Statistical analyses of motion-corrupted MRI relaxometry data

Consistent noise variance across data points (i.e. homoscedasticity) is required to ensure the validity of statistical analyses of MRI data conducted using linear regression methods. However, head motion leads to degradation of image quality, introducing noise heteroscedasticity into ordinary-least square analyses. The recently introduced QUIQI method restores noise homoscedasticity by means of weighted least square analyses in which the weights, specific for each dataset of an analysis, are computed from an index of motion-induced image quality degradation. QUIQI was first demonstrated in the context of brain maps of the MRI parameter R2*, which were computed from a single set of images with variable echo time. Here, we extend this framework to quantitative maps of the MRI parameters R1, R2*, and MTsat, which are computed from multiple sets of images. QUIQI allows for optimization of the noise model by using metrics quantifying heteroscedasticity and free energy. QUIQI restores homoscedasticity more effectively than insertion of an image quality index in the analysis design and yields higher sensitivity than simply removing the datasets most corrupted by head motion from the analysis. In sum, QUIQI provides an optimal approach to group-wise analyses of a range of quantitative MRI parameter maps that is robust to inherent homoscedasticity.