Modeling microdamage behavior of cortical bone

Bone is a complex material which exhibits several hierarchical levels of structural organization. At the submicron-scale, the local tissue porosity gives rise to discontinuities in the bone matrix which have been shown to influence damage behavior. Computational tools to model the damage behavior of bone at different length scales are mostly based on finite element (FE) analysis, with a range of algorithms developed for this purpose. Although the local mechanical behavior of bone tissue is influenced by microstructural features such as bone canals and osteocyte lacunae, they are often not considered in FE damage models due to the high computational cost required to simulate across several length scales, i.e., from the loads applied at the organ level down to the stresses and strains around bone canals and osteocyte lacunae. Hence, the aim of the current study was twofold: First, a multilevel FE framework was developed to compute, starting from the loads applied at the whole bone scale, the local mechanical forces acting at the micrometer and submicrometer level. Second, three simple microdamage simulation procedures based on element removal were developed and applied to bone samples at the submicrometer-scale, where cortical microporosity is included. The present microdamage algorithm produced a qualitatively analogous behavior to previous experimental tests based on stepwise mechanical compression combined with in situ synchrotron radiation computed tomography. Our results demonstrate the feasibility of simulating microdamage at a physiologically relevant scale using an image-based meshing technique and multilevel FE analysis; this allows relating microdamage behavior to intracortical bone microstructure.     

Strain Concentrations Surrounding an Ellipsoid Model of Lacunae and Osteocytes

Direct cell sensing of tissue matrix strains is one possible signaling mechanism for mechanically mediated bone adaptation. We utilized homogenization theory lo estimate bone tissue matrix strains surrounding osteocytes using two sets of models. The first set of models estimated the strain levels surrounding the lacunae and canaliculi, taking into account variations in lamellar properties. The second set estimated strain levels in the osteocyte and the surrounding matrix for different cellular mechanical properties. The results showed that the strain levels found in and surrounding osteocytes, 1700 to 2700 microstrain (denoted as μe; 1 =.0001% strain), were significantly greater than the trabecular tissue level strains of [1325 μe, 287 μe, 87 μe] used for model input. Variation in lamellar properties did not affect strain levels, except at lamellar boundaries. Strain in and surrounding the osteocyte was not significantly affected by cellular stiffness ranging between 28 and 28,000 Pascals (Pa). Strain levels surrounding lacunae and canaliculi were approximately equivalent.     

Multilevel finite element modeling for the prediction of local cellular deformation in bone

The underlying mechanisms by which bone cells respond to mechanical stimuli or how mechanical loads act on osteocytes housed in lacunae in bone are not well understood. In this study, a multilevel finite element (FE) approach is applied to predict local cell deformations in bone tissue. The local structure of the matrix dictates the local mechanical environment of an osteocyte. Cell deformations are predicted from detailed linear FE analysis of the microstructure, consisting of an arrangement of cells embedded in bone matrix material. This work has related the loads applied to a whole femur during the stance phase of the gait cycle to the strain of a single lacuna and of canaliculi. The predicted bone matrix strains around osteocyte lacunae and canaliculi were nonuniform and differed significantly from the macroscopically measured strains. Peak stresses and strains in the walls of the lacuna were up to six times those in the bulk extracellular matrix. Significant strain concentrations were observed at sites where the process meets the cell body.     

Strain Concentrations Surrounding an Ellipsoid Model of Lacunae and Osteocytes

Direct cell sensing of tissue matrix strains is one possible signaling mechanism for mechanically mediated bone adaptation. We utilized homogenization theory to estimate bone tissue matrix strains surrounding osteocytes using two sets of models. The first set of models estimated the strain levels surrounding the lacunae and canaliculi, taking into account variations in lamellar properties. The second set estimated strain levels in the osteocyte and the surrounding matrix for different cellular mechanical properties. The results showed that the strain levels found in and surrounding osteocytes, 1700 to 2700 microstrain (denoted as μe; 1 μe =.0001% strain), were significantly greater than the trabecular tissue level strains of {1325 μe, 287 μe, 87 μe} used for model input. Variation in lamellar properties did not affect strain levels, except at lamellar boundaries. Strain in and surrounding the osteocyte was not significantly affected by cellular stiffness ranging between 28 and 28, 000 Pascals (Pa). Strain levels surrounding lacunae and canaliculi were approximately equivalent.     

