The paper presents the results of experimental studies of water-salt solutions of serum albumin (SAC), which is considered as an analogue of body fluids. The observed structural effects in dehydrated films are considered taking into account the concept of the supramolecular organization of the polymer body and its multilevel structure. To study the samples, a single complex technique was developed and tested, including studies of the supramolecular structure of the entire drop at the optical level (microlevel) and the morphology of the globular structural elements of the albumin film (nanolevel) by atomic force microscopy (AFM). Processing of SAC facies with the help of the Morpho hardware and software complex allowed us to establish the dependence of the NM facies on the albumin concentration. At the optical level, it was possible to observe a complex-step mechanism of changes in the supramolecular structure of water-salt facies of albumin. The study showed that with an increase in protein concentration, the area of the crystallization area of dendrites decreases. At a concentration of 10 % SAC, a structural transition occurs: the dendritic-fractal morphology is replaced by a system of cracks and individual nodules. The globular structure of the protein matrix was revealed by atomic force microscopy. The size of a single globule and protein associates, and the density of their packaging, depending on the concentration, were estimated.

According to the PAMELA experiment, precipitation of electrons from the Earth's radiation belt was detected at the moments of recording gamma-ray bursts of extraterrestrial origin, which gives rise to a hypothesis about the relationship of these phenomena. The work provides estimates of the number of electrons that have experienced interaction with gamma quanta through the Compton effect and have changed their energy and trajectories in the so-called approximation. «toy model» A formula has been obtained for determining the cross section for the interaction of a gamma quantum and a stationary electron depending on the electron emission angle and the energy spectrum of the emitted electrons. In the energy distribution of secondary electrons, a narrow peak is observed near the maximum energy, which is close to the energy of the initial gamma quantum. An estimate of the upper limit for the contribution of the process under consideration to the excess of the electron count rate over the background value recorded in the PAMELA experiment was carried out. It was found that the proposed mechanism does not explain the observed effect; the calculated electron count rate is several orders of magnitude lower, which is explained by the small Compton scattering cross section.

In order to validate new radiotherapeutic techniques, a large number of studies using ionizing radiation are required. Such studies are often carried out using small laboratory animals, such as mice and rats, that is cause the ethical questions of the international scientific community. In this regard, the application of artificial animal models is relevant. It is allow to reduce the number of animals used. In previous studies, homogeneous monolithic test objects were fabricated and dosimetric tests were performed. 3D-printing parameters and materials were determined for the most accurate imitation of biological tissues. This study proposes to use fused filament fabrication techniques for design and creation of heterogeneous objects from different materials, which will allow the fabrication of phantoms with high accuracy in a short period of time. In this work, the male rat dosimetric phantom was designed and created. Its tomographic and dosimetric tests were carried out. The possibility of manufacturing dosimetric phantoms of small laboratory animals by fused filament fabrication methods was shown

Nonlinear unsteady equations of mathematical physics with three independent variables containing the first derivative in time and a quadratic combination of the second derivatives in spatial variables of the Monge – Ampere type are investigated. Separate equations of this type are found, for example, in electron magnetohydrodynamics and differential geometry. In this paper, an eleven-parameter transformation preserving the form of the class of nonlinear equations under study is described. Two-dimensional and one-dimensional reductions leading to simpler partial differential equations with two independent variables or ordinary differential equations are considered. Self-similar and other invariant solutions are obtained. By methods of generalized separation of variables, a number of exact solutions are constructed, many of which are expressed in terms of elementary functions.

MRI (magnetic resonance imaging) plays a crucial role in planning radiosurgical treatment. MRI is used to create a contour of the tumour and critical structures. This imaging method allows the boundaries of the pathological lesion to be defined with high accuracy, but there are certain factors (inhomogeneity of the permanent magnetic field, nonlinearity of the gradient field, etc.) that make MR images more susceptible to spatial distortions compared to images obtained by computed tomography (CT). Determining geometric distortion in MRI images is a critical step in ensuring the accuracy of radiosurgical treatment. One way to determine distortion is to perform MRI and CT scans of a special phantom with plastic rods inside and then analyze the position of the rods on the MRI and CT images. As a rule, MRI and CT images of the phantom are compared visually, which is a rather subjective and inaccurate assessment. The purpose of our work was to develop software to automate the performance of this MRI quality assurance test. The developed software was used to compare MRI in two modes T1 and T2 with CT scans. Magnetic resonance imaging (MRI) is widely used for target delineation in stereotactic radiotherapy treatment planning. The calculated discrepancies between coordinates of the CT, T1 and T2 weighted images exceeded 1 mm in 3.5% and 0.1% of the points, respectively. Discrepancies’ magnitude and directions were assessed. The largest discrepancies between T1 and CT are observed in the lower-right part of the phantom’s axial slice, they are directed primarily to the higher-left part of the slice and reach maximum magnitude of 1.5 mm, the mean discrepancy is 0.5 mm. The discrepancies between T2 and CT are primarily directed to the higher-central part of the slice. These results are acceptable for stereotactic radiosurgery 15 planning. Using this software will speed up the procedure of verifying MRI quality and eliminate visual assessment of the discrepancies.

Currently, radiation therapy is often used for treating cancer. In this method, ionizing radiation affects cancer cells, slowing down their reproduction; however, healthy tissues are also exposed to the irradiation. Therefore, an important stage of treatment planning is to ensure control over the energy distribution of the beam in the transverse plane. In order to obtain the transverse profile of the beam various detectors are created. However, most of them do not meet all the requirements for modern medical detectors, which include the high energy and spatial resolution, as well as the minimalizing of data processing and result obtaining. The multi-angle scanning method could be a solution of this problem. This method is based on repeated linear displacement of the detector in a plane perpendicular to the beam propagation axis at different angles. The data processing involves the reconstruction of beams’ intensities image in the form of pixels of different brightness in grayscale from the data obtained in the experiment. The purpose of this study is to assess the applicability of the main types of mathematical transformations for the implementation of the multi-angle scanning method. This article presents the results of a comparison of the iterative method and the filtered back-projection method with the comprehensive and limited data given. It was found that the filtered back-projection method is less accurate in the presence of comprehensive dataset in contrast to the iterative method, but it still provides better image resolution when there is a limited data.

Exact solutions of various mathematical equations are considered (algebraic, trigonometric, ordinary differential, first order partial derivatives, mathematical physics, integral, functional, delay differential, functional differential, etc.). Particular attention is paid to equations that are found in various fields of natural and engineering sciences (in the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical technology, etc.) and equations of a fairly general form, which depend on several free parameters or arbitrary functions. Equations that are studied in universities and technical colleges are also considered.