BMC Neuroscience

, 16:P156 | Cite as

Pattern recognition of Hodgkin-Huxley equations by auto-regressive Laguerre Volterra network

Open Access
Poster presentation

Keywords

Simulated Annealing Refractory Period Algorithm Simulated Annealing Convergence Problem Cross Term 
A nonparametric, data-driven nonlinear auto-regressive Volterra (NARV) [1] model has been successfully applied for capturing the dynamics in the generation of action potentials, which is classically modeled by Hodgkin-Huxley (H-H) equations. However, the compactness still need to be improved for further interpretations. Therefore, we propose a novel Auto-regressive Sparse Laguerre Volterra Network (ASLVN) model (shown in Figure 1A), which is developed from traditional Laguerre Volterra Network (LVN) and principal dynamic mode (PDM) framework [2].
Figure 1

A Structure of ASLVN for modeling H-H equations, where the input x(n) is the randomly injected current and the output y*(n) is the membrane potential. B The predictions results, z(1) represents the exogenous output, z(2) represents the autoregressive output and z(x) represents the cross term output.

We adopt stochastic global optimization algorithm Simulated Annealing [3] to train the ASLVN instead of Back-propagation method [2] to avoid local minima and convergence problems. We also use lasso regularization [4] to enhance the spasity of the network and prune redundant branches for parsimony. The prediction results are shown in Fig.1B, it can be seen that the exogenous output z(1) represents the subthreshold dynamics in phase III, and the autoregressive output z(2) dominates in the spike shape in phase I, and the cross term output z(x) helps to maintain the refractory period by cancelling the effect of z(1) in phase II and we also observe that refractory inhibition effect decays after initiation of AP, which explains the absolute refractory period and relative refractory period in physiology.

References

  1. 1.
    Eikenberry SE, Marmarelis VZ: A nonlinear autoregressive Volterra model of the Hodgkin-Huxley equations. Journal of computational neuroscience. 2013, 34 (1): 163-183.PubMedCrossRefGoogle Scholar
  2. 2.
    Marmarelis VZ: Nonlinear dynamic modeling of physiological systems. John Wiley & Sons. 2004, 10:Google Scholar
  3. 3.
    Kirkpatrick S: Optimization by simmulated annealing. science. 1983, 220 (4598): 671-680.PubMedCrossRefGoogle Scholar
  4. 4.
    Tibshirani R: Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B (Methodological). 1996, 267-288.Google Scholar

Copyright information

© Geng and Marmarelis 2015

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Authors and Affiliations

  1. 1.Biomedical Engineering DepartmentUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Biomedical Simulations ResourceLos AngelesUSA

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