Microstructure.jl: A Julia package for probabilistic microstructure model fitting with diffusion MRI

Microstructure.jl is a Julia package designed for probabilistic estimation of tissue microstructural parameters from diffusion or combined diffusion-relaxometry MRI data. It provides a flexible and extensible framework for defining compartment models and includes robust and unified estimators for parameter fitting and uncertainty quantification. The package incorporates several established models from the literature, such as the spherical mean technique (SMT), standard model imaging (SMI), and soma and neurite density imaging (SANDI), along with their extensions for analyzing combined diffusion and T2 mapping data acquired at multiple echo times. For parameter estimation, it features methods such as Markov Chain Monte Carlo (MCMC) sampling and Monte Carlo dropout with neural networks, which provide probabilistic estimates by approximating the posterior distributions of model parameters. In this study, we introduce the major modules, functionality, and design of this package. We demonstrate its usage in optimizing acquisition protocols and evaluating fitting performance with synthesized ex vivo datasets for estimating the axon diameter index. We also demonstrate its practical applications for parameter estimation and uncertainty quantification with publicly available in vivo datasets: (1) SMT on 3 b-shell and 1.25-mm isotropic resolution data from the human connectome project, (2) SANDI on 2.0-mm isotropic resolution microstructure data from the high-gradient Connectome 1.0 scanner, and (3) SMI with a free water compartment on 2 b-shell, multi-echo-time, 2.5-mm isotropic resolution data from a Prisma scanner. Microstructure.jl is applicable to in vivo and ex vivo imaging data acquired with typical research, high-performance, or pre-clinical scanners.