Models for magnetic resonance observation of diffusion in cellular environments

Diffusion tensor imaging (DTI) is a widely used way of mapping anatomical connectivity in the brain. However, it is based on two basic features that limit the validity of the model : (i) It is a Gaussian based model. However, studies show that the diffusion in tissue has a restrictive character. (ii) Multiple fiber directions are indistinguishable within a single voxel since Gaussian probability distribution gives only one directional maximum. This thesis consists of two parts. In the first part, a model alternative to DTI will be suggested to characterize diffusion anisotropy. Diffusion-attenuated MR signal for molecules under the influence of a parabolic potential will be discussed. Signal expression under such potential can be obtained by solving the modified Bloch-Torrey equation via multiple correlation function (MCF) framework with the addition of a potential term . Diffusion anisotropy is introduced by a stiffness tensor rather than a diffusion tensor. In the second part, an alternative diffusion sensitization mechanism is provided by employing rotating field gradiens (RFGs) which leads to a way of measuring the diffusion orientation distribution function (dODF) directly. Then, RFG results for both free and restricted diffusion model (proposed model in the first part) will be compared with results obtained by traditional pulsed field gradient (PFG) based models: Q-ball imaging (QBI) and its extension to constant solid angles (CSA).