In vivo quantitation of metabolites with an incomplete model function

Metabolites can serve as biomarkers. Estimation of metabolite concentrations from an in vivo magnetic resonance spectroscopy (MRS) signal often uses a reference signal to estimate a model function of the spectral lineshape. When no reference signal is available, the a priori unknown in vivo lineshape must be inferred from the data at hand. This makes quantitation of metabolites from in vivo MRS signals a semi-parametric estimation problem which, in turn, implies setting of hyper-parameters by users of the software involved. Estimation of metabolite concentrations is usually done by nonlinear least-squares (NLLS) fitting of a physical model function based on minimizing the residue. In this work, the semi-parametric task is handled by complementing the usual criterion of minimal residue with a second criterion acting in tandem with it. This second criterion is derived from the general physical knowledge that the width of the line is limited. The limit on the width is a hyper-parameter; its setting appeared not critical so far. The only other hyper-parameter is the relative weight of the two criteria. But its setting too is not critical. Attendant estimation errors, obtained from a Monte Carlo calculation, show that the two-criterion NLLS approach successfully handles the semi-parametric aspect of metabolite quantitation.