Error images for spectroscopic imaging by LCModel using Cramer–Rao bounds

Abstract

The results of spectroscopic imaging (SI) measurements are often presented as metabolic images. If the spectra quality is not sufficient, the calculated concentrations are biased and the metabolic images show an incorrect metabolite distribution. To simplify the quality analysis of spectra measured by SI, an error image, reflecting the accuracy of the computed concentrations, can be displayed along with the metabolite image. In this paper the relevance of Cramer-Rao bounds (CRBs) calculated by the LCModel program to describe errors in estimated concentrations is validated using spectra simulations. The relation between the average CRBs and standard deviations (STD) of metabolite concentrations from 100 simulated spectra for various signal to noise ratio and line broadening conditions is evaluated. A parameter for calculating error images for metabolite ratios is proposed and an effective way to display error images is shown. The results suggest that the average CRBs are strongly correlated with the standard deviations and hence that CRB values reflect the relative uncertainty of the calculated concentrations. The error information can be integrated directly into a metabolite image by displaying only those areas of the metabolite image with corresponding CRBs below a selected threshold or by mapping CRBs as a transparency of the metabolite image. The concept of error images avoids extensive examination of each SI spectrum and helps to reject low quality spectra.