Shining light on degeneracies and uncertainties in quantifying both exchange and restriction with time-dependent diffusion MRI using Bayesian inference

Diffusion MRI (dMRI) biophysical models hold promise for characterizing gray matter tissue microstructure. Yet, the reliability of estimated parameters 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 two acquisition protocols from the literature, on both simulated and in vivo data. We employ $\mu$GUIDE, a Bayesian inference framework based on deep learning, to quantify model uncertainty and detect parameter degeneracies, enabling a more interpretable assessment of fitted parameters. Our results show that while some microstructural parameters, such as extra-cellular diffusivity and neurite signal fraction, are robustly estimated, others, such as exchange time and soma radius, are often associated with high uncertainty and estimation bias, especially under realistic noise conditions and reduced acquisition protocols. Comparisons with non-linear least squares fitting underscore the added value of uncertainty-aware methods, which allow for the identification and filtering of unreliable estimates. These findings emphasize the need to report uncertainty and consider model degeneracies when interpreting model-based estimates. Our study advocates for the integration of probabilistic fitting approaches in neuroscience imaging pipelines to improve reproducibility and biological interpretability.

$μ$GUIDE: a framework for microstructure imaging via generalized uncertainty-driven inference using deep learning

This work proposes $\mu$GUIDE: a general Bayesian framework to estimate posterior distributions of tissue microstructure parameters from any given biophysical model or MRI signal representation, with exemplar demonstration in diffusion-weighted MRI. Harnessing a new deep learning architecture for automatic signal feature selection combined with simulation-based inference and efficient sampling of the posterior distributions, $\mu$GUIDE bypasses the high computational and time cost of conventional Bayesian approaches and does not rely on acquisition constraints to define model-specific summary statistics. The obtained posterior distributions allow to highlight degeneracies present in the model definition and quantify the uncertainty and ambiguity of the estimated parameters.

Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements

Effective characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in diffusion MRI (dMRI). Solving the problem of relating the dMRI signal with cytoarchitectural characteristics calls for the definition of a mathematical model that describes brain tissue via a handful of physiologically-relevant parameters and an algorithm for inverting the model. To address this issue, we propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model. As opposed to other approaches from the literature, our algorithm yields not only an estimation of the parameter vector $\theta$ that best describes a given observed data point $x_0$, but also a full posterior distribution $p(\theta|x_0)$ over the parameter space. This enables a richer description of the model inversion, providing indicators such as credible intervals for the estimated parameters and a complete characterization of the parameter regions where the model may present indeterminacies. We approximate the posterior distribution using deep neural density estimators, known as normalizing flows, and fit them using a set of repeated simulations from the forward model. We validate our approach on simulations using dmipy and then apply the whole pipeline on two publicly available datasets.