Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation

The adaptive variation of the gradient intensity with the diffusion time at a constant optimal b-value is proposed to enhance the contribution of the nuclei diffusing across permeable barriers, to the pulsed-gradient spin-echo (PGSE) signal. An exact simple formula the PGSE signal is derived under the narrow pulse approximation in the case of one-dimensional diffusion across a single permeable barrier. The barrier contribution to the signal is shown to be maximal at a particular b-value. The exact formula is then extended to multiple permeable barriers, while the PGSE signal is shown to be sensitive to the permeability and to the inter-barrier distance. Potential applications of the protocol to survey diffusion in three-dimensional domains with permeable membranes are illustrated through numerical simulations.