Advertisement

Journal of Computational Neuroscience

, Volume 46, Issue 2, pp 197–209 | Cite as

Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability

  • Yue Liu
  • John Milton
  • Sue Ann CampbellEmail author
Article
  • 261 Downloads

Abstract

We formulate a conductance-based model for a 3-neuron motif associated with Childhood Absence Epilepsy (CAE). The motif consists of neurons from the thalamic relay (TC) and reticular nuclei (RT) and the cortex (CT). We focus on a genetic defect common to the mouse homolog of CAE which is associated with loss of GABAA receptors on the TC neuron, and the fact that myelination of axons as children age can increase the conduction velocity between neurons. We show the combination of low GABAA mediated inhibition of TC neurons and the long corticothalamic loop delay gives rise to a variety of complex dynamics in the motif, including bistability. This bistability disappears as the corticothalamic conduction delay shortens even though GABAA activity remains impaired. Thus the combination of deficient GABAA activity and changing axonal myelination in the corticothalamic loop may be sufficient to account for the clinical course of CAE.

Keywords

Childhood absence epilepsy Time delay 

Notes

Acknowledgments

We thank Samuel Berkovic and Peter Camfield for useful comments on the clinical history and inheritance of children with CAE and Anthony Burre for help with the numerical simulations. SAC and YL acknowledge the support of the Natural Sciences and Engineering Research Council of Canada. JM acknowledges support from the William R Kenan, Jr Charitable Trust.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

