The trouble with free-water elimination using single-shell diffusion MRI data: A case study in ageing

Free-water elimination (FWE) modelling for diffusion tensor imaging (DTI) can be used to estimate the free-water (FW) volume fraction, as well as FW-compensated DTI parameters. Single-shell (SS) diffusion magnetic resonance imaging (MRI) acquisitions are more common in clinical cohorts due to time constraints, but the FWE-DTI model is a two-compartment model, hence only well posed for multi-shell (MS) data. A regularised gradient descent (RGD) method is often applied to SS datasets and has been used to study healthy ageing, Alzheimer's and Parkinson's disease, amongst others, largely ignoring the methodological limitations of this approach. In this study, we compared the performance of RGD fitting with SS data, to a non-linear least squares (NLS) fitting applied to MS data, using simulations and data from 620 participants aged 18 to 88 years. Consistent with previous studies, our simulations show that RGD fitting using SS data flattens the relationship between mean diffusivity (MD) estimates and their ground truth values, and introduces an artificial positive correlation between fractional anisotropy (FA) estimates and the underlying tissue ground truth MD. Neither of these biases were observed when NLS fitting was applied to MS data. In human data, a smaller number of significant voxels with positive correlations between MD and age were observed when the RGD SS algorithm was used, which is consistent with the flattening of MD profiles observed in simulations. FW-compensated FA maps produced strikingly different results depending on the method employed: the maps obtained with RGD SS identified some brain areas with a strong positive association with age, while no such positive correlations were found with MS NLS. While similar positive correlations between age and FW-compensated FA maps obtained with SS RGD have been reported, these results are only replicated when the RGD SS was used, suggesting that this apparent FA increase was likely an artefact introduced by inappropriate modelling using SS data. Our study, therefore, suggests that previous findings reported in the literature using the RGD approach should be interpreted with extreme care.