A study of age-related architectural changes that are most damaging to bones

Osteoporosis-related bone damage causes major socioeconomic problems. For efficient use of therapeutic agents, it is necessary to be able to reliably identify patients with high propensity for nontraumatic fracture. Age-related bone loss imposes several architectural changes in bone; one of the few ways to estimate damage due to individual changes, and hence determine the most serious types of damage, is via the analysis of suitable mathematical models. Anatomical sites such as the vertebral body, proximal femur, and distal radius are locations where most age-related fractures occur. The inner porous (or trabecular) bone from these sites, which resemble disordered cubic networks, play a significant role in load transmission at these sites. Analysis of a mathematical model of porous bone is used to show that perforation of elements of the network is the most damaging architectural change to a bone. We also show that an expression for bone strength, derived on this basis, can capture changes in strength caused by the inclusion of other features like thinning of trabecular bone and the anisotropy of the network. We finally argue that bone density, which is currently the most routinely used diagnostic, cannot be a reliable surrogate for bone strength.     

Mechanisms of reduced implant stability in osteoporotic bone

The determining factors for the fixation of uncemented screws in bone are the bone-implant interface and the peri-implant bone. The goal of this work was to explore the role of the peri-implant bone architecture on the mechanics of the bone-implant system. In particular, the specific aims of the study were to investigate: (i) the impact of the different architectural parameters, (ii) the effects of disorder, and (iii) the deformations in the peri-implant region. A three-dimensional beam lattice model to describe trabecular bone was developed. Various microstructural features of the lattice were varied in a systematic way. Implant pull-out tests were simulated, and the stiffness and strength of the bone-implant system were computed. The results indicated that the strongest decrease in pull-out strength was obtained by trabecular thinning, whereas pull-out stiffness was mostly affected by trabecular removal. These findings could be explained by investigating the peri-implant deformation field. For small implant displacements, a large amount of trabeculae in the peri-implant region were involved in the load transfer from implant to bone. Therefore, trabecular removal in this region had a strong negative effect on pull-out stiffness. Conversely, at higher displacements, deformations mainly localized in the trabeculae in contact with the implant; hence, thinning those trabeculae produced the strongest decrease in the strength of the system. Although idealized, the current approach is helpful for a mechanical understanding of the role played by peri-implant bone.     

How morphology predicts mechanical properties of trabecular structures depends on intra-specimen trabecular thickness variations

Two observations underlie this work. First, that the architecture of trabecular bone can accurately predict the mechanical stiffness characteristics of bone specimens when considering the combination of volume fraction and fabric, which is a measure of architectural anisotropy. Second, that the same morphological measures could not accurately predict the mechanical properties of porous structures in general. We hypothesize that this discrepancy can be explained by the special nature of trabecular bone as a structure in remodeling equilibrium relative to the external loads. We tested this hypothesis using a generic model of trabecular bone. Five series of 153 different architectures were created with this model. Each architecture was subjected to morphological analysis, and four different fabric measures were calculated to evaluate their effectiveness in characterizing the architecture. Relationships were determined relating morphology to the elastic constants. The quality of these relationships was tested by correlating the predicted elastic constants with those determined from finite element analysis. We found that the four fabric measures used could estimate the mechanical properties almost equally well. So the suggestion that fabric measures based on trabecular bone volume better represent the architecture than mean intercept length could not be affirmed. We conclude that for structures with equally sized elliptical voids the mechanical properties can be predicted well only if trabecular thickness variations within each structure are limited. These structures closely resemble previously developed models of trabecular bone. Furthermore, they are stiff in the principal fabric direction, hence, according to Cowin (J. Biomech. Eng. (108) (1986) 83), they are in remodeling equilibrium. These structures are also stiff over a large range of loading orientations, hence, are relatively insensitive to deviations in direction of loading.     

