Local strain and damage mapping in single trabeculae during three-point bending tests

The use of bone mineral density as a surrogate to diagnose bone fracture risk in individuals is of limited value. However, there is growing evidence that information on trabecular microarchitecture can improve the assessment of fracture risk. One current strategy is to exploit finite element analysis (FEA) applied to 3D image data of several mm-sized trabecular bone structures obtained from non-invasive imaging modalities for the prediction of apparent mechanical properties. However, there is a lack of FE damage models, based on solid experimental facts, which are needed to validate such approaches and to provide criteria marking elastic-plastic deformation transitions as well as microdamage initiation and accumulation. In this communication, we present a strategy that could elegantly lead to future damage models for FEA: direct measurements of local strains involved in microdamage initiation and plastic deformation in single trabeculae. We use digital image correlation to link stress whitening in bone, reported to be correlated to microdamage, to quantitative local strain values. Our results show that the whitening zones, i.e. damage formation, in the presented loading case of a three-point bending test correlate best with areas of elevated tensile strains oriented parallel to the long axis of the samples. The average local strains along this axis were determined to be (1.6±0.9)% at whitening onset and (12±4)% just prior to failure. Overall, our data suggest that damage initiation in trabecular bone is asymmetric in tension and compression, with failure originating and propagating over a large range of tensile strains.     

Elastic strains in antler trabecular bone determined by synchrotron X-ray diffraction

The microstructure and associated mechanical properties of antler trabecular bone have been studied using a variety of techniques. The local trabeculae properties, as well as the three-dimensional architecture were characterized using nanoindentation and X-ray microtomography, respectively. An elastic modulus of 10.9+/-1.1 GPa is reported for dry bone, compared with 5.4+/-0.9 GPa for fully hydrated bone. Trabeculae thickness and separation were found to be comparable to those of bovine trabecular bone. Uniaxial compression conducted in situ during X-ray microtomography showed that antler can undergo significant architectural rearrangement, dominated by trabeculae bending and buckling, due to its low mineral content. High-energy synchrotron X-ray diffraction was used to measure elastic strains in the apatite crystals of the trabeculae, also under in situ uniaxial compression. During elastic loading, strain was found to be accommodated largely by trabeculae aligned parallel to the loading direction. Prior to the macroscopic yield point, internal strains increased as trabeculae deformed by bending, and load was also found to be redistributed to trabeculae aligned non-parallel to the loading direction. Significant bending of trabecular walls resulted in tensile strains developing in trabeculae aligned along the loading direction.     

Comparison of the influences of structural characteristics on bulk mechanical behaviour: experimental study using a bone surrogate

An experimental study was conducted to classify the influence of trabecular architecture and cortical shell thickness on the mechanical properties using a bone surrogate. Thirty-six rectangular prisms and 18 vertebral-shaped specimens were fabricated with fused deposition modelling (FDM) as a bone surrogate with controlled structural characteristics (cortical wall thickness, strut spacing, strut angle and strut orientation). The apparent density of the FDM specimens was evaluated using quantitative computed tomography (QCT) imaging and related to the apparent elastic modulus measured with compression testing. The effects of the structural parameters on the apparent elastic modulus were analysed using analysis of variance (ANOVA). The results obtained corroborate that the structural parameters have a significant effect on the apparent mechanical properties of the bulk material. The cortical shell thickness was found to have more influence than trabecular architecture. Therefore, accurate modelling of the cortical shell thickness should be considered more important than trabecular architecture in development of bone finite element models and bone surrogates.     

Mechanical properties of OI type III bone tissue measured by nanoindentation

Nanoindentation was used to characterize the intrinsic mechanical properties of bone tissue from eight (8) children with type III Osteogenesis Imperfecta (OI). The bone samples were harvested from the cortex portion at the site of bowing (the mid 2/3 of the shaft of the tibia/femur). Unlike normal bone tissue, OI type III cortical bone exhibited more isotropic material properties. Young's modulus and hardness values measured in the longitudinal direction did not show significant differences from the transverse measurements. No differences were observed in modulus or hardness in an analysis of the cortical and trabecular samples. The deformation patterns of the OI type III bone during nanoindentation were found to be similar to those of normal adult bone in an analysis of the ratio of modulus to hardness. No correlation was found between nanoindentation measurement and age in an analysis of regression.     

