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.     

On Automatic Continuity and Three Problems of “The Scottish Book” Concerning the Boundedness of Polynomial Functionals

In this paper we introduce and study the notions of isotropic mapping and essential kernel. In addition some theorems on the Borel graph and Baire mapping for polynomial operators are proved. It is shown that a polynomial functional from an infinite dimensional complex linear space into the field of complex numbers vanishes on some infinite dimensional affine subspace.     

Metathetical Reactions in the System Na(K)PF6 – LiBF4 – Aprotic Media

¹⁹F NMR spectroscopy, X‐ray powder diffraction, elemental analysis, and ab initio quantum chemical calculations were used to study metathetical reactions between potassium or sodium hexafluorophosphate and lithium tetrafluoroborate in a mixture of propylene carbonate (PC) – dimethyl carbonate (DMC). It was shown that the increase in size of the cations in the second coordination sphere from Na⁺ to K⁺ results in an increase of the equilibrium conversion. This is in agreement with the influence of the cation size on the solubility of tetrafluoroborates in the media investigated.     

Asymptotics of Running Maxima for φ-Subgaussian Random Double Arrays

Methodology and Computing in Applied Probability - The article studies the running maxima $Y_{m,j}=\max_{1 \le k \le m, 1 \le n \le j} X_{k,n} - a_{m,j}$ where {Xk,n,k ≥?1,n...     

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing (\(R=0.98\) for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining \(R=0.73\) compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to \(R=0.93\). Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple \(\hbox {p}K_{\text {a}}\) correction improved agreement with experiment from \(R=0.54\) to \(R=0.66\), despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.     

Theoretical study of the cosolvent effect on the partial molar volume change of staphylococcal nuclease associated with pressure denaturation

We explain the molecular mechanism of the effect of urea and glycerol cosolvents on the partial molar volume (PMV) change associated with the pressure denaturation of staphylococcal nuclease (SNase) protein recently observed in experiments. Native and denatured conformations of SNase are produced by using molecular dynamics simulations in water, and the PMV is obtained from the integral equation theory of molecular liquids called 3D-RISM, which is based on statistical mechanics. The PMV of the native SNase in water predicted by 3D-RISM theory is in good agreement with experiment. The PMV changes associated with pressure denaturation in water and in water-urea and water-glycerol mixtures are qualitatively reproduced. By analyzing the results obtained, we found two interesting cosolvent effects on the PMV: (1) both urea and glycerol cosolvents increase the PMVs of both native and denatured SNase compared to those in water and (2) both urea and glycerol cosolvents increase the PMV of denatured SNase more than that of native SNase. We also showed that these two observations can be explained in terms of the thermal volume, which is related to the packing effect of solvent molecules.     

On the system cerium-platinum-silicon

Phase relations in the ternary system Ce-Pt-Si have been established for the isothermal section at 800 °C based on X-ray powder diffraction, metallography, scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) techniques on about 120 alloys, which were prepared by various methods employing arc-melting under argon or powder reaction sintering. Nineteen ternary compounds were observed. Atom order in the crystal structures of τ₁₈-Ce₅(Pt,Si)₄ (Pnma; a=0.77223(3) nm, b=1.53279(8) nm c=0.80054(5) nm), τ₃-Ce₂Pt₇Si₄ (Pnma; a=1.96335(8) nm, b=0.40361(4) nm, c=1.12240(6) nm) and τ₁₀-CePtSi₂ (Cmcm; a=0.42943(2) nm, b=1.67357(5) nm, c=0.42372(2) nm) was determined by direct methods from X-ray single-crystal CCD data and found to be isotypic with the Sm₅Ge₄-type, the Ce₂Pt₇Ge₄-type and the CeNiSi₂-type, respectively. Rietveld refinements established the atom arrangement in the structures of Pt₃Si (Pt₃Ge-type, C2/m, a=0.7724(2) nm, b=0.7767(2) nm, c=0.5390(2) nm, β=133.86(2)°), τ₁₆-Ce₃Pt₅Si (Ce₃Pd₅Si-type, Imma, a=0.74025(8) nm, b=1.2951(2) nm, c=0.7508(1) nm) and τ₁₇-Ce₃PtSi₃ (Ba₃Al₂Ge₂-type, Immm, a=0.41065(5) nm, b=0.43221(5) nm, c=1.8375(3) nm). Phase equilibria in Ce-Pt-Si are characterised by the absence of cerium solubility in platinum silicides. Cerium silicides and cerium platinides, however, dissolve significant amounts of the third component, whereby random substitution of the almost equally sized atom species platinum and silicon is reflected in extended homogeneous regions at constant Ce content such as for τ₁₃-Ce(Pt_xSi_1−x)₂, τ₆-Ce₂Pt_3+xSi_5−x or τ₇-CePt_2−xSi_2+x.