Parametric estimation of cross-frequency coupling

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.

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.

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.

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.

The GLM forms an adequate and computationally efficient approach for detecting cross-frequency coupling with the flexibility to add other explanatory variables of interest.