Abstract

Cross-frequency coupling (CFC) has recently attracted a lot of attention in neuroscience, since it  enriches the cooperative behavior of neuronal networks and apparently plays 
an important functional role in neuronal computation, communication, and learning.
A number of methods to detect CFC have been proposed and criticaly evaluated , 
however, aprroaches for inferring its directionality are just beening developed.
We compare cross-frequency directionality (CFD), based on the phase slope index (PSI)
 with the conditional mutual information (CMI) known also as transfer entropy. The two methods
give contradictory results when applied to intracranial EEG data from an animal experiment.
We explain this contradiction using simulated data from unidirectionally coupled nonlinear
oscillators and demonstrate that, in nonlinear systems, the lead-lag relationship is not equivalent
to causality or the direction of coupling.