Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ a²/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.