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Dynamic mechanism of epileptic seizures generation and propagation after ischemic stroke

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Abstract

Epilepsy is the second largest neurological disease which seriously threatens human life and health. The one important reason of inducing epileptic seizures is ischemic stroke which causes insufficient oxygen supply from blood vessels to neurons. However, few studies focus on the underlying mechanism of the generation and propagation of epileptic seizures after ischemic stroke by utilizing modeling methods. To explore the mechanism, this paper establishes a coupled network model consisting of neurons and astrocytes, and introduces a blood vessel to simulate the condition of ischemic stroke. First, we study the effect of the degree of vascular blockage on the generation of epileptic seizures. The results demonstrate that the important reason of epileptic seizures after ischemic stroke is the disruption of ion concentration gradient. Then, we study three factors that influence the epileptic seizures propagation after ischemic stroke: massive glutamate release, excessive receptor activation and high extracellular potassium concentration. The results demonstrate that massive glutamate acting on postsynaptic neurons and the excessive activation of glutamate receptors on postsynaptic neurons promote the epileptic seizures propagation in neuronal population, and massive glutamate acting on astrocytes and excessive activation of metabotropic glutamate receptors on presynaptic neurons inhibit the epileptic seizures propagation, and the potassium uptake by astrocytes suppresses the epileptic seizures propagation. The results are consistent with the experimental phenomena. The simulation results also shed light on the fact that astrocytes have neuroprotective effect. Our results on the generation and propagation of epileptic seizures after ischemic stroke could offer theoretical guidelines for the treatment of epileptic seizures after ischemic stroke.

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Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Li, J., Song, J., Tan, N., Cao, C., Du, M., Xu, S., Wu, Y.: Channel block of the astrocyte network connections accounting for the dynamical transition of epileptic seizures. Nonlinear Dyn. 105, 3571–3583 (2021). https://doi.org/10.1007/s11071-021-06737-0

    Article  Google Scholar 

  2. Scheffer, I.E., Berkovic, S., Capovilla, G., Connolly, M.B., French, J., Guilhoto, L., Hirsch, E., Jain, S., Mathern, G.W., Moshé, S.L., Nordli, D.R., Perucca, E., Tomson, T., Wiebe, S., Zhang, Y.-H., Zuberi, S.M.: ILAE classification of the epilepsies: Position paper of the ILAE commission for classification and terminology. Epilepsia 58, 512–521 (2017). https://doi.org/10.1111/epi.13709

    Article  Google Scholar 

  3. Assis, T.M.R., Bacellar, A., Costa, G., Nascimento, O.J.M.: Mortality predictors of epilepsy and epileptic seizures among hospitalized elderly. Arq. Neuro-Psiquiatr. 73, 510–515 (2015). https://doi.org/10.1590/0004-282X20150043

    Article  Google Scholar 

  4. Stefan, H., May, T.W., Pfäfflin, M., Brandt, C., Füratsch, N., Schmitz, B., Wandschneider, B., Kretz, R., Runge, U., Geithner, J., Karakizlis, C., Rosenow, F., Kerling, F.: Epilepsy in the elderly: comparing clinical characteristics with younger patients. Acta Neurol. Scand. 129, 283–293 (2014). https://doi.org/10.1111/ane.12218

    Article  Google Scholar 

  5. Menon, B., Shorvon, S.D.: Ischaemic stroke in adults and epilepsy. Epilepsy Res. 87, 1–11 (2009). https://doi.org/10.1016/j.eplepsyres.2009.08.007

    Article  Google Scholar 

  6. Graham, N.S.N., Crichton, S., Koutroumanidis, M., Wolfe, C.D.A., Rudd, A.G.: Incidence and associations of poststroke epilepsy. Stroke 44, 605–611 (2013). https://doi.org/10.1161/STROKEAHA.111.000220

    Article  Google Scholar 

  7. GBD 2016 Lifetime Risk of Stroke Collaborators: Global, regional, and country-specific lifetime risks of stroke. N. Engl. J. Med. 379, 2429–2437 (2018). https://doi.org/10.1056/NEJMoa1804492

    Article  Google Scholar 

  8. Adelöw, C., Andersson, T., Ahlbom, A., Tomson, T.: Prior hospitalization for stroke, diabetes, myocardial infarction, and subsequent risk of unprovoked seizures. Epilepsia 52, 301–307 (2011). https://doi.org/10.1111/j.1528-1167.2010.02757.x

