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This article is part of the supplement: Seventeenth Annual Computational Neuroscience Meeting: CNS*2008

Open Access Poster presentation

Comparison of methods to calculate exact spike times in integrate-and-fire neurons with exponential currents

Alexander Hanuschkin1*, Susanne Kunkel1*, Moritz Helias1, Abigail Morrison2 and Markus Diesmann12

Author Affiliations

1 Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University, 79104 Freiburg, Germany

2 Computational Neuroscience Group, RIKEN Brain Science Institute, Wako City, Saitama 351-0198, Japan

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BMC Neuroscience 2008, 9(Suppl 1):P131  doi:10.1186/1471-2202-9-S1-P131

The electronic version of this article is the complete one and can be found online at:

Published:11 July 2008

© 2008 Hanuschkin et al; licensee BioMed Central Ltd.

Poster presentation

Discrete-time neuronal network simulation strategies typically constrain spike times to a grid determined by the computational step size. This approach can have the effect of introducing artificial synchrony [1]. However, time-continuous approaches can be computationally demanding, both with respect to calculating future spike times and to event management, particularly for large network sizes. To address this problem, Morrison et al. [2] presented a general method of handling off-grid spiking in combination with exact subthreshold integration in discrete time driven simulations [3,4]. Within each time step an event-driven environment is emulated to process incoming spikes, whereas the timing of outgoing spikes is based on interpolation. Therefore, the computation step size is a decisive factor for both integration error and simulation time.

An alternative approach for calculating the exact spike times of integrate-and-fire neurons with exponential currents was recently published by Brette [5]. The problem of accurate detection of the first threshold crossing of the membrane potential is converted into finding the largest root of a polynomial. Common numerical means like Descartes' rule and Sturm's theorem are applicable. Although this approach was developed in the context of event-driven simulations, we take advantage of its ability to predict future threshold crossings in the time-driven environment of NEST [3]. We compare the accuracy of the two approaches in single-neuron simulations and the efficiency in a balanced random network of 10,000 neurons [6]. We show that the network simulation time when using the polynomial method depends only weakly on the computational step size, and the single neuron integration error is independent of it. Although the polynomial method attains the maximum precision expected from double numerics for all input rates and computation step sizes, the interpolation method is more efficient for input rates above a critical value. For applications where a lesser degree of precision is acceptable, the interpolation method is more efficient for all input rates.


Partially funded by DIP F1.2, BMBF Grant 01GQ0420 to the Bernstein Center for Computational Neuroscience Freiburg, and EU Grant 15879 (FACETS).


  1. Hansel D, Mato G, Meunier C, Neltner L: On numerical simulations of integrate-and-fire neural networks.

    Neural Comput 1998, 10(2):467-483. PubMed Abstract | Publisher Full Text OpenURL

  2. Morrison A, Straube S, Plesser HE, Diesmann M: Exact subthreshold integration with continuous spike times in discrete-time neural network simulations.

    Neural Comput 2007, 19(1):47-79. PubMed Abstract | Publisher Full Text OpenURL

  3. Gewaltig M-O, Diesmann M: NEST.

    Scholarpedia 2007, 2(4):1430. OpenURL

  4. Rotter S, Diesmann M: Exact digital simulation of time-invariant linear systems with applications to neuronal modeling.

    Biol Cybern 1999, 81(5–6):381-402. PubMed Abstract | Publisher Full Text OpenURL

  5. Brette R: Exact simulation of integrate-and-fire models with exponential currents.

    Neural Comput 2007, 19(10):2604-2609. PubMed Abstract | Publisher Full Text OpenURL

  6. Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.

    J Comput Neurosci 2000, 8(3):183-208. PubMed Abstract | Publisher Full Text OpenURL