References

  1. Arakaki, T., Mahon, S., Charpier, S., Leblois, A., Hansel, D. (2016). The role of striatal feedforward inhibition in the maintenance of absence seizures. Journal of Neuroscience, 36, 9618–9623.PubMedGoogle Scholar
  2. Beenhakker, M.P., & Huguenard, J.R. (2009). Neurons that fire together also conspire together: is normal sleep circuitry hijacked to generate epilepsy? Neuron, 62, 612–632.PubMedPubMedCentralGoogle Scholar
  3. Behrens, T.E.S., Johansen-Berg, H., Woolrich, M.W., Smith, S.M., Wheeler-Kingshott, C.A.M., Boulby, P.A., Barker, G.J., Sillery, E.L., Sheehan, K., Ciccarelli, O., Thompson, A.J., Brady, J.M., Matthews, P.M. (2003). Non-invasive mapping of connections between human thalamus and cortex using diffusion imaging. Nature Neuroscience, 6, 750–757.PubMedGoogle Scholar
  4. Berkovic, S.F. (1993). Childhood absence epilepsy and juvenile absence epilepsy. In E. Wyllie (Ed.) The treatment of epilepsy: principles and practice (pp. 547–551). Philadelphia: Lea & Febiger.Google Scholar
  5. Bouwman, B.M., Suffczynski, P., Lopes da Silva, F.H., Maris, E., Rijn, C.M. (2007). GABAErgic mechanisms in absence epilepsy: a computational model of absence epilepsy simulating spike and wave discharges after vigabatrin in WAG/rij rats. European Journal of Neuroscience, 25, 2783–2790.PubMedGoogle Scholar
  6. 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.PubMedGoogle Scholar
  7. Chen, Y., Parker, W.D., Wang, K. (2014). The role of T-type calcium channel genes in absence seizures. Frontiers in Neurology, 5, 45.PubMedPubMedCentralGoogle Scholar
  8. Chen, M., Cao, D., Xia, Y., Yao, D. (2017). Control of absence seizures by the thalamic feed-forward inhibition. Frontiers of Computational Neuroscience, 11, Article 31.Google Scholar
  9. Chkhenkeli, S.A., & Milton, J. (2003). Dynamic epileptic systems versus static epileptic foci. In J. Milton, & P. Jung (Eds.) Disease, epilepsy as a dynamic (pp. 25–36). New York: Springer.Google Scholar
  10. Crick, F. (1984). Function of the thalamic reticular complex: the searchlight hypothesis. Proceedings of the National Academy of Sciences (USA), 81, 4586–4590.Google Scholar
  11. Crunelli, V., & Leresche, N. (2002). Childhood absence epilepsy. Genes, channels, neurons and networks. Nature Reviews Neuroscience, 3, 371–381.PubMedGoogle Scholar
  12. da Silva, F.H.L., Blanes, W., Kalitzin, S., Gomez, J.P., Suffczynski, P., Velis, F.J. (2002). Epilepsies as dynamical diseases of brain systems: basic models of the transitions between normal and epileptic activity. Epilepsia, 44(Suppl 12), 72–83.Google Scholar
  13. da Silva, F.H.L., Blanes, W., Kalitzin, S., Gomez, J.P., Suffczynski, P., Velis, F.J. (2003). Dynamical diseases of brain systems: different routes to epileptic seizures. IEEE Transactions of Biomedical Engineering, 50, 540–548.Google Scholar
  14. Depaulis, A., & Charpier, S. (2018). Pathophysiology of absence epilepsy: Insights from genetic models. Neuroscience Letters, 667, 53–65.PubMedGoogle Scholar
  15. Depaulis, A., David, O., Charpier, S. (2016). The genetic absence epilepsy rat from Strassberg as a model to decipher the neuronal and network mechanisms of generalized epilepsies. Journal of Neuroscience Methods, 260, 159–174.PubMedGoogle Scholar
  16. Destexhe, A. (1998). Spike-and-wave oscillations based on the properties of GABAB receptors. Journal of Neuroscience, 18, 9099–9111.PubMedGoogle Scholar
  17. Destexhe, A. (2008). Corticothalamic feedback: a key to explain absence seizures. In I. Soltesz, & K. Staley (Eds.) Computational neuroscience in epilepsy (pp. 184–214). New York: Academic Press.Google Scholar
  18. Destexhe, A., & Babloyantz, A. (1991). A model of the inward current Ih and its possible role in thalamocortical oscillations. Neuroreport, 4, 223–226.Google Scholar
  19. Destexhe, A., Babloyantz, A., Sejnowski, T.J. (1993). Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons. Biophysical Journal, 65, 1538–1552.PubMedPubMedCentralGoogle Scholar
  20. Destexhe, A., Contreras, D., Sejnowski, T.J., Steriade, M. (1994). Modeling the control of reticular thalamic oscillations by neuromodulators. Neuroreport, 5, 2217–2220.PubMedGoogle Scholar
  21. 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.PubMedGoogle Scholar
  22. Destexhe, A., Contreras, D., Steriade, M. (1998). Mechanisms underlying the synchronizing action of corticothalamic feedback through inhibition of thalamic relay cells. Journal of Neurophysiology, 79, 999–1016.PubMedGoogle Scholar
  23. Destexhe, A., Mainen, Z., Sejnowski, T., Segev, I. (1998). Kinetic models of synaptic transmission. In C. Koch (Ed.) Methods in neuronal modeling: from synapses to networks (pp. 1–26). Cambridge: MIT Press.Google Scholar
