Q-space quantitative diffusion MRI measures using a stretched-exponential representation

TL;DR

This paper introduces a mathematical framework for analyzing diffusion MRI data using a stretched-exponential model, enabling more accurate characterization of tissue microstructure at high b-values under non-Gaussian diffusion assumptions.

Contribution

It analytically derives higher-order statistics of the diffusion signal with a stretched-exponential model, facilitating improved Q-space measures in non-Gaussian regimes.

Findings

Enables handling of high b-value diffusion data

Provides analytical formulas for RTOP, QMSD, QMFD

Supports early diagnosis of neurodegenerative diseases

Abstract

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.