The study of polymers’ rheological properties is of paramount importance both for the problems of their industrial production as well as for their practical application. Two polymers used for embolization of arteriovenous malformations (AVMs) are studied in this work: Onyx-18^® and Squid-12^®. Viscosity curve tests and computational fluid dynamics (CFD) were used to uncover viscosity law as a function of shear rate as well as behavior of the polymers in catheter or pathological tissue models. The property of thermal activation of viscosity was demonstrated, namely, the law of dependence of viscosity on temperature in the range from 20 ${}^{°}$C to 37 ${}^{°}$C was established. A zone of viscosity nonmonotonicity was identified, and a physical interpretation of the dependence of the embolic polymers’ viscosity on the shear rate was given on the basis of Cisco’s model. The obtained empirical constants will be useful for researchers based on the CFD of AVMs. A description of the process of temperature activation of the embolic polymers’ viscosity is important for understanding the mechanics of the embolization process by practicing surgeons as well as for producing new prospective embolic agents.

The aorta is the main vessel in the human circulatory system which plays a critical role in oxygen and nutrient supply to all abdominal organs and to the lower limbs. A critical pathology of this vessel is an aneurysm. An important problem in medical practice is to predict aortic aneurysm rupture and plan surgery since aneurysm rupture outside a hospital, as a rule, leads to a lethal outcome. To develop adequate mathematical models that predict such an outcome, it is necessary to determine the strength characteristics of tissues of the aorta, aortic aneurysm, and iliac arteries at various stages of aneurysm growth based on individual patient data. The strength characteristics of the tissues of the human aorta, aortic aneurysm, and common iliac arteries have been studied. It has been experimentally proved that in healthy aorta tissue specimens, the differences between the ultimate relative strains in the axial and circumferential directions are statistically significant (\(p=0.033\)), which is not observed in the case of the aortic aneurysm. The results can also be treated as remodeling of the aortic aneurysm wall compared to the healthy aorta. These data can be used to develop predictive models for aortic aneurysm rupture in personalized hydroelastic modeling.

Background: Cerebral aneurysms (CA) are a widespread vascular disease affecting 50 per 1000 population. The study of the influence of histological, morphological and hemodynamic factors on the status of the aneurysm has been the subject of many works. However, an accurate and generally accepted relationship has not yet been identified. Methods: In our work, the results of mechanical and spectroscopic measurements are considered. Total investigated 14 patients and 36 their samples of CA tissue. Results: The excitation–emission matrix of each specimen was evaluated, after which the strength characteristics of the samples were investigated. Conclusions: It has been shown that there is a statistically significant difference in the size of the peaks of two components, which characterizes the status of the aneurysms. In addition, a linear regression model has been built that describes the correlation of the magnitude of the ultimate strain and stress with the magnitude of the peaks of one of the components. The results of this study will serve as a basis for the non-invasive determination of the strength characteristics of the cerebral tissue aneurysms and determination of their status.

This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are useful for describing viscous fluid motion in long pipes, thus considering geometric parameters like pipe diameter and characteristic length. This study provides a representation for the vorticity vector and energy dissipation in the flow problem for a curved channel, thereby determining the magnitude of vorticity and energy dissipation depending on the channel’s central line curvature and torsion. The accuracy of the asymptotic formulas are estimated in terms of small parameter powers. Numerical calculations for helical tubes demonstrate the effectiveness of the asymptotic formulas.

Since, in modern high-performance sports, the technical component is decisive, the ski running surface is an important element of cross-country skiing. This paper presents a review of papers on sliding mechanics, discusses modern methods for improving it, and considers the prospects for the development of this area under current energy and environmental conditions. Various factors affecting the sliding mechanics, in particular, snow cover albedo, and microroughness of the ski running surface are analyzed in detail.