T(2)-relaxometry for myelin water fraction extraction using wald distribution and extended phase graph

Quantitative assessment of myelin density in the white matter is an emerging tool for neurodegenerative disease related studies such as multiple sclerosis and Schizophrenia. For the last two decades, T2 relaxometry based on multi-exponential fitting to a single slice multi-echo sequence has been the most common MRI technique for myelin water fraction (MWF) mapping, where the short T2 is associated with myelin water. However, modeling the spectrum of the relaxations as the sum of large number of impulse functions with unknown amplitudes makes the accuracy and robustness of the estimated MWF's questionable. In this paper, we introduce a novel model with small number of parameters to simultaneously characterize transverse relaxation rate spectrum and B1 inhomogeneity at each voxel. We use mixture of three Wald distributions with unknown mixture weights, mean and shape parameters to represent the distribution of the relative amount of water in between myelin sheets, tissue water, and cerebrospinal fluid. The parameters of the model are estimated using the variable projection method and are used to extract the MWF at each voxel. In addition, we use Extended Phase Graph (EPG) method to compensate for the stimulated echoes caused by B1 inhomogeneity. To validate our model, synthetic and real brain experiments were conducted where we have compared our novel algorithm with the non-negative least squares (NNLS) as the state-of-the-art technique in the literature. Our results indicate that we can estimate MWF map with substantially higher accuracy as compared to the NNLS method.