Trusting the Inverse: Reliability-Aware Mapping for Simulation-Based Microstructure Estimation in Diffusion MRI

Abstract

Diffusion-weighted MRI can probe tissue microstructure non-invasively, however interpreting microstructural parameter estimates remains challenging due to the intrinsic ambiguity of the inverse problem. While simulation-based approaches can incorporate increasingly realistic tissue models, they still lack voxel-wise characterisation of the reliability and degeneracy of the inferred parameters. Here, we introduce a reliability framework for simulation-based microstructure estimation based on three complementary scores that identify distinct sources of unreliability in the estimation process: out-of-distribution signals, local signal mismatch, and parameter degeneracy. The framework was implemented using a Monte Carlo dictionary of 1,050 synthetic voxels generated from geometrically realistic substrates, with parameter ranges grounded in electron microscopy measurements of rat corpus callosum. The dictionary spans biologically plausible axon radii (0.25-0.85 $μ$m), microscopic angular spread (0-10$^\circ$), packing densities (60-92%), and intrinsic diffusivities (1.75-3.0 $μ$m$^2$/ms). On synthetic data, the resulting Reliability Index correlated with actual estimation error (Spearman $ρ= -0.742$) and distinguished between extrapolation, poor local interpolation, and parameter degeneracy. Applied to in vivo corpus callosum DW-MRI in rat (256 voxels, four animals) and human (MGH-USC HCP, 18,765 voxels, nine subjects), 91% and 73% of voxels respectively exceeded $R > 0.5$. These results demonstrate how reliability-aware analysis can support the interpretation and future development of simulation-based diffusion MRI microstructure models.