Physiological significance of changes in bone volume associated with deformation

The changes of volume and the compressibility characteristics of the compact bone tissue of the human tibia in longitudinal tension have been investigated in six different zones of the cross section. It has been established that when a man is walking the relative volume deformation of the bone is comparable with the volume of blood flowing through the tibia during the load-bearing period. It is suggested that the forced cyclic deformations of the bone tissue may significantly modify the level and character of the blood flow through the bone.     

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.     

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.     

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.     

Differences and correlations between the elastic characteristics of the compact bone tissue of the human tibia

Pair t tests have been carried out on experimental data indicating nonuniformity of the distribution of the elastic properties of the compact bone tissue over the cross section of the human tibia. The elastic characteristics obtained by nondestructive and destructive testing have been subjected to a linear correlation analysis. It is shown, with statistical reliability, that the compact bone tissue has a degree of anisotropy of the elastic properties higher than transverse isotropy.     

Technology and Some Mechanical Properties of Biocomposites Based on Mineral Components

Two types of new composite implant materials are investigated. Their mechanical characteristics, biocompatibility, and the dynamics of bond strength between the biocomposites and a live bone tissue are determined. The first type of the biomaterials is based on silicate glass and hydroxyapatite. Both the natural and a synthetic hydroxyapatite were used. The second type of the biomaterials was made of an ultrahigh-molecular polyethylene and the synthetic hydroxyapatite. Composite materials of both the types were implanted in the rabbit femur. The bond strength between the bone tissue and the implants was determined in 2, 4, 10, and 25 weeks.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 273–282, March–April, 2005.     

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.     

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.     

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.     

Effect of moisture content on the microdeformation of compact bone tissue in tension

Conclusions The x-ray diffraction results indicate the following major features for the microdeformation of bone tissue. The total deformation in the elastic region is determined by the microdeformation of the mineral bone tissue component. The large yield of the mineral component indicates its relatively low elasticity modulus. The shape of the deformation curves for both dry and moist bone tissue is a factor of the combined deformation of the mineral and organic components. While the total deformation up to fracture in dry bone tissue is determined largely by microdeformation of the crystalline mineral phase, such behavior is found for moist bone tissue only in the first segment of the curve. Deformation in the second, more curved segment of the deformation curve is a factor largely of deformation of the organic bone-tissue component.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 530–535, May–June, 1983.     

Changes of ultrasound velocity in children's tibial bone due to hypodynamia

The ultrasound propagation velocity was measured in the medial surface of tibial bone of 58 children's shins, ages 3 to 16 years. The children had uninterrupted bed rest from 1 to 52 months because of osteochondropathies of femoral head. The average ultrasound velocity in tibia decreased with the term of hypodynamia, due to diminishing of the amount of hydroxyapatite in the bone. This insignificant relationship could not completely charaterize pathological changes in the bone. Therefore the bone acoustical nonuniformity was analyzed by approximation of the experimental data by polynomial equations. Four different types of ultrasound velocity distribution along the bone were found. Type 1 (maximal velocity in the midpart of diaphysis) was characteristic after short term hypodynamia, when the adaption of the bone remained to the normal loading conditions. For type 2 a characteristic diminishing of the ultrasound velocity in the midpart of diaphysis was found, which gave evidence about beginning bone adaption to the hypodynamia. Type 3 (maximal velocity in the distal epiphysis) was revealed for children after long term bed rest. Distribution of the velocity for type 4 (maximal velocity in the proximal epiphysis) was characteristic for sensible osteoporosis and indicated pathological changes in children's bones after very long term hypodynamia (from 3 to 4 years). The investigations of the ultrasound velocity distribution nonuniformity in tibia from the point of view of functional adaptation showed that there were at least three stages of response of bone tissue to hypodynamia: normal adaption, reversible, and pathological nonreversible changes. Such approach improves the results of ultrasound diagnostics of the bone tissue state. Latvian Medical Academy, Riga, Latvia. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 5, pp. 696–708, September–October, 1996.     

Effect of the rate of deformation on the mechanical properties of compact bone tissue

Conclusions The results of this study show that the ultimate stress increases with increasing deformation rate from 10^–5 to 1 sec^–1 but the initial elasticity modulus remains virtually constant. A characteristic feature of bone tissue is the significant increase or even maximum in specific deformation energy for destruction in the range of deformation rates corresponding to normal physiological conditions for bone function. The deformation diagrams of human bone tissue for the same values of moisture content and deformation rate in tensile testing do not differ from the analogous curves for the bone tissue of cattle. Quantitatively, the ultimate stress ₁₁ and the initial elasticity modulus E₁ are 5–10% and 15–25% greater, respectively, than for cattle bone tissue, while the ultimate deformation eu is virtually the same. An increase in the moisture content of bone tissue leads to a more pronounced dependence of the mechanical parameters on the deformation rate.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 512–517, May–June, 1982.     

