Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems

Over the last decades several techniques have been developed to analyze interactions in multivariate dynamic systems. These analysis techniques have been applied to empirical data recorded in various branches of research, ranging from economics to biomedical sciences. Investigations of interactions between different brain structures are of strong interest in neuroscience. The information contained in electromagnetic signals may be used to quantify the information transfer between those structures. When investigating such interactions, one has to face an inverse problem. Usually the distinct features and different conceptual properties of the underlying processes generating the empirical data and therefore the appropriate analysis technique are not known in advance. The performance of these methods has mainly been assessed on the basis of those model systems they have been developed for. To draw reliable conclusions upon application to empirical time series, understanding the properties and performances of the time series analysis techniques is essential. To this aim, the performances of four representative multivariate linear signal processing techniques in the time and frequency domain have been investigated in this study. The partial cross-spectral analysis and three different quantities measuring Granger causality, i.e. a Granger causality index, partial directed coherence, and the directed transfer function are compared on the basis of different model systems. To capture distinct properties in the dynamics of brain neural networks, we have investigated multivariate linear, multivariate nonlinear as well as multivariate non-stationary model systems. In an application to neural data recorded by electrothalamography and electrocorticography from juvenile pigs under sedation, directed as well as time-varying interactions have been studied between thalamic and cortical brain structures. The time-dependent alterations in local activity and changes in the interactions have been analyzed by the Granger causality index and the partial directed coherence. Both methods have been shown to be most suitable for this application to brain neural networks based on our model systems investigated. The results of this investigation contribute to the long-term goal to understand the relationships in neural structures in an abnormal state of deep sedation.