Book Description
Magnetic resonance imaging (MRI) plays an integral role in the study, diagnosis and treatment of neurological diseases. Neuroimaging analyses involve high-dimensional, large-scale data that contain rich spatial and temporal information about the dynamic and integrated systems in the brain. Therefore, it has become imperative to develop and optimize analytical approaches drawn from engineering and mathematics to more precisely model these complex patterns and interactions, which will advance our understanding of functional brain organization in health and disease. Chapter 1 provides an overview and background of MRI, with a particular focus on the use of resting-state functional magnetic resonance imaging (rs-fMRI) to capture and characterize brain connectivity. Previous work of statistical methods developed for fMRI analysis are reviewed. Chapter 2 presents an analysis of changes in functional connectivity and behavioral outcomes in patients of stroke who undergo brain-computer interface (BCI) interventional therapy. This work employs a widely used network-based inference method for fMRI analysis that serves as motivation for subsequent work to overcome statistical challenges associated with its use to more effectively model and characterize brain network dynamics and organization in a robust manner. Chapter 3 presents a novel application of differential covariance trajectory analysis as promising framework for brain network modeling using rs-fMRI data. The proposed algorithm models functional connectivity as trajectories on the manifold and employs a localization procedure to search over and identify subsets of first- and second-order differences in brain connectivity features between patients with Temporal Lobe Epilepsy (TLE) and healthy control subjects. Chapter 4 extends the work presented in the previous chapter to apply the combined differential covariance trajectory and scan statistics framework to characterize the Alzheimer's Disease connectome. We demonstrate the utility and robustness of this method to study altered brain network organization in large-scale functional networks in a different and older clinical population, which is notably of smaller sample size, where the statistical signal may be weak. Chapter 5 discusses conclusions and key takeaways of the work, along with potential future avenues of research.
