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.     

Numerical simulation of elastic linear micropolar media based on the pore space length scale assumption

The 3D micropolar theory numerical simulations have been performed on the brittle isotropic materials (amorphous glass, brittle rock and two different lightweight concretes) with different pore sizes using the cylindrical models under uniaxial compressive loading. To pursue this goal, it is assumed that first, second and third microrotation constants (α, β, and γ), which appear in the couple stress equilibrium equation, are proportional to the square of average pore diameter or so called characteristic length. Unexpectedly such an assumption leads to a constant polar ratio and consequently, the polar ratio cannot be accounted for as a material constant. The present phenomenon substantiates the existence of a redundant material constant for the 3D micropolar media. Accordingly, the micropolar shear constant κ is a material constant. Different coupling numbers N, with relevant domain are numerically investigated to explore the characteristic features of the micropolar shear constant κ. According to the results obtained, the present methodology shows a very good convergence and is consistent with the physically accepted results for the heterogeneous and homogeneous materials including nano-and microscale pores, whereas several unconverted or discontinuous stress fields are found out when using mesoscale pores. The latter disadvantage is believed to be caused by the impact of voids’ ratio variation under quasistatic loading. __________ Translated from Problemy Prochnosti, No. 4, pp. 43–60, July–August, 2008.     

Modelling Young’s modulus for porous bones with microstructural variation and anisotropy

A structural model with three compositional phases and two levels of hierarchical organization is proposed for predicting Young’s modulus of porous bones with microstructural variations and anisotropy based on their geometric similarity to metal foams. It has been shown that the proposed single model provides predictions of Young’s modulus with high accuracy up to ±30% for cortical and cancellous bones compared with measured data from the literature. In addition, the conversion of the solid bone shape from “Plate-like” to “Rod-like” at a porosity of 70% or higher (BV/TV 30% or lower)—verified by observations—can be predicted using the proposed model.     

Hydroxyapatite bone substitutes developed via replication of natural marine sponges

The application of synthetic cancellous bone has been shown to be highly successful when its architecture mimics that of the naturally interconnected trabeculae bone it aims to replace. The following investigation demonstrates the potential use of marine sponges as precursors in the production of ceramic based tissue engineered bone scaffolds. Three species of natural sponge, Dalmata Fina (Spongia officinalis Linnaeus, Adriatic Sea), Fina Silk (Spongia zimocca, Mediterranean) and Elephant Ear (Spongia agaricina, Caribbean) were selected for replication. A high solid content (80 %wt), low viscosity (126 mPas) hydroxyapatite slurry was developed, infiltrated into each sponge species and subsequently sintered, producing a scaffold structure that replicated pore architecture and interconnectivity of the precursor sponge. The most promising of the ceramic tissue engineered bone scaffolds developed, Spongia agaricina replicas, demonstrated an overall porosity of 56–61% with 83% of the pores ranging between 100 and 500 μm (average pore size 349 μm) and an interconnectivity of 99.92%.     

A 3D multilevel model of damage and strength of wood: Analysis of microstructural effects

A 3D hierarchical computational model of damage and strength of wood is developed. The model takes into account the four scale microstructures of wood, including the microfibril reinforced structure at nanoscale, multilayered cell walls at microscale, hexagon-shape-tube cellular structure at mesoscale and annual rings at the macroscale. With the use of the developed hierarchical model, the influence of the microstructure, including microfibril angle (MFA), the cell shape and the wood density (annual ring structure), differences between earlywood and latewood as well as microstructural arrangements and cellulose strength distributions on the tensile strength of wood is studied numerically. Good agreement of the theoretical results with experimental data has been obtained.     

Fibrillar level fracture in bone beyond the yield point

The nanoscale deformation and fracture mechanisms of parallel fibered bone are investigated using a novel combination of in-situ tensile testing to failure combined with high brilliance synchrotron X-ray scattering. The technique enables the simultaneous measurement of strain at two length scales – in the mineralized collagen fibrils (~100 nm diameter) along with the macroscopic strain (~1 mm diameter). Under constant rate tensile loading, we find that fibril strain saturates beyond the macroscopic yield point of bone at ~0.5 %, providing a correlation between the failure mechanisms at the nanoscale and the bulk structural properties. When bone stretched beyond the yield point is unloaded back to zero stress, the fibrils are contracted relative to their original state. We examine the findings in the context of a fiber – matrix shearing model at the nanometer level.     

