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International Journal of Neuroscience Volume 12, 1981 - Issue 2
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Original Article

Simplified Reaction-Diffusion Equations for Potassium and Calcium Ion Concentrations During Spreading Cortical Depression

Henry C. Tuckwell Department of Mathematics, Monash University, Clayton, Victoria, Australia, 3168View further author information
Pages 95-107 | Received 11 Jun 1980, Published online: 07 Jul 2009

Citations (17)

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HENRYC. TUCKWELL. (1988) Use of Green's function matrices for systems of diffusion equations. International Journal of Systems Science 19:8, pages 1663-1666.
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Articles from other publishers (16)

Pratyush Suryavanshi, Katelyn M. Reinhart, C. William Shuttleworth & K. C. Brennan. (2022) Action Potentials Are Critical for the Propagation of Focally Elicited Spreading Depolarizations. The Journal of Neuroscience 42:11, pages 2371-2383.
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Reza Torabi & Jörn Davidsen. (2019) Pattern formation in reaction-diffusion systems in the presence of non-Markovian diffusion. Physical Review E 100:5.
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Markus A. Dahlem. 2017. Neurobiological Basis of Migraine. Neurobiological Basis of Migraine 285 305 .
Rosemary O’Connell & Yoichiro Mori. (2016) Effects of Glia in a Triphasic Continuum Model of Cortical Spreading Depression. Bulletin of Mathematical Biology 78:10, pages 1943-1967.
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Yoichiro Mori. (2015) A multidomain model for ionic electrodiffusion and osmosis with an application to cortical spreading depression. Physica D: Nonlinear Phenomena 308, pages 94-108.
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Markus A. Dahlem, Bernd Schmidt, Ingo Bojak, Sebastian Boie, Frederike Kneer, Nouchine Hadjikhani & Jürgen Kurths. (2015) Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized. Frontiers in Computational Neuroscience 9.
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Bas-Jan Zandt, Bennie ten Haken, Michel J.A.M. van Putten & Markus A. Dahlem. (2015) How does spreading depression spread? Physiology and modeling. Reviews in the Neurosciences 26:2.
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Bas-Jan Zandt, Bennie ten Haken & Michel J. A. M. van Putten. (2013) Diffusing Substances during Spreading Depolarization: Analytical Expressions for Propagation Speed, Triggering, and Concentration Time Courses. The Journal of Neuroscience 33:14, pages 5915-5923.
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Jos? Antonio Villacorta-Atienza & Valeri A. Makarov. (2013) Wave-Processing of Long-Scale Information by Neuronal Chains. PLoS ONE 8:2, pages e57440.
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D.E. Postnov, D.D. Postnov & L. Schimansky-Geier. (2012) Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression. Brain Research 1434, pages 200-211.
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Markus A. Dahlem, Rudolf Graf, Anthony J. Strong, Jens P. Dreier, Yuliya A. Dahlem, Michaela Sieber, Wolfgang Hanke, Klaus Podoll & Eckehard Sch?ll. (2010) Two-dimensional wave patterns of spreading depolarization: Retracting, re-entrant, and stationary waves. Physica D: Nonlinear Phenomena 239:11, pages 889-903.
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Hewerson Zansávio Teixeira, Antônio-Carlos Guimarães Almeida, Antonio Fernando Catelli Infantosi, Michelle Almeida Vasconcelos & Mário Antônio Duarte. (2004) Simulation of the effect of Na + and Cl   on the velocity of a spreading depression wave using a simplified electrochemical model of synaptic terminals . Journal of Neural Engineering 1:2, pages 117-126.
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George G. Somjen. (2001) Mechanisms of Spreading Depression and Hypoxic Spreading Depression-Like Depolarization. Physiological Reviews 81:3, pages 1065-1096.
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Henry C Tuckwell. (1988) Perturbative analysis of random nonlinear reaction-diffusion systems. Physica Scripta 37:3, pages 321-322.
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Henry C. Tuckwell. 1988. Biomathematics and Related Computational Problems. Biomathematics and Related Computational Problems 581 590 .
Ronald J. MacGregor. 1987. Neural and Brain Modeling. Neural and Brain Modeling 108 131 .

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