Neural network prediction of load from the morphology of trabecular bone

Bone adaptation models are often solved in the forward direction, meaning that the response of bone to a given set of loads is determined by running a bone tissue adaptation model. The model is generally solved using a numerical technique such as the finite element model. Conversely, one may be interested in the loads that have resulted in a given state of bone. This is the inverse of the former problem. Even though the inverse problem has several applications, it has not received as much attention as the forward problem, partly because solving the inverse problem is more difficult. A nonlinear system identification technique is needed for solving the inverse problem. In this study, we use artificial neural networks for prediction of tissue adaptation loads from a given density distribution of trabecular bone. It is shown that the proposed method can successfully identify the loading parameters from the density distribution of the tissue. Two important challenges for all load prediction algorithms are the non-uniqueness of the solution of the inverse problem and the inaccuracies in the measurement of the morphology of the tissue. Both challenges are studied, and it is shown that the load prediction technique proposed in this paper can overcome both.     

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.     

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.     

Strength of fresh bone and bone preserved by freezing

The bending strength of 85 plates obtained from the tibias of human cadavers has been determined and compared with the strength of plates of bone tissue from the same bone stored at temperatures from ?25 to ?30°C for 3 months (44 cases), 6.5 months (32 cases), and 9.5 months (32 cases). It is found that the strength of the deep-frozen bone decreases with time.     

Isotropic continuum damage/repair model for alveolar bone remodeling

Several authors have proposed mechanical models to predict long term tooth movement, considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to either an adaptative elasticity behavior or an update of the elasticity constants with density evolution. However, tooth movements obtained through orthodontic appliances result from a complex biochemical process of bone structure and density adaptation to its mechanical environment, called bone remodeling. This process is far from linear reversible elasticity. It leads to permanent deformations due to biochemical actions. The proposed biomechanical constitutive law, inspired from Doblaré and García (2002) [30], is based on a elasto-viscoplastic material coupled with Continuum isotropic Damage Mechanics (Doblaré and García (2002) [30] considered only the case of a linear elastic material coupled with damage). The considered damage variable is not actual damage of the tissue but a measure of bone density. The damage evolution law therefore implies a density evolution. It is here formulated as to be used explicitly for alveolar bone, whose remodeling cells are considered to be triggered by the pressure state applied to the bone matrix. A 2D model of a tooth submitted to a tipping movement, is presented. Results show a reliable qualitative prediction of bone density variation around a tooth submitted to orthodontic forces.     

Healing times for circular wounds on plane and spherical bone surfaces

A mathematical model is developed for the rate of healing of a circular wound in a spherical “skull”. The motivation for this model is based on experimental studies of the “critical size defect” (CSD) in animal models; this has been defined as the smallest intraosseous wound that does not heal by bone formation during the lifetime of the animal [1]. For practical purposes, this timescale can usually be taken as one year. In [2], the definition was further extended to a defect which has less than ten percent bony regeneration during the lifetime of the animal. CSDs can “heal” by fibrous connective tissue formation, but since this is not bone, it does not have the properties (strength, etc.) that a completely healed defect would. Earlier models of bone wound healing [3,4] have focused on the existence (or not) of a CSD based on a steady-state analysis, so the time development of the wound was not addressed. In this paper, the time development of a circular cylindrical wound is discussed from a general point of view. An integro-differential equation is derived for the radial contraction rate of the wound in terms of the wound radius and parameters related to the postulated healing mechanisms. This equation includes the effect of the curvature of the (spherical) skull, since it is clear from the experimental evidence that the size of the CSD increases monotonically with the size of the calvaria. Certain special cases for a planar wound are highlighted to illustrate the qualitative features of the model, in particular, the dependence of the wound healing time on the initial wound size and the thickness of the healing rim.     

Acoustic emission in human bone tissue subjected to longitudinal extension

A review of papers relating to the rupture of bone tissue subjected to various forms of stress is presented. The degree of development of microcracks in bone tissue subject to longitudinal extension is estimated for the first time by the acoustic-emission method. Three characteristic regions of deformation are established. The rupture process (?₁₁/? ₁₁ ^* >0.94) takes part with a practically constant acoustic emission intensity of 210 pulses/sec.