    Article  Google Scholar 

  9. Stefanidou, M., Das, R.R., Beiser, A.S., Sundar, B., Kelly-Hayes, M., Kase, C.S., Devinsky, O., Seshadri, S., Friedman, D.: Incidence of seizures following initial ischemic stroke in a community-based cohort: the framingham heart study. Seizure 47, 105–110 (2017). https://doi.org/10.1016/j.seizure.2017.03.009

    Article  Google Scholar 

  10. Campbell, B.C.V., De Silva, D.A., Macleod, M.R., Coutts, S.B., Schwamm, L.H., Davis, S.M., Donnan, G.A.: Ischaemic stroke. Nat. Rev. Dis. Primers 5, 70 (2019). https://doi.org/10.1038/s41572-019-0118-8

    Article  Google Scholar 

  11. Bélanger, M., Allaman, I., Magistretti, P.J.: brain energy metabolism: focus on astrocyte-neuron metabolic cooperation. Cell Metab. 14, 724–738 (2011). https://doi.org/10.1016/j.cmet.2011.08.016

    Article  Google Scholar 

  12. Attwell, D., Buchan, A.M., Charpak, S., Lauritzen, M., MacVicar, B.A., Newman, E.A.: Glial and neuronal control of brain blood flow. Nature 468, 232–243 (2010). https://doi.org/10.1038/nature09613

    Article  Google Scholar 

  13. Myint, P.K., Staufenberg, E.F.A., Sabanathan, K.: Post-stroke seizure and post-stroke epilepsy. Postgrad. Med. J. 82, 568–572 (2006). https://doi.org/10.1136/pgmj.2005.041426

    Article  Google Scholar 

  14. Lees, G.J.: Inhibition of sodium-potassium-ATPase: a potentially ubiquitous mechanism contributing to central nervous system neuropathology. Brain Res. Rev. 16, 283–300 (1991). https://doi.org/10.1016/0165-0173(91)90011-V

    Article  Google Scholar 

  15. Kamp, M.A., Dibué, M., Schneider, T., Steiger, H.-J., Hänggi, D.: Calcium and potassium channels in experimental subarachnoid hemorrhage and transient global ischemia. Stroke Res. Treat. 2012, e382146 (2012). https://doi.org/10.1155/2012/382146

    Article  Google Scholar 

  16. Szydlowska, K., Tymianski, M.: Calcium, ischemia and excitotoxicity. Cell Calcium 47, 122–129 (2010). https://doi.org/10.1016/j.ceca.2010.01.003

    Article  Google Scholar 

  17. Zlokovic, B.V.: The blood-brain barrier in health and chronic neurodegenerative disorders. Neuron 57, 178–201 (2008). https://doi.org/10.1016/j.neuron.2008.01.003

    Article  Google Scholar 

  18. Lu, X.-C.M., Williams, A.J., Yao, C., Berti, R., Hartings, J.A., Whipple, R., Vahey, M.T., Polavarapu, R.G., Woller, K.L., Tortella, F.C., Dave, J.R.: Microarray analysis of acute and delayed gene expression profile in rats after focal ischemic brain injury and reperfusion. J. Neurosci. Res. 77, 843–857 (2004). https://doi.org/10.1002/jnr.20218

    Article  Google Scholar 

  19. Trevelyan, A.J., Sussillo, D., Yuste, R.: Feedforward inhibition contributes to the control of epileptiform propagation speed. J. Neurosci. 27, 3383–3387 (2007). https://doi.org/10.1523/JNEUROSCI.0145-07.2007

    Article  Google Scholar 

  20. Khoo, H.M., von Ellenrieder, N., Zazubovits, N., He, D., Dubeau, F., Gotman, J.: The spike onset zone: the region where epileptic spikes start and from where they propagate. Neurology 91, e666–e674 (2018). https://doi.org/10.1212/WNL.0000000000005998

    Article  Google Scholar 

  21. Reato, D., Cammarota, M., Parra, L.C., Carmignoto, G.: Computational model of neuron-astrocyte interactions during focal seizure generation. Front. Comput. Neurosci. (2012). https://doi.org/10.3389/fncom.2012.00081