Nanoscale research in South Africa: A mapping exercise based on scientometrics

This article reports the findings of a scientometric analysis of nanoscale research in South Africa during the period 2000–2005. The ISI databases were identified as the most appropriate information platform for the objectives of the investigation and have been interrogated for the identification of South African authors publishing in the field. The article identifies trends over time, major institutional contributors, journals in which South African authors publish their research, international collaborators and performance in comparison to four comparator countries (India, Brazil, South Korea and Australia). The major findings of the investigation are as follows: nanoscale research in South Africa is driven by individual researchers interests up to date and it is in its early stages of development; the country’s nanoscale research is below what would one expect in light of its overall publication output; the country’s nano-research is distributed to a number of Universities with subcritical concentration of researchers.     

Actuation of polypyrrole nanowires

Nanoscale actuators are essential components of the NEMS (nanoelectromechanical systems) and nanorobots of the future, and are expected to become a major area of development within nanotechnology. This paper demonstrates for the first time that individual polypyrrole (PPy) nanowires with diameters under 100 nm exhibit actuation behavior, and therefore can potentially be used for constructing nanoscale actuators. PPy is an electroactive polymer which can change volume on the basis of its oxidation state. PPy-based macroscale and microscale actuators have been demonstrated, but their nanoscale counterparts have not been realized until now. The research reported here answers positively the fundamental question of whether PPy wires still exhibit useful volume changes at the nanoscale. Nanowires with a 50?nm diameter and a length of approximately 6?μm, are fabricated by chemical polymerization using track-etched polycarbonate membranes as templates. Their actuation response as a function of oxidation state is investigated by electrochemical AFM (atomic force microscopy). An estimate of the minimum actuation force is made, based on the displacement of the AFM cantilever.     

Cancellous bone from porous T{i}6Al4V by multiple coating technique

A highly porous T{i}6Al4V with interconnected porous structure has been developed in our previous study. By using a so-called “Multiple coating” technique, the porous T{i}6Al4V can be tailored to resemble cancellous bone in terms of porous structure and mechanical properties. A thin layer of T{i}6Al4V slurry was coated on the struts of base porous T{i}6Al4V to improve the pore structure. After two additional coating, pore sizes ranged from 100 μm to 700 μm, and the porosity was decreased from ∼90% to ∼ 75%, while the compressive strength was increased from 10.3 ± 3.3 MPa to 59.4 ± 20.3 MPa and the Young's modulus increased from 0.8 ± 0.3 GPa to 1.8 ± 0.3 GPa. The pore size and porosity are similar to that of cancellous bone, meanwhile the compressive strength is higher than that of cancellous bone, and the Young's modulus is between that of cancellous bone and cortical bone. Porosity, pore size and mechanical properties can be controlled by the parameters in such multiple coating processes. Therefore the porous T{i}6Al4V with the characteristics of cancellous bone is expected to be a promising biomaterial for biomedical applications. Author to whom all correspondence should be addressed.     

Nonparametric inference with generalized likelihood ratio tests

The advance of technology facilitates the collection of statistical data. Flexible and refined statistical models are widely sought in a large array of statistical problems. The question arises frequently whether or not a family of parametric or nonparametric models fit adequately the given data. In this paper we give a selective overview on nonparametric inferences using generalized likelihood ratio (GLR) statistics. We introduce generalized likelihood ratio statistics to test various null hypotheses against nonparametric alternatives. The trade-off between the flexibility of alternative models and the power of the statistical tests is emphasized. Well-established Wilks’ phenomena are discussed for a variety of semi- and non-parametric models, which sheds light on other research using GLR tests. A number of open topics worthy of further study are given in a discussion section. This invited paper is discussed in the comments available at: , , , , , , , , . The work was supported by the NSF grants DMS-0354223, DMS-0532370 and DMS-0704337. The paper was initiated when Jiancheng Jiang was a research fellow at Princeton University.     

Investigation on the mechanical properties and frictional performance of Ni–Cu–Si alloy

The microstructure evolution, mechanical properties and dry sliding behaviour of Ni–30Cu–xSi alloy have been investigated systematically. As the volume fraction of microscale second-phase particles and nanoscale precipitates increases, the hardness, yield strength and ultimate tensile strength of alloy are improved significantly but elongation is reduced. Through confocal laser scanning microscope and atomic force microscope, it is suggested that the wear mode changes from the mixture of abrasive and adhesive wear to single abrasive wear. Owing to the existence of netlike microscale second-phase particles which are more likely to split the matrix, the Ni–30Cu–5.5Si alloy exhibits an abnormal higher wear rate even with the highest hardness. The netlike structure which deteriorates the friction performance should be avoided in wear-resistant materials.     

