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Graph Signal Processing for Studying the Relationship between Brain Connectomes

Yang Li

Supervised by Gonzalo Mateos

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https://rochester.zoom.us/j/7718850098?pwd=c0NkMmZ2WUVmbzZWRkduZzFZYTVaUT09

The human brain is a complex yet efficient information processing network, whose distributed organization entails different regions conducting individual tasks while actively interacting with each other. This integrative nature of brain function along with recent advances in neuroimaging, motivate well the adoption of graph-centric signal and information processing tools to study the interplay between brain structure (of neural connections often referred to as the structural connectome) and functional connectivity. This dissertation contributes to this effort by studying the relationship between brain connectomes from the perspective of graph signal processing (GSP), and thus facilitates revealing some of the brain’s organizing principle at the system level.

In the first part of this dissertation, we introduce a supervised graph representation learning framework to model the relationship between brain structural connectivity (SC) and functional connectivity (FC) via a graph encoder-decoder system, where the SC is used as input to predict empirical FC. A trainable graph convolutional encoder captures direct and indirect interactions between brain regions-of-interest that mimic actual neural communications, and it integrates information from both the structural network topology as well as nodal (i.e., region-specific) attributes. The encoder learns node-level SC embeddings which are combined to generate (whole brain) graph-level representations for reconstructing empirical FC networks. The proposed end-to-end model utilizes a multi-objective loss function to jointly reconstruct FC networks and learn discriminative graph representations of the SC-to-FC mapping for downstream subject (i.e., graph-level) classification. Comprehensive experiments demonstrate that the learnt representations of said relationship capture valuable information from the intrinsic properties of the subject’s brain networks and lead to improved accuracy in classifying a large population of heavy drinkers and non-drinkers from the Human Connectome Project. We extend the developed model and further design a siamese network framework to learn graph embeddings that preserve inter-graph similarity, effectively increasing the number of training samples and expanding the flexibility to incorporate additional prior information.

The study of the interplay between SC and FC is a timely application do-main, where it is possible but costly to measure structural and functional networks separately due to different spatiotemporal resolutions, running time, and acquisition methods. In the second part of this thesis, we study the problem of identifying brain structural networks from signals measured by resting-state functional magnetic resonance imaging (fMRI). Our GSP approach builds on a model for the measured statistical dependencies among functional signals, which postulates they are generated by linear diffusion on the structural network we wish to recover. The nature of the diffusion model implies that the signal covariance matrix (i.e., the FC) is an unknown polynomial function of the structural network’s adjacency matrix. Accordingly, we advocate a network deconvolution approach whereby we: (i) estimate the eigenvectors of the structural network from those of the signal covariance matrix; and (ii) solve a convex, sparsity-regularized inverse problem to recover the eigenvalues that were obscured by diffusion, enabling the full recovery of the SC topology. We carry out comprehensive experiments on a large population of subjects from the Human Connectome Project, and show that our methods deliver superior performance in recovering both the network topology and connection strengths than the baseline methods.

To summarize, in this dissertation, we i) explore the estimation of brain FC from SC and learn the representations of the SC-FC relationship via graph neural networks; and ii) infer the SC topology from FC using net- work deconvolution. Understanding brain function is one of the fundamental scientific challenges of this century. Results in this work offer new perspectives for exploring the underpinnings of brain connectomes, and support the promising prospect of using GSP to seamlessly integrate brain structure and function in network neuroscience studies.