Comparison of nanoindentation measurements between osteogenesis imperfecta Type III and Type IV and between different anatomic locations (femur/tibia versus iliac crest)

Nanoindentation was used to compare the intrinsic mechanical properties of bone tissue (iliac crest biopsy) from children with type III and type IV osteogenesis imperfecta (OI). Young's modulus and hardness values were not significantly different between the two clinical severity groups on either cortical or trabecular measurement. In comparing the ratio of modulus over hardness (E/H) between OI type III and IV. The type III bone showed a marginally significant decrease for cortical bone and significant decrease for trabecular bone, which indicated that the OI type III bone was more brittle than OI type IV bone at the tissue level. In addition, nanoindentation measurements of the bone tissue harvested at femur/tibia from the same patients were compared with the results from the iliac crest biopsy. Young's modulus and hardness values were not significantly different between the two anatomic locations in either cortical or trabecular measurements. The ratio of E/H was not significantly different between the two groups. Results indicate that intrinsic modulus, hardness, and indentation deformation pattern (E/H) of OI bone tissues are not significantly different at long bone (midshaft of femur/tibia) and iliac crest. We observed that age (1.9 to 13.2 years) did not influence OI bone tissue intrinsic mechanical properties.     

Comparison of Nanoindentation Measurements Between Osteogenesis Imperfecta Type III and Type IV and Between Different Anatomic Locations (Femur/Tibia versus Iliac Crest)

Nanoindentation was used to compare the intrinsic mechanical properties of bone tissue (iliac crest biopsy) from children with type III and type IV osteogenesis imperfecta (OI). Young's modulus and hardness values were not significantly different between the two clinical severity groups on either cortical or trabecular measurement. In comparing the ratio of modulus over hardness (E/H) between OI type III and IV. The type III bone showed a marginally significant decrease for cortical bone and significant decrease for trabecular bone, which indicated that the OI type III bone was more brittle than OI type IV bone at the tissue level. In addition, nanoindentation measurements of the bone tissue harvested at femur/tibia from the same patients were compared with the results from the iliac crest biopsy. Young's modulus and hardness values were not significantly different between the two anatomic locations in either cortical or trabecular measurements. The ratio of E/H was not significantly different between the two groups. Results indicate that intrinsic modulus, hardness, and indentation deformation pattern (E/H) of OI bone tissues are not significantly different at long bone (midshaft of femur/tibia) and iliac crest. We observed that age (1.9 to 13.2 years) did not influence OI bone tissue intrinsic mechanical properties.     

Non-destructive characterization of microdamage in cortical bone using low field pulsed NMR

The microcracking and damage accumulation process in human cortical bone was characterized by performing cyclic loading under four-point bending at ambient temperature. A non-destructive nuclear magnetic resonance (NMR) spin-spin (T(2)) relaxation technique was applied to quantify the apparent changes in bone porosity as a function of cyclic loading and prior damage accumulation, first to unloaded cortical bone to quantify the initial porosity and then to fatigued cortical bone that was subjected to cyclic loading to various levels of modulus degradation and microdamage in the form of microcracks. The NMR T(2) relaxation time and amplitude data of the fatigued bone were compared against the undamaged state. The difference in the T(2) relaxation time data was taken as a measure of the increase in pore size, bone porosity or microcrack density due to microdamage induced by cyclic loading. A procedure was developed to deduce the number and size distributions of microcracks formed in cortical bone. Serial sectioning of the fatigued bone showed the formation of microcracks along the cement lines or within the interstitial tissue. The results on the evolution of microdamage derived from NMR measurements were verified by independent experimental measurements of microcrack density using histological characterization techniques. The size distribution and population of the microcracks were then utilized in conjunction with an analytical model to predict the degradation of the elastic modulus of cortical bone as a function of damage accumulation.     

