truccolo, W., Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy, Neurons and Cognition, (2017)
[42] Quilichini, P. P.; Diabira, D.; Chiron, C.; Milh, M.; Ben-Ari, Y.; Gozlan, H., Effects of antiepileptic drugs on refractory seizures in the intact immature corticohippocampal formation in vitro, Epilepsia, 44, 1365-1374, (2003)
[43] Santhakumar, V.; Aradi, I.; Soltesz, I., Role of mossy fiber sprouting and mossy cell loss in hyperexcitability: A network model of the dentate gyrus incorporating cell types and axonal topography, J. Neurophysiol., 93, 437-453, (2005)
[44] Silvia, C.; Gustavo, D., Large-scale neural model for visual attention: integration of experimental single-cell and fMRI data, Cereb. Cort., 12, 339-348, (2002)
[45] Song, Y. L.; Tade, M. O.; Zhang, T. J., Bifurcation analysis and spatio-temporal patterns of nonlinear oscillations in a delayed neural network with unidirectional coupling, Nonlinearity, 22, 975-1001, (2009) · Zbl 1171.34058
[46] Suh, M.; Ma, H.; Zhao, M.; Sharif, S.; Schwartz, T. H., Neurovascular coupling and oximetry during epileptic events, Molecul. Neurobiol., 33, 181-197, (2006)
[47] Tang, J.; Zhang, J.; Ma, J.; Zhang, G.; Yang, X., Astrocyte calcium wave induces seizure-like behavior in neuron network, Sci. China Technol. Sci., 60, 1011-1018, (2017)
[48] Taylor, P. N.; Goodfellow, M.; Wang, Y.; Baier, G., Towards a large-scale model of patient-specific epileptic spike-wave discharges, Biol. Cybern., 107, 83-94, (2013)
[49] Terry, J. R.; Benjamin, O.; Richardson, M. P., Seizure generation: the role of nodes and networks, Epilepsia, 53, e166-e169, (2012)
[50] Touboul, J.; Wendling, F.; Chauvel, P.; Faugeras, O., Neural mass activity, bifurcations, and epilepsy, Neural Comput., 23, 3232-3286, (2011)
[51] Traub, R. D.; Duncan, R.; Russell, A. J.; Baldeweg, T.; Tu, Y.; Cunningham, M. O.; Whittington, M. A., Spatiotemporal patterns of electrocorticographic very fast oscillations (\(>\)80\[hz) consistent with a network model based on electrical coupling between principal neurons, Epilepsia, 51, 1587-1597, (201\]
[52] Vanhatalo, S.; Holmes, M. D.; Tallgren, P.; Voipio, J.; Kaila, K.; Miller, J. W., Very slow EEG responses lateralize temporal lobe seizures: an evaluation of non-invasive DC-EEG, Neurology, 60, 1098-1104, (2003)
[53] van Drongelen, W.; Lee, H. C.; Hereld, M.; Chen, Z.; Elsen, F. P.; Stevens, R. L., Emergent epileptiform activity in neural networks with weak excitatory synapses, IEEE Trans. Neural Syst. Rehabil. Engin., 13, 236-241, (2005)
[54] van Drongelen, W.; Lee, H. C.; Stevens, R. L.; Hereld, M., Propagation of seizure-like activity in a model of neocortex, J. Clin. Neurophysiol., 24, 182-188, (2007)
[55] Wang, X.; Buzsaki, G., Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model, J. Neurosci., 16, 6402-6413, (1996)
[56] Wang, X., Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory, J. Neurosci., 19, 9587-9603, (1999)
[57] Wang, Y.; Goodfellow, M.; Taylor, P. N.; Baier, G., Dynamic mechanisms of neocortical focal seizure onset, PLoS Comput. Biol., 10, e1003787, (2014)
[58] Wang, Y.; Trevelyan, A. J.; Valentin, A.; Alarcon, G.; Taylor, P. N., Mechanisms underlying different onset patterns of focal seizures, PLoS Comput. Biol., 13, e1005475, (2017)
[59] Wendling, F.; Bartolomei, F.; Mina, F.; Huneau, C.; Benquet, P., Interictal spikes, fast ripples and seizures in partial epilepsies-combining multi-level computational models with experimental data, Eur. J. Neurosci., 36, 2164-2177, (2012)
[60] Yang, D.; Robinson, P., Critical dynamics of Hopf bifurcations in the corticothalamic system: transitions from normal arousal states to epileptic seizures, Phys. Rev. E, 95, 042410, (2017)
[61] Zhang, L.; Fan, D.; Wang, Q., Transition dynamics of a dentate gyrus-CA3 neuronal network during temporal lobe epilepsy, Front. Comput. Neurosci., 11, 61, (2017)
[62] Zhao, M.; Nguyen, J.; Ma, H.; Nishimura, N.; Schaffer, C. B.; Schwartz, T. H., Preictal and ictal neurovascular and metabolic coupling surrounding a seizure focus, J. Neurosci., 31, 13292-13300, (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.