Biomechanical consequences of developmental changes in trabecular architecture and mineralization of the pig mandibular condyle

Young's modulus of trabecular bone at the tissue level: A review

The tissue-level Young's modulus of trabecular bone is important for detailed mechanical analysis of bone and bone-implant mechanical interactions. However, the heterogeneity and small size of the trabecular struts complicate an accurate determination. Methods such as micro-mechanical testing of single trabeculae, ultrasonic testing, and nanoindentation have been used to estimate the trabecular Young's modulus. This review summarizes and classifies the trabecular Young's moduli reported in the literature. Information on species, anatomic site, and test condition of the samples has also been gathered. Advantages and disadvantages of the different methods together with recent developments are discussed, followed by some suggestions for potential improvement for future work. In summary, this review provides a thorough introduction to the approaches used for determining trabecular Young's modulus, highlights important considerations when applying these methods and summarizes the reported Young's modulus for follow-up studies on trabecular properties.

STATEMENT OF SIGNIFICANCE

The spongy trabecular bone provides mechanical support while maintaining a low weight. A correct measure of its mechanical properties at the tissue level, i.e. at a single-trabecula level, is crucial for analysis of interactions between bone and implants, necessary for understanding e.g. bone healing mechanisms. In this study, we comprehensively summarize the Young's moduli of trabecular bone estimated by currently available methods, and report their dependency on different factors. The critical review of different methods with recent updates is intended to inspire improvements in estimating trabecular Young's modulus. It is strongly suggested to report detailed information on the tested bone to enable statistical analysis in the future.

Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone

The aim of this study was to explore the hierarchical arrangement of structural properties in cortical and trabecular bone and to determine a mathematical model that accurately predicts the tissue's mechanical properties as a function of these indices. By using a variety of analytical techniques, we were able to characterize the structural and compositional properties of cortical and trabecular bones, as well as to determine the suitable mathematical model to predict the tissue's mechanical properties using a continuum micromechanics approach. Our hierarchical analysis demonstrated that the differences between cortical and trabecular bone reside mainly at the micro- and ultrastructural levels. By gaining a better appreciation of the similarities and differences between the two bone types, we would be able to provide a better assessment and understanding of their individual roles, as well as their contribution to bone health overall.

Effect of intraspecimen spatial variation in tissue mineral density on the apparent stiffness of trabecular bone

This study investigated the effects of intraspecimen variations in tissue mineral density(TMD) on the apparent-level stiffness of human trabecular bone. High-resolution finite element (FE) models were created for each of 12 human trabecular bone specimens,using both microcomputed tomography (lCT) and “gold-standard” synchrotron radiation lCT (SRlCT) data. Our results confirm that incorporating TMD spatial variation reduces the calculated apparent stiffness compared to homogeneous TMD models. This effect exists for both lCT- and SRlCT-based FE models, but is exaggerated in lCT based models. This study provides a direct comparison of lCT to SRlCT data and is thereby able to conclude that the influence of including TMD heterogeneity is overestimated in lCT-based models.

Biomimetic mineralization of woven bone-like nanocomposites: role of collagen cross-links

Ideal biomaterials for bone grafts must be biocompatible, osteoconductive, osteoinductive and have appropriate mechanical properties. For this, the development of synthetic bone substitutes mimicking natural bone is desirable, but this requires controllable mineralization of the collagen matrix. In this study, densified collagen films (up to 100 μm thick) were fabricated by a plastic compression technique and cross-linked using carbodiimide. Then, collagen-hydroxyapatite composites were prepared by using a polymer-induced liquid-precursor (PILP) mineralization process. Compared to traditional methods that produce only extrafibrillar hydroxyapatite (HA) clusters on the surface of collagen scaffolds, by using the PILP mineralization process, homogeneous intra- and extrafibrillar minerals were achieved on densified collagen films, leading to a similar nanostructure as bone, and a woven microstructure analogous to woven bone. The role of collagen cross-links on mineralization was examined and it was found that the cross-linked collagen films stimulated the mineralization reaction, which in turn enhanced the mechanical properties (hardness and modulus). The highest value of hardness and elastic modulus was 0.7 ± 0.1 and 9.1 ± 1.4 GPa in the dry state, respectively, which is comparable to that of woven bone. In the wet state, the values were much lower (177 ± 31 and 8 ± 3 MPa) due to inherent microporosity in the films, but still comparable to those of woven bone in the same conditions. Mineralization of collagen films with controllable mineral content and good mechanical properties provide a biomimetic route toward the development of bone substitutes for the next generation of biomaterials. This work also provides insight into understanding the role of collagen fibrils on mineralization.