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions.     

Comparison of the structure and mechanical properties of bovine femur bone and antler of the North American elk (Cervus elaphus canadensis)

Antler and limb bone have a similar microstructure and chemical composition. Both are primarily composed of type I collagen and a mineral phase (carbonated apatite), arranged in osteons in compact (cortical bone) sections and a lamellar structure in the cancellous (spongy or trabecular bone) sections. The mineral content is lower in antler bone and it has a core of cancellous bone surrounded by compact bone running through the main beam and tines. The mineral content is higher in the compact compared with the cancellous bone, although there is no difference in ratios of the mineral elements with calcium. Mechanical tests (bend and compression) on longitudinal and transverse orientations of dry and rehydrated compact bone of North American elk (Cervus elaphus canadensis) antlers are compared with known data on other antlers as well as bovine femora. Both dry and rehydrated bones are highly anisotropic, with the bending and compressive strength and elastic modulus higher in the longitudinal than in the transverse direction. There is no significant difference between the bend strength and elastic modulus between dry and rehydrated samples tested in the transverse direction. The elastic modulus measured from the bending tests is compared with composite models. The elastic modulus and bend strengths are lower in the rehydrated condition, but the strain to failure and fracture toughness is much higher compared with dry samples. All antler bone mechanical properties are lower than that of bovine femora. The antler has a much higher fracture toughness compared with bovine femora, which correlates with their main function in intraspecific combat as a high impact resistant, energy absorbent material. A model of compression deformation is proposed, which is based on osteon sliding during shear.     

Mechanical and morphological variation of the human lumbar vertebral cortical and trabecular bone.

The nanoindentation technique was used to characterize the variation in the elastic modulus and hardness of human lumbar vertebral cortical and trabecular bone. The elastic modulus (and in most cases, the hardness as well) of axially aligned trabeculae cut in the transverse direction was significantly greater than in other orientations of vertebral cortical and trabecular bone. In all cases, the elastic modulus and hardness of bone in the load-bearing direction was greater than in corresponding bone types cut in the other directions. Scanning electron micrographs of cortical shell revealed the Haversian-like canal systems expected in secondary cortical bone, but it was difficult to differentiate by morphology cortical from trabecular bone in the human lumbar vertebrae.     

Characterization of the mechanical and ultrastructural properties of heat-treated cortical bone for use as a bone substitute.

Heat-treated bovine cortical bone has been proposed as an alternative to bone grafts and synthetic bone substitutes because it may combine the advantages of allografts (high stiffness and strength) and synthetic materials (abundant supply, reduced risk of rejection and disease transfer). Its mechanical properties and ultrastructure, however, are not well characterized. To address this, we compared the compressive (n = 20, bovine bone) and tensile (n = 26, bovine bone) mechanical properties and the ultrastructure (n = 12, human bone) of intact versus 350 degrees C heat-treated cortical bone. The 350 degrees C heat-treated bone had a mean +/- SD elastic modulus similar to the intact bone for both compression (16.3 +/- 2.2 GPa, pooled; p = 0.68) and tension (16.3 +/- 3.7 GPa, pooled; p = 0.95). It also maintained 63% of the intact strength in compression but only 9% in tension (p < 0.001). Infrared scans and X-ray diffraction patterns showed no differences between the 350 degrees C heat-treated and intact bone but large differences between ashed (700 degrees C) and intact bone. Similarly, heat-treated bone previously has been shown to be biocompatible and osteoconductive. We conclude, therefore, that 350 degrees C heat-treated cortical bone may be an excellent load-bearing bone substitute provided that it is loaded in compression only in vivo and is shown by future work to have acceptable fatigue properties.     

