Alzheimer's dementia is a rising public health crisis that will have an unprecedented social and economic impact in the near future, as elderly individuals make up the fastest growing segment of the population worldwide. The greatest single risk factor for Alzheimer's disease is age, though many genetic and environmental factors also influence disease onset and progression. While current treatment options are sparse and no cure exists, it is critical to (1) identify the disease at its earliest stages, before irreversible brain degeneration has occurred and (2) to develop alternative strategies for reducing dementia risk based on aspects of health that are currently modifiable, such as cardiovascular health as one example. If we can identify individuals who are at high risk for developing Alzheimer's dementia, but who have not yet experienced major neurodegeneration, then it may be possible to apply these alternative strategies to preserve brain health into old age.

In regards to the first aim, brain MRI scans identify robust signatures of Alzheimer's dementia at early stages. In my work, we have expanded upon existing brain-based MRI biomarkers by demonstrating changes in caudate nucleus shape in Alzheimer's disease and by showing that patterns of thinner cortical gray matter are associated with longitudinal expansion of the lateral ventricles. The caudate nucleus is a subcortical gray matter structure typically associated with motor planning, but is also involved in procedural memory, and is affected by the molecular pathology of Alzheimer's disease. The lateral ventricles are a fluid-filled space located at the center of the brain, which expand as brain tissue is lost in aging and dementia, within the fixed volume of the skull. Both of these biomarkers can be automatically measured from brain scans with high reliability and often with less manual intervention compared to other brain structures (such as the hippocampus). These biomarkers makes are candidates for use in clinical trials or, in the case of the lateral ventricles, even in an individual to assist in dementia diagnosis. My studies provide further validation for the use of these biomarkers with additional information on the clinical implications of structural changes in these structures.

For the second aim, I investigated blood levels of two potentially modifiable compounds (thyroid hormones and homocysteine) that have been linked to dementia risk and cognition in the elderly. Alterations in thyroid hormone levels and elevated homocysteine levels have separately been associated with increased dementia risk and cognitive decline in the elderly. My results demonstrate that homocysteine and thyroid hormones levels measured are significantly associated with structural brain differences in the elderly. I found that elderly individuals with elevated homocysteine levels were more likely to have reduced cortical gray matter in bilateral frontal, right temporal, bilateral sensory, motor, and visual areas. In another study, we found that higher levels of thyroid hormone (free thyroxine, fT4) within the normal range were associated with both brain tissue expansion and contraction relative to lower levels. These two compounds are modifiable because interventions exist to modify the levels of these compounds and it's possible to measure their levels using a blood test. While these interventions are not without risk and involve special consideration in the elderly, it is important to understand the relationship between these modifiable health factors and brain structure in the elderly. As more evidence accumulates, if the connection between these health factors, dementia risk and brain deterioration is strong enough, we may discover new avenues for preserving brain health into old age.

The advent of neuroimaging has provided an invaluable tool for investigating brain disorders with quantitative measurements. Neuroimaging-derived measures can not only serve as biomarkers to track the progression of brain disorders like Alzheimer's disease, but also provide quantitative, intermediate phenotypes or endophenotypes close to the biology of disease, which can be utilized for finding new genes in association with brain pathology. The latter has led to the creation of a new and expanding field called neuroimaging genetics. Most methodologies for the application of neuroimaging and other biomarkers to disease diagnosis and clinical trial design utilize only single biomarkers. Similarly, in neuroimaging genetics studies, genetic variants are typically considered one by one, in association with neuroimaging phenotypes. My dissertation introduces new automated, machine learning and multivariate approaches, which potentially offer more power to biomarker-based diagnosis and clinical trial design as well as discovery and risk prediction in neuroimaging genetics.

