Microstructure.jl: a Julia Package for Probabilistic Microstructure Model Fitting with Diffusion MRI

Abstract: 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 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 like 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 model fitting performance with synthesized datasets. We also showcase practical applications with publicly available datasets. Microstructure.jl is applicable to in vivo and ex vivo imaging data acquired with typical research, high-performance, or pre-clinical scanners.