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.     

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.     

An experimental study of the effect of fracture and operative intervention on acoustical properties of human tibial bone

Conclusions 1. The differences between the ultrasonic parameters c and determined for the right and left tibial bones as well as between values obtained directly on the bone and through the skin are statistically insignificant (p>0.1).2. Experimental fracture of the tibia leads to a significant decrease in the ultrasound speed (p<0.001) and increase in the ultrasound damping coefficient (p<0.001).3. Operative intervention, as a whole, and any of the surgical manipulations, in particular, significantly alter the initial acoustic parameters of the tibia with fracture or after osteotomy relative to fracture or osteotomy without osteosynthesis. These groups of patients should have different criteria for the degree of fracture repair.4. Weakening of the stability of the fixation of a fracture by screwing in or loosening screws attaching a splint plate to the bone cause an increase in the damping coefficient. This sign is rather sensitive for use in clinical practice to diagnose weakening of the rigidity of fixation.5. The ultrasound parameters c and depend on the magnitude of the cross-sectional defect of the diaphysis and in conjunction may be used for diagnosis of the degree of adhesion of a fracture or operation site after corrective osteotomy.6. The values for c and found for undamaged bone may be used to evaluate their values for a diaphysis used for preparing bone samples.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. 1, pp. 88–96, January–February, 1978.     

Theory of the biomechanism of fractures of the diaphysis of long tubular bones

A new theoretical basis is proposed for the biomechanism of fractures of the diaphysis of long tubular bones resulting from bending deformation. Bone damage is shown to result from the concentration of maximum tensile stresses on the tension side and shear stresses in the compression zone. The origin of fan-shaped cracks and oblique fractures, occurring individually or in combination, is explained in these terms.Altai State Medical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 318–322, March–April, 1971.     

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.     

Investigation of the nonuniform distribution of the elastic and strength characteristics over the cross section of the diaphysis of the human tibia

The elastic, deformation, and strength properties of six different zones of the cross section of the diaphysis of the human tibia have been experimentally investigated. It is shown that when the compact bone tissue is stressed in tension all these properties differ significantly from zone to zone. The greatest values of the initial modulus of elasticity and the tensile strength correspond to the frontal-outer zones of the bone. The nonlinear stress-strain curves are analytically approximated. The secant and tangent moduli are shown to depend on the stress intensity.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 940–946, September–October, 1971.     

Use of ultrasonic surface waves for studying the properties of the human tibia

A method of determining the ultrasonic surface-wave velocity by means of exponential concentrators is proposed for determining the properties of human tibia in vitro. The effect of the radiation frequency and the thickness of the surface layer of bone tissue on the surface-wave propagation velocity is studied. For measurement purposes the tibia is divided into 24–28 vertical levels and six to seven horizontal zones. The variation of the surface-wave velocity with the measuring point is investigated. Relations are established between the distribution of surface-wave velocities and the statistical parameters characterizing the dispersion of the results, on the one hand, and biological age and the source of the bone (right or left leg), on the other.     

Optimum selection of the dental implant diameter and length in the posterior mandible with poor bone quality – A 3D finite element analysis

This study aimed to evaluate continuous and simultaneous variations of dental implant diameter and length, and to identify their relatively optimal ranges in the posterior mandible under biomechanical consideration. A 3D finite element model of a posterior mandibular segment with dental implant was created. Implant diameter ranged from 3.0 to 5.0 mm, and implant length ranged from 6.0 to 16.0 mm. The results showed that under axial load, the maximum Von Mises stresses in cortical and cancellous bones decreased by 76.53% and 72.93% respectively, with the increasing of implant diameter and length; and under buccolingual load, by 83.97% and 84.93%, respectively. Under both loads, the maximum displacements of implant-abutment complex decreased by 58.09% and 75.53%, respectively. The results indicate that in the posterior mandible, implant diameter plays more significant roles than length in reducing cortical bone stress and enhancing implant stability under both loads. Meanwhile, implant length is more effective than diameter in reducing cancellous bone stress under both loads. Moreover, biomechanically, implant diameter exceeding 4.0 mm and implant length exceeding 12.0 mm is a relatively optimal combination for a screwed implant in the posterior mandible with poor bone quality.     

