Characteristics of mineral particles in the human bone/cartilage interface

Bone and cartilage consist of different organic matrices, which can both be mineralized by the deposition of nano-sized calcium phosphate particles. We have studied these mineral particles in the mineralized cartilage layer between bone and different types of cartilage (bone/articular cartilage, bone/intervertebral disk, and bone/growth cartilage) of individuals aged 54 years, 12 years, and 6 months. Quantitative backscattered electron imaging and scanning small-angle X-ray scattering at a synchrotron radiation source were combined with light microscopy to determine calcium content, mineral particle size and alignment, and collagen orientation, respectively. Mineralized cartilage revealed a higher calcium content than the adjacent bone (p<0.05 for all samples), whereas the highest values were found in growth cartilage. Surprisingly, we found the mineral platelet width similar for bone and mineralized cartilage, with the exception of the growth cartilage sample. The most striking result, however, was the abrupt change of mineral particle orientation at the interface between the two tissues. While the particles were aligned perpendicular to the interface in cartilage, they were oriented parallel to it in bone, reflecting the morphology of the underlying organic matrices. The tight bonding of mineralized cartilage to bone suggests a mechanical role for the interface of the two elastically different tissues, bone and cartilage.     

Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions

Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. However, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.     

Patterns in ontogeny of human trabecular bone from SunWatch Village in the Prehistoric Ohio Valley: general features of microarchitectural change

Although adult skeletal morphological variation is best understood within the framework of age-related processes, relatively little research has been directed towards the structure of and variation in trabecular bone during ontogeny. We report here new quantitative and structural data on trabecular bone microarchitecture in the proximal tibia during growth and development, as demonstrated in a subadult archaeological skeletal sample from the Late Prehistoric Ohio Valley. These data characterize the temporal sequence and variation in trabecular bone structure and structural parameters during ontogeny as related to the acquisition of normal functional activities and changing body mass. The skeletal sample from the Fort Ancient Period site of SunWatch Village is composed of 33 subadult and three young adult proximal tibiae. Nondestructive microCT scanning of the proximal metaphyseal and epiphyseal tibia captures the microarchitectural trabecular structure, allowing quantitative structural analyses measuring bone volume fraction, degree of anisotropy, trabecular thickness, and trabecular number. The microCT resolution effects on structural parameters were analyzed. Bone volume fraction and degree of anisotropy are highest at birth, decreasing to low values at 1 year of age, and then gradually increasing to the adult range around 6-8 years of age. Trabecular number is highest at birth and lowest at skeletal maturity; trabecular thickness is lowest at birth and highest at skeletal maturity. The results of this study highlight the dynamic sequential relationships between growth/development, general functional activities, and trabecular distribution and architecture, providing a reference for comparative studies.     

Fetal and postnatal mouse bone tissue contains more calcium than is present in hydroxyapatite

It has been shown for developing enamel and zebrafish fin that hydroxyapatite (HA) is preceded by an amorphous precursor, motivating us to examine the mineral development in mammalian bone, particularly femur and tibia of fetal and young mice. Mineral particle thickness and arrangement were characterized by (synchrotron) small-angle X-ray scattering (SAXS) combined with wide-angle X-ray diffraction (WAXD) and X-ray fluorescence (XRF) analysis. Simultaneous measurements of the local calcium content and the HA content via XRF and WAXD, respectively, revealed the total calcium contained in HA crystals. Interestingly, bones of fetal as well as newborn mice contained a certain fraction of calcium which is not part of the HA crystals. Mineral deposition could be first detected in fetal tibia at day 16.5 by environmental scanning electron microscopy (ESEM). SAXS revealed a complete lack of orientation in the mineral particles at this stage, whereas 1 day after birth particles were predominantly aligned parallel to the longitudinal bone axis, with the highest degree of alignment in the midshaft. Moreover, we found that mineral particle length increased with age as well as the thickness, while fetal particles were thicker but much shorter. In summary, this study revealed strong differences in size and orientation of the mineral particles between fetal and postnatal bone, with bulkier, randomly oriented particles at the fetal stage, and highly aligned, much longer particles after birth. Moreover, a part of the calcium seems to be present in other form than HA at all stages of development.     

