Diffusion magnetic resonance imaging (dMRI) is a relatively modern technique used to study tissue microstructure in a non-invasive way. Non-Gaussian diffusion representation is related to the restricted diffusion and can provide information about the underlying tissue properties. In this paper, we analytically derive n-th order statistics of the signal considering a stretched-exponential representation of the diffusion. Then, we retrieve the Q-space quantitative measures such as the Return-To-the-Origin Probability (RTOP), Q-space mean square displacement (QMSD), Q-space mean fourth-order displacement (QMFD). The stretched-exponential representation enables the handling of the diffusion contributions from a higher b-value regime under a non-Gaussian assumption, which can be useful in diagnosing or prognosis of neurodegenerative diseases in the early stages. Numerical implementation of the method is freely available at https://github.com/TPieciak/Stretched.
@article{arxiv.2009.07376,
title = {Q-space quantitative diffusion MRI measures using a stretched-exponential representation},
author = {Tomasz Pieciak and Maryam Afzali and Fabian Bogusz and Aja-Fernández and Derek K. Jones},
journal= {arXiv preprint arXiv:2009.07376},
year = {2020}
}