Spatial mapping of translational diffusion coefficients using diffusion tensor imaging: A mathematical description

摘要: In this article, we discuss the theoretical background for diffusion weighted imaging and tensor imaging. Molecular is a random process involving thermal Brownian motion. biological tissues, underlying microstructures restrict of water molecules, making directionally dependent. Water in tissue mathematically characterized by tensor, elements which contain information about magnitude direction function coordinate system. Thus, it possible to generate contrast based primarily on effects. Expressing terms measured coefficient (eigenvalue) any one can lead errors. Nowhere more evident than white matter, due preferential orientation myelin fibers. The directional dependency removed diagonalization then yields set three eigenvalues eigenvectors, representing orthogonal axes ellipsoid, respectively. For example, eigenvalue corresponding eigenvector along long axis fiber corresponds qualitatively with least restriction. Determination principal values various anisotropic indices provides structural information. We review use measurements using modified Stejskal-Tanner equation. anisotropy analyzed decomposing symmetrical properties describing geometry tensor. further describe visualizing tract organization human brain.