Stress-concentrating effect of resorption lacunae in trabecular bone

Analyses of the distributions of stress and strain within individual bone trabeculae have not yet been reported. In this study, four trabeculae were imaged and finite elements models were generated in an attempt to quantify the variability of stress/strain in real trabeculae. In three of these trabeculae, cavities were identified with depths comparable to values reported for resorption lacunae ( approximately 50 microm)-although we cannot be certain, it is most probable that they are indeed resorption lacunae. A tensile load was applied to each trabeculum to simulate physiological loading and to ensure that bending was minimized. The force carried by each trabecula was calculated from this value using the average cross sectional area of each trabecula. The analyses predict that very high stresses (>100 MPa) existed within bone trabecular tissue. Stress and strain distributions were highly heterogeneous in all cases, more so in trabeculae with the presumptive resorption lacunae where at least 30% of the tissue had a strain greater than 4000 micoepsilon in all cases. Stresses were elevated at the pit of the lacunae, and peak stress concentrations were located in the longitudinal direction ahead of the lacunae. Given these high strains, we suggest that microdamage is inevitable around resorption lacunae in trabecular bone, and may cause the bone multicellular unit to proceed to resorb a packet of bone in the trabeculum rather than just resorb whatever localized area was initially targeted.     

Osteocyte lacunae tissue strain in cortical bone

Current theories suggest that bone modeling and remodeling are controlled at the cellular level through signals mediated by osteocytes. However, the specific signals to which bone cells respond are still unknown. Two primary theories are: (1) osteocytes are stimulated via the mechanical deformation of the perilacunar bone matrix and (2) osteocytes are stimulated via fluid flow generated shear stresses acting on osteocyte cell processes within canaliculi. Recently, much focus has been placed on fluid flow theories since in vitro experiments have shown that bone cells are more responsive to analytically estimated levels of fluid shear stress than to direct mechanical stretching using macroscopic strain levels measured on bone in vivo. However, due to the complex microstructural organization of bone, local perilacunar bone tissue strains potentially acting on osteocytes cannot be reliably estimated from macroscopic bone strain measurements. Thus, the objective of this study was to quantify local perilacunar bone matrix strains due to macroscopically applied bone strains similar in magnitude to those that occur in vivo. Using a digital image correlation strain measurement technique, experimentally measured bone matrix strains around osteocyte lacunae resulting from macroscopic strains of approximately 2000 microstrain are significantly greater than macroscopic strain on average and can reach peak levels of over 30,000 microstrain locally. Average strain concentration factors ranged from 1.1 to 3.8, which is consistent with analytical and numerical estimates. This information should lead to a better understanding of how bone cells are affected by whole bone functional loading.     

Three‐dimensional characterization of osteocyte volumes at multiple scales,and its relationship with bone biology and genome evolution in ray‐finned fishes

