Russian version English version
Volume 15   Issue 2   Year 2020
Kapustnikov A.A.1,2, Sysoeva M.V.1,3, Sysoev I.V.1,2

The Modeling of Spike-Wave Discharges in Brain with Small Oscillatory Neural Networks

Mathematical Biology & Bioinformatics. 2020;15(2):138-147.

doi: 10.17537/2020.15.138.


  1. Helal M., Hingant E., Pujo-Menjouet L., Webb G.F. Alzheimer’s disease: analysis of a mathematical model incorporating the role of prions. Journal of Mathematical Biology. 2014;69:1207-1235. doi: 10.1007/s00285-013-0732-0
  2. Stam C.J., Jelles B., Achtereekte H.A.M., Rombouts S.A.R.B., Slaets J.P.J., Keunen R.W.M. Investigation of EEG non-linearity in dementia and Parkinson's disease. Electroencephalography and Clinical Neurophysiology. 1995;95(5):309-317. doi: 10.1016/0013-4694(95)00147-Q
  3. Proske J.H., Jeanmonod D., Verschure P.F. A Computational Model of Thalamocortical Dysrhythmia. The European Journal of Neuroscience. 2011;33(7):1281-1290. doi: 10.1111/j.1460-9568.2010.07588.x
  4. Destexhe A. Spike-and-wave oscillations based on the properties of GABAB receptors. Journal of Neuroscience. 1998;18:9099-9111. doi: 10.1523/JNEUROSCI.18-21-09099.1998
  5. Karlov V.A., Gnezditski V.V. Absence epilepsy in children and rats. Presservis, 2005.
  6. Volnova A.B., Lenkov D.N. Absence epilepsy: mechanisms of hypersynchronization of neuronal networks. Medical Academic Journal. 2012;12(1):7-19.
  7. Suffczynski P., Kalitzin S., Lopes da Silva F. Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience. 2004;126(2):467-484. doi: 10.1016/j.neuroscience.2004.03.014
  8. Taylor P.N., Wang Y., Goodfellow M., Dauwels J., Moeller F., Stephani U., Baier G. A Computational Study of Stimulus Driven Epileptic Seizure Abatement. PLoS ONE. 2014;9(12). Article No. e114316. doi: 10.1371/journal.pone.0114316
  9. Destexhe A. Network models of absence seizures. In: Neuronal Networks in Brain Function, CNS Disorders, and Therapeutics. Academic Press, 2014. P. 11-35. doi: 10.1016/B978-0-12-415804-7.00002-2
  10. Medvedeva T.M., Sysoeva M.V., van Luijtelaar G., Sysoev I.V. Modeling spike-wave discharges by a complex network of neuronal oscillators. Neural Networks. 2018;98:271-282. doi: 10.1016/j.neunet.2017.12.002
  11. Kolosov A.V., Nujdel I.V., Yakhno V.G. Research of dynamic modes in the mathematical model of elementary thalamocortical cell. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016;24(5):72-83. doi: 10.18500/0869-6632-2016-24-5-72-83
  12. Kuznetsova G.D., Pelinovskij D.E., Yakhno V.G. Mathematical models of the dynamics of the spreading depression waves in cerebrum cortex. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(3):86-99.
  13. Abbasova K., Chepurnov S., Chepurnova N., van Luijtelaar G. The role of perioral afferentation in the occurrence of spike-wave discharges in the WAG/Rij model of absence epilepsy. Brain Research. 2010;1366:257-262. doi: 10.1016/j.brainres.2010.10.007
  14. Luttjohann A., van Luijtelaar G. The dynamics of cortico-thalamo-cortical interactions at the transition from pre-ictal to ictal LFPs in absence epilepsy. Neurobiology of Disease. 2012;47:47-60.
  15. Sysoeva M.V., Luttjohann A., van Luijtelaar G., Sysoev I.V. Dynamics of directional coupling underlying spike-wave discharges. Neuroscience. 2016;314:75-89. doi: 10.1016/j.neuroscience.2015.11.044
  16. Luttjohann A., van Luijtelaar G. Dynamics of networks during absence seizure's on- and offset in rodents and man. Frontiers in Physiology. 2015;6:16. doi: 10.3389/fphys.2015.00016
  17. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal. 1961;1:445-466. doi: 10.1016/S0006-3495(61)86902-6
  18. Nagumo J., Arimoto S., Yoshizawa S. An active pulse transmission line simulating nerve axon. Proceedings of the IRE. 1962;50:2061-2070. doi: 10.1109/JRPROC.1962.288235
  19. Dahlem M.A., Hiller G., Panchuk A., Schöll E. Dynamics of delay-coupled excitable neural systems. International Journal of Bifurcation and Chaos. 2009;19(2):745-753. doi: 10.1142/S0218127409023111
  20. Kulminskiy D.D., Ponomarenko V.I., Prokhorov M.D., Hramov A.E. Synchronization in ensembles of delay-coupled nonidentical neuronlike oscillators. Nonlinear Dynamics. 2019;98(1):735-748. doi: 10.1007/s11071-019-05224-x
  21. Medvedeva T.M., Sysoeva M.V., Sysoev I.V. Coupling analysis between thalamus and cortex in mesoscale model of spike-wave discharges from time series of summarized activity of model neurons. In: 2nd School on Dynamics of Complex Networks and their Application in Intellectual Robotics, DCNAIR 2018. IEEE, 2018. P. 137-138. doi: 10.1109/DCNAIR.2018.8589208
  22. van Drongelen W., Lee H.C., Hereld M., Chen Zh., Elsen F.P., Stevens R.L. Emergent epileptiform activity in neural networks with weak excitatory synapses. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2005;13(2):236-241. doi: 10.1109/TNSRE.2005.847387
  23. Virtanen P., Gommers R., Oliphant T.E., Haberland M., Reddy T., Cournapeau D., Burovski E., Peterson P., Weckesser W., Bright J. et al. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods. 2020;17:261-272. doi: 10.1038/s41592-019-0686-2
  24. Morris C., Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 1981;35(1):193-213. doi: 10.1016/S0006-3495(81)84782-0
  25. Hindmarsh J.L., Rose R.M. A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B. 1984;221(1222):87-102. doi: 10.1098/rspb.1984.0024
  26. Dmitrichev A.S., Kasatkin D.V., Klinshov V.V., Kirillov S.Yu, Maslennikov O.V., Shchapin D.S., Nekorkin V.I. Nonlinear dynamical models of neurons: Review. Izvestiya VUZ. Applied Nonlinear Dynamics. 2018;26(4):5-58. doi: 10.18500/0869-6632-2018-26-4-5-58
  27. Sargsyan A., Sitnikova E., Melkonyan A., Mkrtchian H., van Luijtelaar G. Simulation of sleep spindles and spike and wave discharges using a novel method for the calculation of field potentials in rats. Journal of Neuroscience Methods. 2007;164(1):161-176. doi: 10.1016/j.jneumeth.2007.03.023
  28. Sysoeva M.V., Kuznetsova G.D., Sysoev I.V. The modeling of rat EEG signals in absence epilepsy in the analysis of brain connectivity. Biophysics. 2016;61(4):661-669. doi: 10.1134/S0006350916040230
  29. Meeren H., van Luijtelaar G., Lopes da Silva F., Coenen. A. Evolving concepts on the pathophysiology of absence seizures: the cortical focus theory. Archives of Neurology. 2005;62:371-376. doi: 10.1001/archneur.62.3.371
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2020.15.138
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)


  Copyright IMPB RAS © 2005-2022