On the use of Cramér–Rao minimum variance bounds for the design of magnetic resonance spectroscopy experiments

Abstract

Localized Magnetic Resonance Spectroscopy (MRS) is in widespread use for clinical brain research. Standard acquisition sequences to obtain one-dimensional spectra suffer from substantial overlap of spectral contributions from many metabolites. Therefore, specially tuned editing sequences or two-dimensional acquisition schemes are applied to extend the information content. Tuning specific acquisition parameters allows to make the sequences more efficient or more specific for certain target metabolites. Cramér-Rao bounds have been used in other fields for optimization of experiments and are now shown to be very useful as design criteria for localized MRS sequence optimization. The principle is illustrated for one-and two dimensional MRS, in particular the 2D separation experiment, where the usual restriction to equidistant echo time spacings and equal acquisition times per echo time can be abolished. Particular emphasis is placed on optimizing experiments for quantification of GABA and glutamate. The basic principles are verified by Monte Carlo simulations and in vivo for repeated acquisitions of generalized two-dimensional separation brain spectra obtained from healthy subjects and expanded by bootstrapping for better definition of the quantification uncertainties. Use of Cramer Rao bound criteria to optimize in vivo MR spectroscopy experiments  Method illustrated for 1D and 2D MRS, in particular 2D separation (2DJ) experiments  2DJ generalized to non-equidistant echo times and unequal numbers of scans per TE  Experiment optimizations discussed for GABA and glutamate as target metabolites  In vivo verification for sets of human brain spectra expanded by bootstrapping

Olanzapine antipsychotic treatment of adolescent rats causes long term changes in glutamate and GABA levels in the nucleus accumbens

“…In order to obtain an index of the reliability of our calculation of the contribution of GABA and GLU to the measured spectra in the LCModel, we determined the percent standard deviation (the Cramér-Rao lower bounds [CRLB]) of each component (Bolliger et al, 2013; Cavassila et al, 2001). In the rat brain, we consider a CRLB value of <20 % as an acceptable level of quantitation reliability (Provencher, 1993, 2001).…”

Optimizing acquisition and fitting conditions for 1H MR spectroscopy investigations in global brain pathology

“…In vivo data were collected from 10 healthy subjects (aged 28 ± 12 years). Eight different voxels, placed above the ventricles ( Figure 1A), with sizes ranging from 8 to 99 cm 3 (8,32,48,60,75,85, 88 and 99 cm 3 ) and with a constant thickness of 2 cm in the head/feet-direction (localized by the nonadiabatic RF pulse), were measured for each subject with the acquisition parameters of TE = 51 ms (minimum TE for the specific hyperbolic secant RF pulses and power available) and TR = 3000 ms. VAPOR water suppression was used with a bandwidth of 135 Hz, and 32 acquisitions were averaged for each measurement. Additionally, a single-shot measurement of the nonsuppressed water signal with the same gradients played out as for the water-suppressed scans was recorded for each case.…”

“…In addition, they also offer insight into the beneficial effect of prior knowledge constraints. 7,8 This study uses CRLB as an indicator for optimal acquisition conditions reflected in the lowest fitting uncertainty, to investigate the optimal VS as a compromise of the different aspects of spectral quality.…”

Disturbed cingulate glutamate metabolism in adults with high-functioning autism spectrum disorder: evidence in support of the excitatory/inhibitory imbalance hypothesis

“…Metabolites were considered only for further statistical analysis if the Cramér-Rao bounds were below 20%. 83 First, all dependent variables of interest were tested for normality of distribution using the Kolmogorov--Smirnov test. Then, the data were analyzed with multiple analysis of covariance (MANCOVA).…”