Models for magnetic resonance observation of diffusion in cellular environments

Abstract

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 di usion in tissue has a restrictive character. (ii) Multiple ber directions are indistinguishable within a single voxel since Gaussian probability distribution gives only one directional maximum. This thesis consists of two parts. In the rst part, a model alternative to DTI will be suggested to characterize di usion anisotropy. Di usionattenuated MR signal for molecules under the in uence of a parabolic potential will be discussed. Signal expression under such potential can be obtained by solving the modi ed Bloch-Torrey equation via multiple correlation function (MCF) framework with the addition of a potential term . Di usion anisotropy is introduced by a sti ness tensor rather than a di usion tensor. In the second part, an alternative di usion sensitization mechanism is provided by employing rotating eld gradiens (RFGs) which leads to a way of measuring the di usion orientation distribution function (dODF) directly. Then, RFG results for both free and restricted di usion model (proposed model in the rst part) will be compared with results obtained by traditional pulsed eld gradient (PFG) based models: Q-ball imaging (QBI) and its extension to constant solid angles (CSA).