Delayed bone regeneration and low bone mass in a rat model of insulin-resistant type 2 diabetes mellitus is due to impaired osteoblast function

Patients with diabetes mellitus have an impaired bone metabolism; however, the underlying mechanisms are poorly understood. Here, we analyzed the impact of type 2 diabetes mellitus on bone physiology and regeneration using Zucker diabetic fatty (ZDF) rats, an established rat model of insulin-resistant type 2 diabetes mellitus. ZDF rats develop diabetes with vascular complications when fed a Western diet. In 21-wk-old diabetic rats, bone mineral density (BMD) was 22.5% (total) and 54.6% (trabecular) lower at the distal femur and 17.2% (total) and 20.4% (trabecular) lower at the lumbar spine, respectively, compared with nondiabetic animals. BMD distribution measured by backscattered electron imaging postmortem was not different between diabetic and nondiabetic rats, but evaluation of histomorphometric indexes revealed lower mineralized bone volume/tissue volume, trabecular thickness, and trabecular number. Osteoblast differentiation of diabetic rats was impaired based on lower alkaline phosphatase activity (-20%) and mineralized matrix formation (-55%). In addition, the expression of the osteoblast-specific genes bone morphogenetic protein-2, RUNX2, osteocalcin, and osteopontin was reduced by 40-80%. Osteoclast biology was not affected based on tartrate-resistant acidic phosphatase staining, pit formation assay, and gene profiling. To validate the implications of these molecular and cellular findings in a clinically relevant model, a subcritical bone defect of 3 mm was created at the left femur after stabilization with a four-hole plate, and bone regeneration was monitored by X-ray and microcomputed tomography analyses over 12 wk. While nondiabetic rats filled the defects by 57%, diabetic rats showed delayed bone regeneration with only 21% defect filling. In conclusion, we identified suppressed osteoblastogenesis as a cause and mechanism for low bone mass and impaired bone regeneration in a rat model of type 2 diabetes mellitus.     

Can deterministic mechanical size effects contribute to fracture and microdamage accumulation in trabecular bone?

Failure of bone under monotonic and cyclic loading is related to the bone mineral density, the quality of the bone matrix, and the evolution of microcracks. The theory of linear elastic fracture mechanics has commonly been applied to describe fracture in bone. Evidence is presented that bone failure can be described through a non-linear theory of fracture. Thereby, deterministic size effects are introduced. Concepts of a non-linear theory are applied to discern how the interaction among bone matrix constituents (collagen and mineral), microcrack characteristics, and trabecular architecture can create distinctively differences in the fracture resistance at the bone tissue level. The non-linear model is applied to interpret pre-clinical data concerning the effects of anti-osteoporotic agents on bone properties. The results show that bisphosphonate (BP) treatments that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is reduced. Selective estrogen receptor modulators (SERMs) that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is increased. The consequences of these changes are reflected in bone mechanical response and predictions are consistent with experimental observations in the animal model which show that BP treatment is associated with more brittle fracture and microcracks without altering the average length of the cracks, whereas SERM treatments lead to a more ductile fracture and mainly increase crack length with a smaller increase in microcrack density. The model suggests that BPs may be more effective in cases in which bone mass is very low, whereas SERMS may be more effective when milder osteoporotic symptoms are present.     

Dietary pseudopurpurin improves bone geometry architecture and metabolism in red-bone Guishan goats

Red-colored bones were found initially in some Guishan goats in the 1980s, and they were designated red-boned goats. However, it is not understood what causes the red color in the bone, or whether the red material changes the bone geometry, architecture, and metabolism of red-boned goats. Pseudopurpurin was identified in the red-colored material of the bone in red-boned goats by high-performance liquid chromatography-electrospray ionization-mass spetrometry and nuclear magnetic resonance analysis. Pseudopurpurin is one of the main constituents of Rubia cordifolia L, which is eaten by the goats. The assessment of the mechanical properties and micro-computed tomography showed that the red-boned goats displayed an increase in the trabecular volume fraction, trabecular thickness, and the number of trabeculae in the distal femur. The mean thickness, inner perimeter, outer perimeter, and area of the femoral diaphysis were also increased. In addition, the trabecular separation and structure model index of the distal femur were decreased, but the bone mineral density of the whole femur and the mechanical properties of the femoral diaphysis were enhanced in the red-boned goats. Meanwhile, expression of alkaline phosphatase and osteocalcin mRNA was higher, and the ratio of the receptor activator of the nuclear factor kappa B ligand to osteoprotegerin was markedly lower in the bone marrow of the red-boned goats compared with common goats. To confirm further the effect of pseudopurpurin on bone geometry, architecture, and metabolism, Wistar rats were fed diets to which pseudopurpurin was added for 5 months. Similar changes were observed in the femurs of the treated rats. The above results demonstrate that pseudopurpurin has a close affinity with the mineral salts of bone, and consequently a high level of mineral salts in the bone cause an improvement in bone strength and an enhancement in the structure and metabolic functions of the bone.     

