Dynamic Network Analysis: Analyzing the Chronnectome

Networks describe interactions between objects: they can for example describe connections between people, as in social networks; capture dependencies in biological processes such as gene regulation; or represent the interplay and connectivity of different structural and functional areas in the brain. Numerous methods for network analysis have been developed using different quantitative approaches. However, many of these methods are still predominantly available for the analysis of static networks, i.e., snapshots of a network at a particular point in time. However, to assess how networks such as those in the brain change over time, improved methods for dynamic network analysis are required. This project will develop mathematical approaches motivated by the driving biological problem of analyzing temporal change of structural and functional brain connectivity, the chronnectome. Structural connectivity includes white matter connections in the brain and hence the underlying cabling enabling information exchange. Functional brain connectivity on the other hand describes how tasks influence brain activity and how different brain areas behave similarly under tasks. Quantifying changes in structural and/or functional connectivity over time can improve understanding of brain diseases, which deviate from normality. Moreover, the approaches developed here will have general use for other dynamic networks, from other biological networks to social networks and beyond. To maximize impact, the computational methods developed here will be made available in open-source form, with a software license permitting free commercial and non-commercial use. The project also includes research training and courses for students in network science.

Networks are commonly described as graphs, with nodes describing entities in a system and edges node relationships. Networks range from unstructured and rapidly changing social networks to structured slowly varying networks capturing structural brain connectivity. Network science seeks to develop methods to mine information from interaction patterns, for example, extracting tightly coupled nodes in communities. Time-dependent network data is increasingly available; however, sufficient analysis methods are still lacking as the majority of approaches have focused on static data, with ongoing development of methods for time-dependent networks having become more common only recently. The goal of this project is to advance general time-dependent network analysis, with brain chronnectome analysis as the guiding driving problem to motivate the technical development. Current approaches for the analysis of time-dependent networks lack several key properties required for chronnectome analysis: e.g., (i) the ability to analyze longitudinal network data, where networks are available for multiple subjects at multiple timepoints, (ii) the ability to include domain-specific prior information (such as prior knowledge of connectivity patterns), and (iii) the ability to deal with inhomogeneous subject groups and discontinuities in time. To address these shortcomings, this project will develop customized network analysis approaches based on (i) extensions to the stochastic block model approach of network analysis, and (ii) regression models for network-valued data.