Quality of alveolar bone--Structure-dependent material properties and design of a novel measurement technique

The evidence for the efficiency of clinical methods used to assess the quality of alveolar bone in terms of a density measure prior to and during dental implant surgery is limited. The aim of this paper is to describe the biomechanical background which can be used as a basis for determining the bone quality by measuring the elastic properties of the bone and to design a novel device for the determination of the bone quality during dental implant surgery. Applying material mechanical equations for porous and cellular structured models, the elastic material properties (modulus of elasticity) of cellular and cortical bone as porous structures were approximated over the whole range of relative bone mineral density of trabecular and cortical bone. Based on a circular disc with a central hole reflecting a horizontal cross-section of an implant socket, the mechanical effects of expanding the central hole were studied. Subsequently, the clinical situation of a socket prepared for the placement of a dental implant (depth: 10?mm; diameter 3.5?mm) was simulated using three-dimensional (3D) finite element analysis. A loading device (thickness: 3.5?mm) was placed in the trabecular part of the socket and expanded, while the resulting pressure was recorded and used for the calculation of an elastic modulus. Finite element analysis revealed that it was possible to estimate the bone quality by applying the measurement technique proposed. Maximum deviations of 6% of the experimentally determined elastic modulus from the setpoint elastic modulus were found. Measuring the internal pressure in a drill hole, e.g., in an implant socket caused by a defined expansion of a rotational symmetric loading device, could be used for establishing a clinically meaningful test system for the objective classification of alveolar bone.     

Material properties of the human cranial vault and zygoma

The material properties of cortical bone from the diaphyses of long bones (e.g., the femur and tibia) vary by direction, such that bone is stiffer and stronger along its long axis. This configuration improves the abilities of these structures to resist axial compressive loads coupled with bending. As in long bones, cortical bone from the cranial vault is subject to mechanical loads from various orofacial functions and the contraction of attached muscles. However, experimental studies suggest that the resulting bone strains are at least an order of magnitude smaller than those found in the midshafts of the femur or tibia. The characteristics of the three-dimensional elastic properties of cortical bone are largely unexplored in regions of low bone strain, including the cranial vault, in which little is known regarding cortical structure and function. In the present study we examined variations in the cortical microstructure and material properties of the bone of the human cranial vault, including the parietal, frontal, temporal, and occipital bones. A facial bone, the zygoma, was also included to contrast the properties of the cranial vault with another craniofacial intramembranous bone that experiences larger strains. Cortical specimens from the outer cortical plate of the cranial vault were removed from 15 frozen human crania. We measured cortical thicknesses and densities, and determined the primary direction of stiffness within the bone specimens prior to ultrasonic testing to determine their elastic properties. There were statistically significant differences in elastic properties between bones and, in some cases, sites within bones, which for most variables were clustered by bone or region. In striking contrast to this pattern, elastic moduli in the direction of primary stiffness were larger in cortical regions underlying muscle attachments than in regions without muscle attachments. Few sites in the cranial vault or zygoma showed a consistent orientation of the material axes among individuals, although specimens from many regions had directional differences similar to those in cortical bone from the mandible, femur, or tibia.     

Mechanical properties of human trabecular bone lamellae quantified by nanoindentation.

Improved preventive and therapeutic strategies for skeletal diseases such as osteoporosis rely on a better understanding of the mechanical properties of trabecular bone and their influence on cell mediated adaptation processes. The mechanical properties of trabecular bone are determined by composition as well as structural (trabecular architecture), microstructural (trabecular packets) and nanostructural (lamellae) organization. Density is the major predictor of the mechanical properties of trabecular structures and has been extended to the concept of fabric to include architectural anisotropy and improve even further the power of prediction. Recent advances in QCT and MRI technologies allow for precise assessment of 3D trabecular architecture and the mechanical consequences of structural changes can be increasingly well quantified by the means of computational methods. While single trabeculae have been tested using various techniques with contrasting results, little is known about the intrinsic mechanical properties of trabecular bone lamellae on which these computational methods rely. For instance, water and mineral content have a significant effect on the elastic, viscous, yield and postyield properties of bone tissue. In addition, collagen fiber orientation affects the mechanics of single remodeling units. Variations in composition and organization determined by age, accumulated damage or disease may therefore reduce the mechanical integrity of trabecular bone and deserve more attention. The aim of this work was to utilize a nanoindentation technique to quantify elastic modulus and hardness of human trabecular bone lamellae.     

