Brane World Cosmology - Gauge-Invariant Formalism for Perturbation

In the present paper the gauge-invariant formalism is developed for perturbations of the brane-world model in which our universe is realized as a boundary of a higher-dimensional spacetime. For the background model in which the bulk spacetime is $(n+m)$-dimensional and has the spatial symmetry corresponding to the isometry group of a $n$-dimensional maximally symmetric space, gauge-invariant equations are derived for perturbations of the bulk spacetime. Further for the case corresponding to the brane-world model in which $m=2$ and the brane is a boundary invariant under the spatial symmetry in the unperturbed background, relations between the gauge-invariant variables describing the bulk perturbations and those for brane perturbations are derived from Israel's junction condition under the assumption of \ZR_2 symmetry. In particular, for the case in which the bulk spacetime is a constant-curvature spacetime, it is shown that the bulk perturbation equations reduce to a single hyperbolic master equation for a master variable, and that the physical condition on the gauge-invariant variable describing the intrinsic stress perturbation of the brane yield a boundary condition for the master equation through the junction condition. On the basis of this formalism it is pointed out that it seems to be difficult to suppress brane perturbations corresponding to massive excitations for a brane motion giving a realistic expanding universe model.Comment: 25 pages, no figures, typos corrected, to appear in Phys.Rev.

Diagnostic Performance and Safety of Positron Emission Tomography Using 18F-Fluciclovine in Patients with Clinically Suspected High- or Low-grade Gliomas: A Multicenter Phase IIb Trial

Objective(s): The study objective was to assess the diagnostic performance of positron emission tomography (PET) for gliomas using the novel tracer 18F-fluciclovine (anti-[18F]FACBC) and to evaluate the safety of this tracer in patients with clinically suspected gliomas.Methods: Anti-[18F]FACBC was administered to 40 patients with clinically suspected high- or low-grade gliomas, followed by PET imaging. T1-weighted, contrast-enhanced T1-weighted, and fluid-attenuated inversion recovery (or T2-weighted) magnetic resonance imaging (MRI) scans were obtained to plan for the tissue collection. Tissues were collected from either “areas visualized using anti-[18F]FACBC PET imaging but not using contrast-enhanced T1-weighted imaging” or “areas visualized using both anti-[18F]FACBC-PET imaging and contrast-enhanced T1-weighted imaging” and were histopathologically examined to assess the diagnostic accuracy of anti-[18F]FACBC-PET for gliomas.Results: The positive predictive value of anti-[18F]FACBC-PET imaging for glioma in areas visualized using anti-[18F]FACBC-PET imaging, but not visualized using contrast-enhanced T1- weighted images, was 100.0% (26/26), and the value in areas visualized using both contrastenhanced T1-weighted imaging and anti- [18F]FACBC-PET imaging was 87.5% (7/8). Twelve adverse events occurred in 7 (17.5%) of the 40 patients who received anti-[18F]FACBC. Five events in five patients were considered to be adverse drug reactions; however, none of the events were serious, and all except one resolved spontaneously without treatment.Conclusion: This Phase IIb trial showed that anti-[18F]FACBC-PET imaging was effective for the detection of gliomas in areas not visualized using contrast-enhanced T1-weighted MRI and the tracer was well tolerated