Investigation of the relations between the various mechanical properties and the biochemical composition of human bone tissue

Nondestructive and destructive methods have been used to establish a series of elastic and strength characteristics of the compact bone tissue in six zones of the cross section of the diaphysis of the human tibia. The quantity of five characteristic biochemical substances present in each zone has been determined. The experiments show that, from the standpoint of continuum mechanics, the compact bone tissue is an orthotropic material and that the bone is nonhomogeneous with respect to biochemical composition. The rank correlation coefficients between the mechanical characteristics and the biochemical concentrations are subjected to a detailed analysis. The important effect of the common glycoproteins on the elastic and strength properties of bone tissue in tension is established.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 138–145, January–February, 1973.     

Comparison of the mechanical and biochemical characteristics of human brain arteries

The major characteristics of the mechanical properties of extracranial and intracranial arteries relative to aging were determined experimentally. In a parallel study, the quantitative content of biochemical components of the arterial walls was determined, and an analysis of the rank correlation coefficients between the major characteristics of the mechanical properties and the biochemical components was carried out.     

Technological aspects of the study of the mechanical properties of the human abdominal aorta

Conclusions 1. It was experimentally established that upon the monoxial stretching of individual layers of the abdominal aorta, the tensile strength and tangential elasticity modulus upon breakage are higher in the atherosclerotic layer. The deformative properties are higher in the uninjured layer.2. With increasing age, the capacity for deformation and the tensile strength of both layers of the wall of the abdominal aorta decrease.3. The technique developed for determining the resistance to separation into layers of the wall of the abdominal aorta indicates that the bonding strength of the layers of the aorta depends on the stage of atherosclerosis and increases with advancing stages of the atherosclerotic process.Report presented at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.N. É. Bauman Moscow Higher Technological School. Translated from Mekhanika Polimerov, No. 4, pp. 693–698, July–August, 1977.     

Effect of the biochemical composition of the wall of the vessels of the human thigh on its mechanical properties

The principal characteristics of the mechanical properties of the walls of the human femoral artery and great saphenous vein and their variation with age have been experimentally determined. Macroscopic and microscopic analyses have revealed characteristic age-related changes in the artery and vein walls. The concentrations of six principal biochemical components of the vessel walls have been determined for each age group and the rank correlation coefficients for the principal mechanical properties and biochemical components have been analyzed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga; Riga Institute of Traumatology and Orthopedics. Translated from Mekhanika Polimerov, No. 2, pp. 316–327, March–April, 1974.     

Effect of age on the mechanical properties and biochemical composition of human cardiac arteries

Conclusions 1. The human left coronary arterial wall in subjects from age 15 to 28 has better deformative properties than the right artery.2. With increasing age, a worsening of mechanical properties of the walls is observed specifically for the left coronary artery in comparison with the right coronary artery.3. Quantitative biochemical analysis of the major components of the connective tissue of the human coronary arteries (fibrillar and nonfibrillar proteins and glycoproteins) also disclosed differences among the age groups and the position of the artery (left or right).4. As a result of a dispersion analysis carried out by computer, it was found that both age and position of the artery have a significant effect on the elastin content in the arterial wall and only the age of the subject has a significant effect on the contents of collagen, tyrosine, and hexuronic acids.5. Neither age nor type of artery have a significant effect on the contents of arginine, hexosamines, and hexoses in the arterial wall.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Riga Scientific-Research Institute of Traumatology and Orthopedics. Translated from Mekhanika Polimerov, No. 3, pp. 502–506, May–June, 1978.     

Deformation of human abdominal aorta at biaxial tensioning

An experimental procedure is suggested for studying biaxial tensioning of soft biopolymeric material. The experimental data found at a monaxial and biaxial tensioning are compared.     

Mechanical properties of the wall of the human abdominal aorta after endarterectomy

The deformation and strength properties of the wall of the human aorta have been studied after open endarterectomy. Specimens cut from the aorta wall and specimens subjected to endarterectomy at the levels of both the inner and outer elastic membranes were investigated. It was found that endarterectomy at the level of the inner elastic membrane does not affect the deformation properties of the wall but leads to an increase in strength as compared with the atherosclerotic wall. Endarterectomy at the level of the outer elastic membrane sharply reduces the deformability in the transverse direction as compared with the intact aorta.     

Morphological and functional aspects of the study of some mechanical properties of the human aorta

Some mechanical properties (strength, stretchability, rupture stress, and the like) of the walls of various sections of the aorta have been studied by application of methods and apparatus used in textile materials science. In experiments on unpedigreed dogs, the possibility was studied of recording pulsed oscillations of aorta walls by rheographic methods. The method of polyrheoaortography, which allows, during one's lifetime, determination of the viscoelastic properties of the walls of the human aorta at its various levels, was suggested and tested. High correlation was shown upon comparison of the results of morphological and functional studies. Data have been obtained on the age, individual, and topographic features of the mechanical properties of the aorta, which allows determination of the hemodynamic state in different sections of the aorta for different states of the organism.     

Correlations between the velocities of ultrasonic surface waves and the characteristics of the mechanical properties of human bone tissue

The correlation between the ultrasonic surface wave velocities in the human tibia, on the one hand, and the characteristics of the mechanical properties of compact bone tissue, the ultrasonic longitudinal wave velocities, and the principal biochemical components of the bone, on the other, has been investigated. The regression equations obtained make it possible to estimate the state of the bone tissue on the basis of the data of one of the most convenient methods of nondestructive materials testing.     

Connection between the Kadomtsev-Petviashvili and Johnson equations

The equivalence of the Kadomtsev-Petviashvili and Johnson equations is established in the class of rapidly decreasing Cauchy data. As an illustration of the isomorphism cited the Hamiltonian structure of the Johnson equation is studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 150, pp. 70–75, 1986.We thank M. A. Sall' for helpful discussions.     

Relationship between strength characteristics of unidirectional glass-reinforced plastics and their composition

The article discusses the effect of the amount of binder present and the porosity of the glass reinforced plastic on the usable strength of the glass fibers, the tensile strength, and the elasticity module in stretching. It is shown that a relationship exists over the whole range tested between the volume ratio of the components (binder and glass fiber), certain strength characteristics, and porosity. A method is suggested for the comparison of glass-reinforced plastics according to their usable fiber strength which can be used for the selection of the best binder, the glass material, the glass composition, glass fibers, the lubricant, the technological scheme, etc.Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 477–480, May–June, 1970.     

Connection between the Fokker-Planck-Kolmogorov and nonlinear Langevin equations

We recall the general proof of the statement that the behavior of every holonomic nonrelativistic system can be described in terms of the Langevin equation in Euclidean (imaginary) time such that for certain initial conditions, the different stochastic correlators (after averaging over the stochastic force) coincide with the quantum mechanical correlators. The Fokker-Planck-Kolmogorov (FPK) equation that follows from this Langevin equation is equivalent to the Schrödinger equation in Euclidean time if the Hamiltonian is Hermitian, the dynamics are described by potential forces, the vacuum state is normalizable, and there is an energy gap between the vacuum state and the first excited state. These conditions are necessary for proving the limit and ergodic theorems. For three solvable models with nonlinear Langevin equations, we prove that the corresponding Schrödinger equations satisfy all the above conditions and lead to local linear FPK equations with the derivative order not exceeding two. We also briefly discuss several subtle mathematical questions of stochastic calculus.     

Connection between the kinetic equations and the equations of hydrodynamics

One investigates the Cauchy problem for the nonlinear Boltzmann equation

Connection between commutative algebra and topology

The main aim of this paper is to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.