Brain connectivity methods have tremendous potential to expand our understanding of the brain, especially when added to existing knowledge gained through more traditional structural and functional brain imaging methods. Instead of examining isolated brain regions performing a function or individual regions affected by a disease, a network-level approach appreciates the complex organization and interactions of the brain. Through diffusion weighted imaging, we can visualize the white matter pathways of the brain in vivo, thus modeling the structural highways and roads that support efficient brain function. Understanding how these measures of structural connectivity change with development is key for a fuller understanding of healthy brain development, as structure, function, and connectivity all interact. Additionally, it is necessary for determining how and when dysfunction occurs in neurodevelopmental disorders. As many of these disorders are genetically influenced, examining how risk genes affect brain connectivity might shed light on the mechanisms by which these genes have their effect. Lastly, one of the hallmarks of development is sharpening cognitive skills, which are often significantly impaired in neurodevelopmental disorders. In order to understand both typical and atypical development, determining how connectivity supports cognition is key. Especially with new brain metrics, such as those in graph theory, the association between brain connectivity and cognition is not well known, and presents exciting research potential. Altogether, determining the development, genetic, and cognitive correlates of structural brain connectivity will integrate with existing knowledge about brain structure and function to give us a fuller understanding of the interrelated processes that occur throughout development. This will form a foundation from which we can base future investigations into how connectivity is affected in neurodevelopmental disorders.

We present a collection of methods that model and interpret information represented in structural magnetic resonance imaging (MRI) and diffusion MRI images of the living human brain. Our solution to the problem of brain segmentation in structural MRI combines artificial life and deformable models to develop a customizable plan for segmentation realized as cooperative deformable organisms. We also present work to represent and register white matter pathways as described in diffusion MRI. Our method represents these pathways as maximum density paths (MDPs), which compactly represent information and are compared using shape based registration for population studies. In addition, we present a group of methods focused on connectivity in the brain. These include an optimization for a global probabilistic tractography algorithm that computes fibers representing connectivity pathways in tissue, a novel maximum-flow based measure of connectivity, a classification framework identifying Alzheimer's disease based on connectivity measures, and a statistical framework to find the optimal partition of the brain for connectivity analysis. These methods seek to advance our understanding and analysis of neuroimaging data from crucial pre-processing steps to our fundamental understanding of connectivity in the brain.

Objective: To determine if exercise reduces body weight and to examine the dose-response relationships between changes in exercise and changes in total and regional adiposity. Methods and Results: Questionnaires on weekly running distance and adiposity from a large prospective study of 3,973 men and 1,444 women who quit running (detraining), 270 men and 146 women who started running (training) and 420 men and 153 women who remained sedentary during 7.4 years of follow-up. There were significant inverse relationships between change in the amount of vigorous exercise (km/wk run) and changes in weight and BMI in men (slope+-SE:-0.039+-0.005 kg and -0.012+-0.002 kg/m2 per km/wk, respectively) and older women (-0.060+-0.018 kg and -0.022+-0.007 kg/m2 per km/wk) who quit running, and in initially sedentary men (-0.098+-0.017 kg and -0.032+-0.005 kg/m2 per km/wk) and women (-0.062+-0.023 kg and -0.021+-0.008 kg/m2 per km/wk) who started running. Changes in waist circumference were also inversely related to changes in running distance in men who quit (-0.026+-0.005 cm per km/wk) or started running (-0.078+-0.017 cm per km/wk). Conclusions. The initiation and cessation of vigorous exercise decrease and increase body weight and intra-abdominal fat, respectively, and these changes are proportional to the change in exercise dose.

Over the past decade, billions of dollars from public and private funding institutions have been invested in the fields of neuroimaging and human genetics. Recently, researchers have realized that quantitative measures from imaging methods are a useful substrate for testing how genes influence brain structure, behavior, and susceptibility to disease. However, properly merging the two well-developed fields requires complex new methods and statistical models. Many studies in imaging genetics are simplistic in that they generally focus on individual association tests of a small set of genetic variants (usually single nucleotide polymorphisms, SNPs) on a single summary measure of the brain. These studies are great at bridging the gap between the two fields, but they often fail to utilize advanced methods from either field. For example, in genetics we know that our genes interact with each other in complex pathways, only in very rare circumstances is a single mutation or variant responsible for observable differences in phenotype. Modeling genetic associations using simple linear regression to test the effect of a single SNP at a time on an imaging phenotype is a good first step, but methods that more accurately represent the underlying biology will test the joint effect of multiple genetic variants simultaneously. The flipside of this is a similar problem, our brains are under strong genetic control, but our differences are extremely complex; using quantitative summary measures from imaging data will miss fine-grained differences between subjects.

