• | Hodgkin-Huxley with dynamic ion concentrations (Hubel and Dahlem, 2014) |
References and models cited by this paper | References and models that cite this paper | |||||||||||||||||||||||||||
Barreto E, Cressman JR (2011) Ion concentration dynamics as a mechanism for neuronal bursting. J Biol Phys 37:361-73 [Journal] [PubMed]
Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (2004) Potassium model for slow (2-3 Hz) in vivo neocortical paroxysmal oscillations. J Neurophysiol 92:1116-32 [Journal] [PubMed] Chang JC, Brennan KC, He D, Huang H, Miura RM, Wilson PL, Wylie JJ (2013) A mathematical model of the metabolic and perfusion effects on cortical spreading depression. PLoS One 8:e70469 [Journal] [PubMed] Charles AC, Baca SM (2013) Cortical spreading depression and migraine. Nat Rev Neurol 9:637-44 [Journal] [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. J Comput Neurosci 26:159-70 [Journal] [PubMed]
Dahlem MA, Graf R, Strong AJ, Dreier JP, Dahlem YA, Sieber M, Hanke W, Podoll K, Scholl E (2010) Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves Physica D 239:889-903 Dahlem MA, Hadjikhani N (2009) Migraine aura: retracting particle-like waves in weakly susceptible cortex. PLoS One 4:e5007 [Journal] [PubMed] Dahlem MA, Isele TM (2013) Transient localized wave patterns and their application to migraine. J Math Neurosci 3:7 [Journal] [PubMed] Dahlem MA, Schumacher J, Hübel N (2014) Linking a genetic defect in migraine to spreading depression in a computational model. PeerJ 2:e379 [Journal] [PubMed]
Dahlem YA, Dahlem MA, Mair T, Braun K, Müller SC (2003) Extracellular potassium alters frequency and profile of retinal spreading depression waves. Exp Brain Res 152:221-8 [Journal] [PubMed] DiFrancesco D, Noble D (1985) A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc Lond B Biol Sci 307:353-98 [Journal] [PubMed]
Dokos S, Celler BG, Lovell NH (1993) Modification of DiFrancesco-Noble equations to simulate the effects of vagal stimulation on in vivo mammalian sinoatrial node electrical activity. Ann Biomed Eng 21:321-35 [PubMed] Dreier JP (2011) The role of spreading depression, spreading depolarization and spreading ischemia in neurological disease. Nat Med 17:439-47 [Journal] [PubMed] Ermentrout GB, Terman DH (2010) Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics, Antman SS:Marsden JE:Sirovich L:Wiggins, ed. pp.1 [Journal]
Fröhlich F, Bazhenov M (2006) Coexistence of tonic firing and bursting in cortical neurons. Phys Rev E Stat Nonlin Soft Matter Phys 74:031922 [Journal] [PubMed] Fröhlich F, Bazhenov M, Iragui-Madoz V, Sejnowski TJ (2008) Potassium dynamics in the epileptic cortex: new insights on an old topic. Neuroscientist 14:422-33 [Journal] [PubMed] Grafstein B (1963) Neuronal release of potassium during spreading depression Brain Function Cortical Excitability And Steady Potentials, Brazier MAB, ed. pp.87 Hadjikhani N, Sanchez Del Rio M, Wu O, Schwartz D, Bakker D, Fischl B, Kwong KK, Cutrer FM, Rosen BR, Tootell RB, Sorensen AG, Moskowitz MA (2001) Mechanisms of migraine aura revealed by functional MRI in human visual cortex. Proc Natl Acad Sci U S A 98:4687-92 [Journal] [PubMed] Hindriks R, Meijer HG, van Gils SA, van Putten MJ (2013) Phase-locking of epileptic spikes to ongoing delta oscillations in non-convulsive status epilepticus. Front Syst Neurosci 7:111 [Journal] [PubMed] Hoffmann U, Sukhotinsky I, Atalay YB, Eikermann-Haerter K, Ayata C (2012) Increased glucose availability does not restore prolonged spreading depression durations in hypotensive rats without brain injury. Exp Neurol 238:130-2 [Journal] [PubMed] Hübel