Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ. (2004). Potassium model for slow (2-3 Hz) in vivo neocortical paroxysmal oscillations. Journal of neurophysiology. 92 [PubMed]
Binder DK, Steinhäuser C. (2006). Functional changes in astroglial cells in epilepsy. Glia. 54 [PubMed]
Boussouf A, Lambert RC, Gaillard S. (1997). Voltage-dependent Na(+)-HCO3- cotransporter and Na+/H+ exchanger are involved in intracellular pH regulation of cultured mature rat cerebellar oligodendrocytes. Glia. 19 [PubMed]
Chen KC, Nicholson C. (2000). Spatial buffering of potassium ions in brain extracellular space. Biophysical journal. 78 [PubMed]
Cressman JR, Ullah G, Ziburkus J, Schiff SJ, Barreto E. (2009). The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics. Journal of computational neuroscience. 26 [PubMed]
Dronne MA, Boissel JP, Grenier E. (2006). A mathematical model of ion movements in grey matter during a stroke. Journal of theoretical biology. 240 [PubMed]
Dronne MA, Grenier E, Dumont T, Hommel M, Boissel JP. (2007). Role of astrocytes in grey matter during stroke: a modelling approach. Brain research. 1138 [PubMed]
Ermentrout B. (2010). http://www.math.pitt.edu/~bard/xpp/xpp.html.
Ermentrout GB, Terman DH. (2010). Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics. 35
FRANKENHAEUSER B, HODGKIN AL. (1956). The after-effects of impulses in the giant nerve fibres of Loligo. The Journal of physiology. 131 [PubMed]
Fertziger AP, Ranck JB. (1970). Potassium accumulation in interstitial space during epileptiform seizures. Experimental neurology. 26 [PubMed]
Florence G, Dahlem MA, Almeida AC, Bassani JW, Kurths J. (2009). The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: a computational study. Journal of theoretical biology. 258 [PubMed]
Fröhlich F, Bazhenov M. (2006). Coexistence of tonic firing and bursting in cortical neurons. Physical review. E, Statistical, nonlinear, and soft matter physics. 74 [PubMed]
Fröhlich F, Bazhenov M, Iragui-Madoz V, Sejnowski TJ. (2008). Potassium dynamics in the epileptic cortex: new insights on an old topic. The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry. 14 [PubMed]
Fröhlich F, Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ. (2006). Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability. The Journal of neuroscience : the official journal of the Society for Neuroscience. 26 [PubMed]
Grisar T, Guillaume D, Delgado-Escueta AV. (1992). Contribution of Na+,K(+)-ATPase to focal epilepsy: a brief review. Epilepsy research. 12 [PubMed]
Hahn PJ, Durand DM. (2001). Bistability dynamics in simulations of neural activity in high-extracellular-potassium conditions. Journal of computational neuroscience. 11 [PubMed]
Hunter P, Robbins P, Noble D. (2002). The IUPS human Physiome Project. Pflugers Archiv : European journal of physiology. 445 [PubMed]
Jensen MS, Yaari Y. (1997). Role of intrinsic burst firing, potassium accumulation, and electrical coupling in the elevated potassium model of hippocampal epilepsy. Journal of neurophysiology. 77 [PubMed]
Johnston D, Wu SMS. (2001). Foundations of cellular neurophysiology. Cambridge: MIT Press.
