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Non-linear auto-regressive models for cross-frequency coupling in neural time series

Author

Listed:
  • Tom Dupré la Tour
  • Lucille Tallot
  • Laetitia Grabot
  • Valérie Doyère
  • Virginie van Wassenhove
  • Yves Grenier
  • Alexandre Gramfort

Abstract

We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling.Author summary: Neural oscillations synchronize information across brain areas at various anatomical and temporal scales. Of particular relevance, slow fluctuations of brain activity have been shown to affect high frequency neural activity, by regulating the excitability level of neural populations. Such cross-frequency-coupling can take several forms. In the most frequently observed type, the power of high frequency activity is time-locked to a specific phase of slow frequency oscillations, yielding phase-amplitude-coupling (PAC). Even when readily observed in neural recordings, such non-linear coupling is particularly challenging to formally characterize. Typically, neuroscientists use band-pass filtering and Hilbert transforms with ad-hoc correlations. Here, we explicitly address current limitations and propose an alternative probabilistic signal modeling approach, for which statistical inference is fast and well-posed. To statistically model PAC, we propose to use non-linear auto-regressive models which estimate the spectral modulation of a signal conditionally to a driving signal. This conditional spectral analysis enables easy model selection and clear hypothesis-testing by using the likelihood of a given model. We demonstrate the advantage of the model-based approach on three datasets acquired in rats and in humans. We further provide novel neuroscientific insights on previously reported PAC phenomena, capturing two mechanisms in PAC: influence of amplitude and directionality estimation.

Suggested Citation

  • Tom Dupré la Tour & Lucille Tallot & Laetitia Grabot & Valérie Doyère & Virginie van Wassenhove & Yves Grenier & Alexandre Gramfort, 2017. "Non-linear auto-regressive models for cross-frequency coupling in neural time series," PLOS Computational Biology, Public Library of Science, vol. 13(12), pages 1-32, December.
  • Handle: RePEc:plo:pcbi00:1005893
    DOI: 10.1371/journal.pcbi.1005893
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    References listed on IDEAS

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    4. Laura Lee Colgin & Tobias Denninger & Marianne Fyhn & Torkel Hafting & Tora Bonnevie & Ole Jensen & May-Britt Moser & Edvard I. Moser, 2009. "Frequency of gamma oscillations routes flow of information in the hippocampus," Nature, Nature, vol. 462(7271), pages 353-357, November.
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