Problems of the dynamic behavior of blood vessels as shells

Problems of the dynamic behavior of blood vessels as deformable shells with a viscous fluid flowing in them are investigated. A multicoat elastic shell in which an active (muscular) coat is distinguished is proposed as a model of the vessel. Problems that can be solved on the basis of the model are discussed.N. E. Zhukovskii Military-Air Academy. Translated from Mekhanika Polimerov, No. 2, pp. 373–379, March–April, 1970.     

Mechanical properties of the canine internal carotid artery under constant load regimes

Conclusions 1. A method was developed for the study of the mechanical properties of narrow blood vessels under intravascular pressure and axial stretching.2. A real difference in the deformative properties of the individual segments of the canine internal carotid artery was found experimentally.3. It follows from the analysis of the experimental data that, under identical tension levels within the normal physiological range, the mechanical properties in the circumferential direction are similar in all the arterial segments.4. It was found that 30% more energy is required to deform the flexure of the canine internal carotid artery under its topographical and anatomic conditions than that required for the cervical, intraosseous, and intracranial segments of this artery.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 702–706, July–August, 1976.     

The mechanical properties of human blood vessels relative to their location

The major characteristics of the mechanical properties of strips of the common and internal carotid arteries, anterior and posterior segments of the abdominal aorta wall, the common iliac and femoral arteries, and a large subcutaneous vein in man were experimentally determined. A comparison was carried out of the strength and deformative properties of these vessels, and a correlational analysis of the major indices of the mechanical properties was undertaken.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 320–325, March–April, 1975.     

Numerical Analysis of Myocardial Blood Supply on a Graph of Elastic Vessels

We analyze a mathematical model of blood supply to the arterial part of the myocardium. The model is defined on a graph of elastic vessels that includes the vessel radii and geometry. A numerical analysis of myocardial blood supply is carried out allowing for the elasticity of the blood vessels and for some pathologies of blood supply to the myocardium.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 66–73, 2004.     

Changes in the mechanical properties of human coronary arteries with age

Conclusions We were the first to experimentally find that the greatest changes in E₂, E_2(K) ^tan, _2(K), and W_(K) of the human cardial coronary arteries are observed in people who have reached the age of 40 years. To compare the experimental data, all the parameters of the mechanical properties of the coronary arteries were determined at one and the same stress level — 0.01 kgf/mm², which on an average corresponds to an increased intravascular pressure of within 200 to 240 mm Hg. Under elinical conditions, this pressure is considered critical for arterial vessels affected by atherosclerosis. The most marked shifts in the changes of the mechanical properties were found in the superior part of the left coronary artery. At the age of 40, a considerable decrease in the deformability of the arterial walls in the circular direction is observed, and the walls become more rigid. At the same time, the vessel wall becomes thicker, especially because of increase in its internal layer — the intima. All this facilitates the development of intravascular thrombosis in people suffering from coronary sclerosis and leads to the development of acute stenosis, frequently exceeding 75% of the clearance area of the vessel, or to a complete obstruction of the superior part of the left coronary artery. If the inferior part of this vessel still retains a fair deformability, it is possible to perform a reconstructive operation, by means of which normal blood circulation is restored from the initial part of the ascending aorta to the inferior section of the corresponding coronary artery. From the experimentally found characteristics of the mechanical properties of the inferior parts of coronary vessels, we can select the best autoplastic material — a vessel segment derived from the patient himself — with properties similar to those of the affected vessel, which ensures the successful performance of such an operation, namely, the reconstruction of the human coronary vessels.Lecture delivered at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2,, pp. 277–282, March–April, 1977.     

Concerning the investigation of the supermolecular structure of polymers with a three-dimensional network

The results of an investigation of the structure and properties of a series of crosslinked polymers are presented. It is shown that the structure is determined by the chemical structure of the starting components and the method of synthesis.Institute of Chemistry of High-Molecular Compounds, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 934–936, September–October, 1970.     

On the construction of a variant of the theory of fracture

A theory of long-time strength that takes into account the accumulation of damage in the material in different directions is used as a basis for obtaining isochronous fatigue strength curves in stress space for complex states of stress.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 648–653, July–August, 1970.     

