In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line ℝ+. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyadic wavelets with the Haar, Daubechies, and biorthogonal 9/7 wavelets are prepared.
The aim of this work was to optimize the prognosis of early recurrences of uterine cancer by searching for informative laboratory biomarkers. The study included 343 patients with I-IV stages FIGO endometrial adenocarcinoma the ages of 53 and 76 years. In patients before surgery, as well as 3 and 6 months after the end of primary treatment, the concentration of oncological markers CA-125, HE4, DJ-1, DKK-1 was determined in blood serum by ELISA and electrochemiluminescence immunoassay. We analyzed the predictive informativeness of monitoring markers to assess the risk of early recurrences of cancer within two years after surgery. In patients with uterine cancer with the stage of the disease and the degree of tumor differentiation in the blood serum, the concentration of DJ-1 is changed. With myometrial invasion of more than 50%, increased serum levels of three markers - CA-125, HE4, and DJ-1. Depending on the risk of disease recurrence, the assessment of which was determined by intraoperative and histological characteristics, a difference was revealed in the content of HE4 and DJ-1 markers in the blood. It was found that the risk of early recurrence of uterine cancer increased (p<0,05) when the concentration of CA-125 exceeded the level of 29,3 U/ml, HE4 was above 79,3 pmol/l, DJ-1 was above 90,0 ng/ml and DKK-1 above 47,3 pg/ml 6 months after the end of primary treatment. The highest predictive information value was found for monitoring DJ-1 and HE4 in blood serum, which indicates that they are promising for use in continuous monitoring of the course of cancer.
X-ray photodynamic therapy (XPDT) has been recently considered as an efficient alternative to conventional radiotherapy of malignant tissues. Nanocomposites for XPDT typically consist of two components—a nanophosphor which re-emits X-rays into visible light that in turn is absorbed by the second component, a photosensitizer, for further generation of reactive oxygen species. In this study, BaGdF5 nanophosphors doped with different Eu:Gd ratios in the range from 0.01 to 0.50 were synthesized by the microwave route. According to transmission electron microscopy (TEM), the average size of nanophosphors was ~12 nm. Furthermore, different coatings with amorphous SiO2 and citrates were systematically studied. Micro-CT imaging demonstrated superior X-ray attenuation and sufficient contrast in the liver and the spleen after intravenous injection of citric acid-coated nanoparticles. In case of the SiO2 surface, post-treatment core–shell morphology was verified via TEM and the possibility of tunable shell size was reported. Nitrogen adsorption/desorption analysis revealed mesoporous SiO2 formation characterized by the slit-shaped type of pores that should be accessible for methylene blue photosensitizer molecules. It was shown that SiO2 coating subsequently facilitates methylene blue conjugation and results in the formation of the BaGdF5: 10% Eu3+@SiO2@MB nanocomposite as a promising candidate for application in XPDT.
Herein we report the development of a nanocomposite for X-ray-induced photodynamic therapy (X-PDT) and computed tomography (CT) based on PEG-capped GdF3:Tb3+ scintillating nanoparticles conjugated with Rose Bengal photosensitizer via electrostatic interactions. Scintillating GdF3:Tb3+ nanoparticles were synthesized by a facile and cost-effective wet chemical precipitation method. All synthesized nanoparticles had an elongated “spindle-like” clustered morphology with an orthorhombic structure. The structure, particle size, and morphology were determined by transmission electron microscopy (TEM), X-ray diffraction (XRD), and dynamic light scattering (DLS) analysis. The presence of a polyethylene glycol (PEG) coating and Rose Bengal conjugates was proved by Fourier-transform infrared spectroscopy (FTIR), thermogravimetric analysis (TG), and ultraviolet–visible (UV-vis) analysis. Upon X-ray irradiation of the colloidal PEG-capped GdF3:Tb3+–Rose Bengal nanocomposite solution, an efficient fluorescent resonant energy transfer between scintillating nanoparticles and Rose Bengal was detected. The biodistribution of the synthesized nanoparticles in mice after intravenous administration was studied by in vivo CT imaging.
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