A new algebraic method for quantitative proton density mapping using multi-channel coil data.

A difficult problem in quantitative MRI is the accurate determination of the proton density, which is an important quantity in measuring brain tissue organization. Recent progress in estimating proton density in vivo has been based on using the inverse linear relationship between the longitudinal relaxation rate T1 and proton density. In this study, the same type of relationship is being used, however, in a more general framework by constructing 3D basis functions to model the receiver bias field. The novelty of this method is that the basis functions developed are suitable to cover an entire range of inverse linearities between T1 and proton density. The method is applied by parcellating the human brain into small cubes with size 30mm x 30mm x 30mm. In each cube the optimal set of basis functions is determined to model the receiver coil sensitivities using multi-channel (32 element) coil data. For validation, we use arbitrary data from a numerical phantom where the data satisfy the conventional MR signal equations. Using added noise of different magnitude and realizations, we show that the proton densities obtained have a bias close to zero and also low noise sensitivity. The obtained root-mean-square-error rate is less than 0.2% for the estimated proton density in a realistic 3D simulation. As an application, the method is used in a small cohort of MS patients, and proton density values for specific brain structures are determined.