The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-396

“Quantifications of Self-diffusion Processes in Brain White Tracts with Finite Element Method”

by Shahryar Karimi-Ashtiani

August 2009

Diffusion MRI (D-MRI) opened a new front for uncovering the convoluted structure of the central nervous system by providing the capability for non-invasive identification of geometries of white tracts in the brain. It is well understood that, this imaging modality is characterized by the shape of the self-diffusion (SD) profile within the brain fibers. Despite previous efforts in the literature for quantification of this physical phenomenon, most current methods suffer from a number of constraints which severely limit the extent of their practical applicability. Here, by relaxing limitations of previous work, we address the solution of the SD process in its most general partial differential equation (PDE) form. To this end, we develop an approach based on the finite elements methodology (FEM) to obtain the numerical SD solution in multi-compartments models of white tracts. Our method provides more flexibility for geometry and material of different white tracts compartments than existing techniques. Due to the finite resolution of D-MRI signals, reconstruction of the SD profile is voxel-wise rather than point-wise. We formulate this problem in terms of parameters of microstructures of white tracts, passing through a voxel. Consequently, the developed method can easily accommodate challenging situations such as tract crossings and demyelinations into computing the voxel aggregate propagators.

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