N, Schöll E, Dahlem MA (2014) Bistable dynamics underlying excitability of ion homeostasis in neuron models. PLoS Comput Biol 10:e1003551 [Journal] [PubMed] Kager H, Wadman WJ, Somjen GG (2000) Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J Neurophysiol 84:495-512 [Journal] [PubMed] Kager H, Wadman WJ, Somjen GG (2002) Conditions for the triggering of spreading depression studied with computer simulations. J Neurophysiol 88:2700-12 [Journal] [PubMed] Kager H, Wadman WJ, Somjen GG (2007) Seizure-like afterdischarges simulated in a model neuron. J Comput Neurosci 22:105-28 [Journal] [PubMed] Leao AAP (1944) Spreading depression of activity in the cerebral cortex J Neurophysiol 7:359-390 [Journal] Lee J, Kim SJ (2010) Spectrum measurement of fast optical signal of neural activity in brain tissue and its theoretical origin. Neuroimage 51:713-22 [Journal] [PubMed] Martins-Ferreira H, Nedergaard M, Nicholson C (2000) Perspectives on spreading depression. Brain Res Brain Res Rev 32:215-34 [PubMed] Reshodko LV, Bures J (1975) Computer simulation of reverberating spreading depression in a network of cell automata. Biol Cybern 18:181-9 [PubMed] Shapiro BE (2001) Osmotic forces and gap junctions in spreading depression: a computational model. J Comput Neurosci 10:99-120 [PubMed] Somjen GG, Kager H, Wadman WJ (2008) Computer simulations of neuron-glia interactions mediated by ion flux. J Comput Neurosci 25:349-65 [Journal] [PubMed]
Sukhotinsky I, Yaseen MA, Sakadzic S, Ruvinskaya S, Sims JR, Boas DA, Moskowitz MA, Ayata C (2010) Perfusion pressure-dependent recovery of cortical spreading depression is independent of tissue oxygenation over a wide physiologic range. J Cereb Blood Flow Metab 30:1168-77 [Journal] [PubMed] Timofeev I, Bazhenov M, Sejnowski T, Steriade M (2002) Cortical hyperpolarization-activated depolarizing current takes part in the generation of focal paroxysmal activities. Proc Natl Acad Sci U S A 99:9533-7 [Journal] [PubMed] Tuckwell HC, Miura RM (1978) A mathematical model for spreading cortical depression. Biophys J 23:257-76 [Journal] [PubMed] Ullah G, Schiff SJ (2010) Assimilating seizure dynamics. PLoS Comput Biol 6:e1000776 [Journal] [PubMed] Yao W, Huang H, Miura RM (2011) A continuum neuronal model for the instigation and propagation of cortical spreading depression. Bull Math Biol 73:2773-90 [Journal] [PubMed] Zandt BJ, ten Haken B, van Dijk JG, van Putten MJ (2011) Neural dynamics during anoxia and the "wave of death". PLoS One 6:e22127 [Journal] [PubMed]
| Buchin A, Chizhov A, Huberfeld G, Miles R, Gutkin BS (2016) Reduced Efficacy of the KCC2 Cotransporter Promotes Epileptic Oscillations in a Subiculum Network Model. J Neurosci 36:11619-11633 [Journal] [PubMed]
Conte C, Lee R, Sarkar M, Terman D (2018) A mathematical model of recurrent spreading depolarizations. J Comput Neurosci 44:203-217 [Journal] [PubMed]
Hübel N, Andrew RD, Ullah G (2016) Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na+/K+ pumps-dependent manner. J Comput Neurosci 40:177-92 [Journal] [PubMed]
Hübel N, Hosseini-Zare MS, Žiburkus J, Ullah G (2017) The role of glutamate in neuronal ion homeostasis: A case study of spreading depolarization. PLoS Comput Biol 13:e1005804 [Journal] [PubMed]
Joos B, Barlow BM, Morris CE (2018) Calculating the Consequences of Left-Shifted Nav Channel Activity in Sick Excitable Cells. Handb Exp Pharmacol 246:401-422 [Journal] [PubMed]
Solbrå A, Bergersen AW, van den Brink J, Malthe-Sørenssen A, Einevoll GT, Halnes G (2018) A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons. PLoS Comput Biol 14:e1006510 [Journal] [PubMed]
|