New methods for analysis of source localization and brain connectivity ; towards invariance against volume conduction artifacts ; Neue Methoden für Quellenlokalisierung und die Analyse von Hirnkonnektivität ; mit Invarianz gegenüber Artefakten der Volumenleitung

Due to the artifacts of volume conduction, localization of interacting brain sources is an intricate issue in inverse calculations of EEG and MEG data. Since non-interacting brain sources do not contribute systematically, i.e. apart from random fluctuations around zero, to the imaginary part of cross-spectrum calculated from EEG/MEG data, these measures are powerful tools to study functional brain connectivity from noninvasive electrophysiological data. MUltiple SIgnal Classification (MUSIC), is a standard localization method.In one of the MUSIC variants called Recursively Applied and Projected MUSIC (RAP-MUSIC), multiple iterations are proposed in order to decrease the location estimation uncertainties introduced by subspace estimation errors. Since we are interested in the interacting sources, I propose to apply the existing subspace method “RAP-MUSIC” to the subspace found from the dominant singular vectors of the imaginary part of cross-spectrum. Secondly, to estimate the specific sources interacting with each other, I use a modified LCMV-beamformer approach in which the source direction for each voxel is determined by maximizing the imaginary part of coherency with respect to a given reference. Subspace based algorithms, such as MUSIC and RAP-MUSIC are very sensitive to the choice of subspace. In case the subspace is not accurately estimated, the sources which best explain the data are not localized optimally. RAP-MUSIC is therefore applicable in this form, i.e. on the subspace spanned by the eigenvectors of the imaginary part of cross-spectrum rather than the eigenvectors of covariance matrix, only if the number of interacting sources is even. The reason is that the imaginary part of cross-spectrum is antisymmetric and all eigenvalues occur in pairs. To solve this issue, a new method called Self-Consistent MUSIC (SC-MUSIC) is suggested which is based on the idea that the presence of several sources has a bias on the localization of each source through the bias on the estimation of the subspace. This bias ...