KEYNES RD. (1951). The ionic movements during nervous activity. The Journal of physiology. 114 [PubMed]
Kager H, Wadman WJ, Somjen GG. (2000). Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. Journal of neurophysiology. 84 [PubMed]
Kager H, Wadman WJ, Somjen GG. (2002). Conditions for the triggering of spreading depression studied with computer simulations. Journal of neurophysiology. 88 [PubMed]
Kager H, Wadman WJ, Somjen GG. (2007). Seizure-like afterdischarges simulated in a model neuron. Journal of computational neuroscience. 22 [PubMed]
Lauf PK, Adragna NC. (2000). K-Cl cotransport: properties and molecular mechanism. Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry, and pharmacology. 10 [PubMed]
Lebovitz RM. (1996). Quantitative examination of dynamic interneuronal coupling via single-spike extracellular potassium ion transients. Journal of theoretical biology. 180 [PubMed]
Lloyd CM, Halstead MD, Nielsen PF. (2004). CellML: its future, present and past. Progress in biophysics and molecular biology. 85 [PubMed]
Lux HD, Heinemann U, Dietzel I. (1986). Ionic changes and alterations in the size of the extracellular space during epileptic activity. Advances in neurology. 44 [PubMed]
Nadkarni S, Jung P, Levine H. (2008). Astrocytes optimize the synaptic transmission of information. PLoS computational biology. 4 [PubMed]
Newman EA. (1991). Sodium-bicarbonate cotransport in retinal Müller (glial) cells of the salamander. The Journal of neuroscience : the official journal of the Society for Neuroscience. 11 [PubMed]
Orkand RK, Nicholls JG, Kuffler SW. (1966). Effect of nerve impulses on the membrane potential of glial cells in the central nervous system of amphibia. Journal of neurophysiology. 29 [PubMed]
Ottersen OP, Einevoll GT, Omholt SW, Østby I, Øyehaug L. (2009). Modeling of astrocytic mechanisms explaining neural activity-induced shrinkage of extracellular space and clearance of excess extracellular potassium. Meeting abstract, 2nd INCF Congress of Neuroinformatics, Pilsen, Czech Republic, 6–8 September .
Pangrsic T, Potokar M, Haydon PG, Zorec R, Kreft M. (2006). Astrocyte swelling leads to membrane unfolding, not membrane insertion. Journal of neurochemistry. 99 [PubMed]
Park EH, Durand DM. (2006). Role of potassium lateral diffusion in non-synaptic epilepsy: a computational study. Journal of theoretical biology. 238 [PubMed]
Postnov DE et al. (2008). Giant glial cell: new insight through mechanism-based modeling. Journal of biological physics. 34 [PubMed]
Rose CR, Kovalchuk Y, Eilers J, Konnerth A. (1999). Two-photon Na+ imaging in spines and fine dendrites of central neurons. Pflugers Archiv : European journal of physiology. 439 [PubMed]
Somjen GG. (2004). Ions in the brain: Normal function, seizures and stroke.
Somjen GG, Kager H, Wadman WJ. (2008). Computer simulations of neuron-glia interactions mediated by ion flux. Journal of computational neuroscience. 25 [PubMed]
Ullah G, Schiff SJ. (2010). Assimilating seizure dynamics. PLoS computational biology. 6 [PubMed]
Volman V, Ben-Jacob E, Levine H. (2007). The astrocyte as a gatekeeper of synaptic information transfer. Neural computation. 19 [PubMed]
Ziburkus J, Cressman JR, Barreto E, Schiff SJ. (2006). Interneuron and pyramidal cell interplay during in vitro seizure-like events. Journal of neurophysiology. 95 [PubMed]
Zuckermann EC, Glaser GH. (1970). Activation of experimental epileptogenic foci. Action of increased K+ in extracellular spaces of the brain. Archives of neurology. 23 [PubMed]
Østby I et al. (2009). Astrocytic mechanisms explaining neural-activity-induced shrinkage of extraneuronal space. PLoS computational biology. 5 [PubMed]
Halnes G et al. (2016). Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue. PLoS computational biology. 12 [PubMed]
Halnes G, Ostby I, Pettersen KH, Omholt SW, Einevoll GT. (2013). Electrodiffusive model for astrocytic and neuronal ion concentration dynamics. PLoS computational biology. 9 [PubMed]
Kelley C, Newton AJH, Hrabetova S, McDougal RA, Lytton WW. (2022). Multiscale Computer Modeling of Spreading Depolarization in Brain Slices eNeuro. 9 [PubMed]
Kim CM, Nykamp DQ. (2017). The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons. Journal of computational neuroscience. 43 [PubMed]
Solbrå A et al. (2018). A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons. PLoS computational biology. 14 [PubMed]
Stein W, Harris AL. (2022). Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits Journal of computational neuroscience. 50 [PubMed]
Sætra MJ, Einevoll GT, Halnes G. (2021). An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain PLoS computational biology. 17 [PubMed]
Wei Y, Ullah G, Ingram J, Schiff SJ. (2014). Oxygen and seizure dynamics: II. Computational modeling. Journal of neurophysiology. 112 [PubMed]