  24. Driver, R.D., Sasser, D.W., Slater, M.L. (1973). The equation x (t) = a x(t) + b x(tτ) with small delay. American Mathematics Monthly, 80, 990–995.Google Scholar
  25. Eissa, T.I., Dijkstra, K., Brune, C., Emerson, R.G., van Putten, M.J.A.M., Goodman, R.R, McKhann, GM Jr, Schevon, C.A., van Drongelen, W., van Gils, S.A. (2017). Cross-scale effects of neural interactions during human neocortical seizure activity. Proceedings National Academy Science (USA), 114, 10761–10766.Google Scholar
  26. Ermentrout, B. (2002). Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. Philadelphia: SIAM.Google Scholar
  27. Ermentrout, B., & Terman, D.H. (2010). Mathematical foundations of neuroscience. New York: Springer.Google Scholar
  28. Fan, D., Liu, S., Wang, Q. (2016). Stimulus-induced epileptic spike-wave discharges in thalamocortical model with disinhibition. Scientific Reports, 6, 37703.PubMedPubMedCentralGoogle Scholar
  29. Foss, J., & Milton, J. (2000). Multistability in recurrent inhibitory loops arising from delay. Journal of Neurophysiology, 84, 975–985.PubMedGoogle Scholar
  30. Foss, J., Longtin, A., Mensour, B., Milton, J. (1996). Multistability and delayed recurrent feedback. Physical Review Letters, 76, 708–711.PubMedGoogle Scholar
  31. Foss, J., Moss, F., Milton, J. (1997). Noise, multistability and delayed recurrent loops. Physical Review E, 55, 4536–4543.Google Scholar
  32. Gupta, D., Ossenblok, P., van Luijtelaar, G. (2011). Space-time network connectivity and cortical activations preceding spike wave discharges in human absence epilepsy. Medical Biology Engineering Computation, 49, 555–565.Google Scholar
  33. Hashemi, M., Hutt, A., Hight, D., Sleigh, S. (2017). Anesthetic action on the transmission delay between cortex and thalamus explains the beta-fuzz observed under propofol anesthesia. PLoS ONE, e0179286, 12.Google Scholar
  34. Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500–544.PubMedGoogle Scholar
  35. Hogan, T., & Sundram, M. (1989). Rhythmic auditory stimulation in generalized epilepsy. Electroencephalography clinical Neurophysiology, 72, 455–458.PubMedGoogle Scholar
  36. Hortnagl, H., Tasan, R.O., Wieselthaler, A., Kirchmair, E., Sieghart, W., Sperk, G. (2013). Patterns of mRNA and protein expression for GABAA receptor subunits in the mouse brain. Neuroscience, 236, 345–372.PubMedPubMedCentralGoogle Scholar
  37. Houssaini, K.E., Ivanov, A.I., Bernard, C., Jirsa, V.K. (2015). Seizures, refractory status epilepticus, and depolarization block as endogeneous brain activities. Physical Review E, 91, 010701.Google Scholar
  38. Huguenard, J.R., & Prince, D.A. (1991). Slow inactivation of a TEA-sensitive K current in acutely isolated rat thalamic relay neurons. Journal of Neurophysiology, 66(4), 1316–1328.PubMedGoogle Scholar
  39. Huguenard, J.R., & Prince, D.A. (1992). A novel T-type current underlies prolonged Ca(2 +)-dependent burst firing in GABAergic neurons of rat thalamic reticular nucleus. Journal of Neuroscience, 12, 3804–3804.PubMedGoogle Scholar
  40. Insperger, T. (2015). On the approximation of delayed systems by Taylor series expansion. Journal of Computational and Nonlinear Dynamics, 10, 024503.Google Scholar
  41. Jirsa, V.K., Proix, T., Perdikis, D., Woodman, M.M., Wang, H., Gonzalez-Martinez, J., Bernard, C., Bénar, C., Guye, M., Chauvel, P., Bartolomei, F. (2017). The virtual patient: individualized whole-brain models of epilepsy spread. NeuroImage, 145, 377–388.PubMedGoogle Scholar
  42. Jirsa, V.K., Stacey, W.C., Quilichini, P.P., Ivanov, A.I., Bernard, C. (2014). On the nature of seizure dynamics. Brain: A Journal of Neurology, 137, 2210–2230.Google Scholar
  43. Kandel, E., Schwartz, J., Jessell, T. (2000). Principles of neural science. New York: McGraw-Hill.Google Scholar
  44. Koepp, M.J., Caciagli, L., Pressler, R.M., Lehnertz, K., Beniczky, S. (2016). Reflex seizures, traits, and epilepsies: from physiology to pathology. Lancet Neurology, 15, 92–105.PubMedGoogle Scholar
  45. Kostopoulos, G.K. (2000). Spike-and-wave discharges of absence seizures as a transformation of sleep spindles: the continuing development of a hypothesis. Clinical Neurophysiology, 111(Suppl. 2), S27–S38.PubMedGoogle Scholar
  46. Kreindler, A. (1965). Experimental epilepsy. New York: Elsevier.Google Scholar
  47. Kurzweil, J. (1971). Small delays don’t matter. In D. Chillingworth (Ed.) Proceedings of the symposium on differential equations and dynamical systems, lecture notes in mathematics (pp. 47–49). New York: Springer.Google Scholar