An expression relating breaking stress and density of trabecular bone

Bone mineral density (BMD) is the principal diagnostic tool used in clinical settings to diagnose and monitor osteoporosis. Experimental studies on ex vivo bone samples from multiple skeletal locations have been used to propose that their breaking stress bears a power-law relationship to volumetric BMD, with a location-dependent index. We argue that a power-law cannot represent effects of trabecular removal, which is one of the leading causes of reduction in bone strength. A new expression, proposed on the basis of theoretical and numerical analysis of a mathematical model, is tested using previously published data on bone samples from iliac crest and vertebral body. It represents the experimental biomechanical data at least as well as the power-law, and provides means for extrapolating results from small biopsy samples to an entire bone. In addition, changes caused by trabecular thinning and anisotropy can be modeled by the expression.     

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

The purpose of the present study was to examine the changes in apparent mechanical properties of trabecular bone in the mandibular condyle during fetal development and to investigate the contributions of altering architecture, and degree and distribution of mineralization to this change. Three-dimensional, high-resolution micro-computed tomography (microCT) reconstructions were utilized to assess the altering architecture and mineralization during development. From the reconstructions, inhomogeneous finite element models were constructed, in which the tissue moduli were scaled to the local degree of mineralization of bone (DMB). In addition, homogeneous models were devised to study the separate influence of architectural and DMB changes on apparent mechanical properties. It was found that the bone structure became stiffer with age. Both the mechanical and structural anisotropies pointed to a rod-like structure that was predominantly oriented from anteroinferior to posterosuperior. Resistance against shear, also increasing with age, was highest in the sagittal plane. The reorganization of trabecular elements, which occurred without a change in bone volume fraction, contributed to the increase in apparent stiffness. The increase in DMB, however, contributed more dominantly. Incorporating the observed inhomogeneous distribution of mineralization decreased the apparent stiffness, but increased the mechanical anisotropy. This denotes that there might be a directional dependency of the DMB of trabecular elements, i.e. differently orientated trabecular elements might have different DMBs. In conclusion, the changes in DMB and its distribution are important to consider when studying mechanical properties during development and should be considered in other situations where differences in DMB are expected.     

The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone.

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology--or architecture--and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a negligible effect on the apparent elastic properties of cancellous bone. The question addressed in this paper is whether this is actually true. If it is, then micromechanical finite element analysis (micro-FEA) models, representing trabecular architecture, using an 'effective isotropic tissue modulus' should be able to predict apparent elastic properties of cancellous bone. To test this, accurate multi-axial compressive mechanical tests of 29 whale bone specimens were simulated with specimen-specific micro-FEA computer models built from true three-dimensional reconstructions. By scaling the micro-FEA predictions by a constant tissue modulus, 92% of the variation of Young's moduli determined experimentally could be explained. The correlation even increased to 95% when the micro-FEA moduli were scaled to the isotropic tissue moduli of individual specimens. Excellent agreement was also found in the elastic symmetry axes and anisotropy ratios. The prediction of Poisson's ratios was somewhat less precise at 85% correlation. The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one. They also suggest that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization. Future studies must clarify how specific the tissue modulus should be for different types of bone if adequate predictions of elastic behavior are to be made in this way.     

Simulation of vertebral trabecular bone loss using voxel finite element analysis

Trabecular bone loss in human vertebral bone is characterised by thinning and eventual perforation of the horizontal trabeculae. Concurrently, vertical trabeculae are completely lost with no histological evidence of significant thinning. Such bone loss results in deterioration in apparent modulus and strength of the trabecular core. In this study, a voxel-based finite element program was used to model bone loss in three specimens of human vertebral trabecular bone. Three sets of analyses were completed. In Set 1, strain adaptive resorption was modelled, whereby elements which were subject to the lowest mechanical stimulus (principal strain) were removed. In Set 2, both strain adaptive and microdamage mechanisms of bone resorption were included. Perforation of vertical trabeculae occurred due to microdamage resorption of elements with strains that exceeded a damage threshold. This resulted in collapse of the trabecular network under compression loading for two of the specimens tested. In Set 3, the damage threshold strain was gradually increased as bone loss progressed, resulting in reduced levels of microdamage resorption. This mechanism resulted in trabecular architectures in which vertical trabeculae had been perforated and which exhibited similar apparent modulus properties compared to experimental values reported in the literature. Our results indicate that strain adaptive remodelling alone does not explain the deterioration in mechanical properties that have been observed experimentally. Our results also support the hypothesis that horizontal trabeculae are lost principally by strain adaptive resorption, while vertical trabeculae may be lost due to perforation from microdamage resorption followed by rapid strain adaptive resorption of the remaining unloaded trabeculae.     

