Validity of the Gaussian phase distribution approximation for analysis of isotropic diffusion encoding applied to restricted diffusion in a cylinder

The Gaussian phase distribution approximation enables analysis of restricted diffusion encoded by general gradient waveforms but fails to account for the diffraction-like features that may occur for simple pore geometries. We investigate the range of validity of the approximation by random walk simulations of restricted diffusion in a cylinder using isotropic diffusion encoding sequences as well as conventional single gradient pulse pairs and oscillating gradient waveforms. The results show that clear deviations from the approximation may be observed at relative signal attenuations below 0.1 for one-dimensional sequences with few oscillation periods. Increasing the encoding dimensionality and/or number of oscillations while extending the total duration of the waveform diminishes the non-Gaussian effects while preserving the low apparent diffusivities characteristic of restriction.