On the effect of marrow in the mechanical behavior and crush response of trabecular bone

The present paper focuses on the mechanical behavior analysis of bones at mesoscopic scale, paying a special attention to the trabecular bone and the bone marrow filling the porosities. Uni-axial quasi-static compression tests under unconfined conditions have been performed to identify the mechanical behavior of 46 trabecular bone samples. The bone marrow for 22 samples has been preserved to analyze the fluid flow effects on the crushing response. Although deformation patterns do not differ significantly, the average crush behavior of the trabecular bone shows an unexpected decrease of the mechanical properties when the marrow is kept in the sample (26% for the elastic modulus (E(a)), 38% for the maximum compressive stress (σ(max)) and 33% for the average stress (σ(mean))). An explanation is given by analyzing the contribution of the bone marrow viscosity which smooths the mechanical response. A numerical analysis on an idealized trabecula confirms that the marrow induces transverse pressure and extra local stress on trabeculae during its flow, causing the premature collapse of the trabecular network.     

Vertebral Osteoporosis and Trabecular Bone Quality

Vertebral fractures due to osteoporosis commonly occur under non-traumatic loading conditions. This problem affects more than 1 in 3 women and 1 in 10 men over a lifetime. Measurement of bone mineral density (BMD) has traditionally been used as a method for diagnosis of vertebral osteoporosis. However, this method does not fully account for the influence of changes in the trabecular bone quality, such as micro-architecture, tissue properties and levels of microdamage, on the strength of the vertebra. Studies have shown that deterioration of the vertebral trabecular architecture results in a more anisotropic structure which has a greater susceptibility to fracture. Transverse trabeculae are preferentially thinned and perforated while the remaining vertical trabeculae maintain their thickness. Such a structure is likely to be more susceptible to buckling under normal compression loads and has a decreased ability to withstand unusual or off-axis loads. Changes in tissue material mechanical properties and levels of microdamage due to osteoporosis may also compromise the fracture resistance of vertebral trabecular bone. New diagnostic techniques are required which will account for the influence of these changes in bone quality. This paper reviews the influence of the trabecular architecture, tissue properties and microdamage on fracture risk for vertebral osteoporosis. The morphological characteristics of normal and osteoporotic architectures are compared and their potential influence on the strength of the vertebra is examined. The limitations of current diagnostic methods for osteoporosis are identified and areas for future research are outlined.     

Analysis of anisotropic viscoelastoplastic properties of cortical bone tissues

Bone fractures affect the health of many people and have a significant social and economic effect. Often, bones fracture due to impacts, sudden falls or trauma. In order to numerically model the fracture of a cortical bone tissue caused by an impact it is important to know parameters characterising its viscoelastoplastic behaviour. These parameters should be measured for various orientations in a bone tissue to assess bone's anisotropy linked to its microstructure. So, the first part of this study was focused on quantification of elastic-plastic behaviour of cortical bone using specimens cut along different directions with regard to the bone axis-longitudinal (axial) and transverse. Due to pronounced non-linearity of the elastic-plastic behaviour of the tissue, cyclic loading-unloading uniaxial tension tests were performed to obtain the magnitudes of elastic moduli not only from the initial loading part of the cycle but also from its unloading part. Additional tests were performed with different deformation rates to study the bone's strain-rate sensitivity. The second part of this study covered creep and relaxation properties of cortical bone for two directions and four different anatomical positions-anterior, posterior, medial and lateral-to study the variability of bone's properties. Since viscoelastoplasticity of cortical bone affects its damping properties due to energy dissipation, the Dynamic Mechanical Analysis (DMA) technique was used in the last part of our study to obtain magnitudes of storage and loss moduli for various frequencies. Based on analysis of elastic-plastic behaviour of the bovine cortical bone tissue, it was found that magnitudes of the longitudinal Young's modulus for four cortical positions were in the range of 15-24 GPa, while the transversal modulus was lower--between 10 and 15 GPa. Axial strength for various anatomical positions was also higher than transversal strength with significant differences in magnitudes for those positions. Quantitative data obtained in creep and relaxation tests exhibited no significant position-specific differences. DMA results demonstrated relatively low energy-loss capability due to viscosity of bovine cortical bone that has a loss factor in the range of 0.035-0.1.     

