Understanding the anatomical changes in the connectional network of the human brain is an important research problem in cognitive and clinical neuroscience that could give improved insights onto human development, progression of neurological diseases and effects of traumatic injuries over time. Modeling the variability of human brain "connectivity" over a population can also help understand the effects of demographic or genetic variables on human anatomy and enable early diagnosis of possible anomalies. In the past two decades, diffusion tensor imaging (DTI) has been widely used to understand the neuroanatomy of human brain, mostly in terms of tensor-derived scalar maps such as fractional anisotropy (FA) or apparent diffusion coefficient (ADC) providing additional quantitative information about the tissue structures; or fiber tractography, a DTI based methodology aiming to represent a symbolic version of neuro-connectivity. Due to the lack of mathematical tools able to cope with the complex nature of DTI data and numerous challenges involved in diffusion weighted image processing, population and longitudinal studies based on DTI acquisitions classically simplify the problem onto a simpler domains. However, it is widely acknowledged that the bias in diffusion data introduced by the acquisition and post--processing steps renders different analysis approaches incompatible, and possibly inaccurate.;In this thesis, I present new paradigms and an accompanying suite of tools to realize a robust approach to DTI analysis from groupwise variability modeling perspective. The first part of the thesis describes the problems involved in diffusion weighted image and diffusion tensor image processing and why DTI data can not be directly used in a statistical analysis framework performing as a black box. These problems include different types of distortions involved in data acquisitions, unification and assessment of a variety of DTI acquisition protocols, problems involved in diffusion weighted data interpolation, the bias introduced by physiological noise and the data bias. In the second part, these challenges are analyzed in detail and either processing solutions are methodologies to incorporate their effects into statistical frameworks are provided. Efficient and robust algorithms required for multi-data DTI analysis have been developed in the following sections, focusing on spatial alignment of tensor data and computation of tensorial statistics enabling voxel or region-wise variability analysis using DTI data.;The complete DTI processing and variability analysis framework developed here was applied to DTI studies for understanding the differences in human brain due to demographic variables.
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