Stejskal-tanner equation derived in full

The pulsed field gradient spin‐echo nuclear magnetic resonance method is used to measure the translational diffusion of solvents and solutes in homogeneous and heterogeneous systems. It is widely used in the characterization of molecules and materials in general, via phenomena such as ‘diffusion int...

Full description

Saved in:
Bibliographic Details
Published inConcepts in magnetic resonance. Part A, Bridging education and research Vol. 40A; no. 5; pp. 205 - 214
Main Authors Kuchel, Philip W., Pagès, Guilhem, Nagashima, Kaz, Velan, Sendhil, Vijayaragavan, Vimalan, Nagarajan, Vijayasarathi, Chuang, Kai Hsiang
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.09.2012
Wiley
Subjects
Atomic Physics
Chemical Physics
Chemical Sciences
Diffusion
Engineering Sciences
Fick's equation
magnetization
Mathematica
Physics
pulsed field gradient
Radiochemistry
Signal and Image processing
fick's equation
diffusion
magnetization
mathematica
pulsed field gradient
Online AccessGet full text

Cover

More Information
Summary:The pulsed field gradient spin‐echo nuclear magnetic resonance method is used to measure the translational diffusion of solvents and solutes in homogeneous and heterogeneous systems. It is widely used in the characterization of molecules and materials in general, via phenomena such as ‘diffusion interference’. It is also the basis of tissue discrimination in magnetic resonance imaging, via diffusion tensor imaging. The mathematical equation used to analyze data from a simple noninteracting solute (using a pair of magnetic field gradient pulses that are applied in the experiment) was first derived by Stejskal and Tanner. However, in the article and in subsequent presentations the basic derivation, which we call the the “theoretical physics” of the theory, is not presented in extenso. Conversely, many papers in which the exploration of the effects of magnetic field gradient pulses of shapes other than simple rectangles generally begin with the time‐dependent integral that emerges from the original theoretical physics. To fill this “pedagogical gap” we use here a rigorous step‐by‐step approach to the theoretical physics of the Stejskal–Tanner equation and indicate how it was based on earlier theories. We also take the opportunity to indicate a contemporary approach to deriving new relationships between user‐defined magnetic field gradient pulse shapes and the diffusion coefficient; and we show how these can be rapidly and accurately derived using symbolic computation. © 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40A: 205–214, 2012.
Bibliography:istex:456FBABCA0536E9EE98FEBCF1A44A038F68F2163
We also bring the reader's attention to the fact that JE Tanner's PhD Thesis entitled "Use of a pulsed magnetic-field gradient for measurements of self-diffusion by spin-echo nuclear magnetic resonance with applications to restricted diffusion in several tissues and emulsions," The University of Wisconsin, 1966, is available through University Microfilms, Ann Arbor, Michigan, as 66-5, 951.
ark:/67375/WNG-0L6XKJ2J-9
ArticleID:CMR21241
We also bring the reader's attention to the fact that JE Tanner's PhD Thesis entitled “Use of a pulsed magnetic‐field gradient for measurements of self‐diffusion by spin‐echo nuclear magnetic resonance with applications to restricted diffusion in several tissues and emulsions,” The University of Wisconsin, 1966, is available through University Microfilms, Ann Arbor, Michigan, as 66‐5, 951.
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1546-6086
1552-5023
DOI:10.1002/cmr.a.21241