Multiple-Scale Analysis on the Fractal Structure of the Brain using Diffusion Magnetic Resonance Imaging

The primary goal of this dissertation is to develop better descriptors of the brain’s self-similar structure. We approach this goal through theory, in vitro, ex vivo, and in silico experimentation to describe the brain at both a cellular and a global level. This is done in hopes of deriving better biomarkers for structural changes in the brain due to healthy aging, neurodegeneration, or other pathologies. To this end, we approach this from two general directions. First, we expand on the standard diffusion tensor imaging (DTI) and apply the well described continuous time random walk (CTRW) model to the brain. It is well known that signal decay is not mono-exponential and so CTRW provides a model that is both flexible to characterize changes in jump length and waiting time. This dissertation examines the CTRW model using fiber phantoms and an ex vivo Huntington’s mouse model, as well as validating the CTRW findings through electron microscopy to confirm the assumptions being made about the physics and theory behind the model. In both of these cases, we find that with increase boundaries, we decrease the time fractional derivative and thus have a marker for tissue hetereogeneity. From a global perspective of the brain structure, we look at graph theory and improve on the idea of community estimation and hub analysis. While typically defined by somewhat arbitrary limits, we look at a scale dependent metric that uses multiple scales to describe the near decomposibility of the human brain. While the brain is nearly decomposable overall, select components of the human brain connectome further exhibit relative “embeddedness”. These regions heavily overlap with the recently proposed “revised limbic system” (Catani, Dell’Acqua, and Thiebaut de Schotten 2013) model for memory, emotion and behavior. Finally, we look to visualize the intrinsic topology of the brain. As the nervous system develops, the brain changes from the neural plate (a 2D structure) to the neural tube (a 3D structure) to the human brain, a complex structure that has multiple tissue types and a known fractal dimension (Ha et al. 2005) based on the many gyri and sulci spanning its surface. In this study we simplify the brain by using dimensionality reduction to view the intrinsic topology, free of obfuscation from the anatomical space. We expect that by combining this examination of the brain through multiple scales, we can get a more holistic picture of the overall structure of the brain.