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.

The trouble with quality filtering based on relative Cramér-Rao lower bounds.

Cramér Rao Lower Bounds (CRLB) have become the standard for expression of uncertainties in quantitative MR spectroscopy. If properly interpreted as a lower threshold of the error associated with model fitting, and if the limits of its estimation are respected, CRLB are certainly a very valuable tool to give an idea of minimal uncertainties in magnetic resonance spectroscopy (MRS), although other sources of error may be larger. Unfortunately, it has also become standard practice to use relative CRLB expressed as a percentage of the presently estimated area or concentration value as unsupervised exclusion criterion for bad quality spectra. It is shown that such quality filtering with widely used threshold levels of 20% to 50% CRLB readily causes bias in the estimated mean concentrations of cohort data, leading to wrong or missed statistical findings-and if applied rigorously-to the failure of using MRS as a clinical instrument to diagnose disease characterized by low levels of metabolites. Instead, absolute CRLB in comparison to those of the normal group or CRLB in relation to normal metabolite levels may be more useful as quality criteria. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.

Non-water-suppressed proton MR spectroscopy improves spectral quality in the human spinal cord

Magnetic resonance spectroscopy enables insight into the chemical composition of spinal cord tissue. However, spinal cord magnetic resonance spectroscopy has rarely been applied in clinical work due to technical challenges, including strong susceptibility changes in the region and the small cord diameter, which distort the lineshape and limit the attainable signal to noise ratio. Hence, extensive signal averaging is required, which increases the likelihood of static magnetic field changes caused by subject motion (respiration, swallowing), cord motion, and scanner-induced frequency drift. To avoid incoherent signal averaging, it would be ideal to perform frequency alignment of individual free induction decays before averaging. Unfortunately, this is not possible due to the low signal to noise ratio of the metabolite peaks. In this article, frequency alignment of individual free induction decays is demonstrated to improve spectral quality by using the high signal to noise ratio water peak from non-water-suppressed proton magnetic resonance spectroscopy via the metabolite cycling technique. Electrocardiography (ECG)-triggered point resolved spectroscopy (PRESS) localization was used for data acquisition with metabolite cycling or water suppression for comparison. A significant improvement in the signal to noise ratio and decrease of the Cramér Rao lower bounds of all metabolites is attained by using metabolite cycling together with frequency alignment, as compared to water-suppressed spectra, in 13 healthy volunteers.

Lower complexity bounds in justification logic

Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pure justification logics is typically lower than that of the corresponding modal logics. Moreover, the so-called reflected fragments, which still contain complete information about the respective justification logics, are known to be in~NP for a wide range of justification logics, pure and hybrid alike. This paper shows that, under reasonable additional restrictions, these reflected fragments are NP-complete, thereby proving a matching lower bound. The proof method is then extended to provide a uniform proof that the corresponding full pure justification logics are $\Pi^p_2$-hard, reproving and generalizing an earlier result by Milnikel.

IgE-bearing cells in bronchoalveolar lavage fluid and allergen-specific IgE levels in sera from RAO-affected horses

Recurrent airway obstruction (RAO) is a common condition in stabled horses characterized by small airway inflammation, airway neutrophilia and obstruction following exposure of susceptible horses to mouldy hay and straw and is thus regarded as a hypersensitivity reaction to mould spores. However, the role of immunoglobulin E antibodies (IgE) in the pathogenesis of RAO is unclear. We hypothesized that the number of cells with receptor-bound IgE in bronchoalveolar lavage fluid (BALF) and IgE levels in serum would be higher in RAO-affected than in healthy horses living in the same environment. Therefore, IgE-positive (+) cells were identified by immunocytochemistry on cytospins from BALF and counted. IgE levels against the mould extracts Aspergillus fumigatus (Asp. f.) and Alternaria alternata (Alt. a.) and the recombinant mould allergen Aspergillus fumigatus 8 (rAsp f 8) were measured by enzyme-linked immunosorbent assay (ELISA) in the sera of seven RAO-affected and 22 clinically healthy mature horses housed in the same conventional stable environment. After correcting for the number of neutrophils, there were no significant differences in IgE+ cells on cytospins from BALF between both groups of horses (5% versus 7%, P > 0.1). Serum IgE levels against the mould extracts were significantly higher in RAO-affected than in clinically healthy horses [median = 119 versus 66 relative ELISA units (REU), P < 0.05]. Furthermore, significantly more RAO-affected than healthy horses had detectable serum IgE against the recombinant allergen rAsp f 8 (4/7 and 3/22, respectively, P < 0.05). Age had no significant effect on BALF cell ratios or on specific serum IgE levels. These results show that high IgE levels against mould antigens are associated with RAO under controlled environmental conditions but ranges of mould-specific serum IgE levels overlapped too much between diseased and clinically healthy animals to be of any diagnostic value. Further studies are needed to assess whether IgE-mediated reactions contribute to the pathogenesis of RAO.

Differential association of MUC5AC and CLCA1 expression in small cartilaginous airways of RAO-affected and control horses

REASONS FOR PERFORMING STUDY: Airway mucus accumulation is associated with indoor irritant and allergen exposure in horses with recurrent airway obstruction (RAO). Epidermal growth factor receptor (EGFR) and a chloride channel (calcium activated, family member 1; CLCA1) are key signalling molecules involved in mucin gene expression. OBJECTIVES: We hypothesised that exposure to irritants and aeroallergens would lead to increased expression of the mucin gene eqMUC5AC and increased stored mucosubstance in the airways of RAO-affected horses, associated with increased neutrophils and CLCA1 and EGFR mRNA levels. METHODS: We performed quantitative RT-PCR of eqMUC5AC, CLCA1 and EGFR; volume density measurements of intraepithelial mucosubstances; and cytological differentiation of intraluminal inflammatory cells in small cartilaginous airways from cranial left and right and caudal left and right lung lobes of 5 clinically healthy and 5 RAO-affected horses that had been exposed to indoor stable environment for 5 days before euthanasia. RESULTS: Neutrophils were increased in RAO-affected horses compared to clinically healthy controls. EqMUC5AC mRNA levels were positively correlated with both CLCA1 and EGFR mRNA levels in RAO-affected horses but only with CLCA1 in controls. The relationship between eqMUC5AC and CLCA1 differed in the 2 groups of horses with RAO-affected animals overexpressing CLCA1 in relation to eqMUC5AC. CONCLUSIONS: These data implicate CLCA1 as a signalling molecule in the expression of eqMUC5AC in horses but also suggest differential regulation by CLCA1 and EGFR between horses with RAO and those with milder degrees of airway inflammation.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.