From Micro to Macro: A Study of Human Brain Structure Based on Diffusion MRI and Neuronal Networks

A study on the human brain is carried out through the use of diffusion weighted magnetic resonance imaging (MRI). The brain is studied at three different levels: micro, mid, and macro. At the micro-level, we utilize the theory of continuous time random walk to describe the anomalous diffusive behavior of water molecules in different brain tissues. This behavior is measured through multiple b-value diffusion weighted MRI experiments. Two anisotropic models were derived through the introduction of fractional calculus into the Bloch-Torrey equation. The obtained models are used to describe the complex structure of the brain white and gray matter tissues through the introduction of new biometrics. The models allow the quantification of the tortuosity and porosity of the brain tissues in different directions. At the mid-level, a recent model, the tensor distribution function, is used to extract the brain white matter fiber tracts. A new algorithm is designed to extract different complex fibers in the brain. The algorithm is able to solve the fiber crossing problem at many locations. Moreover, a new metric is suggested to measure fiber incoherence. The measure is then compared to the traditional metric, fractional anisotropy, derived from the classical diffusion tensor model. At the macro-level, the brain network community structure is studied. A new metric to extract the modular structure of networks is derived. The metric is then applied on brain networks to extract the human connectome community structure. Using the ability to extract connectome community structure, a framework is designed to allow the detection of alterations on the nodal and modular levels occurring in in group studies. The framework is then applied on two datasets, bipolar and depression. Significant results were found in agreement with previous clinical studies revealing the importance of the modular analysis of the human connectome.