Regeneration of trabecular bone using porous ceramics

As health care is improving, our life expectancy is increasing but as we get older we lose bone density due to osteoporosis. At present the treatment for severe cases of osteoporosis is the total hip replacement. This has been one of the most successful surgical procedures in the history of medicine, but it uses bio-inert materials to replace damaged bone. These materials cause further loss in bone density and eventually the replacement needs to be replaced. A patient that has a hip replacement at the age of 60 may need several revision operations by the time they reach ninety. For large done defects an alternative is transplantation, but there are limitations of a lack of donors and morbidity of the donor site. Both of these techniques are tissue replacement techniques. A shift in thinking is required from tissue replacement to the regeneration of tissues to their original state and function. One path to follow is the regeneration of bone using ceramic and glass scaffolds that mimic the structure of bone mineral, bond to bone and in some cases activate the genes within bone cells to stimulate new bone growth.     

Influence of density, elasticity, and structure on ultrasound transmission through trabecular bone cylinders

The aim of this in vitro study is to evaluate the potentiality of quantitative ultrasound (QUS) to separate information on density, elasticity, and structure on specimens of trabecular bone. Fifteen cylinders of spongy bone extracted from equine vertebrae were progressively demineralized and subjected to QUS, micro computed tomography (muCT), Dual energy X-ray absorptiometry (DXA) at various mineralization levels. Eventually all cylinders underwent a compression test to calculate the Young's modulus. Correlation analysis shows that speed of sound (SOS) is strictly associated to bone mineral density (BMD), Young's modulus, and all muCT parameters except for degree of anisotropy (DA). Fast wave amplitude (FWA) is directly correlated with bone surface and total volume ratio (BS/TV) and trabecular separation (Tb Sp), and inversely correlated with trabecular number (Tb N). Because muCT parameters were strictly correlated to BMD and Young's modulus data, partial correlation analysis was performed between SOS, FWA, and structural and elastic data in order to eliminate the effect of density. SOS was significantly correlated to bone volume and total volume ratio (BV/TV), BS/TV, and Young's modulus, and FWA was significantly correlated to Tb Sp only. These results show that SOS is strongly influenced by volumetric mineral bone density and elastic modulus of the specimen, and FWA is mainly affected by trabecular separation independently on density. Therefore, SOS and FWA are able to provide different and complementary information, at least on trabecular bone samples.     

谱自相关法估计骨小梁间距

1引言骨质疏松症是引起骨的脆性增加及骨折危险性增加的一种全身性骨骼疾病[1,2]。患这种疾病后骨小梁变细,髓腔增宽,骨的硬度和弹性下降。因此,测量松质骨的微结构,可为松质骨状况的评价及骨质疏松症的诊断提供有效的手段,其中骨小梁间距是评     

Characterization of trabecular bone using the backscattered spectral centroid shift

Ultrasonic attenuation in bone in vivo is generally measured using a through-transmission method at the calcaneus. Although attenuation in calcaneus has been demonstrated to be a useful predictor for osteoporotic fracture risk, measurements at other clinically important sites, such as hip and spine, could potentially contain additional useful diagnostic information. Through-transmission measurements may not be feasible at these sites due to complex bone shapes and the increased amount of intervening soft tissue. Centroid shift from the backscattered signal is an index of attenuation slope and has been used previously to characterize soft tissues. In this paper, centroid shift from signals backscattered from 30 trabecular bone samples in vitro were measured. Attenuation slope also was measured using a through-transmission method. The correlation coefficient between centroid shift and attenuation slope was -0.71. The 95% confidence interval was (-0.86, -0.47). These results suggest that the backscattered spectral centroid shift may contain useful diagnostic information potentially applicable to hip and spine.     

The geometry of nonlinear elasticity

Elasticity is the prototype of constitutive models in Continuum Mechanics. In the nonlinear range, the elastic model claims for a geometrically consistent physico-mathematical formulation providing also the logical premise for linearized approximations. A theoretic framework is envisaged here with the aim of contributing a conceptually clear, physically consistent, and computationally convenient formulation. A reasoning about the physics of the model, from a geometric point of view, leads to conceive constitutive relations as instantaneous incremental responses to a finite set of tensorial state variables and to their time rates along the space-time motion. Integrability of the tangent elastic compliance, existence of an elastic stress potential, and conservativeness of the elastic response, under the conservation of mass, are given a brand new treatment. Finite elastic strains have no physical interpretation in the new rate theory, and referential local placements are appealed to, just as loci for operations of linear calculus. Frame invariance is assessed with a consistent geometric treatment, and the clear distinction between the new notion and the property of isotropy is pointed out, thus overcoming the improper statement of material frame indifference. Extension of the theory to elasto-visco-plastic constitutive models is briefly addressed. Basic computational steps are described to illustrate feasibility and convenience of calculations according to the new theory of elasticity.     

