Uncertainties of calculated Cramér-Rao lower bounds: implications for quantitative MRS.

ABSTRACT

PURPOSE: To investigate the uncertainties on relative Cramér-Rao lower bound (rCRB) estimates and demonstrate their biasing effects in MRS quantification. THEORY AND METHODS: Simulations were performed to calculate the distribution of the computed rCRB (noted rCRB*) for several rCRB levels. One hundred thousand simulations per rCRB value were performed on simulated NMR signals containing either 1 signal (singlet) or 2 partially overlapping signals. False-positive and false-negative risks were compiled for different threshold levels. rCRB* distribution was experimentally checked on a deuterated water sample using a 9.4 Tesla vertical magnet. RESULTS: Simulations showed that (1) rCRB* distribution is asymmetrical, with a right-tailed distribution increasing the risk of accepting false-positive data (i.e., accepting an rCRB* value whereas the true rCRB value is higher than the threshold level) and (2) distribution broadness increases with increasing rCRB level. Simulations with overlapped peaks lead to more inaccuracy in the rCRB estimation. Probabilities of false detection increase with increasing threshold level. CONCLUSION: Analyzing results thanks to a CRB (or rCRB) based on experimental measurements might lead to misinterpretations. To exploit the rCRB* as rejection criteria, a conservative threshold level of 20% is recommended in order to limit the probability of false alarms.