Pulsed-gradient spin-echo monitoring of restricted diffusion 
in multilayered structures

D. S. Grebenkov

Laboratoire de Physique de la Matiere Condensee,
CNRS -- Ecole Polytechnique, F-91128 Palaiseau, France

Email: denis.grebenkov@polytechnique.edu

A general mathematical basis is developed for computation of the
pulsed-gradient spin-echo signal attenuated due to restricted
diffusion in multilayered structures (e.g., multiple slabs,
cylindrical or spherical shells).  Individual layers are characterized
by (different) diffusion coefficients and relaxation times, while
boundaries between adjacent layers are characterized by (different)
permeabilities.  Arbitrary temporal profile of the applied magnetic
field can be incorporated.  The signal is represented in a compact
matrix form and the explicit analytical formulas for the elements of
the underlying matrices are derived.  The implemented algorithm is
faster and much more accurate than classical techniques such as Monte
Carlo simulations or numerical resolutions of the Bloch-Torrey
equation.  The algorithm can be applied for studying restricted
diffusion in biological systems which exhibit a multilayered
structure such as composite tissues, axons and living cells.

Reference

D. S. Grebenkov, Pulsed-gradient spin-echo monitoring of restricted 
diffusion in multilayered structures, J. Magn. Reson. (accepted).