Nanostructural analysis of trabecular bone

The mechanical properties of bone are dictated by the size, shape and organization of the mineral and matrix phases at multiple levels of hierarchy. While much is known about structure–function relations at the macroscopic level, less is known at the nanoscale, especially for trabecular bone. In this study, high resolution transmission electron microscopy (HRTEM) was carried out to analyze shape and orientation of apatite crystals in murine femoral trabecular bone. The distribution and orientation of mineral apatites in trabecular bone were different from lamellar bone and the c-axis of the tablet-like mineral apatite crystals in trabecular bone was arranged with no preferred orientation. The difference in the orientation distribution of apatite crystals of trabecular bone in the present study compared with that of lamellar bone found in the literature can be attributed to the more complex local stress state in trabecular bone. Apatite crystals were also found to be multi-crystalline, not single crystalline, from dark field image analysis. From the observations of this study, it is suggested that Wolff’s law can be applicable to the nanostructural orientation and distribution of apatite crystals in trabecular bone. It was also found that small round crystalline particles observed adjacent to collagen fibrils were similar in size and shape to the apatite crystals in biomimetically nucleated synthetic amorphous calcium phosphate, which suggests that they are bone mineral apatite nuclei.     

Mechanical properties and bone densities of canine trabecular bone

The purposes of this study were (1) to evaluate the mechanical properties of canine epiphyseal cancellous bones from adult canine femoral heads, femoral condyles, tibial plateau, and humeral heads, using indentation and compression tests, and (2) to measure bone densities (apparent density and ash density) of these cancellous bones so as to develop a normal data base of mechanical strength and bone density. The correlations between the two mechanical tests and between these tests and bone densities were also considered. The results showed all of the three mechanical parameters, ultimate load, stiffness, and ultimate strength, measured by the indentation test were higher than those measured by the compression test. Correlation analysis showed that the two sets of mechanical values correlated well (r=0.823–0.952, p<0.01). The apparent density and ash density correlated well with the mechanical parameters determined by the two types of mechanical tests (r=0.737–0.966, p<0.05). © 1998 Chapman & Hall     

Linear stress-strain relations in nonlinear elasticity

Summary Nonlinear strain measures which are compatible with the existence of an elastic potential and lead to a linear stress-strain relation are obtained. An unusual property of these measures is their dependence on material parameters. Standard strain measures commonly used in nonlinear elasticity are shown to be consistent with linear stress-strain relations only for particular cases of Poisson's ratio. Corresponding potentials for these cases are presented.     

An extension of Key's principle to nonlinear elasticity

A variational principle for finite isothermal deformations of anisotropic compressible and nearly incompressible hyperelastic materials is presented. It is equivalent to the nonlinear elastic field (Lagrangian) equations expressed in terms of the displacement field and a scalar function associated with the hydrostatic mean stress. The formulation for incompressible materials is recovered from the compressible one simply as a limit. The principle is particularly useful in the development of finite element analysis of nearly incompressible and of incompressible materials and is general in the sense that it uses a general form of constitutive equation. It can be considered as an extension of Key's principle to nonlinear elasticity. Various numerical implementations are used to illustrate the efficiency of the proposed formulation and to show the convergence behaviour for different types of elements. These numerical tests suggest that the formulation gives results which change smoothly as the material varies from compressible to incompressible.     

Multi-scale modelling of elastic moduli of trabecular bone

We model trabecular bone as a nanocomposite material with hierarchical structure and predict its elastic properties at different structural scales. The analysis involves a bottom-up multi-scale approach, starting with nanoscale (mineralized collagen fibril) and moving up the scales to sub-microscale (single lamella), microscale (single trabecula) and mesoscale (trabecular bone) levels. Continuum micromechanics methods, composite materials laminate theory and finite-element methods are used in the analysis. Good agreement is found between theoretical and experimental results.     

