Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

Benjamin F Moroney; Timothy Stait-Gardner; Bahman Ghadirian; Nirbhay N Yadav; William S Price

doi:10.1016/j.jmr.2013.06.019

Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

J Magn Reson. 2013 Sep:234:165-75. doi: 10.1016/j.jmr.2013.06.019. Epub 2013 Jul 1.

Authors

Benjamin F Moroney¹, Timothy Stait-Gardner, Bahman Ghadirian, Nirbhay N Yadav, William S Price

Affiliation

¹ Nanoscale Organisation and Dynamics Group, University of Western Sydney, Penrith, NSW 2751, Australia.

PMID: 23887027
DOI: 10.1016/j.jmr.2013.06.019

Abstract

Pulsed gradient spin-echo (PGSE) NMR diffusion measurements provide a powerful technique for probing porous media. The derivation of analytical mathematical models for analysing such experiments is only straightforward for ideal restricting geometries and rapidly becomes intractable as the geometrical complexity increases. Consequently, in general, numerical methods must be employed. Here, a highly flexible method for calculating the results of PGSE NMR experiments in porous systems in the short gradient pulse limit based on the finite element method is presented. The efficiency and accuracy of the method is verified by comparison with the known solutions to simple pore geometries (parallel planes, a cylindrical pore, and a spherical pore) and also to Monte Carlo simulations. The approach is then applied to modelling the more complicated cases of parallel semipermeable planes and a pore hopping model. Finally, the results of a PGSE measurement on a toroidal pore, a geometry for which there is presently no current analytical solution, are presented. This study shows that this approach has great potential for modelling the results of PGSE experiments on real (3D) porous systems. Importantly, the FEM approach provides far greater accuracy in simulating PGSE diffraction data.

Keywords: Diffraction; Diffusion; Finite element method; PGSE; Restricted diffusion.