Multiple circular-circular correlation coefficients for the quantification of phase synchronization processes in the brain

Phase synchronization is discussed as a potential mechanism for large-scale integration in the brain. Therefore, the quantification of such synchrony is a crucial topic in brain science research. Furthermore, these cerebral integration processes are likely to involve entire brain areas; therefore, the analysis of multiple couplings is of particular interest. Because phase values are circular variables, it is possible to use circular statistical methods for their examination. In particular, circular-circular correlation coefficients form a suitable measurement to estimate the extent of phase synchronization between different signals. As a multiple circular-circular correlation concept is still pending, two new multiple circular-circular correlation coefficients are presented in this article that can be used to quantify phase couplings between one dependent and an arbitrary number of predictor signals. ̑extcopyright 2013 by Walter de Gruyter Berlin Boston 2013