Hodgkin-Huxley with dynamic ion concentrations (Hubel and Dahlem, 2014)


Hübel N, Dahlem MA. (2014). Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs. PLoS computational biology. 10 [PubMed]

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References and models cited by this paper

Barreto E, Cressman JR. (2011). Ion concentration dynamics as a mechanism for neuronal bursting. Journal of biological physics. 37 [PubMed]

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]

Chang JC et al. (2013). A mathematical model of the metabolic and perfusion effects on cortical spreading depression. PloS one. 8 [PubMed]

Charles AC, Baca SM. (2013). Cortical spreading depression and migraine. Nature reviews. Neurology. 9 [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]

Dahlem MA, Hadjikhani N. (2009). Migraine aura: retracting particle-like waves in weakly susceptible cortex. PloS one. 4 [PubMed]

Dahlem MA, Isele TM. (2013). Transient localized wave patterns and their application to migraine. Journal of mathematical neuroscience. 3 [PubMed]

Dahlem MA, Schumacher J, Hübel N. (2014). Linking a genetic defect in migraine to spreading depression in a computational model. PeerJ. 2 [PubMed]

Dahlem YA, Dahlem MA, Mair T, Braun K, Müller SC. (2003). Extracellular potassium alters frequency and profile of retinal spreading depression waves. Experimental brain research. 152 [PubMed]

DiFrancesco D, Noble D. (1985). A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philosophical transactions of the Royal Society of London. Series B, Biological sciences. 307 [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. Annals of biomedical engineering. 21 [PubMed]

Dreier JP. (2011). The role of spreading depression, spreading depolarization and spreading ischemia in neurological disease. Nature medicine. 17 [PubMed]

Ermentrout GB, Terman DH. (2010). Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics. 35

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]

Graf R et al. (2010). Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves Physica D. 239

Grafstein B. (1963). Neuronal release of potassium during spreading depression Brain Function Cortical Excitability And Steady Potentials.

Hadjikhani N et al. (2001). Mechanisms of migraine aura revealed by functional MRI in human visual cortex. Proceedings of the National Academy of Sciences of the United States of America. 98 [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. Frontiers in systems neuroscience. 7 [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. Experimental neurology. 238 [PubMed]

Hübel N, Schöll E, Dahlem MA. (2014). Bistable dynamics underlying excitability of ion homeostasis in neuron models. PLoS computational biology. 10 [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]

Leao AAP. (1944). Spreading depression of activity in the cerebral cortex J Neurophysiol. 7

Lee J, Kim SJ. (2010). Spectrum measurement of fast optical signal of neural activity in brain tissue and its theoretical origin. NeuroImage. 51 [PubMed]

Martins-Ferreira H, Nedergaard M, Nicholson C. (2000). Perspectives on spreading depression. Brain research. Brain research reviews. 32 [PubMed]

Reshodko LV, Bures J. (1975). Computer simulation of reverberating spreading depression in a network of cell automata. Biological cybernetics. 18 [PubMed]

Shapiro BE. (2001). Osmotic forces and gap junctions in spreading depression: a computational model. Journal of computational neuroscience. 10 [PubMed]

Somjen GG, Kager H, Wadman WJ. (2008). Computer simulations of neuron-glia interactions mediated by ion flux. Journal of computational neuroscience. 25 [PubMed]

Sukhotinsky I et al. (2010). Perfusion pressure-dependent recovery of cortical spreading depression is independent of tissue oxygenation over a wide physiologic range. Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism. 30 [PubMed]

Timofeev I, Bazhenov M, Sejnowski T, Steriade M. (2002). Cortical hyperpolarization-activated depolarizing current takes part in the generation of focal paroxysmal activities. Proceedings of the National Academy of Sciences of the United States of America. 99 [PubMed]

Tuckwell HC, Miura RM. (1978). A mathematical model for spreading cortical depression. Biophysical journal. 23 [PubMed]

Ullah G, Schiff SJ. (2010). Assimilating seizure dynamics. PLoS computational biology. 6 [PubMed]

Yao W, Huang H, Miura RM. (2011). A continuum neuronal model for the instigation and propagation of cortical spreading depression. Bulletin of mathematical biology. 73 [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 [PubMed]

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