Mapping anisotropy of the proximal femur for enhanced image based finite element analysis

Finite element (FE) models of bone derived from quantitative computed tomography (QCT) rely on realistic material properties to accurately predict bone strength. QCT cannot resolve bone microarchitecture, therefore QCT-based FE models lack the anisotropy apparent within the underlying bone tissue. This study proposes a method for mapping femoral anisotropy using high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of human cadaver specimens. Femur HR-pQCT images were sub-divided into numerous overlapping cubic sub-volumes and the local anisotropy was quantified using a ‘direct-mechanics’ method. The resulting directionality reflected all the major stress lines visible within the trabecular lattice, and provided a realistic estimate of the alignment of Harvesian systems within the cortical compartment. QCT-based FE models of the proximal femur were constructed with isotropic and anisotropic material properties, with directionality interpolated from the map of anisotropy. Models were loaded in a sideways fall configuration and the resulting whole bone stiffness was compared to experimental stiffness and ultimate strength. Anisotropic models were consistently less stiff, but no statistically significant differences in correlation were observed between material models against experimental data. The mean difference in whole bone stiffness between model types was approximately 26%, suggesting that anisotropy can still effect considerable change in the mechanics of proximal femur models. The under prediction of whole bone stiffness in anisotropic models suggests that the orthotropic elastic constants require further investigation. The ability to map mechanical anisotropy from high-resolution images and interpolate information into clinical-resolution models will allow testing of new anisotropic material mapping strategies.     

A cellular solid model for modulus reduction due to resorption of trabeculae in bone

In osteoporotic trabecular bone, bone loss occurs by thinning and subsequent resorption of the trabeculae. In this study, we compare the effects of density reductions from uniform thinning of struts or from removal of struts in a random, open-cell, three-dimensional Voronoi structure. The results of this study, combined with those previous studies on other regular and random structures, suggest that the modulus and strength of trabecular bone are reduced more dramatically by density losses from resorption of trabeculae than by those from uniform thinning of trabeculae.     

Alterations in trabecular bone microarchitecture in the ovine spine and distal femur following ovariectomy

Osteoporosis is a bone disease resulting in increased fracture risk as a result of alterations in both quantity and quality of bone. Bone quality is a combination of metabolic and microarchitectural properties of bone that can help to explain the increased susceptibility to fracture. Translational animal models are essential to understanding the pathology and for evaluating potential treatments of this disease. Large animals, such as the ovariectomized sheep, have been used as models for post-menopausal osteoporosis. However, long-term studies have not been carried out to observe the effects of ovariectomy after more than one year. This study employed micro-computed tomography to quantify changes in microarchitectural and mechanical parameters in femoral condyles and vertebral bodies of sheep that were sacrificed one or two years following ovariectomy. In the vertebral body, microarchitectural characteristics were significantly degraded following one year of ovariectomy in comparison to controls. The mechanical anisotropy, determined from micro-scale finite element models, was also greater in the ovariectomized groups, although the fabric tensor anisotropy was similar. There was no greater architectural degradation following two years of ovariectomy compared to one. Ovariectomy had minimal effects on the trabecular architecture of the distal femur even after two years. These results indicate that the vertebral body is the preferred anatomic site for studying bone from the ovariectomized sheep model, and that architectural changes stabilize after the first year.     

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.     