Effects of freeze–thaw and micro-computed tomography irradiation on structure–property relations of porcine trabecular bone

We study the effects of freeze–thaw and irradiation on structure–property relations of trabecular bone. We measure the porosity, apparent density, mineral content, trabecular orientation, trabecular thickness, fractal dimension, surface area, and connectivity of trabecular bone using micro-computed tomography (micro-CT) and relate them to Young?s modulus and ultimate strength measured by uniaxial compression testing. The analysis is done on six-month porcine trabecular bone from femoral heads. The effects of freeze–thaw are studied by using bones from three different groups: fresh bone and bones frozen for one and five years. We find that the porosity and apparent density have most dominant influence on the elastic modulus and strength of fresh bone. Also, five years of freezing lowers both Young?s modulus and ultimate strength of trabecular bone. Additionally, the effects of radiation are investigated by comparing Young?s modulus before and after micro-CT exposure. We find that the micro-CT irradiation has a negligible effect on the Young?s modulus of trabecular bone. These findings provide insights on the effects of tissue preservation and imaging on properties of trabecular bone.     

Altered tissue properties induce changes in cancellous bone architecture in aging and diseases

The mechanical properties of cancellous bone depend on its architecture and the tissue properties of the mineralized matrix. The architecture is continuously adapted to external loads. In this paper, it was assumed that changes in tissue properties leading to changes in tissue deformation can induce adaptation of the architecture. We asked whether changes in cancellous bone architecture with aging and in e.g. early osteoarthrosis can be explained from changes in tissue properties.This was investigated using computer models in which the cancellous architecture was adapted to external loads. Bone tissue with deformations below a certain threshold was resorbed, deformations above another threshold induced formation. Deformations between these two boundaries, in the 'lazy zone', did not induce bone adaptation. The effects of changes in bone tissue stiffness on bone mass, global stiffness and architecture were investigated. The bone gain (40-60%) resulting from a 50% decrease in tissue stiffness (simulating diseased tissue) was much larger than the bone loss (2-30%) resulting from a 50% increase in tissue stiffness (simulating highly mineralized, old tissue). The adaptation induced by a decrease in tissue stiffness resulted in an almost constant stiffness in the main load bearing direction, but the transversal stiffness decreased. An increased tissue stiffness resulted in a higher stiffness in the main direction and overcompensation in the transversal directions: the global stiffness could become even smaller than the stiffness of the original model. Concluding, we showed that changes in trabecular bone in aging and diseases can be partly explained from changes in tissue properties.     

Modeling of dynamic fracture and damage in two-dimensional trabecular bone microstructures using the cohesive finite element method

Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Micro-finite-element models have been used to investigate the elastic and yield properties of trabecular bone but have only seen limited application in modeling the microstructure dependent fracture of trabecular bone. In this research, dynamic fracture in two-dimensional (2D) micrographs of ovine (sheep) trabecular bone is modeled using the cohesive finite element method. For this purpose, the bone tissue is modeled as an orthotropic material with the cohesive parameters calculated from the experimental fracture properties of the human cortical bone. Crack propagation analyses are carried out in two different 2D orthogonal sections cut from a three-dimensional 8 mm diameter cylindrical trabecular bone sample. The two sections differ in microstructural features such as area fraction (ratio of the 2D space occupied by bone tissue to the total 2D space), mean trabecula thickness, and connectivity. Analyses focus on understanding the effect of the rate of loading as well as on how the rate variation interacts with the microstructural features to cause anisotropy in microdamage accumulation and in the fracture resistance. Results are analyzed in terms of the dependence of fracture energy dissipation on the microstructural features as well as in terms of the changes in damage and stresses associated with the bone architecture variation. Besides the obvious dependence of the fracture behavior on the rate of loading, it is found that the microstructure strongly influences the fracture properties. The orthogonal section with lesser area fraction, low connectivity, and higher mean trabecula thickness is more resistant to fracture than the section with high area fraction, high connectivity, and lower mean trabecula thickness. In addition, it is found that the trabecular architecture leads to inhomogeneous distribution of damage, irrespective of the symmetry in the applied loading with the fracture of the entire bone section rapidly progressing to bone fragmentation once the accumulated damage in any trabeculae reaches a critical limit.     