Deriving tissue density and elastic modulus from microCT bone scans

Tissue level density and elastic modulus are intrinsic properties that can be used to quantify bone material and analyses incorporating those quantities have been used to evaluate bone on a macroscopic scale. Micro-computed tomography (microCT) technology has been used to construct tissue level finite element models to simulate macroscopic fracture strength, however, a single method for assigning voxel-specific tissue density and elastic modulus based on those data has not been universally accepted. One method prevalent in the literature utilizes an empirical relationship that derives tissue stiffness as a function of bone calcium content weight fraction. To derive calcium content weight fraction from microCT scans, a measure of tissue density is required and a constant value is traditionally used. However, experimental data suggest a non-trivial amount of tissue heterogeneity suggesting a constant tissue density may not be appropriate. A theoretical derivation for determining the relationship between voxel-specific tissue density and microCT scan data (i.e., microCT derived tissue mineral density (TMD), mgHA/cm(3)) and bone constituent properties is proposed. Constant model parameters used in the derivation include the density of water, ash, and organics (i.e., bone constituents) and the volume fraction of the organics constituent. The effect of incorporating the theoretically derived tissue density (instead of a constant value) in determining voxel-specific elastic modulus resulted in a maximum observed increase of 12GPa (5.9GPa versus 17.9GPa, for the constant value and derived tissue density formulations, respectively) for a measured TMD of 1.02gHA/cm(3). Average and bounding quantities for the four constant model parameters were defined from the literature and the influence of those values on the derived tissue density and elastic modulus relationships were also evaluated. The theoretical relationships of tissue density and elastic modulus, with the average constant model parameters applied, were consistent with previously published empirical relationships derived from experimental data. Tissue density as a function of microCT TMD was formulated as a linear relationship and the density of water and ash was shown to solely influence the proportionality (i.e., slope) between those values. The density of water and organics (i.e., collagen) and the volume fraction of the organics constituent were shown to influence the constant offset (intercept) between tissue density and TMD with no influence from ash density. Incorporating tissue density heterogeneity into the derivation of elastic modulus resulted in a significant increase in predicted modulus (for microCT TMD ranges observed for healthy tissue) as compared to when a constant tissue density was used. The presented approach provides a novel method for deriving tissue-level bone material properties and quantifies the effect of assuming tissue homogeneity when calculating elastic modulus (when using a prevalent method in the literature) from microCT scan data.

Mechanical and microarchitectural analyses of cancellous bone through experiment and computer simulation

The relationship between microarchitecture to the failure mechanism and mechanical properties can be assessed through experimental and computational methods. In this study, both methods were utilised using bovine cadavers. Twenty four samples of cancellous bone were extracted from fresh bovine and the samples were cleaned from excessive marrow. Uniaxial compression testing was performed with displacement control. After mechanical testing, each specimen was ashed in a furnace. Four of the samples were exemplarily scanned using micro-computed tomography (μCT) and three dimensional models of the cancellous bones were reconstructed for finite element simulation. The mechanical properties and the failure modes obtained from numerical simulations were then compared to the experiments. Correlations between microarchitectural parameters to the mechanical properties and failure modes were then made. The Young's modulus correlates well with the bone volume fraction with R² = 0.615 and P value 0.013. Three different types of failure modes of cancellous bone were observed: oblique fracture (21.7%), perpendicular global fracture (47.8%), and scattered localised fracture (30.4%). However, no correlations were found between the failure modes to the morphological parameters. The percentage of error between computer predictions and the actual experimental test was from 6 to 12%. These mechanical properties and information on failure modes can be used for the development of synthetic cancellous bone.

The neonatal ilium-metaphyseal drivers and vascular passengers

At birth the newborn is equipped with a developing locomotor apparatus, which will ultimately become involved in load transfer from the period when the child adopts a sitting posture through to the attainment of a bipedal gait. This load transfer has been considered to influence trabecular bone structural organization by setting up forces, which remodel the internal architecture into a functionally optimized form. However, during the neonatal developmental period the locomotor apparatus is nonweight bearing and instead only supports reflexive movements. Surprisingly, a structural organization has been identified within the internal trabecular architecture and external cortical morphology of the neonatal ilium, which appears to mimic the structural composition of the more mature bone. This study aims to build upon previous qualitative and quantitative investigation of this apparently precocious patterning by further examining structural data obtained from selected volumes of interest within the ilium. Analysis has revealed statistically significant differences in regional trabecular and cortical bone characteristics, which have formed the basis of a possible growth model for the ilium. Volumetric comparison has demonstrated the presence of three progressive "growth regions" and three "restricted growth regions," which appear to relate to metaphyseal and nonmetaphyseal borders of the ilium. Therefore, the structural data and statistical analysis presented in this study challenge the current concept of implied centrifugal ossification within the human ilium and present evidence of an alternative pattern of ossification that is largely dictated and controlled by vascular distribution and growth plate position.

