title: Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation.
abstract: 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.
authors.affiliation: Laboratoire de Physique de la Matière Condensée, CNRS - Ecole Polytechnique, F-91128 Palaiseau, France. Electronic address: denis.grebenkov@polytechnique.edu.
authors.forename: Denis S
authors.initials: DS
authors.lastname: Grebenkov
authors.affiliation: CMAP, Ecole Polytechnique, F-91128 Palaiseau, France.
authors.forename: Dang Van
authors.initials: DV
authors.lastname: Nguyen
authors.affiliation: CMAP, Ecole Polytechnique, F-91128 Palaiseau, France; Neurospin, CEA Saclay, F-91191 Gif sur Yvette, France.
authors.forename: Jing-Rebecca
authors.initials: JR
authors.lastname: Li
mesh_terms: D000465:Algorithms; D001704:Biopolymers / Q000737:chemistry / Q000378:metabolism*; D002462:Cell Membrane / Q000737:chemistry / Q000378:metabolism*; D002463:Cell Membrane Permeability / Q000502:physiology*; D004058:Diffusion; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
chemical_list: D001704:Biopolymers
keywords: Bloch–Torrey equation; Diffusion; Exchange; Permeability