A surface plot of Bundt-gamma distribution, which is a probability distribution that describes the average phase of a group of waves. Image credit: Dimmock et al. (CC BY 4.0)
Phase coherence is a measurement of waves, for example, brain waves, which quantifies the similarity of their oscillatory behaviour at a fixed frequency. That is, while the waves may vibrate the same number of times per minute, the relative timing of the waves with respect to each other may be different (incoherent) or similar (coherent).
In neuroscience, scientists study phase coherence in brain waves to understand how the brain responds to external stimuli, for example if they occur at a fixed frequency during an experiment. To do this, phase coherence is usually quantified with a statistic known as ‘inter-trial phase coherence’ (ITPC). When ITPC equals one, the waves are perfectly coherent, that is, there is no shift between the two waves and the peaks and troughs occur at exactly the same time. When ITPC equals zero, the waves are shifted from each other in an entirely random way.
Phase coherence can also be modelled on phase angles – which describe the shift in each wave relative to a reference angle of zero – and wrapped distributions. Wrapped distributions are probability distributions over phase angles that express their relative likelihood. Wrapped distributions have statistics, including a mean and a variance. The variance of a wrapped distribution can be used to model phase coherence because it explicitly represents the similarity of phase angles relative to the mean: larger variance means less coherence.
While the ITPC is a popular method for analysing phase coherence, it is a so-called ‘summary statistic’. Analyses using the ITPC discard useful information in the trial-to-trial-level data, which might not be lost using phase angles.
Thus, Dimmock, O’Donnell and Houghton set out to determine whether they could create a model of phase coherence that works directly on phase angles (rather than on the ITPC) and yields better results than existing methods.
Dimmock, O’Donnell and Houghton compare their model to the ITPC using both experimental and simulated data. The comparison demonstrates that their model can detect entrainment of the brain to grammatical phrases compared to ungrammatical ones at smaller sample sizes than ITPC, and with fewer false positives. Traditional tools for studying how the brain processes language often yield a lot of noise in the data, which makes it difficult to analyse measurements. Dimmock, O’Donnell and Houghton demonstrates that the brain is not simply responding to the ‘surprise factor’ of words in a phrase, as some have suggested, but also to their grammatical category.
These results of this study will benefit scientists who analyse phase coherence. By using the model in addition to other approaches to study phase coherence, researchers can provide a different perspective on their results and potentially identify new features in their data. This will be particularly powerful in studies with small sample sizes, such as pilot studies where maximising the use of data is important.
