On complexity and phase effects in reconstructing the directionality of coupling in non-linear systems

Abstract

From the theoretical point of view, brain signals measured with electroencephalogram (EEG), or magnetoencephalogram (MEG) can be described as the manifestation of coupled nonlinear systems with time delays in coupling. From the empirical point of view, to understand how the information is processed in the brain, there is a need to characterize the information flow in a network of spatially distinct brain areas. Tools for reconstructing the directionality of coupling, which can be formalized as Granger causality, provide a framework for gaining the insight into the functional organization of the brain networks. In turn, it is not completely understood what kind of effects are captured by causal statistics. Under the context of coupled non-linear oscillating systems with time delay in coupling, we consider two effects that can contribute to the estimation of causality. First, we explore the problem of ambiguity of phase delays observed between the dynamics of the driver and the response, and its effect on the linear, spectral and information-theoretic statistics. Second, we show that the directionality of coupling can be understood as the differences in signal complexity between the driver and response. © 2014 Springer-Verlag Berlin Heidelberg.