Functional connectivity of brain refers to statistical dependence of brain functions among often remote neuronal units. This thesis addresses two novel ways to analyse brain functional connectivity. We provide an entropy based technique called sub-graph entropy to classify brain states. This metric is then used to classify adolescents suffering from obsessive compulsive disorder. The thesis also proposes a new tensor based decomposition to analyse dynamic functional connectivity of brain. In comparison with static connectivity, dynamic analysis assumes that brain network evolves and changes over time. Finally, a combined static-dynamic feature extraction model is used to classify adolescents suffering from major depressive disorder. The first part of the dissertation considers analysis of human brain networks or graphs constructed from time-series collected from functional magnetic resonance imaging (fMRI). In the network of time-series, the nodes describe the regions and the edge weights correspond to the absolute values of correlation coefficients of the time-series of the two nodes associated with the edges. A novel information-theoretic metric, referred as sub-graph entropy is introduced to measure uncertainty associated with a sub-graph. Nodes and edges constitute two special cases of sub-graph structures. Node and edge entropies are used to rank regions and edges in a functional brain network. This work analyzes task-fMRI data collected from 475 subjects in the Human Connectome Project (HCP) study for gambling and emotion tasks. The proposed approach is used to rank regions and edges associated with these tasks. The differential node (edge) entropy metric is defined as the difference of the node (edge) entropy corresponding to two different networks belonging to two different classes. Differential entropy of nodes and edges are used to rank top regions and edges associated with the two classes of data. Using top node and edge entropy features separately, two-class classifiers are designed using support vector machine (SVM) with radial basis function (RBF) kernel and leave-one-out method to classify time-series for emotion task vs. no-task, gambling task vs. no-task and emotion task vs. gambling task. Using node entropies, the SVM classifier achieves classification accuracies of 0.96, 0.97 and 0.98, respectively. Using edge entropies, the classifier achieves classification accuracies of 0.91, 0.96 and 0.94, respectively. Next, we describe two pertinent properties of sub-graph entropy. It is shown that when a graph is divided into multiple smaller graphs, the summation of their sub-graph entropy is always less than a constant. Additionally, this summation is always greater than the corresponding graph entropy. We also demonstrate that node entropy, a special case of sub-graph entropy, is stable. Experiments using both synthetic data and real world brain network data are carried out to further validate these points. Overall, node entropy has better stability compared to other centrality metrics. As a relevant application of static connectivity analysis, we present a novel approach for classifying obsessive-compulsive disorder (OCD) in adolescents from resting-state fMRI data. Currently, the state-of-the-art for diagnosing OCD in youth involves interviews with adolescent patients and their parents by an experienced clinician, symptom rating scales based on Diagnostic and Statistical Manual of Mental Disorders (DSM), and behavioral observation. Discovering signal processing and network-based biomarkers from functional magnetic resonance imaging (fMRI) scans of patients has the potential to assist clinicians in their diagnostic assessments of adolescents suffering from OCD. We investigate the clinical diagnostic utility of a set of univariate, bivariate and multivariate features extracted from resting-state fMRI using an information-theoretic approach in 15 adolescents with OCD and 13 matched healthy controls. Results indicate that an information-theoretic approach based on sub-graph entropy is capable of classifying OCD vs. healthy subjects with high accuracy. Mean time-series were extracted from 85 brain regions and were used to calculate Shannon wavelet entropy, Pearson correlation matrix, network features and sub-graph entropy. In addition, two special cases of sub-graph entropy, namely node and edge entropy, were investigated to identify important brain regions and edges from OCD patients. A leave-one-out cross-validation method was used for the final predictor performance. The proposed methodology using differential sub-graph (edge) entropy achieved an accuracy of 0.89 with specificity 1 and sensitivity 0.80 using leave-one-out cross-validation with in-fold feature ranking and selection. The high classification accuracy indicates the predictive power of the sub-network as well as edge entropy metric. The second part of the thesis explores the predictive capability of dynamic functional connectivity extracted from functional magnetic resonance imaging of the human brain. First, a number of state-of-the-art features extracted from static functional connectivity of brain are employed to predict biological gender and intelligence using publicly available Human Connectome Project (HCP) database. Next, a novel tensor parallel factor (PARAFAC) decomposition model is proposed to decompose sequence of dynamic connectivity matrices into common connectivity components that are orthonormal to each other, common time-courses, and corresponding distinct subject-wise weights. The subject-wise loading of the components are employed to predict biological gender and intelligence using a random forest classifier (respectively, regressor) using 5-fold crossvalidation. The results demonstrate that dynamic functional connectivity can indeed classify biological gender with a high accuracy (0.94, where male identification accuracy was 0.87 and female identification accuracy was 0.97). It can also predict intelligence with smaller normalized mean square error (0.139 for fluid intelligence and 0.031 for fluid ability metrics) compared with other functional connectivity measures (the nearest mean square error were 0.147 and 0.037 for fluid intelligence and fluid ability metrics, respectively using static connectivity approaches). Our work is an important milestone for the understanding of non-stationary behavior of hemodynamic blood-oxygen level dependent (BOLD) signal in brain and how they are associated with biological gender and intelligence. The paper demonstrates that dynamic behavior of brain can contribute substantially towards forming a fingerprint of biological gender and intelligence. We further combine the static and dynamic approaches for classifying major depressive disorder (MDD) for adolescents from resting-state fMRI. This last part investigates various static and dynamic connectivity measures extracted from resting-state fMRI for assisting with MDD diagnosis. First, absolute pearson correlation matrices from 85 brain regions are extracted and they are used to calculate static features. An information-theoretic approach based on sub-graph entropy is found to classify MDD vs. healthy subjects with high accuracy. Next, approaches utilizing dynamic connectivity are employed to extract tensor-based, independent component based and principal component based subject specific attributes. Finally, features from static and dynamic approaches are combined to create a feature vector. A leave-one-out cross-validation method is used for the final predictor performance. Out of 49 adolescents with MDD and 33 matched healthy controls, a support vector machine (SVM) classifier using a radial basis function (RBF) kernel using differential sub-graph entropy combined with dynamic connectivity features achieves an accuracy of 0.82 with specificity 0.79 and sensitivity 0.84 using leave-one-out cross-validation with in-fold feature ranking and selection. The high classification accuracy indicates the predictive power of combining the static and dynamic connectivity features for classification of adolescent MDD.
University of Minnesota Ph.D. dissertation. July 2020. Major: Electrical Engineering. Advisor: Keshab Parhi. 1 computer file (PDF); xxii, 189 pages.
Static and Dynamic Connectivity Analysis of Human Brain via Functional Magnetic Resonance Imaging.
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