Anatomical shape analysis problems are ubiquitous in medical imaging. In brain MRI imaging, the problem arises when comparing cortical features of functional importance, such as gray matter thickness, as well as when performing fine-grained analysis of sub-cortical structures. Two general types of approaches have been developed over the years to perform quantitative shape comparison of anatomy: the first, and more intuitive approach, attempts to bring surface models into dense point-to-point correspondence; the alternative approach avoids the need for dense registration by exploring intrinsic global properties of the shape. Each of these methods has their advantages and disadvantages, and I explore examples from each in applications to brain imaging. The general underlying theme of my work has been spherical parametric shape registration, and other descriptions based on spherical maps. Several times throughout this work I utilize the theory of spherical harmonics, both in their scalar and vector form as a means of parameterizing and describing brain anatomy. Using this theory, I develop several algorithms for rigid and non-rigid shape registration for a variety of brain shapes, which are described in Chapters 1-4.

In Chapter 5, I present an application of the methods developed in previous chapters to developing brain imaging biomarkers of Alzheimer's disease. I show that using the new surface-based features and statistical learning, it is possible to develop biomarkers which outperform all others to date in terms of sensitivity to disease-modifying effects and disease specificity.

A more recent field of application for shape-based analysis comes from human skull models generated from conical CT imaging. The general registration problems are similar in spirit to brain imaging. However, the much lower signal-to-noise ratio and greater topological variability of the shape models require a new set of tools to deal with these shapes in practice. In Chapter 6, I develop an approach to modify the topology of a skull surface while preserving useful features, and again return to the sphere for dense registration and the creation of shape atlases. Due to the noisy nature of the data, a fast non-local non-linear correspondence search is developed for pairs of skull shapes from different subjects. I show that this search is crucial for high-quality registration based on resulting population-based averages and individualized shape analyses.

To understand factors that affect brain connectivity and integrity, it is beneficial to automatically cluster white matter (WM) fibers into anatomically recognizable tracts. Whole brain tractography, based on diffusion-weighted MRI, generates vast sets of fibers throughout the brain; clustering them into consistent and recognizable bundles can be difficult as there are wide individual variations in the trajectory and shape of WM pathways. Here I propose a novel automated tract clustering algorithm based on label fusion - a concept from traditional intensity-based segmentation. Streamline tractography generates many incorrect fibers, so this top-down approach extracts tracts consistent with known anatomy, by mapping multiple hand-labeled atlases into a new dataset. Then, I fuse clustering results from different atlases, using a mean distance fusion scheme. To compute population statistics, I develop a point-wise correspondence method to match, compare, and average WM tracts across subjects.

The complete workflow is demonstrated in two large-scale population studies. In one study, the major 17 tracts were extracted from 105-gradient high angular resolution diffusion images (HARDI) of 198 young normal twins to show the 3-D genetic heritability profile for each tract. In the other study, the fornix tracts of 210 participants were segmented from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database to study its relationship with cognitive decline.

Besides studying the local connectivity with fiber clustering, I also investigate whole brain connectivity from a different perspective. Many connectivity studies parcellate the brain into regions and count fibers extracted between them. The resulting network analyses require validation of the tractography, as well as region and parameter selection. I propose a mathematical formulation based on studying the eigenvalues of the Laplacian matrix of the diffusion tensor field at the voxel level. This voxelwise matrix has over a million parameters, but I derive the Kirchhoff complexity and eigen-spectrum through elegant mathematical theorems, without heavy computation. These novel measures were used to estimate the voxelwise connectivity in multiple biomedical applications such as Alzheimer's disease and intelligence prediction.