Quantitative magnetic resonance spectroscopy: Semi‐parametric modeling and determination of uncertainties

Abstract

A semi-parametric approach for the quantitative analysis of magnetic resonance (MR) spectra is proposed and an uncertainty analysis is given. Single resonances are described by parametric models or by parametrized in vitro spectra and the baseline is determined nonparametrically by regularization. By viewing baseline estimation in a reproducing kernel Hilbert space, an explicit parametric solution for the baseline is derived. A Bayesian point of view is adopted to derive uncertainties, and the many parameters associated with the baseline solution are treated as nuisance parameters. The derived uncertainties formally reduce to Cramé r-Rao lower bounds for the parametric part of the model in the case of a vanishing baseline.The proposed uncertainty calculation was applied to simulated and measured MR spectra and the results were compared to Cramé r-Rao lower bounds derived after the nonparametrically estimated baselines were subtracted from the spectra. In particular, for high SNR and strong baseline contributions the proposed procedure yields a more appropriate characterization of the accuracy of parameter estimates than Cramé r-Rao lower bounds, which tend to overestimate accuracy. Accurate quantitative analysis of in vivo 1 H magnetic resonance spectra is a challenging task and has been the subject of research for a long time; see (1-3) for reviews. In addition to technical advances, such as higher field strength (4) and novel pulse sequences (5), the development of sophisticated quantification approaches (6 -16) has greatly contributed to establishing magnetic resonance spectroscopy (MRS) as a noninvasive tool for medical diagnosis and biochemical analysis. Further improvement of quantification methods is still a topic of interest, and to date a wide variety of methods are in use. Consequently, considerable effort has been undertaken in comparing different approaches of spectrum analysis (17)(18)(19)(20).Typically, parametric models including (parametrized) in vitro spectra are utilized for quantitative analysis of magnetic resonance (MR) spectra. Determination of the unknown MRS parameters is usually done by (nonlinear) least-squares fitting, either in the time or in the frequency domain. A serious difficulty arises-in particular when analyzing spectra acquired at short echo times (TE)-due to the presence of baseline contributions caused by residual water and macromolecules. Generally, no parametric model is available for these baseline contributions, but they can be assumed to be smooth in the frequency domain. Several methods have been proposed for dealing with this task; e.g., successful baseline treatment has been carried out by spline approximation (7) and application of wavelets (12), but incorporation of measured baselines has also been suggested (4,13,14).Characterizing the accuracies of calculated MRS parameter estimates is an important part of quantitative analysis, and reliable uncertainty calculation is mandatory for assessing or comparing individual results. Usually, accuracies of MRS parameter e...

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