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.     

Three-dimensional analytical techniques for evaluation of osseointegrated titanium implants

Abstract

Osseointegration, the direct bonding of titanium implant materials with bone, is critical for implant success where nanostructured surface features contribute to nano-osseointegration. However, we also know that features and processes on the microscale influence the biocompatibility of implant materials. We highlight the advantages of using mutlilength scale analyses, focusing on three-dimensional techniques, ranging from X-ray microcomputed tomography, to focused ion beam, to high resolution electron tomography to identify markers of osseointegration. A titanium implant with modified biomimetic coating studied in vitro and in vivo at various time points is used to exemplify the complementary information gained from three-dimensional analyses from the micro- to nanoscale.     

Stress, stress asymmetry and couple stress: from discrete particles to continuous fields

Explicit and closed expressions for the stress and couple-stress fields for discrete (classical) mechanical systems in terms of the constituents’ degrees of freedom and interactions are derived and compared to previous results. This is done by using an exact and general coarse graining formulation, which allows one to predetermine the resolution of the continuum fields. Since the full dynamics of the pertinent fields is considered, the results are not restricted to static states or quasi-static deformations; the latter comprise mere limiting cases, which are discussed as well. The fields automatically satisfy the equations of continuum mechanics. An explicit expression for the antisymmetric part of the stress field is presented; the question whether the latter vanishes, much like its nature when it does not, have been debated in the literature. Physical explanations of some of the obtained results are offered; in particular, an interpretation of the expression for the stress field provides an argument in favor of its uniqueness, yet another topic of debate in the literature. The formulation and results are valid for single realizations, and can of course be used in conjunction with ensemble averaging. Part of the paper is devoted to a biased discussion of the notion of coarse graining in general, in order to set the presented results in a certain perspective. Although the results can be applied to molecular (nanoscale included) and granular systems alike, the presentation and some simplifying assumptions (which can be easily relaxed) target granular systems. The results should be useful for the analysis of experimental and numerical findings as well as the development of constitutive relations.     

Repair of goat tibial defects with bone marrow stromal cells and β-tricalcium phosphate

Tissue engineering techniques have been proven effective in bone regeneration and repairing load-bearing bone defects. Previous studies, however, have heretofore been limited to the use of slowdegradable or natural biomaterials as scaffolds. There are, however, no reports on using biodegradable, synthetic beta-tricalcium phosphate (β-TCP) as scaffolds to repair weight-bearing bone defects in large animals. In the present study, highly porous β-TCP scaffolds prepared by the polymeric sponge method were used to repair goat tibial defects. Fifteen goats were randomly assigned to one of three groups, and a 26 mm-long defect at the middle part of the right tibia in each goat was created. In Group A (six goats), a porous β-TCP ceramic cylinder that had been loaded with osteogenically induced autologous bone marrow stromal cells (BMSCs) was implanted in the defect of each animal. In Group B (six goats), the same β-TCP ceramic cylinder without any cells loaded was placed in the defect. In Group C (three goats), the defect was left untreated. In Group A, bony union can be observed by gross view, X-ray and micro-computed tomography (Micro-CT) detection, and histological observation at 32 weeks post-implantation. The implanted β-TCP scaffolds were almost completely replaced by tissue-engineered bone. Bone mineral density in the repaired area of Group A was significantly higher (p < 0.05) than that of Group B, in which scant new bone was formed in each defect and the β-TCP hadn’t been completely resorbed at 32 weeks. Moreover, the tissue-engineered bone of Group A had similar biomechanical properties as that of the normal left tibia in terms of bending strength and Young’s modulus (p > 0.05). In Group C, little or no new bone was formed, and non-union occurred, showing that the 26 mm segmental defect of the goat tibia was critical sized at 32 weeks. Thus, it can be concluded that the mechanical properties of the BMSCs/β-TCP composites could be much improved via tissue engineering approach and β-TCP might be used to repair the weight-bearing segmental defects of goat tibias. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Nanoscale fracture analysis by atomic force microscopy of EPDM rubber due to high-pressure hydrogen decompression

