Feasibility of diffusion-NMR surface-to-volume measurements tested by calculations and computer simulations

It has been demonstrated previously that the surface-to-volume ratio S/V can be determined from the derivative of the time-dependent diffusion coefficient D(t), in the limit t --> 0. Several questions arise concerning the practicality of determining S/V by NMR. In particular, how large are the errors generated by (1) working outside the t --> 0 limit and (2) measuring D outside the b --> 0 limit, both for narrow and full-width gradient pulses? Here b is gamma2G2delta2Delta for narrow pulses and gamma2G2t3/12 for broad pulses. These questions are addressed by random-walk computer simulations and numerical calculations in geometries relevant to small-airways of lung. The results demonstrate that one can work well outside the t --> 0 and b --> 0 limits, provided 10-20% accuracy in the measured S/V is sufficient. Emphasis is placed on the useful range of times t for which NMR determinations of lung S/V are feasible.