PhD Dissertation Defense

Analysis of brain network connectivity
using spatial information

Sai Ma

1:00pm Thursday, 18 April 2013, ITE 325b

In current functional magnetic resonance imaging (fMRI) research, one of the most active areas involves exploring statistical dependencies among brain regions, known as functional connectivity analysis. Data-driven methods, especially independent component analysis (ICA), have been successfully applied to fMRI data to extract distributed brain networks and offer an opportunity to investigate functional connectivity on a network level, thus at a multivariate level. However, the independence assumption in ICA is neither necessarily nor typically satisfied in real applications and an extension is desirable. Furthermore, most current ICA-based studies focus on the use of temporal information and second-order statistics for functional connectivity analysis. Taking spatial information and higher-order statistics in fMRI data into account is expected to lead to better understanding of the overall brain network connectivity in healthy controls and also in patients with mental disorders, such as schizophrenia.

We develop a dependent component analysis (DCA) framework to generalize the ICA-based connectivity analysis methods by grouping components into maximally independent clusters. First, we define functional network connectivity as the statistical dependence among spatial components, instead of the typically used temporal correlation. Based on this definition, we use a hypothesis test to automatically generate functional connectivity structure for a large number of brain networks. After that, we separate dependent components within a given cluster using prior information, such as sparsity and experimental paradigm information, to achieve a better decomposition. We also combine this DCA-based clustering analysis with graph-theoretical analysis to discover significant group differences in topological properties of functional connectivity structure. To extend the methodologies currently available for functional connectivity, we propose an independent vector analysis (IVA) based scheme to extract and analyze dynamic functional connectivity.

The methods we develop offer advantages for effective and efficient examination of not only static, but also dynamic functional connectivity among different brain networks. We identify significant differences in functional connectivity structure between healthy controls and patients with schizophrenia, which may prove useful to serve as potential biomarkers for diagnosis. We also find task-induced modulations in functional connectivity when comparing different active states in the brain. Furthermore, we observe temporal variability in functional connectivity structure and physiologically meaningful group differences in dynamic connectivity among several brain networks. Our methods can provide insights to understanding of functional characteristics of the brain network organization in healthy individuals and patients with schizophrenia.

Committee: Dr. Adali (Chair), Dr. Morris, Dr. Rutledge, Dr. LaBerge, Dr. Phlypo, Dr. Calhoun, and Dr. Westlake

PhD Dissertation Defense

Data-driven group analysis of complex-valued fMRI data

Pedro A. Rodriguez

11:00am Tuesday, 16 April 2013, ITE 346, UMBC

Analysis of functional magnetic resonance imaging (fMRI) data in its native, complex form has been shown to increase the sensitivity of the analysis both for data-driven techniques such as independent component analysis (ICA) and for model-driven techniques. The promise of an increase in sensitivity and specificity in clinical studies provides a powerful motivation for utilizing both the phase and magnitude data; however, the unknown and noisy nature of the phase poses a challenge for successful study of the fMRI data. In addition, complex-valued analysis algorithms, such as ICA, suffer from an inherent phase ambiguity, which introduces additional difficulty for group analysis and visualization of the results. We present solutions for these issues, which have been among the main reasons phase information has been traditionally discarded, and show their effectiveness when used as part of a complex-valued group ICA algorithm application. The developed methods become key components of a framework that allows the development of new fully complex data-driven and semi-blind methods to process, analyze, and visualize fMRI data.

In this dissertation, we first introduce the methods developed as part of the fully complex framework for ICA of fMRI data. We introduce a physiologically motivated de-noising method that uses phase quality maps to successfully identify and eliminate noisy voxels—3D pixels—in the fMRI complex images so they can be used in individual and group studies. We also introduce a phase correction scheme that can be either applied sub-sequent to ICA of fMRI data or can be incorporated into the ICA algorithm in the form of prior information to eliminate the need for further processing for phase correction. Finally, we present two visualization methods that are used to augment the sensitivity and specificity in the detection of activated voxels. We show the benefits of using the developed methods on actual complex-valued fMRI data.

In the remainder of the dissertation, we focus on developing constrained ICA (C-ICA) algorithms for complex-valued fMRI data. C-ICA uses prior information, hence providing a balance between model-based and data-driven approaches such as ICA to improve the source estimation performance and robustness to noise. C-ICA algorithms have been used to improve the estimation performance in real-valued fMRI data, but—to our knowledge—have not been applied to complex-valued fMRI data. We develop the first C-ICA algorithm that uses complex-valued references to constrain either the sources or the mixing coefficients. The designed algorithm is not restricted to having a unitary demixing matrix, which is a major assumption in existing C-ICA algorithms. We show, on both simulated and actual fMRI data, how the performance of ICA improves by using prior information about the fMRI paradigm.

Committee: Dr. Adali (Chair), Dr. Morris, Dr. Rutledge, Dr. Laberge, Dr. Phlypo, and Dr. Calhoun

PhD Dissertation Defense

Independent Vector Analysis:
Theory, Algorithms, and Applications

Matthew Anderson

1:45pm Wednesday, 17 April 2013, ITE 325B

The field of blind source separation (BSS) is a well studied discipline within the signal processing community due to its applicability to a variety of problems when the data observation model is poorly known or difficult to model. For example, in the study of the human brain with functional magnetic resonance imaging (fMRI), a neuroimaging sensor, BSS algorithms are able to provide medical researchers and practitioners with a decomposition of a three-dimensional ‘movie’ of the brain that is amenable to analysis. BSS algorithms achieve this decomposition with only a few justifiable assumptions; this is contrary to methods based on the general linear model, which require prespecified models of the expected or desired response to achieve analysis of fMRI data.

Most BSS algorithms consider just a single dataset, but it also desirable to have methods that can analyze multiple subjects or data collections in fMRI jointly, so as to provide insights beyond that achieved with individual analysis of single datasets. Several frameworks for using BSS on multiple datasets jointly have been proposed. The subject of this dissertation is the study of one of these frameworks, which has been termed independent vector analysis (IVA). IVA is a recent extension of the classical independent component analysis (ICA) model to BSS of multiple datasets and it has been the subject of significant research interest. In this dissertation, we provide a formulation of IVA that accounts for sources which possess properties such as a) following Gaussian or non-Gaussian distributions; b) samples are independently and identically distributed (iid) or are dependent; and c) having either linear or nonlinear dependence of sources between datasets. The proposed IVA formulation utilizes the likelihood to define the objective function. This formulation admits to theoretical analysis. In particular, we provide the identification conditions, i.e., we determine when the sources can be ‘blindly’ recovered by IVA, and give a lower bound on the source separation performance.

Several algorithms exist for achieving IVA. We provide several new approaches to developing IVA algorithms and apply these approaches using a Gaussian distribution source model and a more general Kotz distribution model. The former, in addition to leading to efficient IVA algorithms, serves as the distribution model that directly connects canonical correlation analysis (CCA) and ICA.  

Committee: Dr. Tulay Adali (Chair), Dr. Joel Morris, Dr. Aninyda Roy, Dr. Ronald Phlypo, and Dr. Mike Novey