Skip to main content
SpringerLink
Log in

Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains

  • Original Paper
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

An experimentally recorded time series formed by the exact times of occurrence of the neuronal spikes (spike train) is likely to be affected by observational noise that provokes events mistakenly confused with neuronal discharges, as well as missed detection of genuine neuronal discharges. The points of the spike train may also suffer a slight jitter in time due to stochastic processes in synaptic transmission and to delays in the detecting devices. This study presents a procedure aimed at filtering the embedded noise (denoising the spike trains) the spike trains based on the hypothesis that recurrent temporal patterns of spikes are likely to represent the robust expression of a dynamic process associated with the information carried by the spike train. The rationale of this approach is tested on simulated spike trains generated by several nonlinear deterministic dynamical systems with embedded observational noise. The application of the pattern grouping algorithm (PGA) to the noisy time series allows us to extract a set of points that form the reconstructed time series. Three new indices are defined for assessment of the performance of the denoising procedure. The results show that this procedure may indeed retrieve the most relevant temporal features of the original dynamics. Moreover, we observe that additional spurious events affect the performance to a larger extent than the missing of original points. Thus, a strict criterion for the detection of spikes under experimental conditions, thus reducing the number of spurious spikes, may raise the possibility to apply PGA to detect endogenous deterministic dynamics in the spike train otherwise masked by the observational noise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Dayhoff, J.E., Gerstein, G.L.: Favored patterns in spike trains. I. Detection. J. Neurophysiol. 49, 1334–1348 (1983)

    Google Scholar 

  2. Abeles, M., Gerstein, G.: Detecting spatiotemporal firing patterns among simultaneously recorded single neurons. J. Neurophysiol. 60, 909–924 (1988)

    Google Scholar 

  3. Villa, A.E.P., Abeles, M.: Evidence for spatiotemporal firing patterns within the auditory thalamus of the cat. Brain Res. 509, 325–327 (1990)

    Article  Google Scholar 

  4. Prut, Y., Vaadia, E., Bergman, H., Haalman, I., Slovin, H., Abeles, M.: Spatiotemporal structure of cortical activity—properties and behavioral relevance. J. Neurophysiol. 79, 2857–2874 (1998)

    Google Scholar 

  5. Tetko, I.V., Villa, A.E.P.: A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings. J. Neurosci. Methods 105, 15–24 (2001)

    Article  Google Scholar 

  6. Villa, A.E.P., Tetko, I.V., Hyland, B., Najem, A.: Spatiotemporal activity patterns of rat cortical neurons predict responses in a conditioned task. Proc. Natl. Acad. Sci. U. S. A. 96, 1006–1011 (1999)

    Article  Google Scholar 

  7. Villa, A.E.P.: Spatio-temporal patterns of spike occurrences in freely-moving rats associated to perception of human vowels. In: König, R., Heil, P., Budinger, E., Scheich, H. (eds.) Auditory Cortex: [T]owards a Synthesis of Human and Animal Research, chap. 17, pp. 241–254. Lawrence Erlbaum, Oxford (2005)

    Google Scholar 

  8. Tetko, I.V., Villa, A.E.P.: A comparative study of pattern detection algorithm and dynamical system approach using simulated spike trains. Lect. Notes Comput. Sci. 1327, 37–42 (1997)

    Article  Google Scholar 

  9. Tetko, I.V., Villa, A.E.P.: Fast combinatorial methods to estimate the probability of complex temporal patterns of spikes. Biol. Cybern. 76, 397–407 (1997)

    Article  MATH  Google Scholar 

  10. Tetko, I.V., Villa, A.E.P.: A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 1. Detection of repeated patterns. J. Neurosci. Methods 105, 1–14 (2001)

    Article  Google Scholar 

  11. Abeles, M., Gat, I.: Detecting precise firing sequences in experimental data. J. Neurosci. Methods 107, 141–154 (2001)

    Article  Google Scholar 

  12. Asai, Y., Yokoi, T., Villa, A.E.P.: Detection of a dynamical system attractor from spike train analysis. Lect. Notes Comput. Sci. 4131, 623–631 (2006)

