Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks

Aaditya Rangan, David Cai

Research output: Contribution to journalArticle

Abstract

We discuss numerical methods for simulating large-scale, integrate-and-fire (I&F) neuronal networks. Important elements in our numerical methods are (i) a neurophysiologically inspired integrating factor which casts the solution as a numerically tractable integral equation, and allows us to obtain stable and accurate individual neuronal trajectories (i.e., voltage and conductance time-courses) even when the I&F neuronal equations are stiff, such as in strongly fluctuating, high-conductance states; (ii) an iterated process of spike-spike corrections within groups of strongly coupled neurons to account for spike-spike interactions within a single large numerical time-step; and (iii) a clustering procedure of firing events in the network to take advantage of localized architectures, such as spatial scales of strong local interactions, which are often present in large-scale computational models - for example, those of the primary visual cortex. (We note that the spike-spike corrections in our methods are more involved than the correction of single neuron spike-time via a polynomial interpolation as in the modified Runge-Kutta methods commonly used in simulations of I&F neuronal networks.) Our methods can evolve networks with relatively strong local interactions in an asymptotically optimal way such that each neuron fires approximately once in InlineEquation O(N) operations, where N is the number of neurons in the system. We note that quantifications used in computational modeling are often statistical, since measurements in a real experiment to characterize physiological systems are typically statistical, such as firing rate, interspike interval distributions, and spike-triggered voltage distributions. We emphasize that it takes much less computational effort to resolve statistical properties of certain I&F neuronal networks than to fully resolve trajectories of each and every neuron within the system. For networks operating in realistic dynamical regimes, such as strongly fluctuating, high-conductance states, our methods are designed to achieve statistical accuracy when very large time-steps are used. Moreover, our methods can also achieve trajectory-wise accuracy when small time-steps are used.

Original languageEnglish (US)
Pages (from-to)81-100
Number of pages20
JournalJournal of Computational Neuroscience
Volume22
Issue number1
DOIs
StatePublished - Feb 2007

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Neurons
Visual Cortex
Cluster Analysis

Keywords

  • Network architecture
  • Numerical algorithm

ASJC Scopus subject areas

  • Neuroscience(all)

Cite this

Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks. / Rangan, Aaditya; Cai, David.

In: Journal of Computational Neuroscience, Vol. 22, No. 1, 02.2007, p. 81-100.

Research output: Contribution to journalArticle

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