Osteocytes, cells embedded within the bone mineral matrix, inform on key aspects of vertebrate biology. In particular, a relationship between volumes of the osteocytes and bone growth and/or genome size has been proposed for several tetrapod lineages. However, the variation in osteocyte volume across different scales is poorly characterized and mostly relies on incomplete, two‐dimensional information. In this study, we characterize the variation of osteocyte volumes in ray‐finned fishes (Actinopterygii), a clade including more than half of modern vertebrate species in which osteocyte biology is poorly known. We use X‐ray synchrotron micro‐computed tomography (SRµCT) to achieve a three‐dimensional visualization of osteocyte lacunae and direct measurement of their size (volumes). Our specimen sample is designed to characterize variation in osteocyte lacuna morphology at three scales: within a bone, among the bones of one individual and among species. At the intra‐bone scale, we find that osteocyte lacunae vary noticeably in size between zones of organized and woven bone (being up to six times larger in woven bone), and across cyclical bone deposition. This is probably explained by differences in bone deposition rate, with larger osteocyte lacunae contained in bone that deposits faster. Osteocyte lacuna volumes vary 3.5‐fold among the bones of an individual, and this cannot readily be explained by variation in bone growth rate or other currently observable factors. Finally, we find that genome size provides the best explanation of variation in osteocyte lacuna volume among species: actinopterygian taxa with larger genomes (polyploid taxa in particular) have larger osteocyte lacunae (with a ninefold variation in median osteocyte volume being measured). Our findings corroborate previous two‐dimensional studies in tetrapods that also observed similar patterns of intra‐individual variation and found a correlation with genome size. This opens new perspectives for further studies on bone evolution, physiology and palaeogenomics in actinopterygians, and vertebrates as a whole.     

Measurement of microstructural strain in cortical bone

It is well known that mechanical factors affect bone remodeling such that increased mechanical demand results in net bone formation, whereas decreased demand results in net bone resorption. Current theories suggest that bone modeling and remodeling is controlled at the cellular level through signals mediated by osteocytes. The objective of this study was to investigate how macroscopically applied bone strains similar in magnitude to those that occur in vivo are manifest at the microscopic level in the bone matrix. Using a digital image correlation strain measurement technique, experimentally determined bone matrix strains around osteocyte lacuna resulting from macroscopic strains of approximately 2,000 microstrain (0.2%) reach levels of over 30,000 microstrain (3%) over fifteen times greater than the applied macroscopic strain. Strain patterns were highly heterogeneous and in some locations similar to observed microdamage around osteocyte lacuna indicating the resulting strains may represent the precursors to microdamage. This information may lead to a better understanding of how bone cells are affected by whole bone functional loading.     

Comparison of strain measurement in the mouse forearm using subject-specific finite element models,strain gaging,and digital image correlation

Mechanical loading in bone leads to the activation of bone-forming pathways that are most likely associated with a minimum strain threshold being experienced by the osteocyte. To investigate the correlation between cellular response and mechanical stimuli, researchers must develop accurate ways to measure/compute strain both externally on the bone surface and internally at the osteocyte level. This study investigates the use of finite element (FE) models to compute bone surface strains on the mouse forearm. Strains from three FE models were compared to data collected experimentally through strain gaging and digital image correlation (DIC). Each FE model was assigned subject-specific bone properties and consisted of one-dimensional springs representing the interosseous membrane. After three-point bending was performed on the ulnae and radii, moment of inertia was determined from microCT analysis of the bone region between the supports and then used along with standard beam analyses to calculate the Young’s modulus. Non-contact strain measurements from DIC were determined to be more suitable for validating numerical results than experimental data obtained through conventional strain gaging. When comparing strain responses in the three ulnae, we observed a 3–14% difference between numerical and DIC strains while the strain gage values were 37–56% lower than numerical values. This study demonstrates a computational approach for capturing bone surface strains in the mouse forearm. Ultimately, strains from these macroscale models can be used as inputs for microscale and nanoscale FE models designed to analyze strains directly in the osteocyte lacunae.     