The effects of bovine trabecular bone matrix particulates on cortical bone repair

This paper reports the effects of a synthetic bone substitute and bone allograft on cortical bone repair in an experimental model. To test the hypothesis that bovine trabecular bone matrix, BBM, can enhance the repair rate of cortical bone, osteotomies were created in the rabbit fibula and filled with either allograft or BBM particulates or left empty as controls. At five weeks post-surgery, mechanical tests and histological evaluations were performed. No significant differences were observed in the mechanical properties of the healing bone in the three animal groups (n=6). Histologically, the medullary cavity was obstructed and the cross-sectional area ratio of the osteotomies to intact bone was approximately 3 : 1. Highly significant area differences were observed between the intact bone group and both the BBM and the allograft groups . At the junction between the original bone and the newly formed bone, both woven and lamellar bone microstructures were prevalent. However, in the BBM filled defects, the woven bone microstructure was not ostentatious. It is concluded that failure to demonstrate significantly differences between the treatments were due to the small sample sizes and or the efficacy of the tensile analysis.     

Monte Carlo modelling of energy deposition in trabecular bone

This study includes the design and testing of a program that creates quadric-based geometric models of the trabecular region, designed specifically for use with the 2005 version of the Monte Carlo radiation transport code PENELOPE. Our model was tested, by comparison with published data, in two aspects: the distributions of path lengths throughout the geometry and absorbed fraction values from the monoenergetic emission of electrons from within our geometry. In both comparisons, our results show a close agreement with published methods.     

Accurate digital time-of-flight measurement using self-interference

Most ultrasonic distance measurements are based on the determination of the time of flight. This paper presents a novel way for the measurement of the time of flight, based on the detection of the envelope zero in an ultrasonic wave. A particular wave form is produced by supplying two pulse trains subsequently to an acoustic transducer. Distance information is retrieved from the zero, so a fully digital measurement is possible, reducing signal-processing time and resulting in a fast and accurate distance measurement     

Pseudo‐transient continuation for nonlinear transient elasticity

This paper demonstrates how pseudo‐transient continuation improves the efficiency and robustness of a Newton iteration within a non‐linear transient elasticity simulation. Pseudo‐transient continuation improves efficiency by enabling larger time steps than possible with a Newton iteration. Robustness improves because pseudo‐transient continuation recovers the convergence of Newton's method when the initial iterate is not within the region of local convergence. We illustrate the benefits of pseudo‐transient continuation on a non‐linear transient simulation of a buckling cylinder, including a comparison with a line search‐based Newton iteration. Copyright © 2008 John Wiley & Sons, Ltd.     

A stratified model to predict dispersion in trabecular bone

Frequency-dependent phase velocity (dispersion) has previously been measured in trabecular bone by several groups. In contrast to most biologic tissues, phase velocity in trabecular bone tends to decrease with frequency. A stratified model, consisting of alternating layers of bone and marrow (in vivo) or water (in vitro), has been employed in an attempt to explain this phenomenon. Frequency-dependent phase velocity was measured from 300 to 700 kHz in 1) phantoms consisting of regularly spaced thin parallel layers of polystyrene sheets in water and 2) 30 calcaneus samples in vitro. For the polystyrene phantoms, the agreement between theory and experiment was good. For the calcaneus samples, the model has some limited usefulness (uncertainty of about 5%) in predicting average phase velocity. More importantly, the model seems to perform consistently well for predicting the frequency dependence of phase velocity in calcaneus.     

Position and size effects on voids growth in nonlinear elasticity

Numerical studies of multiple voids growth are carried out on a nonlinear hyper-elastic 2D cylinder subjected to an expansionary boundary condition. For certain compressible hyper-elastic material, our numerical experiments on the case of two voids revealed that both the positions and initial sizes of the pre-existing voids can have significant effects on the final grown configuration. We found that, for the initial voids of macroscopic scale both factors affect the final result in a continuous manner and two grown voids of comparable size are commonly observed, and for the initial voids of mesoscopic scale the size effect is no longer continuous and one of the grown voids is always found significantly greater than the other, while for the initial voids of microscopic scale the position effect is essentially decisive on the voids growth and the center positioned void always grows much more rapidly. We also found that the size and position effects are stronger if the material is less compressible, or the load, with the smaller principle stress in alignment with the two voids, is less symmetric.     

A numerical study on dynamics of cavity growth in nonlinear elasticity

A dynamic cavity growth problem in an isotropic compressible nonlinear hyper-elastic material subject to a gradually applied traction is numerically studied. The effects of three parameters, namely the material mass density, the maximum traction, and the loading rate, on the evolution of the cavity radius, especially the maximum cavity radius, are investigated. The numerical results show that, while both the inertia and loading rate have only marginal effect on the onset of cavitation, they do significantly affect the maximum cavity radius. Furthermore, the applied traction eventually leads to a periodic oscillatory cavity growth, and a square root power law for the vibration period as a function of the material mass density is found to hold.