Distributional Variations in Trabecular Architecture of the Mandibular Bone: An In Vivo Micro-CT Analysis in Rats

Purpose

To evaluate the effect of trabecular thickness and trabecular separation on modulating the trabecular architecture of the mandibular bone in ovariectomized rats.

Materials and Methods

Fourteen 12-week-old adult female Wistar rats were divided into an ovariectomy group (OVX) and a sham-ovariectomy group (sham). Five months after the surgery, the mandibles from 14 rats (seven OVX and seven sham) were analyzed by micro-CT. Images of inter-radicular alveolar bone of the mandibular first molars underwent three-dimensional reconstruction and were analyzed.

Results

Compared to the sham group, trabecular thickness in OVX alveolar bone decreased by 27% (P = 0.012), but trabecular separation in OVX alveolar bone increased by 59% (P = 0.005). A thickness and separation map showed that trabeculae of less than 100μm increased by 46%, whereas trabeculae of more than 200μm decreased by more than 40% in the OVX group compared to those in the sham group. Furthermore, the OVX separation of those trabecular of more than 200μm was 65% higher compared to the sham group. Bone mineral density (P = 0.028) and bone volume fraction (p = 0.001) were also significantly decreased in the OVX group compared to the sham group.

Conclusions

Ovariectomy-induced bone loss in mandibular bone may be related to the distributional variations in trabecular thickness and separation which profoundly impact the modulation of the trabecular architecture.     

Differential effects of jump versus running exercise on trabecular architecture during remobilization after suspension-induced osteopenia in growing rats

High-impact exercise is considered to be very beneficial for bones. We investigated the ability of jump exercise to restore bone mass and structure after the deterioration induced by tail suspension in growing rats and made comparisons with treadmill running exercise. Five-week-old male Wistar rats (n = 28) were randomly assigned to four body weight-matched groups: a spontaneous recovery group after tail suspension (n = 7), a jump exercise group after tail suspension (n = 7), a treadmill running group after tail suspension (n = 7), and age-matched controls without tail suspension or exercise (n = 7). Treadmill running was performed at 25 m/min, 1 h/day, 5 days/wk. The jump exercise protocol consisted of 10 jumps/day, 5 days/wk, with a jump height of 40 cm. Bone mineral density (BMD) of the total right femur was measured by dual-energy X-ray absorptiometry. Three-dimensional trabecular bone architecture at the distal femoral metaphysis was evaluated using microcomputed tomography. After 5 wk of free remobilization, right femoral BMD, right hindlimb muscle weight, and body weight returned to age-matched control levels, but trabeculae remained thinner and less connected. Although both jump and running exercises during the remobilization period increased trabecular bone mass, jump exercise increased trabecular thickness, whereas running exercise increased trabecular number. These results indicate that restoration of trabecular bone architecture induced by jump exercise during remobilization is predominantly attributable to increased trabecular thickness, whereas running adds trabecular bone mass through increasing trabecular number, and suggest that jumping and running exercises have different mechanisms of action on structural characteristics of trabecular bone.     

The Role of Muscle Loading on Bone (Re)modeling at the Developing Enthesis

Muscle forces are necessary for the development and maintenance of a mineralized skeleton. Removal of loads leads to malformed bones and impaired musculoskeletal function due to changes in bone (re)modeling. In the current study, the development of a mineralized junction at the interface between muscle and bone was examined under normal and impaired loading conditions. Unilateral mouse rotator cuff muscles were paralyzed using botulinum toxin A at birth. Control groups consisted of contralateral shoulders injected with saline and a separate group of normal mice. It was hypothesized that muscle unloading would suppress bone formation and enhance bone resorption at the enthesis, and that the unloading-induced bony defects could be rescued by suppressing osteoclast activity. In order to modulate osteoclast activity, mice were injected with the bisphosphonate alendronate. Bone formation was measured at the tendon enthesis using alizarin and calcein fluorescent labeling of bone surfaces followed by quantitative histomorphometry of histologic sections. Bone volume and architecture was measured using micro computed tomography. Osteoclast surface was determined via quantitative histomorphometry of tartrate resistant acid phosphatase stained histologic sections. Muscle unloading resulted in delayed initiation of endochondral ossification at the enthesis, but did not impair bone formation rate. Unloading led to severe defects in bone volume and trabecular bone architecture. These defects were partially rescued by suppression of osteoclast activity through alendronate treatment, and the effect of alendronate was dose dependent. Similarly, bone formation rate was increased with increasing alendronate dose across loading groups. The bony defects caused by unloading were therefore likely due to maintained high osteoclast activity, which normally decreases from neonatal through mature timepoints. These results have important implications for the treatment of muscle unloading conditions such as neonatal brachial plexus palsy, which results in shoulder paralysis at birth and subsequent defects in the rotator cuff enthesis and humeral head.     

