Uncertainty propagation in absolute metabolite quantification for in vivo MRS of the human brain

Abstract

Purpose: Absolute spectral quantification is the standard method for deriving estimates of the concentration from metabolite signals measured using in vivo proton MRS (1H-MRS). This method is often reported with minimum variance estimators, specifically the Cramér-Rao lower bound (CRLB) of the metabolite signal amplitude's scaling factor from linear combination modeling. This value serves as a proxy for SD and is commonly reported in MRS experiments. Characterizing the uncertainty of absolute quantification, however, depends on more than simply the CRLB. The uncertainties of metabolite-specific (T1m, T2m), reference-specific (T1ref, T2ref), and sequence-specific (TR, TE) parameters are generally ignored, potentially leading to an overestimation of precision. In this study, the propagation of uncertainty is used to derive a comprehensive estimate of the overall precision of concentrations from an internal reference. Methods: The propagated uncertainty is calculated using analytical derivations and Monte Carlo simulations and subsequently analyzed across a set of commonly measured metabolites and macromolecules. The effect of measurement error from experimentally obtained quantification parameters is estimated using published uncertainties and CRLBs from in vivo 1H-MRS literature. Results: The additive effect of propagated measurement uncertainty from applied quantification correction factors can result in up to a fourfold increase in the concentration estimate's coefficient of variation compared to the CRLB alone. A case study analysis reveals similar multifold increases across both metabolites and macromolecules. Conclusion: The precision of absolute metabolite concentrations derived from 1H-MRS experiments is systematically overestimated if the uncertainties of commonly applied corrections are neglected as sources of error.