Bayesian uncertainty quantification for magnetic resonance fingerprinting.

Magnetic Resonance Fingerprinting (MRF) is a promising technique for fast quantitative imaging of human tissue. In general, MRF is based on a sequence of highly undersampled MR images which are analyzed with a pre-computed dictionary. MRF provides valuable diagnostic parameters such as the $T_1$ and $T_2$ MR relaxation times. However, uncertainty characterization of dictionary-based MRF estimates for $T_1$ and $T_2$ has not been achieved so far, which makes it challenging to assess if observed differences in these estimates are significant and may indicate pathological changes of the underlying tissue. We propose a Bayesian approach for the uncertainty quantification of dictionary-based MRF which leads to probability distributions for $T_1$ and $T_2$ in every voxel. The distributions can be used to make probability statements about the relaxation times, and to assign uncertainties to their dictionary-based MRF estimates. All uncertainty calculations are based on the pre-computed dictionary and the observed sequence of undersampled MR images, and they can be calculated in short time. The approach is explored by analyzing MRF measurements of a phantom consisting of several tubes across which MR relaxation times are constant. The proposed uncertainty quantification is quantitatively consistent with the observed within-tube variability of estimated relaxation times. Furthermore, calculated uncertainties are shown to characterize well observed differences between the MRF estimates and the results obtained from high-accurate reference measurements. These findings indicate that a reliable uncertainty quantification is achieved. We also present results for simulated MRF data and an uncertainty quantification for an in vivo MRF measurement. MATLAB$^{\scriptsize \text{\textregistered}}$ source code implementing the proposed approach is made available.