Contribution of the intra-specimen variations in tissue mineralization to PTH- and raloxifene-induced changes in stiffness of rat vertebrae

The intra-specimen spatial variation in mineralization of bone tissue can be changed by drug treatments that alter bone remodeling. However, the contribution of such changes to the overall biomechanical effect of a treatment on bone strength is not known. To provide insight into this issue, we used a rat model to determine the effects of ovariectomy, parathyroid hormone, and raloxifene (vs. sham) on the contribution of spatial variations in mineralization to treatment-induced changes in vertebral stiffness. Mineral density was measured from 6-microm voxel-sized quantitative micro-CT scans. Whole-vertebral and trabecular stiffness values were estimated using finite element analysis of these micro-CT scans, first including all intra-specimen variations in mineral density in the model and then excluding such variations by using a specimen-specific average density throughout each specimen. As expected, we found appreciable effects of treatment on overall bone stiffness, the effect being greater for the trabecular compartment (up to 52% reduction vs. sham, p<0.0001) than the whole vertebra (p=0.055). Intra-specimen mean mineralization was not changed with treatment but the intra-specimen variation in mineralization was, although the effect was small (4%). Intra-specimen spatial variations in mineralization accounted for 10-12% and 5-6% of overall stiffness of the trabecular compartment and whole vertebral body, respectively. However, after accounting for all treatment effects on bone geometry and trabecular microstructure, any treatment effects due to changes in mineralization were negligible (<2%), although statistically detectable (p<0.02). We conclude that, despite a role in the general biomechanical behavior of bone, the spatial variations in tissue mineralization, as measured by quantitative micro-CT, did not appreciably contribute to ovariectomy-, PTH-, or raloxifene-induced changes in stiffness of the whole bone or the trabecular compartment in these rat vertebrae.

Anticipating bipedalism: trabecular organization in the newborn ilium

Trabecular bone structural organization is considered to be predominantly influenced by localized temporal forces which act to maintain and remodel the trabecular architecture into a biomechanically optimal configuration. In the adult pelvis, the most significant remodelling forces are believed to be those generated during bipedal locomotion. However, during the fetal and neonatal period the pelvic complex is non-weight bearing and, as such, structural organization of iliac trabecular bone cannot reflect direct stance-related forces. In this study, micro-computed tomography scans from 28 neonatal ilia were analysed, using a whole bone approach, to investigate the trabecular characteristics present within specific volumes of interest relevant to density gradients highlighted in a previous radiographic study. Analysis of the structural indices bone volume fraction, trabecular thickness, trabecular spacing and trabecular number was carried out to quantitatively investigate structural composition. Quantification of the neonatal trabecular structure reinforced radiographic observations by highlighting regions of significant architectural form which grossly parallel architectural differences in the adult pattern but which have previously been attributed to stance-related forces. It is suggested that the seemingly organized rudimentary scaffold observed in the neonatal ilium may be attributable to other non-weight bearing anatomical interactions or even to a predetermined genetic blueprint. It must also be postulated that whilst the observed patterning may be indicative of a predetermined inherent template, early non-weight bearing and late stance-related locomotive influences may subsequently be superimposed upon this scaffolding and perhaps reinforced and likely remodelled at a later age. Ultimately, the analysis of this fundamental primary pattern has core implications for understanding the earliest changes in pelvic trabecular architecture and provides a baseline insight into future ontogenetic development and bipedal capabilities.

