Skip to main content
SpringerLink
Log in

Seizures dynamics in a neural field model of cortical-thalamic circuitry

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

The focus of this study is to explore the mechanisms during seizure behavior using a physiologically motivated by corticothalamic circuity. The model is based on the assumption that, the inhibitory projects from thalamus reticular nucleus (TRN) to specific relay nuclei (SRN) are mediated by GABAA and GABAB receptors which react different time scales in synaptic transmission. Secondly, we include the effects of slow modulation on the threshold current of TRN population that were found to generate bursting behavior. Our model can reproduce healthy and pathological dynamics including wake, spindle, deep sleep, and also seizure states. In addition, contour maps are used to explore the transition of different activity states. It is worthy to point out seizure duration is significantly affected by a time-varying delay as illustrated in our numerical simulation. Finally, a reduced model ignoring the cerebral cortex mass can also capture the feature of spike wave discharge as generated in the full network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hauser W A. Epilepsy: A Comprehensive Textbook. Philadelphia: Lippincott-Raven Publishers, 1998

    Google Scholar 

  2. Browne T R, Holmes G L. Handbook of Epilepsy. Philadelphia: Williams and Wilkins, 2000

    Google Scholar 

  3. Aarabi A, He B. Seizure prediction in hippocampal and neocortical epilepsy using a model-based approach. Clin Neurophysiol, 2014, 125: 930–940

    Article  Google Scholar 

  4. Ullah G, Schiff S J. Assimilating seizure dynamics. PLoS Comput Biol, 2010, 6: e1000776

    Article  Google Scholar 

  5. Stefanescu R A, Shivakeshavan R G, Talathi S S. Computational models of epilepsy. Seizure, 2012, 21: 748–759

    Article  Google Scholar 

  6. Silva F L, Blanes W, Kalitzin S N, et al. Epilepsies as dynamical diseases of brain systems: Basic models of the transition between normal and epileptic activity. Epilepsia, 2003, 4: 72–83

    Article  Google Scholar 

  7. Milton J G. Epilepsy as a dynamic disease: A tutorial of the past with an eye to the future. Epilepsy Behav, 2010, 18: 33–44

    Article  Google Scholar 

  8. Taylor P N, Goodfellow M, Wang Y, et al. Towards a large-scale model of patient-specific epileptic spike-wave discharges. Biol Cybern, 2013, 107: 83–94

    Article  Google Scholar 

  9. Taylor P N, Kaiser M, Dauwels J. Structural connectivity based whole brain modelling in epilepsy. J Neurosci Meth, 2014, 236: 51–57

    Article  Google Scholar 

  10. Yan B, Li P. The emergence of abnormal hypersynchronization in the anatomical structural network of human brain. NeuroImage, 2013, 65: 34–51

    Article  Google Scholar 

  11. Baier G, Goodfellow M, Taylor P N, et al. The importance of modeling epileptic seizure dynamics as spatio-temporal patterns. Front Physiol, 2012, 3: 00281

    Article  Google Scholar 

  12. Saillet S, Gharbi S, Charvet G, et al. Neural adaptation to responsive stimulation: A comparison of auditory and deep brain stimulation in a rat model of absence epilepsy. Brain Stimulation, 2013, 6: 241–247

    Article  Google Scholar 

  13. Conte A, Gilio F, Iacovelli E, et al. Effects of repetitive transcranial magnetic stimulation on spike-and-wave discharges. Neurosci Res, 2007, 57: 140–142

    Article  Google Scholar 

  14. Freeman W J. Mass Action in The Nervous System. New York: Academic Press, 1975

    Google Scholar 

  15. Wilson H R, Cowan J D. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 1973, 13: 55–80

    Article  MATH  Google Scholar 

  16. Wendling F, Bartolomei F, Bellanger J J, et al. Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur J Neurosci, 2002, 15: 1499–1508

    Article  Google Scholar 

  17. Jansen B H, Rit V G. Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol Cybern, 1995, 73: 357–366

    Article  MATH  Google Scholar 

  18. Jansen B H, Zouridakis G, Brandt M E. A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol Cybern, 1993, 68: 275–283

    Article  Google Scholar 

  19. Zandt B J, Visser S, van Putten M J A M, et al. A neural mass model based on single cell dynamics to model pathophysiology. J Comput Neurosci, 2014, 37: 549–568

    Article  MathSciNet  Google Scholar 

  20. de Haan W, Mott K, van Straaten E C W, et al. Activity dependent degeneration explains hub vulnerability in alzheimer’s disease. PLoS Comput Biol, 2012, 8: e1002582

    Article  Google Scholar 

  21. Pons A J, Cantero J L, Atienza M, et al. Relating structural and functional anomalous connectivity in the aging brain via neural mass modeling. Neuroimage, 2010, 52: 848–861

    Article  Google Scholar 

  22. Deco G, Jirsa V K, Robinson P A, et al. The dynamic brain: From spiking neurons to neural masses and cortical fields. PLoS Comput Biol, 2008, 4: e1000092