    Article  Google Scholar 

  22. Martinet, L.-E., Fiddyment, G., Madsen, J.R., Eskandar, E.N., Truccolo, W., Eden, U.T., Cash, S.S., Kramer, M.A.: Human seizures couple across spatial scales through travelling wave dynamics. Nat. Commun. 8, 14896 (2017). https://doi.org/10.1038/ncomms14896

    Article  Google Scholar 

  23. Proix, T.: Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy. Nat. Commun. 9, 1–15 (2018)

    Article  Google Scholar 

  24. Bezzi, P., Carmignoto, G., Pasti, L., Vesce, S., Rossi, D., Rizzini, B.L., Pozzan, T., Volterra, A.: Prostaglandins stimulate calcium-dependent glutamate release in astrocytes. Nature 391, 281–285 (1998). https://doi.org/10.1038/34651

    Article  Google Scholar 

  25. Nedergaard, M., Ransom, B., Goldman, S.A.: New roles for astrocytes: redefining the functional architecture of the brain. Trends Neurosci. 26, 523–530 (2003). https://doi.org/10.1016/j.tins.2003.08.008

    Article  Google Scholar 

  26. Du, M.-M., Li, J.-J., Yuan, Z.-X., Fan, Y.-C., Wu, Y.: Astrocyte and ions metabolism during epileptogenesis: a review for modeling studies. Chinese Phys. B. 29, 038701 (2020). https://doi.org/10.1088/1674-1056/ab6961

    Article  Google Scholar 

  27. Du, M., Li, J., Chen, L., Yu, Y., Wu, Y.: Astrocytic Kir4.1 channels and gap junctions account for spontaneous epileptic seizure. PLOS Comput. Biol. 14, e1005877 (2018). https://doi.org/10.1371/journal.pcbi.1005877

    Article  Google Scholar 

  28. Coulter, D.A., Eid, T.: Astrocytic regulation of glutamate homeostasis in epilepsy. Glia 60, 1215–1226 (2012). https://doi.org/10.1002/glia.22341

    Article  Google Scholar 

  29. Kirischuk, S., Kettenmann, H., Verkhratsky, A.: Membrane currents and cytoplasmic sodium transients generated by glutamate transport in Bergmann glial cells. Pflugers Arch. – Eur. J. Physiol. 454, 245–252 (2007). https://doi.org/10.1007/s00424-007-0207-5

    Article  Google Scholar 

  30. Mergenthaler, K., Oschmann, F., Obermeyer, K.: Glutamate uptake by astrocytic transporters. In: De Pittà, M., Berry, H. (eds.) Computational Glioscience, pp. 329–361. Springer, Cham (2019)

    Chapter  Google Scholar 

  31. Sun, L., Zhang, Y., Liu, E., Ma, Q., Anatol, M., Han, H., Yan, J.: The roles of astrocyte in the brain pathologies following ischemic stroke. Brain Inj. 33, 712–716 (2019). https://doi.org/10.1080/02699052.2018.1531311

    Article  Google Scholar 

  32. Hirayama, Y., Ikeda-Matsuo, Y., Notomi, S., Enaida, H., Kinouchi, H., Koizumi, S.: Astrocyte-mediated ischemic tolerance. J. Neurosci. 35, 3794–3805 (2015). https://doi.org/10.1523/JNEUROSCI.4218-14.2015

    Article  Google Scholar 

  33. Rossi, D.J., Brady, J.D., Mohr, C.: Astrocyte metabolism and signaling during brain ischemia. Nat. Neurosci. 10, 1377–1386 (2007). https://doi.org/10.1038/nn2004

    Article  Google Scholar 

  34. Schmidt-Kastner, R., Freund, T.F.: Selective vulnerability of the hippocampus in brain ischemia. Neuroscience 40, 599–636 (1991). https://doi.org/10.1016/0306-4522(91)90001-5

    Article  Google Scholar 

  35. Kelly, K.M.: Poststroke seizures and epilepsy: clinical studies and animal models. Epilepsy Curr. 2, 173–177 (2002). https://doi.org/10.1046/j.1535-7597.2002.00064.x

    Article  Google Scholar 

  36. Meyer, F.B.: Calcium, neuronal hyperexcitability and ischemic injury. Brain Res. Rev. 14, 227–243 (1989). https://doi.org/10.1016/0165-0173(89)90002-7

