Abstract
Mechanisms of epileptic discharge generation and spread are not well known. Interictal and ictal discharges (IIDs and IDs) are determined by neuronal interactions and ionic dynamics. In order to reproduce the discharges in a simplest way, we have recently proposed a minimal mathematical model that is alternative to the known model Epileptor. Our model is of similar complexity, but in contrast to the Epileptor formulated in terms of abstract variables, it attributes physical meaning to the main variables. The model is expressed in ordinary differential equations for four principal variables, extracellular potassium and intracellular sodium concentrations, a mean membrane potential and a short-term depressing synaptic resource. Our model reproduces IIDs as bursts of spikes, and IDs as clusters of spike bursts. Potassium accumulation governs the transition to IDs. Here we generalize the model to the case of spatial propagation. Diffusion of the extracellular potassium concentration is assumed to govern the spatial spread of spiking activity across cortical tissue. Simulations are consistent with experimental registrations of waves in pro-epileptic conditions, propagating at a speed of about 0.5 mm/s.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Trevelyan, A.J., Sussillo, D., Watson, B.O., Yuste, R.: Modular propagation of epileptiform activity: evidence for an inhibitory veto in neocortex. J. Neurosci. 26(48), 12447–12455 (2006)
Trevelyan, A.J., Sussillo, D., Yuste, R.: Feedforward inhibition contributes to the control of epileptiform propagation speed. J. Neurosci. 27(13), 3383–3387 (2007)
Smith, E.H., Liou, J., Davis, T.S., Merricks, E.M., Kellis, S.S., Weiss, S.A., et al.: The ictal wavefront is the spatiotemporal source of discharges during spontaneous human seizures. Nat. Commun. 7, 11098 (2016)
Wenzel, M., Hamm, J.P., Peterka, D.S., Yuste, R.: Reliable and elastic propagation of cortical seizures in vivo. Cell Rep. 19, 2681–2693 (2017)
Wang, Y., Trevelyan, A.J., Valentin, A., Alarcon, G., Taylor, P.N., Kaiser, M.: Mechanisms underlying different onset patterns of focal seizures. PLoS Comput. Biol. 13(5), e1005475 (2017)
Chizhov, A., Amakhin, D., Zaitsev, A.: Computational model of interictal discharges triggered by interneurons. PLoS ONE 12(10), e0185752 (2017)
Wei, Y., Ullah, G., Ingram, J., Schiff, S.J.: Oxygen and seizure dynamics: II. Computational modeling. J. Neurophysiol. 112, 213–223 (2014)
Bazhenov, M.: Potassium model for slow (2–3 Hz) in vivo neocortical paroxysmal oscillations. J. Neurophysiol. 92, 1116–1132 (2004)
Krishnan, G.P., Bazhenov, M.: Ionic dynamics mediate spontaneous termination of seizures and postictal depression state. J Neurosci. 31(24), 8870–8882 (2011)
Chizhov, A.V., Zefirov, A.V., Amakhin, D.V., Smirnova, EYu., Zaitsev, A.V.: Minimal model of interictal and ictal discharges “Epileptor-2”. PLoS CB 14(5), e1006186 (2018)
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)
Müller, B.J., Zhdanov, A.V., Borisov, S.M., Foley, T., Okkelman, I.A., Tsytsarev, V., et al.: Nanoparticle-based fluoroionophore for analysis of potassium ion dynamics in 3D tissue models and in vivo. Adv. Funct. Mater. (2018). 1704598
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(1), 495–512 (2000)
Cressman, J.R., 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(2), 159–170 (2009)
Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans. Neural Netw. 14, 1569–1572 (2003)
Acknowledgments
This work was supported by the Russian Science Foundation (project 16-15-10201).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Chizhov, A.V. (2019). Epileptic Seizure Propagation Across Cortical Tissue: Simple Model Based on Potassium Diffusion. In: Kryzhanovsky, B., Dunin-Barkowski, W., Redko, V., Tiumentsev, Y. (eds) Advances in Neural Computation, Machine Learning, and Cognitive Research II. NEUROINFORMATICS 2018. Studies in Computational Intelligence, vol 799. Springer, Cham. https://doi.org/10.1007/978-3-030-01328-8_38
Download citation
DOI: https://doi.org/10.1007/978-3-030-01328-8_38
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01327-1
Online ISBN: 978-3-030-01328-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)