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Efficient spike tests for linear integrate-and-fire neuron models in time-driven simulations

Susanne Kunkel1, 2*, Moritz Helias3, Markus Diesmann3, 4, 5, 6 and Abigail Morrison1, 2
  • 1 Albert-Ludwig University of Freiburg, Faculty of Biology, Germany
  • 2 Albert-Ludwig University of Freiburg, Bernstein Center Freiburg, Germany
  • 3 Research Center Jülich, Computational and Systems Neuroscience, Germany
  • 4 RIKEN Computational Science Research Program, Japan
  • 5 RIKEN Brain Science Institute, Japan
  • 6 RWTH Aachen University, Medical Faculty, Germany

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.

Traditionally, spikes are incorporated, detected and emitted only at the pre-defined update-and-check points. However, the time-driven environment of the simulator NEST [2] provides an 'off-grid' framework that enables spikes to be be incorporated and emitted at any point in time [3,4]. For each neuron the arrival times of incoming spikes introduce additional update-and-check points.

As the detection of a threshold crossing can only take place at the next check point, time-driven simulation still bears the risk of missing a threshold crossing: a very brief excursion of the membrane potential above threshold may not be detected. This problem is more pronounced in networks with low connectivity and strong coupling as well as in the case of low firing rates.

Here, we investigate spike tests of increasing complexity and specificity that can supplement the standard test for a super-threshold membrane potential at each check point and that guarantee the detection of all threshold crossings. Firstly, we determine the specificities of simple sifting methods for a range of input scenarios. Secondly, we compare the performances of complex spike tests which faithfully indicate the existence of a threshold crossing between the last and the current check point. This stepwise analysis enables us to identify 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.
2. Gewaltig M-O, Diesmann M: NEST (Neural Simulation Tool). Scholarpedia 2007, 2(4):1430.
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.
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.

Keywords: dynamical systems, networks, Neurons, precise spike times, Simulation Technology, time-driven simulation

Conference: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.

Presentation Type: Poster

Topic: neurons, networks and dynamical systems (please use "neurons, networks and dynamical systems" as keywords)

Citation: Kunkel S, Helias M, Diesmann M and Morrison A (2011). Efficient spike tests for linear integrate-and-fire neuron models in time-driven simulations. Front. Comput. Neurosci. Conference Abstract: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011. doi: 10.3389/conf.fncom.2011.53.00049

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Received: 23 Aug 2011; Published Online: 04 Oct 2011.

* Correspondence: Ms. Susanne Kunkel, Albert-Ludwig University of Freiburg, Faculty of Biology, Freiburg i. Br., Germany, su.kunkel@fz-juelich.de