    Article  Google Scholar 

  37. Ingram, J., Zhang, C., Cressman, J.R., Hazra, A., Wei, Y., Koo, Y.-E., Žiburkus, J., Kopelman, R., Xu, J., Schiff, S.J.: Oxygen and seizure dynamics: I. Experiments. J. Neurophysiol. 112, 205–212 (2014). https://doi.org/10.1152/jn.00540.2013

    Article  Google Scholar 

  38. David, Y., Cacheaux, L.P., Ivens, S., Lapilover, E., Heinemann, U., Kaufer, D., Friedman, A.: Astrocytic dysfunction in epileptogenesis: Consequence of altered potassium and glutamate homeostasis? J. Neurosci. 29, 10588–10599 (2009). https://doi.org/10.1523/JNEUROSCI.2323-09.2009

    Article  Google Scholar 

  39. Giaume, C., Koulakoff, A., Roux, L., Holcman, D., Rouach, N.: Astroglial networks: a step further in neuroglial and gliovascular interactions. Nat. Rev. Neurosci. 11, 87–99 (2010). https://doi.org/10.1038/nrn2757

    Article  Google Scholar 

  40. Fitzhugh, R.: Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J. Gen. Physiol. 43, 867–896 (1960). https://doi.org/10.1085/jgp.43.5.867

    Article  Google Scholar 

  41. 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, 159–170 (2009). https://doi.org/10.1007/s10827-008-0132-4

    Article  MathSciNet  Google Scholar 

  42. Wei, Y., Ullah, G., Ingram, J., Schiff, S.J.: Oxygen and seizure dynamics: II. Computational modeling. J. Neurophysiol. 112, 213–223 (2014). https://doi.org/10.1152/jn.00541.2013

    Article  Google Scholar 

  43. Traub, R.D., Wong, R.K., Miles, R., Michelson, H.: A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J. Neurophysiol. 66, 635–650 (1991). https://doi.org/10.1152/jn.1991.66.2.635

    Article  Google Scholar 

  44. Gloveli, T., Dugladze, T., Saha, S., Monyer, H., Heinemann, U., Traub, R.D., Whittington, M.A., Buhl, E.H.: Differential involvement of oriens/pyramidale interneurones in hippocampal network oscillations in vitro: Interneurones and network oscillations. J. Physiol. 562, 131–147 (2005). https://doi.org/10.1113/jphysiol.2004.073007

    Article  Google Scholar 

  45. Chapuisat, G., Dronne, M.A., Grenier, E., Hommel, M., Gilquin, H., Boissel, J.P.: A global phenomenological model of ischemic stroke with stress on spreading depressions. Prog. Biophys. Mol. Biol. 97, 4–27 (2008). https://doi.org/10.1016/j.pbiomolbio.2007.10.004

    Article  Google Scholar 

  46. Fisher, M.: Characterizing the target of acute stroke therapy. Stroke 28, 866–872 (1997). https://doi.org/10.1161/01.STR.28.4.866

    Article  Google Scholar 

  47. Baron, J.-C.: Mapping the ischaemic penumbra with PET: Implications for acute stroke treatment. CED 9, 193–201 (1999). https://doi.org/10.1159/000015955

    Article  Google Scholar 

  48. Götz-Trabert, K., Hauck, C., Wagner, K., Fauser, S., Schulze-Bonhage, A.: Spread of ictal activity in focal epilepsy. Epilepsia 49, 1594–1601 (2008). https://doi.org/10.1111/j.1528-1167.2008.01627.x

    Article  Google Scholar 

  49. Yang, P.-F., Shang, M.-C., Lin, Q., Xiao, H., Mei, Z., Jia, Y.-Z., Liu, W., Zhong, Z.-H.: Three-dimensional intracranial EEG monitoring in presurgical assessment of MRI-negative frontal lobe epilepsy. Medicine (Baltimore) (2016). https://doi.org/10.1097/MD.0000000000005192

    Article  Google Scholar 

  50. Ermentrout, G.B., Terman, D.H.: Mathematical Foundations of Neuroscience. Springer, New York (2010)

    Book  Google Scholar 

  51. Terman, D., Rubin, J.E., Yew, A.C., Wilson, C.J.: Activity patterns in a model for the subthalamopallidal network of the basal ganglia. J. Neurosci. (2002). https://doi.org/10.1523/JNEUROSCI.22-07-02963.2002

