Measuring functional connectivity of the brain

The rich temporal content of measurements of electromagnetic activity, including electroencephalography (EEG) and magnetoencephalography (MEG), allow researchers to study dynamic functional networks in the human brain. However, it is difficult to turn this data into meaningful conclusions about those brain networks. In this dissertation, we describe the theoretical relationships between different interaction measures, followed by development of novel measures to address classical nuisance of cross-talk in brain electrophysiological recordings. ❧ Coherence and phase locking value (PLV) are widely used measures that can reveal interactions between electrophysiological signals within a frequency range of interest. We investigate the statistical properties of the PLV by describing two distributions that are widely used to a priori model phase interactions. The first of these is the von Mises distribution, for which the standard sample PLV is a maximum likelihood estimator. The second is the relative phase distribution derived from bivariate circularly symmetric complex Gaussian data. We derive an explicit expression for the PLV for this distribution and show that it is a function of the coherence between the two signals. We then compare results via local field potential data from a visually-cued motor study in macaque for the two different PLV estimators and conclude that, for this data, the sample PLV provides equivalent information to the coherence of the two complex time series. This result reduces the analysis of time-locked activity between signals to the computation of coherence rather than coherence and PLV. ❧ Since the PLV is a bivariate measure (that is, it is computed pairwise between signals) it cannot differentiate between direct and indirect connections in a multidimensional network. A non-parametric partial phase synchronization index attempted to resolve this problem by extending sample PLV to the multivariate case using the same mechanism relating correlation to partial correlation. Here we derive an analytical expression for partial PLV for a multivariate circular complex Gaussian model and show that partial PLV can be computed from partial coherence. We demonstrate our method in simulations with Roessler oscillators and experimental data of multichannel local field potentials from a macaque monkey. We show that the multivariate circular complex Gaussian model suggests similar synchronization networks. In addition, the circular complex Gaussian model has a lower variance in the estimation of partial PLV. ❧ Interpretation of functional connectivity from EEG/MEG data is challenging due to cross-talk problem between signals of interest. For example, coherence may yield spuriously large values leading false positive connections. Approaches such as imaginary coherence, phase lag index, lagged coherence and orthogonal coherence have been proposed to overcome this problem. The common assumption of these measures is that time-lagged interactions are more robust to cross-talk than instantaneous interactions. However, none of these measures account for the remaining nodes in a multivariate network. While partial coherence quantifies the direct relationship between signals after excluding the linear effect from the remaining signals, it is still significantly affected by cross-talk. Here we combine the cross-talk robustness of lagged coherence with the multivariate framework of partial coherence to form a new measure called partial lagged coherence. Briefly, partial lagged coherence regresses our signals of interest onto the remaining signals so that only the instantaneous contributions from other signals are removed before computing lagged coherence. Our findings on realistic simulations of MEG data indicate a better performance of partial lagged coherence than other approaches in distinguishing direct from indirect connections in the presence of cross-talk.