  48. Landisman, C.E., Long, M.A., Beierlein, M., Deans, M.R., Paul, D.L., Connors, B.W. (2002). Electrical synapses in the thalamic reticular nucleus. Journal of Neuroscience, 22, 1002–1009.PubMedGoogle Scholar
  49. Ma, J., & Wu, J. (2007). Multistability in spiking neuron models of delayed recurrent inhibitory loops. Neural Computation, 19, 2124–2148.PubMedGoogle Scholar
  50. Mak-McCully, R.A., Rolland, M., Sargsyan, A., Gonzalez, C., Magnin, M., Chauvel, P., Rey, M., Bastuji, H., Halgren, E. (2017). Coordination of cortical and thalamic activity during non-REM sleep in humans. Nature Communications, 8, 15499.PubMedPubMedCentralGoogle Scholar
  51. Maljevic, S., Krampfl, K., Cobilanschi, J., Tilgen, N., Beyer, S., Weber, Y.G., Schlesinger, F., Ursu, D., Melzer, W., Cossette, P., Bufler, J., Lerche, H., Helis, A. (2006). A mutation in the GABAA receptor α 1-subunit is associated with absence epilepsy. Annals of Neurology, 59, 983–987.PubMedGoogle Scholar
  52. McCormick, D.A., Wang, Z., Huguenard, J. (1993). Neurotransmitter control of neocortical neuronal activity and excitability. Cerebral Cortex, 3, 387–398.PubMedGoogle Scholar
  53. McDougal, R.A., Morse, T.M., Carnevale, T., Marenco, L., Wang, R., Migliore, M., Miller, P.L., Shepherd, G.M., Hines, M.L. (2017). Twenty years of modelDB and beyond: building essential modeling tools for the future of neuroscience. J Comput Neurosci., 42(1), 1–10.PubMedGoogle Scholar
  54. McKusick, V.A. (2017). Mendelian inheritance in man: a catalogue of human genes and genetic disorders. https://www.omin.org.
  55. Meeren, H.K., Pijn, J.P., Luijtelaar, E.L., Coenen, A.M., da Silva, F.H.L. (2002). Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats. Journal of Neuroscience, 22, 1480–1485.PubMedGoogle Scholar
  56. Milanowski, P., & Suffczynski, P. (2016). Seizures start without common signatures of critical transitions. International Journal of Neurological Systems, 26, 1650053.Google Scholar
  57. Milton, J.G., Gotman, J., Remillard, G.M., Andermann, F. (1987). Timing of seizure recurrence in adult epileptics: a statistical analysis. Epilepsia, 28, 471–478.PubMedGoogle Scholar
  58. Milton, J., & Jung, P. (2003). Epilepsy as a dynamic disease. New York: Springer.Google Scholar
  59. Milton, J., & Ohira, T. (2014). Mathematics as a laboratory tool: dynamics, delays and noise. New York: Springer.Google Scholar
  60. Milton, J., Wu, J., Campbell, S.A., Bélair, L. (2017). Outgrowing neurological diseases: Microcircuits, conduction delay and dynamics diseases. In P. Erdi, S. Bhattacharya, A. Cochran (Eds.) Computational neurology - computational psychiatry: why and how? (pp. 11–47). New York: Springer.Google Scholar
  61. Milton, J.G. (2000). Epilepsy and the multistable nervous system. In J. Walleczek (Ed.) Self-organized biological dynamics and nonlinear control by external stimuli (pp. 374–386). Cambridge: Cambridge University Press.Google Scholar
  62. Milton, J.G., Chkhenkeli, S.A., Towle, V.L. (2007). Andamp; A.R. McIntosh Brain connectivity and the spread of epileptic seizures. In Jirsa, V. K. (Ed.) Handbook of brain connectivity (pp. 477–503). New York: Springer.Google Scholar
  63. Nagaraj, V., Lee, S., Krook-Magnuson, E., Soltesz, I., Benquet, P., Irazoqui, P., Netoff, T. (2015). The future of seizure prediction and intervention: Closing the loop. Journal of Clinical Neurophysiology, 32, 194–206.PubMedPubMedCentralGoogle Scholar
  64. Osorio, I., Frei, M.G., Sornette, D., Milton, J., Lai, Y.C. (2010). Epileptic seizures: quakes of the brain? Physical Review E, 82, 021919.Google Scholar
  65. Osorio, I., Zaveri, H.P., Frei, M.G., Arthurs, S. (2011). Epilepsy: the intersection of neurosciences, biology, mathematics, engineering and physics. New York: CRC Press.Google Scholar
  66. Paz, J.T., Bryant, A.S., Peng, K., Fenno, L., Yizhar, O., Frankel, W.N., Deisseroth, K., Huguenard, J.R. (2011). A new mode of corticothalamic transmission revealed in the Gria44-’- model of absence epilepsy. Nature Neuroscience, 14, 1167–1173.PubMedPubMedCentralGoogle Scholar
  67. Penry, J.K., Porter, R.J., Driefess, F.E. (1975). Simultaneous recording of absence seizures with videotape and electroencephalography. a study of 374 seizures in 48 patients. Brian, 98, 427–440.Google Scholar
  68. Pollack, P.O., Guillemain, J., Hu, E., Deransant, C., Depaulis, A., Charpier, S. (2007). Deep layer somatosensory cortical neurons initiate spike-and-wave discharges in a genetic model of absence seizures. Journal of Neuroscience, 27, 6590–6599.Google Scholar
