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

PLoS Comput Biol. 2017 Dec 11;13(12):e1005893. doi: 10.1371/journal.pcbi.1005893. eCollection 2017 Dec.


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials
  • Brain / physiology*
  • Models, Neurological*
  • Neurons / physiology

Grant support

This work was supported by the European research council ( Starting Grant SLAB ERC-YStG-676943 to AG, the European research council ( Starting Grant MindTime ERC-YStG-263584 to VW, the agence nationale pour la recherche ( ANR-16-CE37-0004-04 AutoTime to VD and VW, and the université Paris-Saclay ( IDEX NoTime to VD, AG and VW. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.