图像相关法测试股骨近端骨小梁压缩特性

目的改善传统方法做压缩测试的不足,更准确地反映骨小梁的压缩弹性模量,探究股骨近端骨小梁的压缩生物力学特性,为临床诊疗提供实验室依据。方法运用微材料力学测试系统,对正常国人(45～60岁)尸体股骨近端骨小梁沿主压力方向及与其垂直方向的压缩性能进行实验研究。结果测得了股骨近端骨小梁在主压力方向压缩弹性模量为(335.26±183.85)MPa,与其垂直方向的压缩弹性模量为(59.27±23.88)MPa,骨小梁在主压力方向上的生物力学性能要明显高于主张力方向;记录了载荷下的骨小梁的位移及应变分布图,负载时骨小梁的位移及应变分布是不均匀的。结论应用微材料力学测试系统测试股骨近端骨小梁压缩弹性模量以更准确地反映其力学性能的方法是可行的,股骨近端骨小梁的压缩性能具有各向异性和不均匀性。     

Use of hydrodynamic forces to engineer cartilaginous tissues resembling the non-uniform structure and function of meniscus

The aim of this study was to demonstrate that differences in the local composition of bi-zonal fibrocartilaginous tissues result in different local biomechanical properties in compression and tension. Bovine articular chondrocytes were loaded into hyaluronan-based meshes (HYAFF-11) and cultured for 4 weeks in mixed flask, a rotary Cell Culture System (RCCS), or statically. Resulting tissues were assessed histologically, immunohistochemically, by scanning electron microscopy and mechanically in different regions. Local mechanical analyses in compression and tension were performed by indentation-type scanning force microscopy and by tensile tests on punched out concentric rings, respectively. Tissues cultured in mixed flask or RCCS displayed an outer region positively stained for versican and type I collagen, and an inner region positively stained for glycosaminoglycans and types I and II collagen. The outer fibrocartilaginous capsule included bundles (up to 2 microm diameter) of collagen fibers and was stiffer in tension (up to 3.6-fold higher elastic modulus), whereas the inner region was stiffer in compression (up to 3.8-fold higher elastic modulus). Instead, molecule distribution and mechanical properties were similar in the outer and inner regions of statically grown tissues. In conclusion, exposure of articular chondrocyte-based constructs to hydrodynamic flow generated tissues with locally different composition and mechanical properties, resembling some aspects of the complex structure and function of the outer and inner zones of native meniscus.     

The ability of quantitative ultrasound to predict the mechanical properties of trabecular bone under different strain rates

The ability of quantitative ultrasound to predict the mechanical properties of trabecular bone under different strain rates was investigated. Ultrasound velocity (UV) and broadband attenuation (BUA) were measured for 60 specimens of human trabecular bone. Samples were divided into two equal groups and loaded in compression at the strain rates of 0.0004 and 0.08 s⁻¹. The ultimate strength, elastic modulus, and energy absorption capacity were determined for each specimen. Specimens tested at 0.08 s⁻¹ had a mean value of strength 63% higher than the specimens tested at 0.0004 s⁻¹. The elastic modulus and energy absorption capacity were 82% and 42% higher, respectively, for the higher strain rate. UV and BUA were significantly associated with most mechanical properties at both strain rates. All mechanical properties were also correlated strongly with a linear combination of UV and BUA for both the low and high loading rates. The use of ultrasound parameters may provide good clinical means for assessing the resistance of trabecular bone to both low and high energy trauma.