Improving reproducibility of proton MRST by optimally averaging temperatures measured from multiple references: theoretical and empirical approaches

Purpose: In 1H 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. Methods: 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 accuracy of frequency measurement. Based on these, we then developed a theoretically optimal weighting factor and suggested an empirical weighting factor for weighted average of temperatures measured from three references in 1H MRS-based thermometry. We assessed the two new weighting factors, together with other two previously proposed weighting factors, by comparing the errors of temperatures measured from individual references and the errors of averaged temperatures using these differing weighting factors. These errors were defined as the standard deviations in repeated measurements and in Monte Carlo studies. We also performed computer simulations to aid error analyses in temperature averaging. Results: Both the proposed theoretical and empirical weighting factors outperformed the other two previously proposed weighting factors as well as the three individual references in all phantom and in vivo experiments. In phantom experiments with 4 Hz or 10 Hz line broadening, the theoretical weighting outperformed the empirical one, but the latter was superior in all other repeated and Monte Carlo tests performed on phantom and in vivo data. Computer simulations offered explanations for the performances of the two new proposed weightings. Conclusion: The proposed two new weighting factors are superior to the two previously proposed weighting factors and can improve the measurement of temperature using 1H MRS-based thermometry.