Bayesian Insights into Exchange and Restriction in Gray Matter Diffusion MRI

TL;DR

This work assesses the reliability of gray-matter diffusion MRI models that incorporate water exchange, focusing on NEXI and SANDIX. It leverages the µGUIDE Bayesian framework to estimate full posterior distributions, quantify uncertainty, and detect parameter degeneracies under two diffusion protocols and realistic noise. The findings show robust estimates for extracellular diffusivity $D_e$ and neurite fraction $f_n$, but limited reliability for exchange time $t_{ex}$ and soma parameters $(r_s, f_s)$, with degeneracies more pronounced under practical acquisition. The study underscores the importance of reporting uncertainty and using uncertainty-aware inference to improve reproducibility and biological interpretability in diffusion MRI analyses.

Abstract

Biophysical models in diffusion MRI (dMRI) hold promise for characterizing gray matter tissue microstructure. Yet, the reliability of their parameter estimates remains largely under-studied, especially in models that incorporate water exchange. In this study, we investigate the accuracy, precision, and presence of degeneracy of two recently proposed gray matter models, NEXI and SANDIX, using established acquisition protocols, on both simulated and \textit{in vivo} data. We employ $μ$GUIDE, a Bayesian inference framework based on deep learning, to quantify parameter uncertainty and detect degeneracies, enabling a more interpretable assessment of model fits. Our results show that while some microstructural parameters, such as extra-cellular diffusivity and neurite signal fraction, are robustly estimated, others, including exchange time and soma radius, are often associated with high uncertainty and estimation bias, particularly under realistic noise conditions and reduced acquisition protocols. Comparison with non-linear least squares fitting highlights the critical advantage of uncertainty-aware methods: the ability to flag and filter out unreliable estimates. Together, these findings emphasize the need to report uncertainty and account for model degeneracies when interpreting model-based estimates. Our study advocates for the integration of probabilistic fitting approaches into imaging pipelines to improve reproducibility and biological interpretability.

Figures (11)

• Figure 1: Graphical representation of the considered gray matter biophysical models, with the following parameters: exchange time $t_{ex}$, neurites signal fraction $f_n$, parallel diffusivity $D_{n}^{\|}$, extra-cellular diffusivity $D_e$, soma signal fraction $f_s$ and soma radius $r_s$.
• Figure 2: Simulated signals of the NEXI (A & B) and SANDIX (C & D) models, without noise, obtained from exemplar gray matter tissues using both acquisition protocols, and posterior distributions obtained with µGUIDE. For each subplot, upper rows: left plots show the signal with b-values inferior to 10 ms/µm$^2$ as a function of $b$, and right subplot shows the signal for b-values superior to 5 ms/µm$^2$ as a function of $b^{-1/2}$. Dots represent the simulated data, solid lines show signals generated from the MAP estimates, and shaded areas encompass all signals corresponding to parameter combinations sampled from the posterior distributions, illustrating their uncertainty. Bottom rows: Posterior distributions of each parameter obtained with µGUIDE. Vertical black dashed lines correspond to the ground truth values. Model parameters used to generate the signals are the following: A) $t_{ex}=43$ ms, $D_{n}^{\|}=2.55$ µm${}^2$/ms, $D_e=0.74$ µm${}^2$/ms, $f_n=0.29$jelescu_neurite_2022; B) $t_{ex}=8.15$ ms, $D_{n}^{\|}=1.45$ µm${}^2$/ms, $D_e=0.55$ µm${}^2$/ms, $f_n=0.525$olesen_diffusion_2022; C) similar to A) with $r_s=15$ µm and $f_s=0.2$; D) $t_{ex}=4.95$ ms, $D_{n}^{\|}=1.0$ µm${}^2$/ms, $D_e=0.9$ µm${}^2$/ms, $f_n=0.54$, $r_s=11.4$ µm and $f_s=0.13$olesen_diffusion_2022.
• Figure 3: Fitting results for the NEXI model using µGUIDE on 1000 test simulations. Results are shown for the extensive ex vivo acquisition protocol (A & C), and the NEXI 3T Connectom protocol (B & D). In each subplot, the top row displays the MAP estimates of the model parameters plotted against their ground truth values, color-coded by their uncertainty values. Red dots indicate cases where the posterior distribution was identified as degenerate. The bottom row shows the distribution of uncertainty values across all test simulations.
• Figure 4: Fitting results for the SANDIX model using µGUIDE on 1000 test simulations. Results are shown for the extensive ex vivo acquisition protocol (A & C), and the NEXI 3T Connectom protocol (B & D). In each subplot, the top row displays the MAP estimates of the model parameters plotted against their ground truth values, color-coded by their uncertainty values. Red dots indicate cases where the posterior distribution was identified as degenerate. The bottom row shows the distribution of uncertainty values across all test simulations.
• Figure 5: Fitting results of the NEXI model on in vivo data from one participant scanned using the 3T Connectom protocol, estimated using µGUIDE. For each model parameter, the MAP estimate and associated uncertainty are shown for a single coronal slice of the brain. Voxels exhibiting degenerate posterior distributions are marked with red dots.