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.     

Age-induced changes in the deformation capacity of the compact bone tissue of the human tibia when subjected to torsion

Changes taking place in the initial shear moduli, maximum shear strains, and maximum specific energies of shear deformation of the compact bone tissue of the human tibia with increasing age are considered. The orthotropic character of the deformation characteristics of this tissue when subjected to torsion are examined in relation to age; also examined is the inhomogeneity of their distribution with respect to the cross-sectional zones of the diaphysis. The results emphasize the importance of preserving mechanical compatibility when transplanting bones.     

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.     

Deformation properties of demineralized human compact bone tissue upon stretching

Conclusions 1. Demineralized human compact bone is a physically nonlinear material with a nonuniform distribution of deformation parameters over the bone cross section.2. At the initial moment of stressing (₁₁=0), the modulus of elasticity of demineralized tissue is 380 times less than that of normal tissue. The minimum value of this parameter is in zone 6 (3.32 kgf/mm²) and the maximum value is in zone 1 (7.12 kgf/mm²). With increasing stress, the tangential modulus of elasticity increases.3. The specific energy of deformation under the same stressing conditions ₁₁/*₁₁ expended is greater for demineralized bone than for normal bone.4. The parameter of cross-sectional deformation ₁₂ upon stressing (at ₁₁/*₁₁ from 0.1 to 0.3) increases for demineralized tissue by a factor of 1.56, while for normal tissue this increase is only by a factor of 1.01. The average values of ₁₂ ^0·1 and ₁₂ ^0·3 for demineralized tissue are 3.3 and 2.2 times, respectively, higher than for normal tissue.5. The greatest correlations for the deformation parameters were found between the internal and external layers of the cross-sectional zones for E ₁ ⁰ (0.94) and ₁₂ ^0·3 (0.87), though the discrepancies in the zones between the internal and external layers are insignificant (p>0.05).6. The changes in the deformation parameters over the cross section have a positive correlation (with the exception of U ₁ ^0.3 ) with the amount of ground substance in normal tissue (determined relative to hexosamine).7. The deformation parameters of demineralized tissue may be described by a multi-dimensional linear equation using quantitative indices of the major biochemical components (hydroxyproline, phosphorus, and hexosamine) of normal tissue, which characterize the amounts of collagen, mineral substance, and ground substance, respectively.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 101–108, January–February, 1978.     

Change in the mechanical properties of human compact bone tissue upon aging

The ultimate tensile strength σ_z, elastic modulus E, maximum deformation ?, and Brinell hardness H_B of human compact bone tissue were determined. The contents of the minerals calcium and phosphorus, nitrogen, and water (relative to mass and volume), as well as the density were studied in the same bone samples. It was found that all the characteristics studied changed with increasing age. It is emphasized that various types of destructive mechanisms are characteristics of different ages.     

Variation of certain mechanical properties of human compact bone tissue with age

The nature of the variation of the moduli of elasticity, shear moduli, and flexural and torsional decrements of human compact bone tissue during biological aging has been investigated. It has been found that the moduli of elasticity and shear moduli increase sharply up to age 20–25 and then progressively fall; the distribution of the modulus of elasticity over the individual zones of the cross section of the tibia changes significantly with age. By investigating the changes in the logarithmic decrements by nondestructive methods it is possible to estimate the changes in the mechanical and structural properties of the bone.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 885–891, September–October, 1974.     

Deformability and strength of compact bone tissue during tensioning

The deformability and strength characteristics of compact bone tissue of human tibia during tensioning along all three main anisotropy axes was determined experimentally. The character of change in the secant moduli of elasticity and specific energies of deformation during the loading process were studied. A correlation was established between the mechanical characteristics and the biochemical composition of the bone tissue.     

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.     

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.