Graph-Spectral Techniques For Analyzing Resting State Functional Neuroimaging Data

Srinivas Govinda Surampudi

Abstract

Human brain is undoubtedly the most magnificent yet delicate arrangement of tissues. This serves as the seat of such a wide span of cognitive functions and behaviors. The neuronal activities within every neuron, collectively observed over network(s) of these interconnected neurons, manifest themselves into patterns at multiple scales of observations. Many brain imaging techniques such as fMRI, EEG, MEG etc. measure these patterns as electro-magnetic responses. These patterns supposedly play the role of unique neuronal signatures of the vast repertoire of cognitive functions. Experimentally, it is observed that different neuronal populations participate coherently to generate a signature for a cognitive function. These signatures could be investigated at the micro-scale corresponding to responses of individual neurons to external-current stimuli, at the meso-scale related to populations of neurons that show similar metabolic activities and in turn these populations, also known as regions of interest (ROIs), communicate via complex arrangement of anatomical fiber pathways leading to signatures at the macro-scale. The holy grail of neuroscience is thus to computationally decipher the interplay of this complex anatomical network and the complex functional patterns corresponding to the cognitive behaviors at various scales/levels. Each scale of observation, depending on the instruments of measurement, has its own rich spatiotemporal dynamics that interacts with higher and lower levels in complex ways. Large-scale anatomical fiber pathways are represented in a matrix that accounts for inter-population fiber strength known as structural connectivity (SC) matrix. One of the popular modalities to capture large-scale functional dynamics is resting-state fMRI, and statistical dependence between these inter-population BOLD signals is captured in functional connectivity (FC) matrix. There are many models that provide computational accounts for the relationship between these two matrices as deciphering this relationship will provide the mechanism by which cognitive functions arise over the structure. On one hand, there are many non-linear dynamical models that describe the biological phenomenon well but are expensive and intractable. On the other hand there are linear models that compromise on the biological richness but are analytically feasible. This thesis is concerned with the analysis of the temporal dynamics of observed resting-state fMRI signals over the large-scale human cortex. We provide a model that has a bio-physical explanation as well as an analytical expression for FC given SC. Reaction-diffusion systems provide a computational framework for the emergence of excitatory-inhibitory activities at the populations as reactions and their interactions as diffusion over space and time. The spatio-temporal dynamics of the BOLD signal governed by this framework is constrained with respect to the anatomical connections thereby separating the spatial and temporal dynamics. Covariancematrix of this signal is estimated thus getting an estimate of the functional connectivity matrix. The covariance matrix or the BOLD signal in general is expressed in terms of the graph-diffusion-kernels thus forming an analytically elegant expression. Most importantly, the model for FC abstracts out biological details and works in the realm of spectral graph theoretic constructs providing the necessary ease for computational analysis. As this model learns the combination parameters of multiple diffusion kernels and kernels themselves, it is called Multiple Kernel Learning (MKL) model. Apart from superior quantitative performance, the model parameters may act as biomarkers for various cognitive studies. Albeit, the model parameters are learned for a cohort, the model preserves subject-specificity. These parameters can be used as a measure for inter-group differences and dissimilarity identification as has been employed for age-group identification as an example in this thesis. Essentially MKL model partitions FC into two constituents: influence of the underlying anatomical structure into diffusion kernels and the cognitive theme of temporal structure into the model parameters, thus predicting FCs specific to subjects within the cognitive conditions of the cohort. Even though MKL is a cohort based model, it maintains sensitivity towards anatomy. Performance of the model drastically drops down with alterations in SC and model parameters, but does not overfit to the cohort. Resting state fMRI BOLD signals have been observed to show non-stationary dynamics. Such multiple spatio-temporal patterns, represented as dynamic FC matrices, are observed to be cyclically repeating in time motivating use of a generic clustering scheme to identify latent states of dynamics. We propose a novel solution that learns parameters specific to the dynamic states using a graph-theoretic model (temporal-Multiple Kernel Learning, tMKL) and finally predicts the grand average FC of the unseen subjects by leveraging a state transition Markov model. We discover the underlying lower-dimensional manifold of the temporal structure which is further parameterized as a set of local density distributions, or latent transient states. tMKL thus learns a mapping between anatomical graph and the temporal structure. Unlike MKL, tMKL model obeys state-specific optimization formulation and yet performs at par or better than MKL for predicting the grand average FC. Like MKL, tMKL also shows sensitivity towards subject-specific anatomy. Finally, both tMKL and MKL models outperform the state-of-the-art in their own ways by providing bio-physical insights.

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