  69. Powell, K.L., & et al. (2009). A Cav3. 2 T-type calcium channel point mutation has splice-variant-specific effects on function and segregates with seizure expression in a polygenic rat model of absence epilepsy. Journal of Neuroscience, 29(2), 371– 380.PubMedGoogle Scholar
  70. Tsakiridou, E., Bertollini, L., de Curtis, M., Avanzini, G., Pape, H. (1995). Selective increase in T-type calcium conductance of reticular thalamic neurons in a rat model of absence epilepsy. Journal of Neuroscience, 15(4), 3110–3117.PubMedGoogle Scholar
  71. Quan, A., Osorio, I., Ohira, T., Milton, J. (2011). Vulnerability to paroxysmal oscillations in delayed neural networks: A basis for nocturnal frontal lobe epilepsy? Chaos, 21, 047512.PubMedPubMedCentralGoogle Scholar
  72. Roberts, J.A., & Robinson, P.A. (2008). Modeling absence seizure dynamics: Implications for basic mechanisms and measurement of thalamocortical and corticothalamic latencies. Journal of Theortical Biology, 253, 189–201.Google Scholar
  73. Robinson, P., 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.Google Scholar
  74. Salami, M., Itami, C., Tsumoto, T., Kimura, F. (2003). Change of conduction velocity be regional myelination yields constant latency irrespective of distance between thalamus and cortex. Proceedings of the National Academy of Sciences (USA), 100, 6174–6179.Google Scholar
  75. Skinner, F.K., Bazzazi, H., Campbell, S.A. (2005). Two-cell to N-cell heterogeneous, inhibitory networks: precise linking of multistable and coherent properties. J. Computational Neuroscience, 18(3), 343–352.Google Scholar
  76. Soltesz, I., & Staley, K. (2008). Computational neuroscience in epilepsy. New York: Academic Press.Google Scholar
  77. Suffczynski, P., Kalitzin, S., Lopes da Silva, F.H. (2004). Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience, 126, 467–484.PubMedGoogle Scholar
  78. Swadlow, H.A., & Waxman, S.G. (2012). Axonal conduction delays. Scholarpedia, 7(6), 1451.Google Scholar
  79. Tenney, J.R., Fujiwara, H., Horn, P.S., Jacobsen, S.E., Glaser, T.A., Rose, D.F. (2013). Focal corticothalamic sources during generalized absence seizures: a MEG study. Epilepsy Research, 106, 113–122.PubMedGoogle Scholar
  80. Traub, R.D., & Miles, R. (1991). Neuronal networks of the hippocampus. New York: Cambridge University Press.Google Scholar
  81. van de Kamp, C., Gawthrop, P.J., Gollee, H., Loram, I.D. (2013). Refractoriness in sustained visuo-manual control. is the refractory duration intrinsic or does it depend on external system parameters? PLoS Computational Biology, e1002843, 9.Google Scholar
  82. Vince, M.A. (1948). The intermittency of control movements and the psychological refractory period. British Journal of Psychology General Section, 38, 149–157.Google Scholar
  83. Wallace, R.H., Marini, C.V., Petrou, S., Harkin, L.A., Bowser, D.N., Panchal, R.G., Williams, D.A., Sutherland, G.R., Mulley, J.C., Scheffer, I.E., Berkovic, S.F. (2001). Mutant GABAA receptor γ2-subunit in childhood absence epilepsy and febrile seizures. Nature Genetics, 28, 49–52.PubMedGoogle Scholar
  84. Wang, X.J., Rinzel, J., Rogawski, M.A. (1991). A model of the T-type calcium current and the low-threshold spike in thalamic neurons. Journal of Neurophysiology, 66, 839–850.PubMedGoogle Scholar
  85. Weir, B. (1964). Spikes-wave from stimulation of reticular core. Archives of Neurology, 11, 209–218.PubMedGoogle Scholar
  86. Weiss, S.A., Banks, G.P., McKhan, G.M. Jr., Goodman, R.R, Emerson, R.G., Trevelyan, A.J., Schevon, C.A. (2013). Ictal high frequency oscillations distinguish two types of seizure territories in humans. Brain, 136, 3796–3808.PubMedPubMedCentralGoogle Scholar
  87. Westmije, I., Ossenblok, P., Gunning, B., van Luijtelaar, G. (2009). Onset and propagation of spike and slow wave discharges in human absence epilepsy: a MEG study. Epilepsia, 50, 2538– 2548.Google Scholar
  88. Williams, D. (1953). A study of thalamic and cortical rhythms in petit mal. Brain: A Journal of Neurology, 76, 50–69.Google Scholar
  89. Yang, D. -P., & Robinson, P.A. (2017). Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures. Physical Review E, 95(4), 042410.PubMedGoogle Scholar
  90. Zhou, C., Ding, L., Deel, M.E., Ferrick, E.A., Emeson, R.B., Gallagher, M.J. (2015). Altered intrathalamic GABAA neurotransmission in a mouse model of a human genetic epilepsy syndrome. Neurobiology of Disease, 73, 407–417.PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Institute of Applied Mathematics and Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.W.M. Keck Science DepartmentThe Claremont CollegesClaremontUSA
  4. 4.Department of Applied Mathematics and Centre for Theoretical NeuroscienceUniversity of WaterlooWaterlooCanada

Personalised recommendations