Fast and robust quantification of uncertainty in non-linear diffusion MRI models

Abstract

Diffusion MRI (dMRI) allows for non-invasive investigation of brain tissue microstructure. By fitting a model to the dMRI signal, various quantitative measures can be derived from the data, such as fractional anisotropy, neurite density and axonal radii maps. We investigate the Fisher Information Matrix (FIM) and uncertainty propagation as a generally applicable method for quantifying the parameter uncertainties in linear and non-linear diffusion MRI models. In direct comparison with Markov Chain Monte Carlo (MCMC) sampling, the FIM produces similar uncertainty estimates at much lower computational cost. Using acquired and simulated data, we then list several characteristics that influence the parameter variances, including data complexity and signal-to-noise ratio. For practical purposes we investigate a possible use of uncertainty estimates in decreasing intra-group variance in group statistics by uncertainty-weighted group estimates. This has potential use cases for detection and suppression of imaging artifacts.

Keywords

• Uncertainty estimates
• Variances
• Diffusion MRI
• Microstructure
• Fisher Information Matrix (FIM)
• Cramér Rao Lower Bound (CRLB)