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

Absolute spectral quantification is the standard method for deriving estimates of the concentration from metabolite signals measured using in vivo proton MRS (¹ H-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 (T_1m , T_2m ), reference-specific (T_1ref , T_2ref ), and sequence-specific (T_R , T_E ) 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.

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 ¹ H-MRS literature.

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.

The precision of absolute metabolite concentrations derived from ¹ H-MRS experiments is systematically overestimated if the uncertainties of commonly applied corrections are neglected as sources of error.