J. Stepisnik, SPIN-ECHO ATTENUATION OF RESTRICTED DIFFUSION AS A DISCORD OF SPIN PHASE-STRUCTURE, Journal of magnetic resonance [1997], 131(2), 1998, pp. 339-346
Citations number
29
Categorie Soggetti
Physics, Atomic, Molecular & Chemical","Biochemical Research Methods
By using the particle probability density we analyze the spin echo att
enuation of particles, diffusing in a bounded region. It provides a me
ans to expand a nonuniform spin phase distribution into a series of wa
ves that characterize the geometry and boundary conditions of confinem
ent. Random motion disrupts the initial phase structure created by app
lied gradients and consequently discords its structure waves. By assum
ing the spin phase fluctuation and/or the randomness of spin phase dis
tribution in the subensemble as a Gaussian stochastic process, we deri
ve a new analytical expression for the echo attenuation related to the
particle velocity correlation. For a diffusion in porous structure we
get the expression featuring the same ''diffusive diffraction'' patte
rns as those being found and explained by P. T. Callaghan and A. Coy (
''Principles of Nuclear Magnetic Resonance Microscopy,'' Oxford Univ,
Press, Oxford (1991); J. Chem. Phys. 101, 4599-4609 (1994)) with the u
se of propagator theory. With the new approach we cast a new light on
the phenomena and derive analitically how the diffusive diffractions a
ppear when the sequence of finite or even modulated gradients are appl
ied. The method takes into account the non-Markovian character of rest
ricted diffusion, and therefore the echo dependence on the diffusion l
engths and on the strength of applied gradient differs from the result
s of authors assuming the Markovian diffusion either by dealing with t
he diffusion propagators or by the computer simulation of Fick's diffu
sion. (C) 1998 Academic Press.