Osteocyte lacuna size and shape in women with and without osteoporotic fracture

Osteocytes have been hypothesized to control the amount and location of bone tissue which is resorbed or formed, based on the strain magnitude they perceive, and therefore may play a role in the bone loss of osteoporosis. The shape of osteocyte lacunae influences the mechanical strain applied to the osteocyte; thus, it is important to quantify their shape to further understand the mechanical environment of this cell. Previous studies of the size and shape of lacunae have been contradictory and limited to two-dimensional measurements on iliac crest biopsies. This investigation measured the size and shape of osteocyte lacunae in trabecular bone near a typical fracture site from three-dimensional image sets obtained by confocal microscopy. Bone tissue specimens were obtained from individuals undergoing hip replacement subsequent to fracture, and matched cadaveric specimens without fracture. After extensive image processing to differentiate the lacunae from the matrix, the volume and anisotropy of the lacuna were determined. No significant difference was found in the size (volume) or shape (anisotropy) of the lacunae between women with and without osteoporotic fracture, although there was a large range of sizes and shapes in both groups. These results suggest that the size or shape of the lacunae, which influences the strain in osteocytes, does not play a role in osteoporotic fracture. In addition, this study provides geometric measures of lacunae that are important in computational modeling of the mechanical environment of osteocytes.     

A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties

At its highest level of microstructural organization—the mesoscale or millimeter scale—cortical bone exhibits a heterogeneous distribution of pores (Haversian canals, resorption cavities). Multi-scale mechanical models rely on the definition of a representative volume element (RVE). Analytical homogenization techniques are usually based on an idealized RVE microstructure, while finite element homogenization using high-resolution images is based on a realistic RVE of finite size. The objective of this paper was to quantify the size and content of possible cortical bone mesoscale RVEs. RVE size was defined as the minimum size: (1) for which the apparent (homogenized) stiffness tensor becomes independent of the applied boundary conditions or (2) for which the variance of elastic properties for a set of microstructure realizations is sufficiently small. The field of elastic coefficients and microstructure in RVEs was derived from one acoustic microscopy image of a human femur cortical bone sample with an overall porosity of 8.5%. The homogenized properties of RVEs were computed with a finite element technique. It was found that the size of the RVE representative of the overall tissue is about 1.5 mm. Smaller RVEs (~0.5 mm) can also be considered to estimate local mesoscopic properties that strongly depend on the local pores volume fraction. This result provides a sound basis for the application of homogenization techniques to model the heterogeneity of cortical microstructures. An application of the findings to estimate elastic properties in the case of a porosity gradient is briefly presented.     

Decrease in the osteocyte lacunar density accompanied by hypermineralized lacunar occlusion reveals failure and delay of remodeling in aged human bone

Aging decreases the human femur’s fatigue resistance, impact energy absorption, and the ability to withstand load. Changes in the osteocyte distribution and in their elemental composition might be involved in age‐related bone impairment. To address this question, we carried out a histomorphometric assessment of the osteocyte lacunar distribution in the periosteal and endosteal human femoral cortexes of 16 female and 16 male donors with regard to age‐ and sex‐related bone remodeling. Measurements of the bone mineral density distribution by quantitative backscattered electron imaging and energy dispersive X‐ray analysis were taken to evaluate the osteocyte lacunar mineral composition and characteristics. Age‐dependent decreases in the total osteocyte lacunar number were measured in all of the cases. This change signifies a risk for the bone’s safety. Cortical subdivision into periosteal and endosteal regions of interest emphasized that, in both sexes, primarily the endosteal cortex is affected by age‐dependent reduction in number of osteocyte lacunae, whereas the periosteal compartment showed a less pronounced osteocyte lacunar deficiency. In aged bone, osteocyte lacunae showed an increased amount of hypermineralized calcium phosphate occlusions in comparison with younger cases. With respect to Frost’s early delineation of micropetrosis, our microanalyses revealed that the osteocyte lacunae are subject to hypermineralization. Intralacunar hypermineralization accompanied by a decrease in total osteocyte lacunar density may contribute to failure or delayed bone repair in aging bone. A decreased osteocyte lacunar density may cause deteriorations in the canalicular fluid flow and reduce the detection of microdamage, which counteracts the bone’s structural integrity, while hypermineralized osteocyte lacunae may increase bone brittleness and render the bone fragile.     

