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

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.

Population-Based Design of Mandibular Plates Based on Bone Quality and Morphology

In this paper we present a new population-based implant design methodology, which advances the state-of-the-art approaches by combining shape and bone quality information into the design strategy. The method enhances the mechanical stability of the fixation and reduces the intra-operative in-plane bending which might impede the functionality of the locking mechanism. The method is presented for the case of mandibular locking fixation plates, where the mandibular angle and the bone quality at screw locations are taken into account. Using computational anatomy techniques, the method automatically derives, from a set of computed tomography images, the mandibular angle and the bone thickness and intensity values at the path of every screw. An optimisation strategy is then used to optimise the two parameters of plate angle and screw position. Results for the new design are presented along with a comparison with a commercially available mandibular locking fixation plate. A statistically highly significant improvement was observed. Our experiments allowed us to conclude that an angle of 126° and a screw separation of 8mm is a more suitable design than the standard 120° and 9mm.

Quantile-Based Optimization of Noisy Computer Experiments with Tunable Precision

This article addresses the issue of kriging-based optimization of stochastic simulators. Many of these simulators depend on factors that tune the level of precision of the response, the gain in accuracy being at a price of computational time. The contribution of this work is two-fold: first, we propose a quantile-based criterion for the sequential design of experiments, in the fashion of the classical expected improvement criterion, which allows an elegant treatment of heterogeneous response precisions. Second, we present a procedure for the allocation of the computational time given to each measurement, allowing a better distribution of the computational effort and increased efficiency. Finally, the optimization method is applied to an original application in nuclear criticality safety. This article has supplementary material available online. The proposed criterion is available in the R package DiceOptim.