A theoretical model for Reynolds-stress and dissipation-rate budgets in near-wall region

A 3-D wave model for the turbulent coherent structures in near-wall region is proposed. The transport nature of the Reynolds stresses and dissipation rate of the turbulence kinetic energy are shown via computation based on the theoretical model. The mean velocity profile is also computed by using the same theoretical model. The theoretical results are in good agreement with those found from DNS, indicating that the theoretical model proposed can correctly describe the physical mechanism of turbulence in near wall region and it thus possibly opens a new way for turbulence modeling in this region.     

Modeling the influence of mineral content and porosity on ultrasound parameters in bone by using synthetic phantoms

Model composite media − 10×15×80 mm³ bone tissue phantoms based on an epoxy resin with fillers—were made to study the influence of porosity and mineral content on ultrasound velocity and attenuation. The pores were simulated by ∼ 1 mm³ particles of a soft rubber, while the mineral content was imitated by a mineral residue of natural bone obtained by burning and grinding. The porosity and mineral content were varied in the range of 0–70% by volume with a step of 10%. The velocity, attenuation, and prevalent frequency of ultrasound were measured by the pulse transition method, using transducers with nominal frequencies 0.1, 0.2, 0.5, and 1.0 MHz. It was experimentally found that the ultrasound velocity decreased nearly exponentially with growth in porosity, while the velocity dispersion was negligible at frequencies >0.2 MHz; the ultrasound attenuation increased linearly with growth in porosity and strongly depended on the frequency; the velocity increased nonlinearly with growth in mineral content above 40%; the attenuation did not exhibit a distinct dependence on the mineral content; the porosity provoked a shift in the prevalent frequency of transducers, tending to the common value of 0.2 MHz, while the mineral content did not excite similar changes. The complex measurement of velocity, frequency-dependent attenvation, and prevenlent frequency of ultrasound is proposed in ultrasonic diagnostics of bone for more precise determination of the influence of the porosity and the degree of mineralization on the bone condition.     

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.     

Modeling the influence of mineral content and porosity on ultrasound parameters in bone by using synthetic phantoms

Model composite media – 10×15×80 mm³ bone tissue phantoms based on an epoxy resin with fillers—were made to study the influence of porosity and mineral content on ultrasound velocity and attenuation. The pores were simulated by 1 mm³ particles of a soft rubber, while the mineral content was imitated by a mineral residue of natural bone obtained by burning and grinding. The porosity and mineral content were varied in the range of 0–70% by volume with a step of 10%. The velocity, attenuation, and prevalent frequency of ultrasound were measured by the pulse transition method, using transducers with nominal frequencies 0.1, 0.2, 0.5, and 1.0 MHz. It was experimentally found that the ultrasound velocity decreased nearly exponentially with growth in porosity, while the velocity dispersion was negligible at frequencies >0.2 MHz; the ultrasound attenuation increased linearly with growth in porosity and strongly depended on the frequency; the velocity increased nonlinearly with growth in mineral content above 40%; the attenuation did not exhibit a distinct dependence on the mineral content; the porosity provoked a shift in the prevalent frequency of transducers, tending to the common value of 0.2 MHz, while the mineral content did not excite similar changes. The complex measurement of velocity, frequency-dependent attenvation, and prevenlent frequency of ultrasound is proposed in ultrasonic diagnostics of bone for more precise determination of the influence of the porosity and the degree of mineralization on the bone condition.Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 211–220, March–April, 1999.     

Numerical Simulation of the Influence of Rough Bone-Callus Interface on the Healing of Fractured Bone

The process of healing of fractured bone is known to be influenced by the mechanical environment and the loads exerted by physical activity of the patient or otherwise. We compute mechanical fields in the soft connective tissue of the healing fracture using Biot's poroelasticity model and a finite element (FE) method for low-frequency loading. A two-scale FE framework is used to model effects of the rough bone-callus contact surface. We look at the difference the interface roughness makes with respect to different possible mechanostimulating agents.     

