THE IMPACT OF GEOMETRY FACTORS ON NMR DIFFUSION MEASUREMENTS BY THE STEJSKAL AND TANNER PULSED GRADIENTS METHOD
Loading...
Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
International Journal of Theoretical Physics, Group Theory and Nonlinear Optics
Abstract
Diffusion imaging and particularly diffusion tensor imaging have become popular
due to their numerous clinical and research applications which span from brain stroke
evaluation to fiber tracking. With few exceptions, these methods are rooted in the
classical Stejskal-Tanner formula for the diffusion-attenuated signal, usually obtained by
solving the Bloch-Torrey partial differential equations. Here we derive the Stejskal-
Tanner formula in the simplest possible manner, avoiding cumbersome integrals and
differential equations. This approach makes it easy to understand the origin of the
diffusion signal attenuation, the effects of various diffusion sequence parameters, and
also the numerous important pitfalls are discussed. This contribution is based on a
mathematical formulation for the analysis of geometry factors in Stejskal-Tanner imaging
sequence. Calculations are based on the direct analytical solution of the Bloch NMR flow
equations by the method of separation of variable in Cartesian, cylindrical and spherical
polar coordinates representing the NMR transverse magnetization. Appropriate
mathematical transformations are involved in the resolution algorithm at different stages.
The mathematical transformations are introduced based on Bessel and Legendre
polynomials.
Description
Staff Publication
Keywords
NMR diffusion equations,, Stejskal-Tanner imaging sequence,, Geometrical factors,, Bessel and Legendre polynomials.