Is partial coherence a viable technique for identifying generators of neural oscillations?

Partial coherence measures the linear relationship between two signals after the influence of a third signal has been removed. Gersch proposed in 1970 that partial coherence could be used to identify sources of driving for multivariate time series. This idea, referred to in this paper as Gersch Causality, has received wide acceptance and has been applied extensively to a variety of fields in the signal processing community. Neurobiological data from a given sensor include both the signals of interest and other unrelated processes collectively referred to as measurement noise. We show that partial-coherence-based Gersch Causality is extremely sensitive to signal-to-noise ratio; that is, for a group of three or more simultaneously recorded time series, the time series with the highest signal-to-noise ratio (i.e., relatively noise free) is often identified as the "driver" of the group, irrespective of the true underlying patterns of connectivity. This hypothesis is tested both theoretically and on experimental time series acquired from limbic brain structures during the theta rhythm.