Practical considerations in T1 mapping of prostate for dynamic contrast enhancement pharmacokinetic analyses

There are many challenges in developing robust imaging biomarkers that can be reliably applied in a clinical trial setting. In the case of dynamic contrast-enhanced (DCE) MRI, one such challenge is to obtain accurate precontrast T₁ maps for subsequent use in two-compartment pharmacokinetic models commonly used to fit the MR enhancement time courses. In the prostate, a convenient and common approach for this task has been to use the same 3D spoiled gradient-echo sequence used to collect the DCE data, but with variable flip angles (VFAs) to collect data suitable for T₁ mapping prior to contrast injection. However, inhomogeneous radiofrequency conditions within the prostate have been found to adversely affect the accuracy of this technique. Herein we demonstrate the sensitivity of DCE pharmacokinetic parameters to precontrast T₁ values and examine methods to improve the accuracy of T₁ mapping with flip angle-corrected VFA SPGR methods, comparing T₁ maps from such methods with “gold standard” reference T₁ maps generated with saturation recovery experiments performed with fast spin-echo (FSE) sequences.     

Linear ultrafilters

Let X be a k-vector space, and U a maximal proper filter of subspaces of X. Then the ring of endomorphisms of X that are “continuous” with respect to U modulo the ideal of those that are “trivial” with respect to U forms a division ring E(U). (These division rings can also be described as the endomorphism rings of the simple left End(X)-modules.) We study this and the dual construction, based on maximal cofiIters of subspaces of X, in particular, the relation between the constructed division rings and the original field or division ring k. We end by examining a more general construction in which X is a module over a general ring, given with both a filter and a cofilter of submodules.     

Aza‐Bambusurils En Route to Anion Transporters

Previous calculations of anion binding with various bambusuril analogs predicted that the replacement of oxygen by nitrogen atoms to produce semiaza‐bambus[6]urils would award these new cavitands with multiple anion binding properties. This study validates the hypothesis by efficient synthesis, crystallography, thermogravimetric analysis and calorimetry. These unique host molecules are easily accessible from the corresponding semithio‐bambusurils in a one‐pot reaction, which converts a single anion receptor into a potential anion channel. Solid‐state structures exhibit simultaneous accommodation of three anions, linearly positioned within the cavity along the main symmetry axis. The ability to hold anions at a short distance of about 4 Å is reminiscent of natural chloride channels in E. coli, which exhibit similar distances between their adjacent anion binding sites. The calculated transition‐state energy for double‐anion movement through the channel suggests that although these host–guest complexes are thermodynamically stable they enjoy high kinetic flexibility to render them efficient anion channels.