    Article  Google Scholar 

  23. Taylor P N, Baier G. A spatially extended model for macroscopic spike-wave discharges. J Comput Neurosci, 2011, 31: 679–684

    Article  Google Scholar 

  24. Taylor P N, Wang Y, Goodfellow M, et al. A computational study of stimulus driven epileptic seizure abatement. PLoS One, 2014, 9: e114316

    Article  Google Scholar 

  25. Velazquez J L P, Huo J Z, Dominguez L G, et al. Typical versus atypical absence seizures: Network mechanisms of the spread of paroxysms. Epilepsia, 2007, 48: 1585–1593

    Article  Google Scholar 

  26. Dulac O. Epileptic encephalopathy. Epilepsia, 2001, 42: 23–26

    Article  Google Scholar 

  27. Loddenkemper T, Fernández I S, Peters J M. Continuous spike and waves during sleep and electrical status epilepticus in sleep. J Clin Neurophysiol, 2011, 28: 154–164

    Article  Google Scholar 

  28. Robinson P A, Rennie C J, Rowe D L. Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E, 2002, 65: 041924

    Article  Google Scholar 

  29. Breakspear M, Roberts J A, Terry J R, et al. A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb Cortex, 2005, 16: 1296–1313

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Kim J W, Robinson P A. Compact dynamical model of brain activity. Phys Rev E, 2007, 75: 031907

    Article  MathSciNet  Google Scholar 

  32. Robinson P A, Wu H, Kim J W. Neural rate equations for bursting dynamics derived from conductance-based equations. J Theor Biol, 2008, 250: 663–672

    Article  MathSciNet  Google Scholar 

  33. Marten F, Rodrigues S, Benjamin O, et al. Onset of polyspike complexes in a mean-field model of human electroencephalography and its application to absence epilepsy. Philos Trans R Soc A-Math Phys Eng Sci, 2009, 367: 1145–1161

    Article  MathSciNet  MATH  Google Scholar 

  34. Kim J W, Robinson P A. Controlling limit-cycle behaviors of brain activity. Phys Rev E, 2008, 77: 051914

    Article  MathSciNet  Google Scholar 

  35. Ursino M, Cona F, Zavaglia M. The generation of rhythms within a cortical region: Analysis of a neural mass model. Neuroimage, 2010, 52: 1080–1094

    Article  Google Scholar 

  36. Robinson P A, Rennie C J, Wright J J. Propagation and stability of waves of electrical activity in the cerebral cortex. Phys Rev E, 1997, 56: 826–840

    Article  Google Scholar 

  37. Destexhe A. Spike-and-wave oscillations based on the properties of GABA(B) receptors. J Neurosci, 1998, 18: 9099–9111

    Google Scholar 

  38. Destexhe A, Huguenard J R. Nonlinear thermodynamic models of voltage dependent currents. J Comp Neurosci, 2000, 9: 259–270

    Article  Google Scholar 

  39. Nunez P L, Srinivasan R. Electric Fields of the Brain: The Neurophysics of EEG. Oxford: Oxford University Press, 2006

    Book  Google Scholar 

  40. Jirsa V K, Haken H. Field theory of electromagnetic brain activity. Phys Rev Lett, 1996, 77: 960–963

    Article  Google Scholar 

  41. Marten F, Rodrigues S, Suffczynski P, et al. Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics. Phys Rev E, 2009, 79: 021911

    Article  MathSciNet  Google Scholar 

  42. Wilson H R, Cowan J D. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J, 1972, 12: 1–24

    Article  Google Scholar 

  43. Rodrigues S, Terry J R, Breakspear M. On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics. Phys Lett A, 2006, 355: 352–357

    Article  Google Scholar 

  44. Zhao X, Robinson P A. Generalized seizures in a neural field model with bursting dynamics. J Comput Neurosci, 2015, 39: 197–216

    Article  MathSciNet  Google Scholar 

  45. Bazhenov M, Timofeev I, Steriade M, et al. Model of thalamocortical slow-wave sleep oscillations and transitions to activated states. J Neurosci, 2002, 22: 8691–8704

    Google Scholar 

  46. Destexhe A, Sejnowski T J. Interactions between membrane conductances underlying thalamocortical slow-wave oscillations. Physiol Rev, 2003, 83: 1401–1453

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Natural and Applied Science, Northwestern Polytechnical University, Shaanxi, 710012, China

    HongHui Zhang

  2. College of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    YanHong Zheng

  3. Department of Mathematics, the University of Texas at Arlington, Arlington, Texas, 76019, USA

    JianZhong Su

  4. Department of Mathematics, University of Evansville, Evansville, Indiana, 47722, USA

    PengCheng Xiao

Authors
  1. HongHui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YanHong Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. JianZhong Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. PengCheng Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to HongHui Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, H., Zheng, Y., Su, J. et al. Seizures dynamics in a neural field model of cortical-thalamic circuitry. Sci. China Technol. Sci. 60, 974–984 (2017). https://doi.org/10.1007/s11431-016-9045-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-016-9045-4

Keywords

Search

Navigation