Mechanics of linear microcracking in trabecular bone

Microcracking in trabecular bone is responsible both for the mechanical degradation and remodeling of the trabecular bone tissue. Recent results on trabecular bone mechanics have demonstrated that bone tissue microarchitecture, tissue elastic heterogeneity and tissue-level mechanical anisotropy all should be considered to obtain detailed information on the mechanical stress state. The present study investigated the influence of tissue microarchitecture, tissue heterogeneity in elasticity and material separation properties and tissue-level anisotropy on the microcrack formation process. Microscale bone models were executed with the extended finite element method. It was demonstrated that anisotropy and heterogeneity of the bone tissue contribute significantly to bone tissue toughness and the resistance of trabecular bone to microcrack formation. The compressive strain to microcrack initiation was computed to increase by a factor of four from an assumed homogeneous isotropic tissue to an assumed anisotropic heterogenous tissue.     

Shear strength and toughness of trabecular bone are more sensitive to density than damage

Microdamage occurs in trabecular bone under normal loading, which impairs the mechanical properties. Architectural degradation associated with osteoporosis increases damage susceptibility, resulting in a cumulative negative effect on the mechanical properties. Treatments for osteoporosis could be targeted toward increased bone mineral density, improved architecture, or repair and prevention of microdamage. Delineating the relative roles of damage and architectural degradation on trabecular bone strength will provide insight into the most beneficial targets. In this study, damage was induced in bovine trabecular bone samples by axial compression, and the effects on the mechanical properties in shear were assessed. The damaged shear modulus, shear yield stress, ultimate shear stress, and energy to failure all depended on induced damage and decreased as the architecture became more rod-like. The changes in ultimate shear strength and toughness were proportional to the decrease in shear modulus, consistent with an effective decrease in the cross-section of trabeculae based on cellular solid analysis. For typical ranges of bone volume fraction in human bone, the strength and toughness were much more sensitive to decreased volume fraction than to induced mechanical damage. While ultimately repairing or avoiding damage to the bone structure and increasing bone density both improve mechanical properties, increasing bone density is the more important contributor to bone strength.     

Analysis of biomechanical effects on bone and on the muscle-bone interactions in small animal models

Animal models are suitable to study many aspects of bone structure and strength. This article reviews some general principles of current bone biomechanics and describes the scope of the available methodology for biomechanical studies of the musculoskeletal system employing those models. The analysis comprises bone and muscle "mass" indicators provided by standard densitometry (DEXA); bone 'mass', 'apparent density', geometry or architectural design and strength and muscle strength indicators that can be determined by peripheral quantitative computed tomography (pQCT), and bone material and structural (whole-bone) properties than can be directly assessed by destructive mechanical tests. Some novel interrelationships that can be investigated that way are discussed, namely, 1. the pathogenetic analysis of the effects on whole-bone strength, 2. the discrimination between mineralization and microstructural factors as determinants of changes in the bone material or structural properties, 3. the evaluation of the interaction of a treatment with the ability of bone 'mechanostat' to optimize the bone architectural design by 'distribution / mass' and 'distribution / quality' curves, and 4. the analysis of effects on the musclebone interactions for a differential diagnosis between 'physiological' or 'disuse' and 'true' osteopenias and osteoporoses.     

Fracture prediction for the proximal femur using finite element models: Part II--Nonlinear analysis.

In Part I we reported the results of linear finite element models of the proximal femur generated using geometric and constitutive data collected with quantitative computed tomography. These models demonstrated excellent agreement with in vitro studies when used to predict ultimate failure loads. In Part II, we report our extension of those finite element models to include nonlinear behavior of the trabecular and cortical bone. A highly nonlinear material law, originally designed for representing concrete, was used for trabecular bone, while a bilinear material law was used for cortical bone. We found excellent agreement between the model predictions and in vitro fracture data for both the onset of bone yielding and bone fracture. For bone yielding, the model predictions were within 2 percent for a load which simulated one-legged stance and 1 percent for a load which simulated a fall. For bone fracture, the model predictions were within 1 percent and 17 percent, respectively. The models also demonstrated different fracture mechanisms for the two different loading configurations. For one-legged stance, failure within the primary compressive trabeculae at the subcapital region occurred first, leading to load transfer and, ultimately, failure of the surrounding cortical shell. However, for a fall, failure of the cortical and trabecular bone occurred simultaneously within the intertrochanteric region. These results support our previous findings that the strength of the subcapital region is primarily due to trabecular bone whereas the strength of the intertrochanteric region is primarily due to cortical bone.     

