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.

Numerical modeling is an effective tool for preoperative planning. The present work is devoted to a retrospective analysis of neurosurgical treatments for the occlusion of cerebral aneurysms using flow-diverters and hemodynamic factors affecting stent endothelization. Several different geometric approaches have been considered for virtual flow-diverters deployment. A comparative analysis of hemodynamic parameters as a result of computational modeling has been carried out basing on the four clinical cases: one successful treatment, one with no occlusion and two with in stent stenosis. For the first time, a quantitative assessment of both: the limiting magnitude of shear stresses that are necessary for the occurrence of in stent stenosis (MaxWSS > 1.23) and for conditions in which endothelialization is insufficiently active and occlusion of the cervical part of the aneurysm does not occur (MaxWSS < 1.68)—has been statistacally proven (p < 0.01).

Highlights. Small cerebral aneurysms (3 mm) and giant (>15 mm) aneurysms and have a higher risk of rupture. This article proves for the first time that the rupture risk criteria developed for giant cerebral aneurysms do not work for small aneurysms. The development of small aneurysms in patients was analyzed and measured morphological features of aneurysms were compared with their calculated hydrodynamic characteristics.Aim. To study the dynamics of development of small cerebral aneurysms, to assess the applicability of existing methods for calculating the risk of rupture, to formulate new clarifying hypotheses for calculating the risk of rupture of small cerebral aneurysms.Methods. Patient data were provided by the Federal Center for Neurosurgery, Novosibirsk. CT angiography was performed using a Philips Ingenuite CT scanner (Philips Medical Systems, USA, 128 slices). Aneurysm size dynamics was assessed by measuring three main sizes with an accuracy of 0.1 mm using the IntelliSpace Portal Philips software environment. Numerical calculations were carried out using ANSYS CFX 2020R2.Results. Hemodynamic characteristics change according to the changes of the aneurysm dome. In the case when morphological characteristics of the aneurysm have not changed, a change in the geometry of the patient's circle of Willis (coW) is observed: the curvature of the arteries, the angles of bifurcations (the structure of coW remained unchanged). The PHASES score (absolute risks of rupture for aneurysms) was found to be unusable for the considered aneurysms.Conclusion. This work formulates and morphologically and hydrodynamically confirms for the first time in the volunteers that the change in risk estimates for such aneurysms is fundamentally affected, even insignificantly, by the change in the circle of Willis: a change in the curvature of individual segments of the cerebral arteries, as well as the angles of their bifurcations. The results obtained are aimed at modifying the existing risk criteria for rupture of cerebral aneurysms.

Coronary artery disease is a widespread cause of death and disability in the population. Angioplasty of the coronary arteries is one of the most common methods of eliminating the cause of ischemia – stenosis of the coronary arteries. As a result of stent installation, a change in the angle of vascular bifurcation occurs usually, as well as a redistribution of volumetric blood flow in the coronary artery system. Considering the high variability of the branching angioarchitecture of these arteries, as well as the structure of their environment, the problem of predicting the specific redistribution of blood flow in these arteries remains unsolved; the main ways of its implementation are computational and experimental hemodynamics. Material and methods. This paper uses an experimental approach to explore the effect of stent placement in a model of coronary artery stenosis, and also provides an analysis of the current level of awareness of the scientific community on this issue. Results and discussion. The experiment showed that the throughput of the model increases by 14 % compared to the model with stenosis, and the redistribution of flows in the model depends not on diameters but on the anatomy of a particular vascular network. The data of the performed mathematical modeling are generally consistent with the results of the experiment before stent installation, when the coronary tree consists of several load-bearing branches, but have quantitative differences for the distal branches of the coronary artery model in the presence of an installed stent. Conclusions. The results of the work can be used to accumulate an experimental data array on the restructuring of blood flow during angioplasty, and can also be used to verify the numerical hemodynamics of the coronary arteries during the virtual installation of a stent in them to resolve stenosis.

The superficial femoral artery, in contrast to the deep femoral artery, is most often affected by atherosclerosis with the formation of hemodynamically significant stenoses or occlusions, which leads to ischemia of the lower limb. The latest Russian and European guidelines for peripheral arterial disease currently recommend an endovascular strategy (angioplasty and stenting) for all lesions shorter than 25 cm. The study of the hemodynamics of the superficial femoral artery is complicated by the fact that it is subject to severe deformation (compression, stretching, torsion) during physiological movements in the hip and knee joints. In this regard, a very urgent task is the numerical modeling of hemodynamics before and after angioplasty and stenting of the affected artery to assess the redistribution of blood flow in the great vessels of the lower limb. The work performed a numerical study of the hemodynamics of the arteries of the lower extremities under normal conditions, with occlusion, and with installed virtual stents of various porosities for a specific patient. It has been established that, depending on the chosen stent, the volume of blood flow through the superficial femoral artery can vary up to 15 %, and in general, the redistribution of blood flow can reach up to 50 % compared to a healthy limb. For stents with a porosity index of 0.1–0.2, the shear stresses in the stent area are up to 5 times higher than for stents for which this value is 0.8, although the maximum WSS over the entire configuration remains comparable, which indicates possible significantly different stent endothelialization scenarios. A deeper understanding of these processes will make it possible to determine the choice of treatment tactics and the type of implanted device, which can ultimately improve the immediate and long-term results of surgical treatment, as well as improve the patient’s rehabilitation status.