title: Parametric estimation of cross-frequency coupling.
abstract: BACKGROUND
  Growing experimental evidence suggests an important role for cross-frequency coupling in neural processing, in particular for phase-amplitude coupling (PAC). Although the details of methods to detect PAC may vary, a common procedure to estimate the significance level is the comparison of observed values to those of at least 100 surrogate time series. When scanning large parts of the frequency spectrum and multiple recording sites, this could amount to very large computation times.
  
  
  METHODS
  We demonstrate that the general linear model (GLM) allows for a parametric estimation of significant PAC. Continuous recordings are split into epochs, of a few seconds duration, on which an F-test can be performed. We compared its performance against traditional non-parametric permutation tests in both simulated and experimental data.
  
  
  RESULTS
  Our method was able to reproduce findings of phase-amplitude coupling in local field potential recordings obtained from the subthalamic nucleus in patients with Parkinson's disease. We also show that PAC may be detected between the subthalamic nucleus and cortical motor areas.
  
  
  CONCLUSIONS
  Although the GLM slightly underestimated significance compared to permutation tests in the simulations, for experimental data the two methods produced highly similar results. Computation times were drastically lower for the GLM. Furthermore, we demonstrate that the GLM can be easily extended by including additional predictors such as low-frequency amplitude to test for amplitude-amplitude coupling.
  
  
  CONCLUSIONS
  The GLM forms an adequate and computationally efficient approach for detecting cross-frequency coupling with the flexibility to add other explanatory variables of interest.
authors: Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, 12 Queen Square, WC1N 3BG London, UK. Electronic address: b.vanwijk@ucl.ac.uk.
authors: B C M
authors: BC
authors: van Wijk
authors: Sobell Department of Motor Neuroscience and Movement Disorders, UCL Institute of Neurology, 33 Queen Square House, Queen Square, WC1N 3BG London, UK.
authors: A
authors: A
authors: Jha
authors: Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, 12 Queen Square, WC1N 3BG London, UK.
authors: W
authors: W
authors: Penny
authors: Wellcome Trust Centre for Neuroimaging, UCL Institute of Neurology, 12 Queen Square, WC1N 3BG London, UK.
authors: V
authors: V
authors: Litvak
mesh_terms: D000978:Antiparkinson Agents / Q000627:therapeutic use; D003198:Computer Simulation; D046690:Deep Brain Stimulation / Q000379:methods; D006801:Humans; D016014:Linear Models; D015225:Magnetoencephalography / Q000379:methods; D009044:Motor Cortex / Q000187:drug effects / Q000503:physiopathology; D010300:Parkinson Disease / Q000503:physiopathology / Q000628:therapy; D012815:Signal Processing, Computer-Assisted; D020531:Subthalamic Nucleus / Q000187:drug effects / Q000503:physiopathology; D013997:Time Factors
chemical_list: D000978:Antiparkinson Agents
keywords: Beta band; Connectivity; Deep brain stimulation (DBS); Magnetoencephalography (MEG); Nested oscillations; Power fluctuations