Improving the reproducibility of proton magnetic resonance spectroscopy brain thermometry: Theoretical and empirical approaches

In proton magnetic resonance spectroscopy (H-1 MRS)-based thermometry of brain, averaging temperatures measured from more than one reference peak offers several advantages, including improving the reproducibility (i.e., precision) of the measurement. This paper proposes theoretically and empirically optimal weighting factors to improve the weighted average of temperatures measured from three references. We first proposed concepts of equivalent noise and equivalent signal-to-noise ratio in terms of frequency measurement and a concept of relative frequency that allows the combination of different peaks in a spectrum for improving the precision of frequency measurement. Based on these, we then derived a theoretically optimal weighting factor and proposed an empirical weighting factor, both involving equivalent noise levels, for a weighted average of temperatures measured from three references (i.e., the singlets of NAA, Cr, and Ch in the H-1 MR spectrum). We assessed these two weighting factors by comparing their errors in measurement of temperatures with the errors of temperatures measured from individual references; we also compared these two new weighting factors with two previously proposed weighting factors. These errors were defined as the standard deviations in repeated measurements or in Monte Carlo studies. Both the proposed theoretical and empirical weighting factors outperformed the two previously proposed weighting factors as well as the three individual references in all phantom and in vivo experiments. In phantom experiments with 4- or 10-Hz line broadening, the theoretical weighting factor outperformed the empirical one, but the latter was superior in all other repeated and Monte Carlo tests performed on phantom and in vivo data. The proposed weighting factors are superior to the two previously proposed weighting factors and can improve the reproducibility of temperature measurement using H-1 MRS-based thermometry.