Biomechanical effect of mineral heterogeneity in trabecular bone

Due to daily loading, trabecular bone is subjected to deformations (i.e., strain), which lead to stress in the bone tissue. When stress and/or strain deviate from the normal range, the remodeling process leads to adaptation of the bone architecture and its degree of mineralization to effectively withstand the sustained altered loading. As the apparent mechanical properties of bone are assumed to depend on the degree and distribution of mineralization, the goal of the present study was examine the influences of mineral heterogeneity on the biomechanical properties of trabecular bone in the human mandibular condyle. For this purpose nine right condyles from human dentate mandibles were scanned and evaluated with a microCT system. Cubic regional volumes of interest were defined, and each was transformed into two different types of finite element (FE) models, one homogeneous and one heterogeneous. In the heterogeneous models the element tissue moduli were scaled to the local degree of mineralization, which was determined using microCT. Compression and shear tests were simulated to determine the apparent elastic moduli in both model types. The incorporation of mineralization variation decreased the apparent Young's and shear moduli by maximally 21% in comparison to the homogeneous models. The heterogeneous model apparent moduli correlated significantly with bone volume fraction and degree of mineralization. It was concluded that disregarding mineral heterogeneity may lead to considerable overestimation of apparent elastic moduli in FE models.

Relationship between tissue stiffness and degree of mineralization of developing trabecular bone

It is unknown how the degree of mineralization of bone in individual trabecular elements is related to the corresponding mechanical properties at the bone tissue level. Understanding this relationship is important for the comprehension of the mechanical behavior of bone at both the apparent and tissue level. The purpose of the present study was, therefore, to determine the tissue stiffness and degree of mineralization of the trabecular bone tissue and to establish a relationship between these two variables. A second goal was to assess the change in this relation during development. Mandibular condylar specimens of four fetal and four newborn pigs were used. The tissue stiffness was measured using nanoindentation. A pair of indents was made in the cores of 15 trabecular elements per specimen. Subsequently, the degree of mineralization of these locations was determined from microcomputed tomography. The mean tissue stiffness was 11.2 GPa (+/-0.5 GPa) in the fetal group and 12.0 GPa (+/-0.8 GPa) in the newborn group, which was not significantly different. The degree of mineralization of the fetal trabecular cores was 744 mg/cm3 (+/-28 mg/cm3). The one in the newborn bone measured 719 mg/cm(3) (+/-34 mg/cm3). Again, the difference was statistically insignificant. A significant relationship between tissue stiffness and degree of mineralization was obtained for fetal (R = 0.42, p < 0.001) and newborn (R = 0.72, p < 0.001) groups. It was concluded that woven bone tissue in fetal and newborn trabecular cores resembles adult trabecular bone in terms of tissue properties and is strongly correlated with degree of mineralization.

Intratrabecular distribution of tissue stiffness and mineralization in developing trabecular bone

The purpose of this study was to investigate the relation between bone tissue stiffness and degree of mineralization distribution and to examine possible changes during prenatal development. Understanding this may provide insight into adaptation processes and into deformation mechanisms of the bone microstructure. Mandibular condyles from four fetal and newborn pigs were used. Tissue stiffness was measured using nanoindentation, the degree of mineralization with microCT. Eight indents were made over the trabecular width of 15 trabeculae in each specimen, leading to a total of 960 indents. Subsequently, the degree of mineralization of these locations was determined. Intratrabecular variations in bone tissue stiffness and degree of mineralization showed a similar pattern; low at trabecular surfaces and higher in the cores. A strong correlation was found between the two variables, which remained unchanged during development. It was concluded that bone tissue in fetal and newborn trabecular cores resembles adult trabecular bone tissue properties and is distributed in a regular radial pattern in trabeculae. For the first time, it was shown that the intratrabecular tissue stiffness develops along the same path as the degree of mineralization. Knowledge regarding intratrabecular tissue stiffness and mineralization results in a better understanding of trabecular bone mechanical behavior on a structural and tissue level.

The Influence of Mineralization on Intratrabecular Stress and Strain Distribution in Developing Trabecular Bone

The load-transfer pathway in trabecular bone is largely determined by its architecture. However, the influence of variations in mineralization is not known. The goal of this study was to examine the influence of inhomogeneously distributed degrees of mineralization (DMB) on intratrabecular stresses and strains. Cubic mandibular condylar bone specimens from fetal and newborn pigs were used. Finite element models were constructed, in which the element tissue moduli were scaled to the local DMB. Disregarding the observed distribution of mineralization was associated with an overestimation of average equivalent strain and underestimation of von Mises equivalent stress. From the surface of trabecular elements towards their core the strain decreased irrespective of tissue stiffness distribution. This indicates that the trabecular elements were bent during the compression experiment. Inhomogeneously distributed tissue stiffness resulted in a low stress at the surface that increased towards the core. In contrast, disregarding this tissue stiffness distribution resulted in high stress at the surface which decreased towards the core. It was concluded that the increased DMB, together with concurring alterations in architecture, during development leads to a structure which is able to resist increasing loads without an increase in average deformation, which may lead to damage.