Experimental determination of the influence of periodic shear deformation and filling on the effective viscosity of solutions of synthetic rubber

The influence of periodic shear deformation on the effective viscosity of filled solutions of synthetic rubber has been studied. The study was carried out on an amplitude-frequency viscosimeter developed by the authors. It has been established that during periodic deformation a linear region exists in which the effective viscosity is independent of the vibration rate, and a nonlinear region where the effective viscosity of the solutions decreases with increase in amplitude of the speed of relative deformation.Presented at the IV Symposium on Rheology of Polymers at the A. V. Topchiev Institute for Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow, May 27–30, 1969.Institute for Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, 514–520, May–June, 1970.     

Apparatus for testing samples of glass plastic subject to high-frequency fatigue in the symmetrical extension-compression mode

Using an instrument of the UM-20 type (made by the Scientific-Research and Design Institute of Testing Instruments, Moscow) as a basis, an apparatus is designed for subjecting glass-plastic samples to high-frequency fatigue tests at frequencies of 10–20 kHz. In order to stabilize the thermal state of the sample, water cooling is incorporated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 756–758, July–August, 1972.     

Conformational transitions associated with the deformation of oriented polyethylene fibers

It is shown that, as the elastic deformation of the polymer increases, the number of gauche isomers in oriented polyethylene fibers decreases linearly.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 170–172, January–February, 1970.     

On the relationship between the strong and scalar almost periodicity of Banach representations of the group of reals

Khar'kov State Academy of Town Economy. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 4, pp. 75–77, October–December, 1995.     

The asymptotic efficiency,in the sense of Bahadur,of estimators of a multidimensional parameter of the spectral density

Institute of Mathematics and Informatics, Lithuanian Academy of Sciences. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), pp. 455–474, July–September, 1991.     

Resolvents of the theory of orthotropic shells with low shear stiffness in force-moments and stress functions

The problem of the theory of orthotropic layered shells with low shear stiffness is reformulated in force-moments and stress functions on the basis of new strain continuity relations constructed with allowance for transverse shears.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 950–952, September–October, 1970.     

On the applicability of two-dimensional applied theories to problems of the stability of axially loaded cylindrical shells made of materials with low shear stiffness

The applicability of two-dimensional applied theories of the Kirchhoff-Love, Timoshenko, and Ambartsumyan types to problems of the stability of shells with low shear stiffness [1] is discussed. The critical loads given by these theories are compared with those recently obtained [6–8] by solving the problem of the stability of a cylindrical shell on the basis of general solutions [3, 4] of the three-dimensional linearized equations of the theory of elasticity [5].Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. L'vov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 141–143, January–February, 1970.     

Topology of the space of nondegenerate curves

Moscow Timiryazev Agriculture Academy. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 26, No. 3, pp. 93–96, July–September, 1992.     

Investigation of the effect of polymer coatings on wear under vibrational loads

The process of friction and wear in the presence of vibration has been investigated on the range of relatively high loads and vibration amplitudes. It is shown that the use of Teflon-based composites completely eliminates damage to the contact surfaces as a result of fretting corrosion.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1029–1035, November–December, 1973.     

Estimation of the constant in the Berry-Esseen inequality

Institute of Mathematics and Computer Science, Lithuanian Academy of Sciences. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 3, pp. 475–482, July–September, 1991.     

The number of components of the complement of the level surface of a harmonic polynomial in three variables

Institute for Problems in Information Transmission, Russian Academy of Sciences. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 2, pp. 52–54, April–June, 1994.     

Particular case of the deformation of a nine-atom model

The dependence of the tensile loading on the length of a nine-atom plane model is calculated. The shapes of the model in tension are determined.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 545–547, May–June, 1975.     

Relation between the elastic deformation of oriented specimens of crystalline polymers and the "large-period" deformation

Illustrative calculations for a specific model of the supermolecular organization of an oriented crystalline polymer are presented as an explanation of the fact that the "large-period" deformation may exceed the macrodeformation of the specimen.Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 579–583, July–August, 1973.