The effects of mechanical stability on the macromolecules of the connective tissue matrices produced during fracture healing. II. The glycosaminoglycans

Summary The glycosaminoglycans secreted into the matrices associated with fractures of the rabbit tibia healing under stable and unstable mechanical conditions have been characterized histochemically using the dye Alcian Blue at pH 5.7 in the presence of increasing concentrations of magnesium chloride, and after enzymatic extractions. These results are compared with those of immunohistochemical experiments using monoclonal antibodies which recognize epitopes specific to various glycosaminoglycans.The results indicate that the fibrous tissues, including those of the cavities of the cancellous bone and periosteum, possess hyaluronate and chondroitin sulphate, but the amounts present are small. The glycosaminoglycans detected in the cortical bone are located mainly around the osteocyte lacunae where chondroitin and keratan sulphates are found. The developing trabeculae of cancellous bone in the callus contain chondroitin and keratan sulphates, but as the trabeculae mature, these glycosaminoglycans are no longer present throughout the matrix; they are found particularly around the osteocyte lacunae.The cartilage in the callus of mechanically unstable fractures contains chondroitin, chondroitin-4- and 6-sulphates and keratan sulphate, though their distribution is variable. The small, transient areas of cartilage in the callus of mechanically stable fractures also contain those glycosaminoglycans, but they appear to be less highly sulphated.The mechanical stability of the fractures appears to affect the amount and degree of sulphation of the glycosaminoglycans, rather than the types of glycosaminoglycan produced. The glycosaminoglycans produced during fracture healing are compared with those produced during embryonic development and other healing processes.     

树鼩的骨元和骨细胞穴微观结构超微影像的定性比较

近年来,由于树鼩与灵长类动物的亲缘关系,它们引起了人类发展和疾病研究的兴趣。在这项对树鼩,鼠,狗,狒狒和人类的骨骼超微形态的比较研究中,我们定性分析了骨骼的微观结构和形态,以评估树鼩对人类的亲近程度。在3只成年雄性树鼩 (滇西亚种) (Tupaia belangeri chinensis）的股骨中,使用荧光素异硫氰酸盐样品制备和染色共聚焦成像研究了皮质骨的骨元结构,并使用酸蚀刻SEM观察了骨细胞穴的形态。总体而言,树鼩中骨样形成物的密度和结构以及骨细胞穴的形态更像鼠, 与人类,狗和狒狒都明显不同。这些发现表明,尽管树鼩在系统发育上比鼠更接近人类,但它们的骨骼超微形态仍与鼠接近。这是除狗和狒狒之外,第一次对树鼩的骨元和骨细胞穴进行超微影像的研究。这个比较研究的结果丰富了我们对早期灵长类动物骨骼发育,适应性和进化的理解。未来有必要进行进一步的定量比较研究来表征树鼩骨骼的微观形态。     

Observations of microdamage around osteocyte lacunae in bone

Tensile microdamage was examined using laser scanning confocal microscopy in beam specimens of bovine, equine and human long bones loaded in vitro and whole specimens of rat ulnae loaded in vivo. Microcracks were observed to initiate frequently at osteocyte lacunae. The implication is that osteocyte lacunae act as stress concentrating features in bone. This association provides a potential mechanism for the detection of strain and/ or damage by osteocytes in bone.     

Trabecular deformations during screw pull-out: a micro-CT study of lapine bone

The mechanical fixation of endosseous implants, such as screws, in trabecular bone is challenging because of the complex porous microstructure. Development of new screw designs to improve fracture fixation, especially in high-porosity osteoporotic bone, requires a profound understanding of how the structural system implant/trabeculae interacts when it is subjected to mechanical load. In this study, pull-out tests of screw implants were performed. Screws were first inserted into the trabecular bone of rabbit femurs and then pulled out from the bone inside a computational tomography scanner. The tests were interrupted at certain load steps to acquire 3D images. The images were then analysed with a digital volume correlation technique to estimate deformation and strain fields inside the bone during the tests. The results indicate that the highest shear strains are concentrated between the inner and outer thread diameter, whereas compressive strains are found at larger distances from the screw. Tensile strains were somewhat smaller. Strain concentrations and the location of trabecular failures provide experimental information that could be used in the development of new screw designs and/or to validate numerical simulations.     

