Generalised calculation of NMR imaging edge effects arising from restricted diffusion in porous media

The theoretical problem of how to describe apparent image spin density under conditions of restricted diffusion, given any general gradient sequence, is intrinsically complex. Here we demonstrate a simple approach to calculating the signal and the corresponding density in nuclear magnetic resonance (NMR) imaging experiments by means of an impulse-propagator method based on matrix multiplication. The multiplication scheme bears a natural and straightforward relationship to the k-space sampling, while the matrices themselves are calculated from the eigenmodes of the pore diffusion equation. Good agreement is found between theoretical predictions and the results of micro-imaging experiments on water trapped in rectangular pores whose walls are spaced by 100 microns along the read direction.