The effect of exercise and nutrition on the mechanostat

In this review, we discuss the effect of increased and decreased loading and nutrition deficiency on muscle and bone mass and strength (and bone length and architecture) independently and combined. Both exercise and nutrition are integral components of the mechanostat model but both have distinctly different roles. Mechanical strain imparted by muscle action is responsible for the development of the external size and shape of the bone and subsequently the bone strength. In contrast, immobilization during growth results in reduced growth in bone length and a loss of bone strength due to large losses in bone mass (a result of endosteal resorption in cortical bone and trabecular thinning) and changes in geometry (bone shafts do not develop their characteristic shape but rather develop a rounded default shape). The use of surrogate measures for peak muscle forces acting on bone (muscle strength, size, or mass) limits our ability to confirm a cause-and-effect relationship between peak muscle force acting on bone and changes in bone strength. However, the examples presented in this review support the notion that under adequate nutrition, exercise has the potential to increase peak muscle forces acting on bone and thus can lead to a proportional increase in bone strength. In contrast, nutrition alone does not influence muscle or bone in a dose-dependent manner. Muscle and bone are only influenced when there is nutritional deficiency--and in this case the effect is profound. Similar to immobilization, the immediate effect of malnutrition is a reduction in longitudinal growth. More specifically, protein and energy malnutrition results in massive bone loss due to endosteal resorption in cortical bone and trabecular thinning. Unlike loading however, there is indirect evidence that severe malnutrition when associated with menstrual dysfunction can shift the mechanostat set point upward, thus leading to less bone accrual for a given amount of bone strain.     

Interrelationship of trabecular mechanical and microstructural properties in sheep trabecular bone

The ability to evaluate fracture risk at an early time point is essential for improved prognostics as well as enhanced treatment in cases of bone loss such as from osteoporosis. Improving the diagnostic ability is inherent upon both high-resolution non-invasive imaging, and a thorough understanding of how the derived indices of structure and density relate to its true mechanical behavior. Using sheep femoral trabecular bone with a range of strength, the interrelationship of mechanical and microstructural parameters was analyzed using multi-directional mechanical testing and micro-computed tomography. Forty-five cubic trabecular bone samples were harvested from 23 adult female sheep, some of whom had received hind-limb vibratory stimuli over the course of 2 years with consequently enhanced mechanical properties. These samples were pooled into a low, medium, or high strength group for further analysis. The findings show that microCT indices that are structural in nature, e.g., structural model index (SMI) (r2=0.85, p<0.0001) is as good as more density oriented indices like bone volume/total volume (BV/TV) (r2=0.81, p<0.0001) in predicting the ultimate strength of a region of trabecular bone. Additionally, those indices more related to global changes in trabecular structure such as connectivity density (ConnD) or degree of anisotropy (DA) are less able to predict the mechanical properties of bone. Interrelationships of trabecular indices such as trabecular number (TbN), thickness (TbTh), and spacing (TbSp) provide clues as to how the trabecular bone will remodel to ultimately achieve differences in the apparent mechanical properties. For instance, the analysis showed that a loss of bone primarily affects the connectedness and overall number of trabeculae, while increased strength results in an increase of the overall thickness of trabeculae while not improving the connectedness. Certainly, the microCT indices studied are able to predict the bulk mechanical properties of a trabecular ROI well, leaving unaccounted only about 15-20% of its inherent variability. Diagnostically, this implies that future work on the early prediction of fracture risk should continue to explore the role of bone quality as the key factors or as an adjuvant to bone quantity (e.g., apparent density).     