Variation of osteocyte lacunae size within the tetrapod skeleton: implications for palaeogenomics

Recent studies have emphasized the ability to reconstruct genome sizes (C-values) of extinct organisms such as dinosaurs, using correlations between known genome sizes and bone cell (osteocyte lacunae) volumes. Because of the established positive relationship between cell size and genome size in extant vertebrates, osteocyte lacunae volume is a viable proxy for reconstructing C-values in the absence of any viable genetic material. However, intra-skeletal osteocyte lacunae size variation, which could cause error in genome size estimation, has remained unexplored. Here, 11 skeletal elements of one individual from each of four major clades (Mammalia, Amphibia, Aves, Reptilia) were examined histologically. Skeletal elements in all four clades exhibit significant differences in the average sizes of their lacunae. This variation, however, generally does not cause a significant difference in the estimated genome size when common phylogenetic estimation methods are employed. On the other hand, the spread of the estimations illustrates that this method may not be precise. High variance in genome size estimations remains an outstanding problem. Additionally, a suite of new methods is introduced to further automate the measurement of bone cells and other microstructural features on histological thin sections.     

The influence of mechanical stimulation on osteocyte apoptosis and bone viability in human trabecular bone

It has been shown previously using in vivo and ex vivo animal models, that cyclical mechanical stimulation is capable of maintaining osteocyte viability through the control of apoptotic cell death. Here we have studied the effect of mechanical stimulation on osteocyte viability in human trabecular bone maintained in a 3-D bioreactor system. Bone samples, maintained in the bioreactor system for periods of 3, 7 and 27 days, were subjected to either cyclical mechanical stimulation which engendered a maximum of 3,000 microstrain in a waveform corresponding to physiological jumping exercise for 5 minutes daily or control unloading. Unloading resulted in a decrease in osteocyte viability within 3 days that was accompanied by increased levels of cellular apoptosis. Mechanical stimulation significantly reduced apoptosis (p< or =0.032) and improved the maintenance of osteocyte viability in bone from all patient samples. The percentage Alkaline Phosphatase (ALP) labelled bone surface was significantly increased (p< or =0.05) in response to mechanical stimulation in all samples as was the Bone Formation Rate (BFR/BS) (p=0.005) as determined by calcein label incorporation in the 27-day experiment. These data indicate that in this model system, mechanical stimulation is capable of maintaining osteocyte viability in human bone.     

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure–function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean±S.D.) 18.7±3.4 GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.     

Machine vision photogrammetry: a technique for measurement of microstructural strain in cortical bone.

Understanding local microstructural deformations and strains in cortical bone may lead to a better understanding of cortical bone damage development, fracture, and remodeling. Traditional experimental techniques for measuring deformation and strain do not allow characterization of these quantities at the microstructural level in cortical bone. This study describes a technique based on digital stereoimaging used to measure the microstructural strain fields in cortical bone. The technique allows the measurement of material surface displacements and strains by comparing images acquired from a specimen at two distinct stress states. The accuracy of the system is investigated by analyzing an undeformed image set; the test image is identical to the reference image but translated by a known pixel amount. An increase in the correlation sub-image train parameter results in an increase in displacement measurement accuracy from 0.049 to 0.012 pixels. Errors in strain calculated from the measured displacement field were between 39 and 564 microstrain depending upon the sub-image train size and applied image displacement. The presence of a microcrack in cortical bone results in local strain at the crack tip reaching 0.030 (30,000 microstrain) and 0.010 (10,000 microstrain) near osteocyte lacunae. It is expected that the use of this technique will allow a greater understanding of bone strength and fracture as well as bone mechanotransduction.