Investigation of physiological pulsatile flow in a model arterial stenosis using large-eddy and direct numerical simulations

Physiological pulsatile flow in a 3D model of arterial stenosis is investigated by using large eddy simulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatile flow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatile flow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3.     

Investigation of the nonunifcrmity of the acoustic properties of the human tibia

Mechanics of Composite Materials - A method is proposed for determining the propagation velocity and coefficient of attenuation of ultrasonic vibrations in both the whole diaphysis of the human...     

Long-time behavior of one-dimensional compressible Bingham flows

Barotropic flows of one-dimensional compressible Bingham fluids are considered. Long-time behavior of the corresponding initial-boundary problem is investigated. The uniform upper and lower bounds for the density and a decay of the kinetic energy are established. We admit a class of mass forces not considered for similar problems to Newtonian fluids. Under additional assumptions on the mass force, we achieve strong estimates for the solution (uniformly in time) and decays of the velocity and its derivatives.     

Anisotropy in the destruction of compact bone material

Conclusions 1. The nature of the destruction of compact bone material upon short-term static compressive and tensile stresses, as well as upon impact bending, is a function of the anistropy of the structure on the osteon level.2. The compact bone material of femoral bones of the age range studied is destroyed by shear for the types of stresses indicated.3. The nature of the destruction of samples of compact bone material for the stresses studied may be generalized for tubular bones.Kurgan Scientific-Research Institute of Experimental and Clinical Orthopedics and Traumatology. Translated from Mekhanika Polimerov, No. 2, pp. 319–324, March–April, 1978.     

Some qualitative effects in the exact solutions of the Lamé problem for large deformations

Qualitative effects in the solution of a number of radially symmetric and plane axisymmetric problems for bodies made of non-linearly elastic incompressible materials are analysed for large deformations. In the case of problems of the axisymmetric plane deformation of cylindrical bodies, the lack of uniqueness of the solution for a given follower load in the case of a Bartenev–Khazanovich material and the existence of a limiting load in the case of a Treloar (neo-Hookian) material have been studied in detail and the dependences of the limiting load on the ratio of the external and internal radii of a hollow cylinder in the undeformed state have been presented. A similar study has been carried out for constitutive relations of a special form that well describe the properties of rubber. For this material, the lack of uniqueness of the solution is revealed for fairly high loads. The axisymmetric problem of the plane stress state of a circular ring made of a Bartenev–Khazanovich material has been solved and a lack of uniqueness of the solution for a given follower load was discovered in the case when the dimensions of the ring are given in the undeformed state. Similar studies have been carried out for Chernykh and Treloar materials in the case of the problem of the radially symmetric deformation of a spherical shell. It was established that, in the case of a Chernykh material, the lack of uniqueness of the solution depends considerably on the constant characterizing the physical non-linearity. The limit case of the deformation of a spherical cavity in an infinitely extended body has been investigated. The effect of an unbounded increase in the boundary stresses is observed for finite external loads, that appears in the case of the problem of the plane axisymmetric deformation of a cylindrical cavity in an infinitely extended body made of a Bartenev–Khazanovich material and in the case of the problem of the radially symmetric deformation of an infinitely extended body made of a Chernykh material with a spherical cavity.     

Flow of a Maxwell fluid between two side walls induced by a constantly accelerating plate

The unsteady flow of a Maxwell fluid induced by a constantly accelerating plate between two side walls perpendicular to the plate is studied. Exact solutions for the velocity field are established by means of the Fourier sine transforms. The adequate tangential stresses are also determined. The similar solutions for a Newtonian fluid are obtained as limiting cases of our solutions. In the absence of the side walls, the similar solutions for the unsteady flow over an infinite flat plate are recovered. Finally, for comparison, the velocity field in the middle of the channel and the shear stresses at the bottom wall and on the side walls are plotted for different values of the material constants.