Perforation of cancellous bone trabeculae by damage-stimulated remodelling at resorption pits: a computational analysis

Loss of trabeculae in cancellous bone is often attributed to a general decline in the bone mass leading to fracture of the thin trabeculae. It has never been investigated whether trabecular perforation may have any other biomechanical mechanism. In this paper, an alternative hypothesis is proposed and tested using a computational model. Taking it as given that osteoclastic resorption is targeted to microdamage, it is hypothesised that the creation of a resorption cavity during normal bone remodelling could cause a stress-concentration in the bone tissue. If the resorption cavities were excessively deep, as is seen during osteoporosis, then this stress concentration may be sufficient to generate more microdamage so that osteoclasts "chase" newly formed damage leading to perforation. If this were true then we should find that, for a given trabecular thickness, there is a critical depth of resorption cavity such that smaller cavities refill whereas deeper cavities cause microdamage accumulation, continued osteoclast activity, and eventual trabecular perforation. Computer simulation is used to test this hypothesis. Using a remodelling stimulus calculated from both strain and damage and a simplified finite element model of a trabeculum with cavities of different sizes, it is predicted that such a critical depth of resorption cavity does indeed exist. Therefore we suggest that an increase in resorption depth relative to the thickness of trabeculae may be responsible for trabecular perforation during osteoporosis, rather than simply trabecular fracture due to insufficient strength.     

Indirect determination of trabecular bone effective tissue failure properties using micro-finite element simulations

Trabecular bone strength is marked not only by the onset of local yielding, but also by post-yield behavior. To study and predict trabecular bone elastic and yield properties, micro-finite element (micro-FE) models were successfully applied. However, trabecular bone strength predictions require micro-FE models incorporating post-yield behavior of trabecular bone tissue. Due to experimental difficulties, such data is currently not available. Here we used micro-FE modeling to determine failure behavior of trabecular bone tissue indirectly, by iteratively fitting FE simulation to experimental results. Failure parameters were fitted to an isotropic plasticity model based on Hill's yield function, using materially and geometrically nonlinear micro-FE models of seven bovine trabecular bone specimens. The predictive value of the averaged effective tissue properties was subsequently tested. The results showed that compression softening had to be included on the tissue level in order to accurately describe the apparent-level behavior of the bone specimens. A sensitivity study revealed that the simulated response was less sensitive to variations in the post-yield properties of the bone tissue than variations in the elastic and yield properties. Due to fitting of the tissue properties, apparent-level behavior could be accurately reproduced for each specimen separately. Predictions based on the averaged and fixed tissue properties were less accurate, due to inter-specimen variations in the tissue properties.     

Recent experimental and clinical findings in the skeleton associated with loss of estrogen hormone or estrogen receptor activity

Studies on rodent models and rare human disorders of estrogen production or response have revealed an increased complexity of the actions of estrogen on bone. ERα disruption in human males results in delayed epiphyseal maturation, tall stature, trabecular thinning, marked cortical thinning, genu valgum and significantly reduced cortical vBMD, but trabecular number is preserved and there is normal to increased periosteal expansion. Aromatase deficiency results overall in a similar phenotype, although less is known about skeletal architecture. Importantly, estrogen replacement in these individuals, even if provided late in the third decade, may normalize aBMD. Less certain is whether there is complete recovery of normal skeletal architecture and strength. Rodent models, in general, are consistent with the human phenotype but are confounded by inherent differences between mouse and human physiology and issues regarding the completeness of the different knock-out lines. Both human and rodent studies suggest that residual effects of estrogen through ERβ, truncated ERα forms or nonclassical estrogen receptors might account for different phenotypes in the hERKO man, aromatase deficient subjects and rodents. Importantly, androgen, particularly by preserving trabecular number and augmenting both periosteal and epiphyseal growth, also has significant actions on bone.