A Review of the Integrateandfire Neuron Model: I. Homogeneous Synaptic Input
 A. N. Burkitt
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The integrateandfire 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 integrateandfire 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 neural processing. A number of variations of the model are discussed, together with the relationship with the Hodgkin–Huxley neuron model and the comparison with electrophysiological data. A brief overview is given of two issues in neural information processing that the integrateandfire neuron model has contributed to – the irregular nature of spiking in cortical neurons and neural gain modulation.
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 Title
 A Review of the Integrateandfire Neuron Model: I. Homogeneous Synaptic Input
 Journal

Biological Cybernetics
Volume 95, Issue 1 , pp 119
 Cover Date
 20060701
 DOI
 10.1007/s0042200600686
 Print ISSN
 03401200
 Online ISSN
 14320770
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Integrateandfire neuron
 Neural models
 Conductance models
 Industry Sectors
 Authors

 A. N. Burkitt ^{(1)} ^{(2)}
 Author Affiliations

 1. The Bionic Ear Institute, 384–388 Albert Street, East Melbourne, VIC, 3002, Australia
 2. Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC, 3010, Australia