    Article  Google Scholar 

  13. Zaslavskii, G.M.: The simplest case of a strange attractor. Phys. Lett. 69A, 145–147 (1978)

    ADS  MathSciNet  Google Scholar 

  14. Ikeda, K.: Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 30, 257–261 (1979)

    Article  ADS  Google Scholar 

  15. Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9, 1465–1466 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Abeles, M.: Local Cortical Circuits. Springer, Heidelberg (1982)

    Google Scholar 

  17. Villa, A.E.P., Tetko, I.V.: Spatiotemporal activity patterns detected from single cell measurements from behaving animals. Proc. SPIE 3728, 20–34 (1999)

    Article  ADS  Google Scholar 

  18. Rapp, P.E.: Chaos in the neurosciences: cautionary tales from the frontier. Biologist 40, 89–94 (1993)

    Google Scholar 

  19. Celletti, A., Villa, A.E.P.: Determination of chaotic attractors in the rat brain. J. Stat. Phys. 84, 1379–1385 (1996)

    Article  ADS  Google Scholar 

  20. Celletti, A., Villa, A.E.P.: Low dimensional chaotic attractors in the rat brain. Biol. Cybern. 74, 387–394 (1996)

    Article  Google Scholar 

  21. Celletti, A., Bajo Lorenzana, V.M., Villa, A.E.P.: Correlation dimension for two experimental time series. J. Stat. Phys. 89, 877–884 (1997)

    MATH  ADS  Google Scholar 

  22. Celletti, A., Froeschlé, C., Tetko, I.V., Villa, A.E.P.: Deterministic behaviour of short time series. Meccanica 34, 145–152 (1999)

    Article  Google Scholar 

  23. Izhikevich, E.M.: Neural excitability, spiking and bursting. Int. J. Bifurc. Chaos 10, 1170–1266 (2000)

    MathSciNet  Google Scholar 

  24. Asai, Y., Yokoi, T., Villa, A.E.P.: Deterministic nonlinear spike train filtered by spiking neuron model. Lect. Notes Comput. Sci. 4668, 924–933 (2007)

    Article  Google Scholar 

  25. Kostelich, E.J., Schreiber, T.: Noise reduction in chaotic time-series data: a survey of common methods. Phys. Rev. E 48, 1752–1763 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  26. Aksenova, T.I., Chibirova, O., Dryga, A.O., Tetko, I.V., Benabid, A., Villa, A.E.P.: An un-supervised automatic method for sorting neuronal spike waveforms in awake and freely moving animal. Methods 30, 178–187 (2003)

    Article  Google Scholar 

  27. Asai, Y., Aksenova, T.I., Villa, A.E.P.: On-line real-time oriented application for neuronal spike sorting with unsupervised learning. Lect. Notes Comput. Sci. 3696, 109–114 (2005)

    Article  Google Scholar 

  28. Segundo, J.P.: Nonlinear dynamics of point process systems and data. Int. J. Bifurc. Chaos 13, 2035–2116 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

This study was partially funded by the binational JSPS/INSERM grant SYRNAN (2007–2008) and the Japan–France Research Cooperative Program.

Author information

Authors and Affiliations

  1. The Center for Advanced Medical Engineering and Informatics, Osaka University, Japan, Machikaneyama 1-3, Toyonaka, Osaka, 560-8531, Japan

    Yoshiyuki Asai

  2. Grenoble Institut des Neurosciences, CR Inserm U 836-UJF-CEA-CHU, Université Joseph Fourier, Equipe 7 - NeuroHeuristic Research Group, UJF Site Santé - La Tronche BP 170, 38042, Grenoble Cedex 9, France

    Alessandro E. P. Villa

  3. Neuroheuristic Research Group, Information Science Institute, HEC-University of Lausanne, Lausanne, Switzerland

    Yoshiyuki Asai & Alessandro E. P. Villa

Authors
  1. Yoshiyuki Asai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alessandro E. P. Villa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessandro E. P. Villa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Asai, Y., Villa, A.E.P. Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains. J Biol Phys 34, 325–340 (2008). https://doi.org/10.1007/s10867-008-9093-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-008-9093-0

Keywords

Search

Navigation