ABSTRACT
The Cramér-Rao lower bounds (CRBs) are the lowest possible standard deviations of all unbiased model parameter estimates obtained from the data. Consequently they give insight into the potential performance of quantitation estimators. Using analytical CRB expressions for spectral parameters of singlets and doublets in noise, one is able to judge the precision as a function of spectral and experimental parameters. We point out the usefulness of these expressions for experimental design. The influence of constraints (chemical prior knowledge) on spectral parameters of the peaks of doublets is demonstrated and the inherent benefits for quantitation are shown. Abbreviations used: CRB Cramér-Rao lower bounds
Subject(s)
Magnetic Resonance Spectroscopy , Signal Processing, Computer-Assisted , Animals , Brain Chemistry , Mathematics , Models, Theoretical , RatsABSTRACT
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Subject(s)
Magnetic Resonance SpectroscopyABSTRACT
We have derived analytical expressions of the Cramer-Rao lower bounds on spectral parameters for singlet, doublet, and triplet peaks in noise. We considered exponential damping (Lorentzian lineshape) and white Gaussian noise. The expressions, valid if a sufficiently large number of samples is used, were derived in the time domain for algebraic convenience. They enable one to judge the precision of any unbiased estimator as a function of the spectral and experimental parameters, which is useful for quantitation objectives and experimental design. The influence of constraints (chemical prior knowledge) on parameters of the peaks of doublets and triplets is demonstrated both analytically and numerically and the inherent benefits for quantitation are shown. Our expressions also enable analysis of spectra comprising many peaks. Copyright 2000 Academic Press.
ABSTRACT
RATIONALE AND OBJECTIVES: This work concerns quantitation of in vivo magnetic resonance spectroscopy signals and the influence of prior knowledge on the precision of parameter estimates. The authors point out how prior knowledge can be used for experiments. METHODS: The Cramer-Rao lower bounds formulae of the noise-related standard deviations on spectral parameters for doublets and triplets were derived. Chemical prior knowledge of the multiplet structures was used. RESULTS: The benefit of chemical prior knowledge was estimated for doublet and triplet structures of arbitrary shape. Then, it was used to quantify in vivo 31P time-series signals of rat brain. CONCLUSIONS: Analytic expressions of errors on parameter estimates were derived, enabling prediction of the benefit of prior knowledge on quantitation results. These formulae allow us to state, for a given noise level, if the quantitation of strongly overlapping peaks such as adenosine triphosphate multiplets can be performed successfully.