    Article  Google Scholar 

  52. Amiri, M., Hosseinmardi, N., Bahrami, F., Janahmadi, M.: Astrocyte- neuron interaction as a mechanism responsible for generation of neural synchrony: a study based on modeling and experiments. J. Comput. Neurosci. 34, 489–504 (2013). https://doi.org/10.1007/s10827-012-0432-6

    Article  MathSciNet  Google Scholar 

  53. Li, Y.X., Rinzel, J.: Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a hodgkin-huxley like formalism. J. Theor. Biol. 166, 461–473 (1994). https://doi.org/10.1006/jtbi.1994.1041

    Article  Google Scholar 

  54. Volman, V., Ben-Jacob, E., Levine, H.: The astrocyte as a gatekeeper of synaptic information transfer. Neural Comput. 19, 303–326 (2007). https://doi.org/10.1162/neco.2007.19.2.303

    Article  MathSciNet  MATH  Google Scholar 

  55. Perea, G., Navarrete, M., Araque, A.: Tripartite synapses: astrocytes process and control synaptic information. Trends Neurosci. 32, 421–431 (2009). https://doi.org/10.1016/j.tins.2009.05.001

    Article  Google Scholar 

  56. Araque, A., Parpura, V., Sanzgiri, R.P., Haydon, P.G.: Tripartite synapses: glia, the unacknowledged partner. Trends Neurosci. 22, 208–215 (1999). https://doi.org/10.1016/S0166-2236(98)01349-6

    Article  Google Scholar 

  57. Araque, A., Carmignoto, G., Haydon, P.G.: Dynamic signaling between astrocytes and neurons. Annu. Rev. Physiol. 63, 795–813 (2001). https://doi.org/10.1146/annurev.physiol.63.1.795

    Article  Google Scholar 

  58. Newman, E.A.: New roles for astrocytes: regulation of synaptic transmission. Trends Neurosci. 26, 536–542 (2003). https://doi.org/10.1016/S0166-2236(03)00237-6

    Article  Google Scholar 

  59. Koizumi, S., Fujishita, K., Tsuda, M., Shigemoto-Mogami, Y., Inoue, K.: Dynamic inhibition of excitatory synaptic transmission by astrocyte-derived ATP in hippocampal cultures. PNAS 100, 11023–11028 (2003). https://doi.org/10.1073/pnas.1834448100

    Article  Google Scholar 

  60. Bladin, C.F., Alexandrov, A.V., Bellavance, A., Bornstein, N., Chambers, B., Coté, R., Lebrun, L., Pirisi, A., Norris, J.W.: Seizures after stroke study group: seizures after stroke: a prospective multicenter study. Arch. Neurol. 57, 1617–1622 (2000). https://doi.org/10.1001/archneur.57.11.1617

    Article  Google Scholar 

  61. Lambrakis, C.C., Lancman, M.E.: The phenomenology of seizures and epilepsy after stroke. J. Epilepsy 11, 233–240 (1998). https://doi.org/10.1016/S0896-6974(98)00029-2

    Article  Google Scholar 

  62. Traynelis, S.F., Dingledine, R.: Potassium-induced spontaneous electrographic seizures in the rat hippocampal slice. J. Neurophysiol. 59, 259–276 (1988). https://doi.org/10.1152/jn.1988.59.1.259

    Article  Google Scholar 

  63. Jensen, M.S., Yaari, Y.: Role of intrinsic burst firing, potassium accumulation, and electrical coupling in the elevated potassium model of hippocampal epilepsy. J. Neurophysiol. 77, 1224–1233 (1997). https://doi.org/10.1152/jn.1997.77.3.1224

    Article  Google Scholar 

  64. Heinemann, U., Lux, H.D., Gutnick, M.J.: Extracellular free calcium and potassium during paroxysmal activity in the cerebral cortex of the cat. Exp. Brain Res. (1977). https://doi.org/10.1007/BF00235500

    Article  Google Scholar 

  65. Ullah, G., Cressman, J.R., Jr., Barreto, E., Schiff, S.J.: The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: II. Network and glial dynamics. J. Comput. Neurosci. 26, 171–183 (2009). https://doi.org/10.1007/s10827-008-0130-6

