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This article is part of the supplement: Twentieth Annual Computational Neuroscience Meeting: CNS*2011

Open Access Poster presentation

Fail-safe detection of threshold crossings of linear integrate-and-fire neuron models in time-driven simulations

Susanne Kunkel12*, Moritz Helias3, Markus Diesmann345 and Abigail Morrison123

Author Affiliations

1 Functional Neural Circuits Group, Faculty of Biology, Albert-Ludwig University of Freiburg, Germany

2 Bernstein Center Freiburg, Albert-Ludwig University of Freiburg, Germany

3 RIKEN Brain Science Institute, Wako, Japan

4 Institute of Neuroscience and Medicine (INM-6), Computational and Systems Neuroscience, Research Center Jülich, Germany

5 RIKEN Computational Science Research Program, Wako, Japan

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BMC Neuroscience 2011, 12(Suppl 1):P229  doi:10.1186/1471-2202-12-S1-P229

The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/12/S1/P229


Published:18 July 2011

© 2011 Kunkel et al; licensee BioMed Central Ltd.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Poster presentation

The characteristics of time-driven simulation are a fixed-size simulation step and a fixed-size communication interval [1]. The former defines update-and-check points, which are the discrete points in time when all neurons update their state variables and check for a super-threshold membrane potential. The latter defines the discrete points in time when all neurons communicate their spikes. The communication interval is a multiple of the simulation step size and limited only by the minimum synaptic transmission delay in the network.

The time-driven environment of the simulator NEST [2] provides an 'on-grid' and an 'off-grid' framework that handle spikes differently. In the on-grid framework, spikes are incorporated, detected and emitted only at the pre-defined update-and-check points. In the off-grid framework, spikes can be incorporated and emitted at any point in time [3]. For each neuron the arrival times of incoming spikes introduce additional update-and-check points. Hence, the simulation step can be increased up to the size of the communication interval. The detection of a threshold crossing can only take place at a check point, but the timing of the referring spike is estimated with precision limited only by the limits of double representation.

In general, a time-driven simulator that supports the off-grid framework performs neural network simulations with the same precision and faster than an event-driven simulator [4]. However, time-driven simulation still bears the risk of missing a threshold crossing as a very brief excursion of the membrane potential above threshold may not be detected at the next check point. In the off-grid framework, this problem is more pronounced in networks with low connectivity and strong coupling as well as in the case of low firing rates. The on-grid framework is even more affected due to fewer check points and the synchronized arrival of spikes.

Here, we present algorithms which are guaranteed to detect all threshold crossings by supplementing the standard test for a super-threshold membrane potential at each check point and that exploit the information about the neuronal state at nearby check points. These additional tests need to be invoked whenever the membrane potential is sub-threshold, which means at virtually all check points. We develop sub-tests of increasing complexity and specificity, starting with simple sifting methods and ending up with a complex expression that faithfully indicates the existence of a threshold crossing between the last and the current check point. An analysis of the test specificities and computational costs results in a cascade of tests which locates all threshold crossings at a low computational cost.

Acknowledgements

Partially funded by BMBF Grant 01GQ0420 to BCCN Freiburg, EU Grant 15879 (FACETS), EU Grant 269921 (BrainScaleS), the Helmholtz Alliance on Systems Biology (Germany), the Next-Generation Supercomputer Project of MEXT (Japan), Neurex, and the Junior Professor Program of Baden-Württemberg.

References

  1. Morrison A, Mehring C, Geisel T, Aertsen AD, Diesmann M: Advancing the boundaries of high-connectivity network simulation with distributed computing.

    Neural Comput 2005, 17(8):1776-1801. PubMed Abstract | Publisher Full Text OpenURL

  2. Gewaltig M-O, Diesmann M: NEST (Neural Simulation Tool).

    Scholarpedia 2007, 2(4):1430. Publisher Full Text OpenURL

  3. 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

  4. Hanuschkin A, Kunkel S, Helias M, Morrison A, Diesmann M: A general and efficient method for incorporating precise spike times in globally time-driven simulations.

    Front. Neuroinform 2010, 4:113. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL