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.

Functional magnetic resonance imaging is a non-invasive tomographic imaging modality that has provided insights into system-level brain function. New analysis methods are emerging to study the dynamic behavior of brain activity. The innovation-driven co-activation pattern (iCAP) approach is one such approach that relies on the detection of timepoints with a significant transient activity to subsequently retrieve spatially and temporally overlapping large-scale brain networks. To recover temporal profiles of the iCAPs for further time-resolved analysis, spatial patterns are fitted back to the activity-inducing signals. In this crucial step, spatial dependences can hinder the recovery of temporal overlapping activity. To overcome this effect, we propose a novel back-projection method that optimally fits activity-inducing signals given a set of transient timepoints and spatial maps of iCAPs, thus taking into account both spatial and temporal constraints. Validation on simulated data shows that transient-based constraints improve the quality of fitted time courses. Further evaluation on experimental data demonstrates that overfitting and underfitting are prevented by the use of optimized spatio-temporal constraints. Spatial and temporal properties of resulting iCAPs support that brain activity is characterized by the recurrent co-activation and co-deactivation of spatially overlapping large-scale brain networks. This new approach opens new avenues to explore the brain's dynamic core.

Modern neuroimaging techniques offer disctinct views on brain structure and function. Data acquired using these techniques can be analyzed in terms of its network structure to identify organizing principles at the systems level. Graph representations are flexible frameworks where nodes are related to brain regions and edges to structural or functional links. Most research to date has focused on analyzing these graphs reflecting structure or function. Graph signal processing (GSP) is an emerging area of research where signals at the nodes are studied atop the underlying graph structure. Here, we review GSP tools for brain imaging data and discuss their potential to integrate brain structure with function. We discuss how brain activity can be meaningfully filtered. We also derive surrogate data as a null model to test significance for graph signals. We review that individuals with less concentration on graph high frequency could switch attention faster.

Modern neuroimaging techniques provide us with unique views on brain structure and function; i.e., how the brain is wired, and where and when activity takes place. Data acquired using these techniques can be analyzed in terms of its network structure to reveal organizing principles at the systems level. Graph representations are versatile models where nodes are associated to brain regions and edges to structural or functional connections. Structural graphs model neural pathways in white matter, which are the anatomical backbone between regions. Functional graphs are built based on functional connectivity, which is a pairwise measure of statistical interdependency between pairs of regional activity traces. Therefore, most research to date has focused on analyzing these graphs reflecting structure or function. Graph signal processing (GSP) is an emerging area of research where signals recorded at the nodes of the graph are studied atop the underlying graph structure. An increasing number of fundamental operations have been generalized to the graph setting, allowing to analyze the signals from a new viewpoint. Here, we review GSP for brain imaging data and discuss their potential to integrate brain structure, contained in the graph itself, with brain function, residing in the graph signals. We review how brain activity can be meaningfully filtered based on concepts of spectral modes derived from brain structure. We also derive other operations such as surrogate data generation or decompositions informed by cognitive systems. In sum, GSP offers a novel framework for the analysis of brain imaging data.

Functional magnetic resonance imaging (fMRI) provides a window on the human brain at work. Spontaneous brain activity measured during resting-state has already provided many insights into brain function. In particular, recent interest in dynamic interactions between brain regions has increased the need for more advanced modeling tools. Here, we deploy a recent fMRI deconvolution technique to express resting-state temporal fluctuations as a combination of large-scale functional network activity profiles. Then, building upon a novel sparse coupled hidden Markov model (SCHMM) framework, we parameterised their temporal evolution as a mix between intrinsic dynamics, and a restricted set of cross-network modulatory couplings extracted in data-driven manner. We demonstrate and validate the method on simulated data, for which we observed that the SCHMM could accurately estimate network dynamics, revealing more precise insights about direct network-to-network modulatory influences than with conventional correlational methods. On experimental resting-state fMRI data, we unraveled a set of reproducible cross-network couplings across two independent datasets. Our framework opens new perspectives for capturing complex temporal dynamics and their changes in health and disease.