    Article  MathSciNet  Google Scholar 

  66. Chever, O., Djukic, B., McCarthy, K.D., Amzica, F.: Implication of Kir4.1 channel in excess potassium clearance: an in vivo study on anesthetized glial-conditional Kir4.1 knock-out mice. J. Neurosci. 30, 15769–15777 (2010). https://doi.org/10.1523/JNEUROSCI.2078-10.2010

    Article  Google Scholar 

  67. Walz, W.: Role of astrocytes in the clearance of excess extracellular potassium. Neurochem. Int. 36, 291–300 (2000). https://doi.org/10.1016/S0197-0186(99)00137-0

    Article  Google Scholar 

  68. Bullock, R., Zauner, A., Woodward, J., Young, H.F.: Massive persistent release of excitatory amino acids following human occlusive stroke. Stroke 26, 2187–2189 (1995). https://doi.org/10.1161/01.STR.26.11.2187

    Article  Google Scholar 

  69. Dávalos, A., Castillo, J., Serena, J., Noya, M.: Duration of glutamate release after acute ischemic stroke. Stroke 28, 708–710 (1997). https://doi.org/10.1161/01.STR.28.4.708

    Article  Google Scholar 

  70. Losi, G., Cammarota, M., Chiavegato, A., Gomez-Gonzalo, M., Carmignoto, G.: A new experimental model of focal seizures in the entorhinal cortex: NMDA-Induced seizure-like events. Epilepsia 51, 1493–1502 (2010). https://doi.org/10.1111/j.1528-1167.2009.02472.x

    Article  Google Scholar 

  71. Koizumi, S., Fujishita, K., Tsuda, M., Shigemoto-Mogami, Y., Inoue, K.: Dynamic inhibition of excitatory synaptic transmission by astrocyte-derived ATP in hippocampal cultures. Proc. Natl. Acad. Sci. (2003). https://doi.org/10.1073/pnas.1834448100

    Article  Google Scholar 

  72. Sun, D.A., Sombati, S., DeLorenzo, R.J.: Glutamate injury-induced epileptogenesis in hippocampal neurons. Stroke 32, 2344–2350 (2001). https://doi.org/10.1161/hs1001.097242

    Article  Google Scholar 

  73. Rose, C.R., Felix, L., Zeug, A., Dietrich, D., Reiner, A., Henneberger, C.: Astroglial glutamate signaling and uptake in the hippocampus. Front. Mol. Neurosci. (2018). https://doi.org/10.3389/fnmol.2017.00451

    Article  Google Scholar 

  74. Iversen, L., Mulvihill, E., Haldeman, B., Diemer, N.H., Kaiser, F., Sheardown, M., Kristensen, P.: Changes in metabotropic glutamate receptor mRNA levels following global ischemia: increase of a putative presynaptic subtype (mGluR4) in highly vulnerable rat brain areas. J. Neurochem. 63, 625–633 (1994). https://doi.org/10.1046/j.1471-4159.1994.63020625.x

    Article  Google Scholar 

  75. Nicholls, J.G., Martin, A.R., Wallace, B.G., Fuchs, P.A.: From Neuron to Brain, 5th edn. Sinauer Associates, Sunderland, MA (2001)

    Google Scholar 

  76. Yu, Y., Yuan, Z., Fan, Y., Li, J., Wu, Y.: Dynamic transitions in neuronal network firing sustained by abnormal astrocyte feedback. Neural Plast. 2020, 1–13 (2020). https://doi.org/10.1155/2020/8864246

    Article  Google Scholar 

  77. Leis, J.A., Bekar, L.K., Walz, W.: Potassium homeostasis in the ischemic brain. Glia 50, 407–416 (2005). https://doi.org/10.1002/glia.20145

    Article  Google Scholar 

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Acknowledgements

We thank Dr. Yeyin Xu for helpful comments.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 12132012 and 11972275).

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Yu, Y., Li, J., Yuan, Z. et al. Dynamic mechanism of epileptic seizures generation and propagation after ischemic stroke. Nonlinear Dyn 109, 3113–3132 (2022). https://doi.org/10.1007/s11071-022-07577-2

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