Mineral heterogeneity affects predictions of intratrabecular stress and strain

Knowledge of the influence of mineral variations (i.e., mineral heterogeneity) on biomechanical bone behavior at the trabecular level is limited. The aim of this study is to investigate how this material property affects the intratrabecular distributions of stress and strain in human adult trabecular bone. Two different sets of finite element (FE) models of trabecular samples were constructed; tissue stiffness was either scaled to the local degree of mineralization of bone as measured with microCT (heterogeneous) or tissue stiffness was assumed to be homogeneous. The influence of intratrabecular mineral heterogeneity was analyzed by comparing both models. Interesting effects were seen regarding intratrabecular stress and strain distributions. In the homogeneous model, the highest stresses were found at the surface with a significant decrease towards the core. Higher superficial stresses could indicate a higher predicted fracture risk in the trabeculae. In the heterogeneous model this pattern was different. A significant increase in stress with increasing distance from the trabecular surface was found followed by a significant decrease towards the core. This suggests trabecular bending during a compression. In both models a decrease in strain values from surface to core was predicted, which is consistent with trabecular bending. When mineral heterogeneity was taken into account, the predicted intratrabecular patterns of stress and strain are more consistent with the expected biomechanical behavior as based on mineral variations in trabeculae. Our findings indicate that mineral heterogeneity should not be neglected when performing biomechanical studies on topics such as the (long-term or dose dependent) effects of antiresorptive treatments.     

Multiscale modeling of bone tissue with surface and permeability control

Natural biological materials usually present a hierarchical arrangement with various structural levels. The biomechanical behavior of the complex hierarchical structure of bone is investigated with models that address the various levels corresponding to different scales. Models that simulate the bone remodeling process concurrently at different scales are in development. We present a multiscale model for bone tissue adaptation that considers the two top levels, whole bone and trabecular architecture. The bone density distribution is calculated at the macroscale (whole bone) level, and the trabecular structure at the microscale level takes into account its mechanical properties as well as surface density and permeability. The bone remodeling process is thus formulated as a material distribution problem at both scales. At the local level, the biologically driven information of surface density and permeability characterizes the trabecular structure. The model is tested by a three-dimensional simulation of bone tissue adaptation for the human femur. The density distribution of the model shows good agreement with the actual bone density distribution. Permeability at the microstructural level assures interconnectivity of pores, which mimics the interconnectivity of trabecular bone essential for vascularization and transport of nutrients. The importance of this multiscale model relays on the flexibility to control the morphometric parameters that characterize the trabecular structure. Therefore, the presented model can be a valuable tool to define bone quality, to assist with diagnosis of osteoporosis, and to support the development of bone substitutes.     

Knockout of Nuclear High Molecular Weight FGF2 Isoforms in Mice Modulates Bone and Phosphate Homeostasis

We previously reported that targeted overexpression of the fibroblast growth factor 2 (FGF2) high molecular weight (HMW) isoforms in osteoblastic lineage cells in mice resulted in phenotypic changes, including dwarfism, rickets, osteomalacia, hypophosphatemia, increased serum parathyroid hormone, and increased levels of the phosphatonin FGF23 in serum and bone. This study examined the effects of genetically knocking out the FGF2HMW isoforms (HMWKO) on bone and phosphate homeostasis. HMWKO mice were not dwarfed and had significantly increased bone mineral density and bone mineral content in femurs and lumbar vertebrae when compared with the wild-type (WT) littermates. Micro-computed tomography analysis of femurs revealed increased trabecular bone volume, thickness, number, and connective tissue density with decreased trabecular spacing compared with WT. In addition, there was significantly decreased cortical porosity and increased cortical thickness and sub-periosteal area in femurs of HMWKO. Histomorphometric analysis demonstrated increased osteoblast activity and diminished osteoclast activity in the HMWKO. In vitro bone marrow stromal cell cultures showed there was a significant increase in alkaline phosphatase-positive colony number at 1 week in HMWKO. At 3 weeks of culture, the mineralized area was also significantly increased. There was increased expression of osteoblast differentiation marker genes and reduced expression of genes associated with impaired mineralization, including a significant reduction in Fgf23 and Sost mRNA. Normal serum phosphate and parathyroid hormone were observed in HMWKO mice. This study demonstrates a significant negative impact of HMWFGF2 on biological functions in bone and phosphate homeostasis in mice.     

