This work involves advances in modeling and estimating white matter fiber orientations for use in tractography studies and axonal microstructure analysis in the human brain. We make use of preferential movement of water along axon fibers rather than across it's membrane as an indirect measure using MRI data acquisition sensitized to diffusion. Over the past decade, several mathematically elegant models have been proposed, with varying acceptance levels from the clinical fraternity. With practical feasibility in mind, the trade-offs between resolution, acquisition time and SNR make the optimization of data capture protocols ever more crucial. We focus on generalizing the current state-of-art models to allow for any acquisition scheme, and go on to understand how the acquisition parameters affect the results.
The Constant Solid Angle -Orientation Distribution Function (CSA-ODF) model provides a vital correction in the Q-ball method for High Angular Resolution Diffusion Imaging (HARDI) data. The HARDI data is decomposed on a modified Spherical Harmonic (SH) basis, due to which the otherwise necessary 3-D inverse Fourier Transform can be easily estimated using a linear approximation of the Funk Radon Transform (FRT) on a single shell. This results in a simple linear-least-squares approximation, prone to over-fitting errors and low SNR. We explore an adaptive regularization scheme to generalize well for the inverse problem of interpolating the q-space data. We use a bi-exponential radial signal decay model, which uses more information about the axonal microstructure than the single-shell approximation. The 'staggered' acquisition scheme increases the angular spread of samples and allows for higher angular resolution of the fiber orientations. A comprehensive analysis of the reconstruction is shown on synthetic data, and the best parameters for acquisition is demonstrated. The optimal level of b-value, number of gradient directions, order of SH decomposition and interpolation is derived
from experiments, and results on a brain data set is shown to validate the method. We hope that this generalization of the CSA-ODF algorithm is going to provide better models of the diffusion process in MR images, and prove to be a guide for setting up the acquisition protocols for the Human Connectome Project and other future studies.