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.     

Creep of compact human bony tissue under tension

The behavior of compact bony tissue from a human tibia with time at various levels of a constant lengthwise stretching load has been studied. The limits of application of the linear viscoelastic theory for bony tissue have been established. Characteristics of the material have been determined which make it possible to describe both active and also retrograde creep.     

Comparative performance of living and dead bony tissue under static and dynamic loading

The dependence of the mechanical properties of bony tissue on different conditions of storing the samples has been studied. As the performance characteristic under static loading we used the ultimate compressive strength of the bony tissue, and under dynamic loading we used the specific impact strength.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.I. M. Sechenov First Moscow Medical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 647–649, July–August, 1975.     

Hardness of the human tibia

The hardness distribution over the compact bone tissue of the human tibia is examined along the length and in six different zones of the cross section of the bone. A correlation is established between the hardness numbers, on the one hand, and the characteristics of the mechanical properties and the biochemical composition of the bone tissue, on the other. The three-dimensional structure of the equal-hardness formations is studied. The results confirm the assumptions of [1] concerning the specific functions of each zone in the rheological adaptation of the bone to physiological loads.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga; Scientific Research Institute of Traumatology and Orthopedics, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1101–1107, November–December, 1973.     

Lateral strain coefficients of human compact bone tissue

The values of all the lateral strain coefficients of the compact bone tissue of the human tibia have been experimentally determined. The variation of these coefficients in six zones of the cross section have been studied at various stress levels, including the ultimate strengths in the corresponding directions. It has been established that the bone tissue possesses orthotropy of the elastic properties. The change in the volume of the bone tissue during deformation has been studied. The bulk moduli for both uniaxial and hydrostatic loading have been determined. A bulk deformation parameter characterizing the strain energy expended in producing a volume change of 100% is introduced. The coefficients of the rank correlation between the lateral strain coefficients and bulk moduli, on the one hand, and the concentrations of a number of biochemical substances found in bone tissue, on the other, are analyzed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1089–1100, November–December, 1973.     

The anisotropy of compact bone material

From the measurements of the main elements of the microstructure of compact bone material, it is concluded that the theoretical model of a transtropic material can be applied to bone tissue. This conclusion is confirmed by the experimental data obtained on compression. The correlation connection between the ultimate strength of compact bone material and the elasticity modulus has been found. It is shown that the anisotropy of the compact material is satisfactorily described by the tensor formula.Scientific-Research Institute of Medical Radiology, Academy of Medical Sciences of the USSR, Obninsk. S. M. Kirov Leningrad Order of Lenin Wood Technology Academy. Translated from Mekhanika Polimerov, No. 4, pp. 711–716, July–August, 1972.     

Effect of material structure on the stability of a laminated-plastic cylindrical shell

A compact equation is proposed for analyzing the stability of layered shells in relation to their structure. The case of a shell with split longitudinal-transverse winding subjected to hydrostatic pressure is investigated.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 1, pp. 147–150, January–February, 1971.     

Compact elements and Cartan subgroups of connected Lie groups

It is established that the number of compact Cartan subgroups of a connected Lie group is determined by the topological size of the set of its compact elements. This fact clarifies the structure of those connected Lie groups in which the set indicated is everywhere dense.Translated from Ukrainskii Matematicheskii Zhurnal, Vol 42, No. 2, pp. 164–168, February, 1990.     

Bernstein–Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifolds

Bernstein–Nikolskii inequalities and Riesz interpolation formula are established for eigenfunctions of Laplace operators and polynomials on compact homogeneous manifolds.     

Experimental determination of the shear modulus of compact bone tissue

Various methods of experimentally determining the shear moduli G₁₂, G₁₃, and G₂₃ of compact human bone tissue have been examined. The results of the study confirm the previous view that compact tissue has properties similar to those of a transversally isotropic material. It has been established that the shear modulus along the diaphysis of the tibia at the level of girdles 9–24 does not change significantly. There is a definite difference in the rigidity characteristics with respect to the regions of the cross section. The highest values for the shear modulus were established in the angle regions of the cross section. There is a linear dependence of the shear stress ₁₂ on the torsional angle ₁ within the experimental range of stresses (₁₂90 kg/cm²).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 697–705, July–August, 1972.     

