Attenuation of MR spin-echo signal by restricted diffusion confined to a laminar system and a large rectangular box

We investigate magnetic resonance (MR) signal attenuation caused by confined by restricted diffusion confined to a laminar system and a large rectangular box using the pulsed gradient spin-echo MR method. Applying asymptotic expansions, we derive corrections up to order $1/L^2$, where $L$ is the characteristic system size, and show that in the limit of large $L$, the attenuation converges to the free diffusion expression. In the fast diffusion regime, where ${\gamma }^2{G}^2{\delta }^{2}D∆\gg 1$, interference effects become significant, limiting the applicability of the asymptotic expansion. Our findings refine diffusion-weighted MRI models and provide insights into confined molecular transport.