Fitting of two-tensor models without ad hoc assumptions to detect crossing fibers using clinical DWI data

Analysis of crossing fibers is a challenging topic in recent diffusion-weighted imaging (DWI). Resolving crossing fibers is expected to bring major changes to present tractography results based on the standard tensor model. Model free approaches, like Q-ball or diffusion spectrum imaging, as well as multi-tensor models are used to unfold the different diffusion directions mixed in a voxel of DWI data. Due to its seeming simplicity, the two-tensor model (TTM) is applied frequently to provide two positive-definite tensors and the relative population fraction modeling two crossing fiber branches. However, problems with uniqueness and noise instability are apparent. To stabilize the fit, several of the 13 physical parameters are fixed ad hoc, before fitting the model to the data. Our analysis of the TTM aims at fitting procedures where ad hoc parameters are avoided. Revealing sources of instability, we show that the model's inherent ambiguity can be reduced to one scalar parameter which only influences the fraction and the eigenvalues of the TTM, whereas the diffusion directions are not affected. Based on this, two fitting strategies are proposed: the parsimonious strategy detects the main diffusion directions without extra parameter fixation, to determine the eigenvalues and the population fraction an empirically motivated condition must be added. The expensive strategy determines all 13 physical parameters of the TTM by a fit to DWIs alone; no additional assumption is necessary. Ill-posedness of the model in case of noisy data is cured by denoising of the data and by L-curve regularization combined with global minimization performing a least-squares fit of the full model. By model simulations and real data applications, we demonstrate the feasibility of our fitting strategies and achieve convincing results. Using clinically affordable diffusion acquisition paradigms (encoding numbers: 21, 2*15, 2*21) and b values (b = 500–1500 s/mm²), this methodology can place the TTM parameters involved in crossing fibers on a more empirical basis than fitting procedures with technical assumptions.     

Electron-vibration effects in Cs2SiF6 : Mn4+

We report a study of the ⁴ A _2g →² T _1g absorption band of Mn⁴⁺ in Cs₂SiF₆. The band shows several lines or groups of lines associated with transitions from the ⁴ A _2g ground state to the spin-orbit components (² T _1g )Γ₈ and (² T _1g )Γ₆ coupled to the three odd-parity vibrations v ₆(t _2u ), v ₄(t _1u ) and v ₃(t _1u ). The absorptions associated with the (² T _1g )Γ₈ electronic state have structure whereas those associated with the (² T _1g )Γ₆ do not. It is shown that the structure is a consequence of splitting of the Γ₈ × v vibronic multiplets by electron-vibration interaction. The intensity of the ⁴ A _2g →(² T _1g )Γ _i + v_j vibronic transitions are expressed in terms of a small number of parameters; two parameters for v(t _1u ) modes and three for v(t _2u ) modes. Plausible but not good fits to the low temperature Zeeman data and vibronic splitting patterns are obtained. The excitation spectrum of the Cs₂SiF₆ : Mn⁴⁺ in the region of the ⁴ A _2g →² E_g and ⁴ A _2g →² T _1g is recorded using a c.w. dye laser. This reveals numerous weaker lines involving combinational modes and even-parity modes v₅ (t _2g ), v ₂(e_g ) and v ₁(a _1g ). Several interesting electron-vibrational effects are observed. These are illustrated and discussed qualitatively.     

An Iterative method for nonlinear variational inequalities arising in elastoplasticity ∗

In this paper, we study an iterative method, which includes the Ka?anov method as a particular case, for solving nonlinear variational inequalities of the second kind. A convergence result is also proved under suitable assumptions. We apply our iterative method to solve an elastoplasticity problem.     

Reusable Nano-Zirconia-Catalyzed Synthesis of Benzimidazoles and Their Antibacterial and Antifungal Activities

In this article, a zirconia-based nano-catalyst (Nano-ZrO₂), with intermolecular C-N bond formation for the synthesis of various benzimidazole-fused heterocycles in a concise method is reported. The robustness of this reaction is demonstrated by the synthesis of a series of benzimidazole drugs in a one-pot method. All synthesized materials were characterized using ¹HNMR, ¹³CNMR, and LC-MS spectroscopy as well as microanalysis data. Furthermore, the synthesis of nano-ZrO₂ was processed using a standard hydrothermal technique in pure form. The crystal structure of nano-ZrO₂ and phase purity were studied, and the crystallite size was calculated from XRD analysis using the Debye–Scherrer equation. Furthermore, the antimicrobial activity of the synthesized benzimidazole drugs was evaluated in terms of Gram-positive, Gram-negative, and antifungal activity, and the results were satisfactory.     