Variability of tissue mineral density can determine physiological creep of human vertebral cancellous bone

Creep is a time-dependent viscoelastic deformation observed under a constant prolonged load. It has been indicated that progressive vertebral deformation due to creep may increase the risk of vertebral fracture in the long-term. The objective of this study was to examine the relationships of creep with trabecular architecture and tissue mineral density (TMD) parameters in human vertebral cancellous bone at a physiological static strain level. Architecture and TMD parameters of cancellous bone were analyzed using microcomputerized tomography (micro-CT) in specimens cored out of human vertebrae. Then, creep and residual strains of the specimens were measured after a two-hour physiological compressive constant static loading and unloading cycle. Creep developed (3877 ± 2158 με) resulting in substantial levels of non-recoverable post-creep residual strain (1797 ± 1391 με). A strong positive linear correlation was found between creep and residual strain (r = 0.94, p < 0.001). The current results showed that smaller thickness, larger surface area, greater connectivity of trabeculae, less mean tissue mineral density (TMD, represented by gray levels) and higher variability of TMD are associated with increasing logarithmic creep rate. The TMD variability (GL(COV)) was the strongest correlate of creep rate (r = 0.79, p < 0.001). This result suggests that TMD variability may be a useful parameter for estimating the long-term deformation of a whole vertebral body. The results further suggest that the changes in TMD variability resulting from bone remodeling are of importance and may provide an insight into the understanding of the mechanisms underlying progressive failure of vertebral bodies and development of a clinical fracture.     

Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.     

Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution

The bone remodeling process takes place at the surface of trabeculae and results in a non-uniform mineral distribution. This will affect the mechanical properties of cancellous bone, because the properties of bone tissue depend on its mineral content. We investigated how large this effect is by simulating several non-uniform mineral distributions in 3D finite element models of human trabecular bone and calculating the apparent stiffness of these models. In the ‘linear model’ we assumed a linear relation between mineral content and Young's modulus of the tissue. In the ‘exponential model’ we included an empirical exponential relation in the model. When the linear model was used the mineral distribution slightly changed the apparent stiffness, the difference varied between an 8% decrease and a 4% increase compared to the uniform model with the same BMD. The exponential model resulted in up to 20% increased apparent stiffness in the main load-bearing direction. A thin less mineralized surface layer (28 μm) and highly mineralized interstitial bone (mimicking mineralization resulting from anti-resorptive treatment) resulted in the highest stiffness. This could explain large reductions in fracture risk resulting from small increases in BMD. The non-uniform mineral distribution could also explain why bone tissue stiffness determined using nano-indentation is usually higher than finite element (FE)-determined stiffness. We conclude that the non-uniform mineral distribution in trabeculae does affect the mechanical properties of cancellous bone and that the tissue stiffness determined using FE-modeling could be improved by including detailed information about mineral distribution in trabeculae in the models.     

Computational simulation of trabecular adaptation progress in human proximal femur during growth

There are a large number of clinical and experimental studies that analyzed trabecular architecture as a result of bone adaptation. However, only a limited amount of quantitative data is currently available on the progress of trabecular adaptation during growth. In this paper, we proposed a two-step numerical simulation method that predicts trabecular adaptation progress during growth using a recently developed topology optimization algorithm, design space optimization (DSO), under the hypothesis that the mechanisms of DSO are functionally equivalent to those of bone adaptation. We applied the proposed scheme to trabecular adaptation simulation in human proximal femur. For the simulation, the full trabecular architecture in human proximal femur was represented by a two-dimensional μFE model with 50 μm resolution. In Step 1, we determined a reference value that regulates trabecular adaptation in human proximal femur. In Step 2, we simulated trabecular adaptation in human proximal femur during growth with the reference value derived in Step 1. We analyzed the architectural and mechanical properties of trabecular patterns through iterations. From the comparison with experimental data in the literature, we showed that in the early growth stage trabecular adaptation was achieved mainly by increasing bone volume fraction (or trabecular thickness), while in the later stage of the development the trabecular architecture gained higher structural efficiency by increasing structural anisotropy with a relatively low level of bone volume fraction (or trabecular thickness). We demonstrated that the proposed numerical framework predicted the growing progress of trabecular bone that has a close correlation with experimental data.