Linking time-varying functional brain activity with underlying neural architecture remains a complex and challenging endeavor. A recent framework for this undertaking is graph signal processing (GSP), where functional activity patterns are treated as signals living on a graph that is characterized by structural connectivity. Then graph spectral filtering can be used to obtain the parts of functional activity that are more or less smooth on the graph; i.e., more coupled or decoupled from brain structure, respectively. Given the time-varying behavior of functional magnetic resonance imaging (fMRI) networks, structure- function coupling may also change over time. Here, we leverage the GSP framework in a sliding-window setting to investigate the dynamics of brain structure-function coupling during resting-state at the node- and edge-wise levels. We conclude that dynamics are captured by both node- and edge-wise metrics of structure-function coupling and we identify principal patterns of dynamic functional connectivity respectively coupled and decoupled from structure.

The study of complex systems greatly benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smallest nonzero eigenvalue and plays a key role for graph clustering. Graph signal processing focuses on the analysis of signals that are attributed to the graph nodes. Again, the eigendecomposition of the graph Laplacian is important to define the graph Fourier transform and extend conventional signal-processing operations to graphs. Here, we introduce the design of Slepian graph signals by maximizing energy concentration in a predefined subgraph given a graph spectral bandlimit. We establish a novel link with classical Laplacian embedding and graph clustering, which provides a meaning to localized graph frequencies.

The Virtual Navigator (VN) technology was used for the fusion of transcranial Ultrasound (US) and brain Magnetic Resonance Images (MRI), with a repeatability error under 0.1 cm. The superimposition of US to the previously acquired MRI volume consisted of external point-based registration, that was subsequently refined with image-based registration of internal brain structures. The common registration procedure with the usage of external fiducial markers acquired with the two modalities was improved using facial anatomical landmarks, with a reduction of the internal targeted structure residual shift (maximum 0.7 cm in the cranio-caudal direction). This allowed the investigation of Deep Cerebral Veins and dural sinuses insonated from the condyloid process of the mandible, a recently introduced US window. The fusion of these vessels to the MRI volume provided their anatomical position and helped excluding false Doppler signal sources.