Thermal stability and UV–Vis-NIR spectroscopy of a new erbium-doped fluorotellurite glass

A new transparent bulk glass from the system 76TeO₂?·?10ZnO?·?9.0PbO?·?1.0PbF₂?·?3.0Na₂O doped with Er³⁺ (TZPPN doped with Er³⁺) has been prepared using the conventional melt-quenching method. Results of differential thermal analysis (DTA) measurements indicate good thermal stability of this glass. The refractive indices at different wavelengths, the optical energy gap, the Sellmeier gap energy and the dispersion energy have been estimated. The Judd–Ofelt parameters, Ω _t (t?=?2,?4,?6) of Er³⁺ were evaluated from optical absorption spectra. Electric dipole, magnetic dipole type transition probabilities, spectroscopic quality factors, branching ratio and radiative lifetimes of several excited states of Er³⁺ have been predicted using intensity Judd–Ofelt parameters. The spectroscopic properties indicate that TZPPN glass doped with Er³⁺ is a promising candidate for laser applications and may be suitable for upconversion fibre optical devices.     

Generalized vector variational-like inequalities and vector optimization in Asplund spaces

Some properties of pseudoinvex functions, defined by means of limiting subdifferential, are obtained. Furthermore, the equivalence between vector variational-like inequalities involving limiting subdifferential and vector optimization problems are studied under pseudoinvexity condition.     

Recent developments in polyetherimide membrane for gas separation

Polyetherimide (PEI) is an extraordinary type of polyimide with excellent thermal and mechanical properties. The polymer is also gas permeable and is considered one of the best membranes for gas separation. Despite the high selectivity, PEI suffers from low permeability due to the trade‐off between phenomena in polymers. To overcome this limitation, fillers are added during the membrane preparation to create voids for better gas transport. In this paper, permeability and selectivity data of PEI membranes for the separation of oxygen, carbon dioxide, and helium are discussed. The paper also summarizes the reported studies for adding fillers to improve the membrane performance.     

Size‐dependent Tumor Response to Photodynamic Therapy and Irinotecan Monotherapies Revealed by Longitudinal Ultrasound Monitoring in an Orthotopic Pancreatic Cancer Model

Longitudinal monitoring of tumor size in vivo can provide important biological information about disease progression and treatment efficacy that is not captured by other modes of quantification. Ultrasound enables high‐throughput evaluation of orthotopic mouse models via fast acquisition of three‐dimensional tumor images and calculation of volume with a reasonable degree of accuracy. Herein, we compare orthotopic pancreatic tumor volume measurements determined by ultrasound with volume measured by calipers and tumor weight, and found strong correlations between the three modalities over a large range of tumor sizes, suggesting ultrasound can accurately quantify tumor volumes in this model. Furthermore, we demonstrate the unique ability of longitudinal treatment monitoring to reveal a tumor size‐dependent response to Benzoporphyrin Derivative photodynamic therapy (BPD‐PDT) and irinotecan. Small tumors (5–35 mm³) were found to respond well to a single round of PDT, while large tumors (35–65 mm³) showed no response to the same treatment. These results highlight the role that tumor size can play in preclinical interpretation of treatment response and more generally suggest that careful evaluation of subtle biological features such as this must be carefully considered in order to grant a more comprehensive understanding of disease biology in vivo.     

68Ga-5, 10, 15, 20-Tetrakis (2, 4, 6-trimethoxy phenyl) porphyrin: a novel radio-labeled porphyrin complex for positron emission tomography

Journal of Radioanalytical and Nuclear Chemistry - Porphyrins and 68Ga have emerged as novel synergic options for PET applications so the idea of preparation of a novel porphyrin complex using this...