The relationship between internal fracture due to high-pressure hydrogen decompression and microstructure of ethylene–propylene–diene–methylene linkage (EPDM) rubber was investigated by atomic force microscopy (AFM). Nanoscale line-like structures were observed in an unexposed specimen, and their number and length increased with hydrogen exposure. This result implies that the structure of the unfilled EPDM rubber is inhomogeneous at a nanoscale level, and nanoscale fracture caused by the bubbles that are formed from dissolved hydrogen molecules after decompression occurs even though no cracks are observed by optical microscopy. Since this nanoscale fracture occurred at a threshold tearing energy lower than that obtained from static crack growth tests of macroscopic cracks (T _s,th), it is supposed that nanoscale structures that fractured at a lower threshold tearing energy (T _nano,th) than T _s,th existed in the rubber matrix, and these low-strength structures were the origin of the nanoscale fracture. From these results, it is inferred that the fracture of the EPDM rubber by high-pressure hydrogen decompression consists of two fracture processes that differ in terms of size scale, i.e., bubble formation at a submicrometer level and crack initiation at a micrometer level. The hydrogen pressures at bubble formation and crack initiation were also estimated by assuming two threshold tearing energies, T _nano,th for the bubble formation and T _s,th for the crack initiation, in terms of fracture mechanics. As a result, the experimental hydrogen pressures were successfully estimated.     

Non-equilibrium Green’s function method for modeling quantum electron transport in nano-scale devices with anisotropic multiband structure

Aggressive scaling of devices has reduced device dimensions into nanometer scale in which the single-band effective mass model is inadequate to simulate quantum transport in such devices. Thus it motivates the use of more realistic full band structures in quantum transport simulations. In this study we perform the analysis of multiband quantum transport in nanoscale devices based on a non-equilibrium Green’s function (NEGF) formalism coupled self-consistently with the Poisson equation. The empirical nearest neighbor sp ³ s ^* tight binding approximation (TBA), where the couplings among atomic orbitals of the host crystal are taken into account, is employed to obtain a realistic multiband structure. The effects of non-parabolic bandstructure as well as anisotropic features of Si are studied and analyzed. Our multiband simulation results on potential and current profiles show significant differences, especially in higher applied bias, with those of conventional effective mass model where only parabolic singleband is considered in the simulation.     

评价松质骨状况的一种背散射频谱方法

采用超声背散射信号的质心偏移量来评价松质骨,并对牛胫骨和人体跟骨中背散射信号的质心偏移量与松质骨表观密度的关系,以及人体跟骨松质骨中背散射信号频谱质心位置与年龄的关系进行了分析讨论。分析结果表明,随松质骨表观密度的增大,背散射信号频谱的质心向低频方向移动;随年龄的增大,质心位置越接近于发射超声的中心频率。根据超声背散射信号质心偏移量的大小,可用于评价松质骨健康状况。     

A comparative study of the physical and mechanical properties of three natural corals based on the criteria for bone–tissue engineering scaffolds

Coral has been used for bone grafts since 1970. Because coral has the advantages of good osteoconduction, biocompatibility, and biodegradation, it is also suitable for scaffolds used in bone–tissue engineering. However, the skeletons of different species of corals often vary significantly, and very few studies focus on the assessment of the permeability and mechanical properties of coral structure. In order to better understand the use of coral in bone tissue–engineering, we selected three typical models (Acropora sp., Goniopora sp., and Porites sp.) to analyze for pore size, porosity, permeability, and mechanical strength. We found Goniopora and Porites had homogenous structure and Acropora had oriented pores and irregular pore size. Acropora had the largest permeability, however, the transverse section was closed and the useful size was limited because of its habitat type. Porites had the smallest pore size and had the lowest permeability. Our data indicated that Goniopora sp. can be considered as the most promising source of scaffolds for bone–tissue engineering because of its high porosity (73%) and that its permeability and mechanics were similar to those in human cancellous bone. In conclusion, we analyzed the impact of the macroporous structure of coral on the permeability and mechanical properties that provide indicators for designing the optimal scaffold for bone–tissue engineering.     

Tuning of the Optical,Electronic, and Magnetic Properties of Boron Nitride Nanosheets with Oxygen Doping and Functionalization

Engineering of the optical, electronic, and magnetic properties of hexagonal boron nitride (h‐BN) nanomaterials via oxygen doping and functionalization has been envisaged in theory. However, it is still unclear as to what extent these properties can be altered using such methodology because of the lack of significant experimental progress and systematic theoretical investigations. Therefore, here, comprehensive theoretical predictions verified by solid experimental confirmations are provided, which unambiguously answer this long‐standing question. Narrowing of the optical bandgap in h‐BN nanosheets (from ≈5.5 eV down to 2.1 eV) and the appearance of paramagnetism and photoluminescence (of both Stokes and anti‐Stokes types) in them after oxygen doping and functionalization are discussed. These results are highly valuable for further advances in semiconducting nanoscale electronics, optoelectronics, and spintronics.