A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input

Biological cybernetics
A N Burkitt

Abstract

The integrate-and-fire neuron model is one of the most widely used models for analyzing the behavior of neural systems. It describes the membrane potential of a neuron in terms of the synaptic inputs and the injected current that it receives. An action potential (spike) is generated when the membrane potential reaches a threshold, but the actual changes associated with the membrane voltage and conductances driving the action potential do not form part of the model. The synaptic inputs to the neuron are considered to be stochastic and are described as a temporally homogeneous Poisson process. Methods and results for both current synapses and conductance synapses are examined in the diffusion approximation, where the individual contributions to the postsynaptic potential are small. The focus of this review is upon the mathematical techniques that give the time distribution of output spikes, namely stochastic differential equations and the Fokker-Planck equation. The integrate-and-fire neuron model has become established as a canonical model for the description of spiking neurons because it is capable of being analyzed mathematically while at the same time being sufficiently complex to capture many of the essential features of neu...Continue Reading

References

Mar 7, 1979·Journal of Theoretical Biology·H C Tuckwell
Dec 1, 1979·Biological cybernetics·D R Brillinger, J P Segundo
Sep 7, 1979·Journal of Theoretical Biology·D K Cope, H C Tuckwell
Mar 1, 1978·Biophysical Journal·H C Tuckwell
Apr 1, 1977·Computers and Biomedical Research, an International Journal·H G Nilsson
Apr 21, 1977·Journal of Theoretical Biology·H C Tuckwell
Feb 1, 1976·British Journal of Clinical Pharmacology·A V Mackay
Sep 1, 1976·The Journal of Physiology·H L Bryant, J P Segundo
Nov 30, 1976·Biological cybernetics·L M Ricciardi
Jan 2, 1976·Biological cybernetics·A V Holden
Apr 1, 1989·Mathematical Biosciences·P Lánský, C E Smith
Oct 1, 1985·Journal of Neurophysiology·D A McCormickD A Prince
Jan 1, 1988·Biological cybernetics·D R Brillinger
Jan 1, 1987·Biological cybernetics·P Lánský, V Lánská
Jul 1, 1986·IEEE Transactions on Bio-medical Engineering·W D O'NeillY C Ma
Jan 1, 1987·Biological cybernetics·P Lánský, T Radil
Jul 1, 1967·Biophysical Journal·D H PerkelG P Moore
Jun 1, 1972·The Journal of General Physiology·B W Knight
Jun 1, 1971·Kybernetik·R M Capocelli, L M Ricciardi
Jul 1, 1968·Journal of Neurophysiology·W H Calvin, C F Stevens
Jun 1, 1969·The Bulletin of Mathematical Biophysics·B K Roy, D R Smith
Mar 1, 1966·Journal of the Experimental Analysis of Behavior·J R Millenson
Apr 21, 1984·Journal of Theoretical Biology·P Lánský
Jan 1, 1982·Biological cybernetics·W J Wilbur, J Rinzel
Apr 7, 1980·Journal of Theoretical Biology·H C Tuckwell, D K Cope
Oct 1, 1995·Biological cybernetics·P LánskýF Tomassetti
Jun 9, 1995·Science·Z F Mainen, T J Sejnowski
Aug 1, 1994·Current Opinion in Neurobiology·M N Shadlen, W T Newsome
Feb 21, 1994·Journal of Theoretical Biology·V LánskáC E Smith
Jul 1, 1996·Neural Computation·B Ermentrout
Dec 1, 1996·Journal of Computational Neuroscience·D H Johnson
Apr 1, 1997·Neural Computation·A Destexhe
Jul 1, 1997·Neural Computation·M E Rudd, L G Brown
Sep 23, 1998·Neural Computation·B Ermentrout
Nov 6, 1998·Journal of Theoretical Biology·N Brunel, S Sergi
Jan 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·W Gerstner

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Citations

Jul 1, 2011·Journal of Mathematical Biology·Robert RosenbaumKrešimir Josić
May 25, 2012·Journal of Mathematical Biology·Susanne Ditlevsen, Priscilla Greenwood
Jun 21, 2012·Journal of Mathematical Biology·Grégory Dumont, Jacques Henry
Aug 25, 2007·Biological cybernetics·Paul FriedelJ Leo van Hemmen
Nov 18, 2008·Biological cybernetics·Laurent BadelMagnus J E Richardson
Jul 21, 2012·Biological cybernetics·Stefano Noventa, Giulio Vidotto
Dec 19, 2012·Biological cybernetics·Elisa Benedetto, Laura Sacerdote
Apr 6, 2013·Biological cybernetics·Christian R Huyck, Peter J Passmore
Nov 15, 2008·Cognitive Processing·Rune W Berg, Jørn Hounsgaard
Jun 12, 2009·Annals of Biomedical Engineering·Vasilis Z MarmarelisTheodore W Berger
Jul 31, 2007·Journal of Computational Neuroscience·Paul Mullowney, Satish Iyengar
Dec 11, 2008·Journal of Computational Neuroscience·Fabien MarpeauKresimir Josić
Dec 17, 2009·Journal of Computational Neuroscience·Douglas ZhouDavid Cai
Apr 12, 2011·Journal of Computational Neuroscience·Patrick JahnSusanne Ditlevsen
Sep 13, 2012·Journal of Computational Neuroscience·Nahal SharafiBenjamin Lindner
Feb 26, 2013·Bulletin of Mathematical Biology·Grégory Dumont, Jacques Henry
Jun 5, 2013·Cognitive Neurodynamics·Maurizio Mattia, Maria V Sanchez-Vives
Aug 12, 2009·Proceedings of the National Academy of Sciences of the United States of America·Simona CoccoRémi Monasson
Jun 1, 2010·Proceedings of the National Academy of Sciences of the United States of America·Raoul-Martin Memmesheimer
Aug 4, 2012·Journal of the Royal Society, Interface·Coraline LlorensOlivier Vincent
Mar 15, 2013·Journal of the Royal Society, Interface·Nitzan RazinOfer Feinerman
Jul 27, 2012·International Journal of Neural Systems·W K WongSys Leung
Jun 8, 2012·Journal of Neurophysiology·Joshua H GoldwynEric Shea-Brown
Sep 22, 2007·Neural Computation·Andreas KaltenbrunnerVicente López
May 12, 2009·Neural Computation·Hans E Plesser, Markus Diesmann
Jun 25, 2009·Neural Computation·Ram Krips, Miriam Furst
May 5, 2009·Neural Computation·Yoram BurakHaim Sompolinsky
Jul 9, 2010·Neural Computation·A BuonocoreL M Ricciardi
Feb 9, 2011·Neural Computation·Robert Rosenbaum, Krešimir Josić
Jul 8, 2011·Neural Computation·Sean ByrnesHamish Meffin
Sep 17, 2011·Neural Computation·Ryota KobayashiPetr Lansky
Feb 2, 2011·PLoS Computational Biology·Srdjan Ostojic, Nicolas Brunel
Apr 26, 2012·PLoS Computational Biology·Raoul-Martin Memmesheimer, Marc Timme
Mar 30, 2012·PLoS Computational Biology·James TrousdaleKrešimir Josić
Apr 18, 2013·PLoS Computational Biology·Adam Ponzi, Jeffery R Wickens

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