Towards EEG source connectivity analysis

Due to its temporal resolution in the millisecond range and other compelling properties such as noninvasiveness, portability and relatively low costs, electroencephalography (EEG) is the tool of choice for studying brain dynamics in humans. However, any neurophysiological interpretation of EEG data is hindered by the fact that the signals related to electrical activity in source brain regions are spread across the EEG sensors due to a process called volume conduction, the inversion of which is an ill-posed inverse problem. In the EEG-based analysis of directed information flow between brain regions, volume conduction poses a serious challenge, since multiple active sources have to be assumed, the contributions of which, however, mix into all EEG sensors. With this thesis we contribute to the field of EEG-based brain connectivity analysis. We start by conducting an extensive survey of relevant approaches and go on to assess their performance on simulated EEG data, which are realistically generated as mixtures of interacting sources. We observe that most of the tested methods are not able to determine the connectivity structure of the underlying sources because either i) the effect of volume conduction is neglected or ii) the assumptions made to estimate mixed sources do not comply with the requirements of source connectivity analysis or even with the physics of the EEG. The central contribution of this thesis is the development of source demixings that meet theoretical requirements for source connectivity analysis and are applicable in practice. We achieve this using two different strategies. In inverse source reconstruction, a given physical model of EEG generation is inverted under physiologically motivated constraints. We derive an inverse methodology, S-FLEX, which is able to recover multiple source of arbitrary shape and depth using a sparsity penalty that assures rotational invariance of the solution. Our method is applicable to entire time series as a preprocessing step to source connectivity analysis. Its favorable localization properties are empirically evaluated on real data as well as in simulations and are demonstrated to be the key to correct source connectivity determination. In the course of the thesis, we also present a blind source separation (BSS) technique, SCSA, which estimates the underlying brain sources and their mixing patterns jointly under assumptions on connectivity structure of the sources. We demonstrate that SCSA performs well on simulated data, if mild assumptions regarding the non-Gaussianity of the source variables hold. By way of an outlook, we present a hybrid approach that combines S-FLEX inverse source reconstruction with SCSA blind source separation and thereby fuses physical and dynamical assumptions on the sources. In the final part of the thesis, we analyze information transfer between sources of the human alpha rhythm during rest. Our analysis of S-FLEX source estimates yields a number of insights which could not have been obtained from mere sensor-space analysis. We observe that generators of alpha band activity are mostly symmetrically distributed on the cortex. However, the strength of the sources nor the corresponding interaction patterns are exclusively symmetric. These findings support the hypothesis of a consistent dominant laterality in the population.