Determination of the elastic characteristics of compact bone tissue by investigation of the natural vibration frequency

The dynamic elastic H and shear G_dyn moduli of compact bone tissue have been determined by investigating the natural vibration frequency of specimens obtained from long tubular human bones. The modulus of elasticity E has also been determined by conducting mechanical bending tests. The value of the H modulus is found to change in the course of storage.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 167–172, January–February, 1971.     

Degree of deformation and strength of compact bone tissue during torsion

This paper discusses the variation in the deformation and strength properties of compact bone tissue during torsion in various zones of the cross section of human tibia. A correlation has been found between the specific energy of deformation consumed during the loading process and the level of stress attained. The degree of correlation between the deformation and strength properties of the bone tissue has been studied as a function of the concentration of certain biochemical substances in its composition.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No.5, pp. 911–918, September–October, 1973.     

Study of the strength and coefficients of friction of metal-containing polymers based on heteropolyacids

The strength and coefficients of friction of new heat-resistant composite materials consisting of metallopolymers of iron and cobalt based on molybdosilicic and tungstosilicic heteropolyacids have been studied. It has been established that the use of a lubricant in the frication of metallopolymers over steel brings about a sharper deerease in the coefficients of friction than in the case of the friction of the compact material; this is due to the ability of the metallopolymers to absorb the lubricant material.Kiev Automobile-Road Institute. Translated from Mekhanika Polimerov, No. 5, pp. 931–933, September–October, 1973.     

Construction and decomposition of biorthogonal vector-valued wavelets with compact support

In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time–frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.     

A Longitudinal Lefschetz Theorem in K-Theory

We give a leafwise Lefschetz theorem in the localized equivariant K-theory of a compact foliated manifold. The method is a generalization of the one adopted by M.F. Atiyah and G. Segal in the nonfoliated case. The main tool is the equivariant version of the Connes–Skandalis longitudinal index theorem for foliations. As a byproduct, we obtain a generalization of the Heitsch–Lazarov measured Lefschetz formula to arbitrary complexes with the explicit formula for the integrand, when the diffeomorphism belongs to a compact Lie group acting on the compact manifold.     

Kähler–Ricci solitons on compact complex manifolds with C 1(M) > 0

In this paper, we discuss the relation between the existence of Kähler–Ricci solitons and a certain functional associated to some complex Monge–Ampère equation on compact complex manifolds with positive first Chern class. In particular, we obtain a strong inequality of Moser–Trudinger type on a compact complex manifold admitting a Kähler–Ricci soliton.Received: October 2004 Revised: February 2005 Accepted: February 2005     

Age aspects of the torsional strength of compact bone tissue

The variation of the strength of specimens of human tibial compact bone tissue with age has been investigated. It is shown that the torsional strength _i ^* increases sharply in childhood, reaches a maximum at age 25–35, and then gradually falls. There is a correlation between _i ^* and the porosity of the bone tissue. The mode of fracture of the bone tissue has been studied in relation to its orientation with respect to the principal axes of anisotropy.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 493–503, May–June, 1975.     

Determination of some dynamic characteristics of forming bone callus by the induced vibration method

Conclusions 1. Upon maturation, bone callus not only goes through a series of morphological chantes but also changes in mechanical properties. This is true primarily for an increase in the elasticity modulus.2. The specific energy of dispersion and loss modulus have maxima which occur after 25 to 30 days. This behavior is apparently related to the fact that bone callus at this period has the nature of spongy bone tissue. For compact bone tissue, on the other hand, these values are equal to zero.3. The area of the hysteresis loop is almost completely independent of the frequency upon cyclic stressing.4. The elasticity modulus is proportional to the x-ray density of the samples, which thus may serve as an objective criterion of the degree of maturity of callus.Smolensk State Medical Institute. Translated from Mekhanika Polimerov, No. 5, pp. 896–900, September–October, 1977.     

Hyperbolic Manifolds, Harmonic Forms, and Seiberg–Witten Invariants

New estimates are derived concerning the behavior of self-dual harmonic 2-forms on a compact Riemannian 4-manifold with nontrivial Seiberg–Witten invariants. Applications include a vanishing theorem for certain Seiberg–Witten invariants on compact 4-manifolds of constant negative sectional curvature.