A sclerostin-based theory for strain-induced bone formation

Bone formation responds to mechanical loading, which is believed to be mediated by osteocytes. Previous theories assumed that loading stimulates osteocytes to secrete signals that stimulate bone formation. In computer simulations this 'stimulatory' theory successfully produced load-aligned trabecular structures. In recent years, however, it was discovered that osteocytes inhibit bone formation via the protein sclerostin. To reconcile this with strain-induced bone formation, one must assume that sclerostin secretion decreases with mechanical loading. This leads to a new 'inhibitory' theory in which loading inhibits osteocytes from inhibiting bone formation. Here we used computer simulations to show that a sclerostin-based model is able to produce a load-aligned trabecular architecture. An important difference appeared when we compared the response of the stimulatory and inhibitory models to loss of osteocytes, and found that the inhibitory pathway prevents the loss of trabeculae that is seen with the stimulatory model. Further, we demonstrated with combined stimulatory/inhibitory models that the two pathways can work side-by-side to achieve a load-adapted bone architecture.     

Interstitial fluid flow in canaliculi as a mechanical stimulus for cancellous bone remodeling: in silico validation

Cancellous bone has a dynamic 3-dimensional architecture of trabeculae, the arrangement of which is continually reorganized via bone remodeling to adapt to the mechanical environment. Osteocytes are currently believed to be the major mechanosensory cells and to regulate osteoclastic bone resorption and osteoblastic bone formation in response to mechanical stimuli. We previously developed a mathematical model of trabecular bone remodeling incorporating the possible mechanisms of cellular mechanosensing and intercellular communication in which we assumed that interstitial fluid flow activates the osteocytes to regulate bone remodeling. While the proposed model has been validated by the simulation of remodeling of a single trabecula, it remains unclear whether it can successfully represent in silico the functional adaptation of cancellous bone with its multiple trabeculae. In the present study, we demonstrated the response of cancellous bone morphology to uniaxial or bending loads using a combination of our remodeling model with the voxel finite element method. In this simulation, cancellous bone with randomly arranged trabeculae remodeled to form a well-organized architecture oriented parallel to the direction of loading, in agreement with the previous simulation results and experimental findings. These results suggested that our mathematical model for trabecular bone remodeling enables us to predict the reorganization of cancellous bone architecture from cellular activities. Furthermore, our remodeling model can represent the phenomenological law of bone transformation toward a locally uniform state of stress or strain at the trabecular level.     

The turnover of mineralized growth plate cartilage into bone may be regulated by osteocytes

During endochondral ossification, growth plate cartilage is replaced with bone. Mineralized cartilage matrix is resorbed by osteoclasts, and new bone tissue is formed by osteoblasts. As mineralized cartilage does not contain any cells, it is unclear how this process is regulated. We hypothesize that, in analogy with bone remodeling, osteoclast and osteoblast activity are regulated by osteocytes, in response to mechanical loading. Since the cartilage does not contain osteocytes, this means that cartilage turnover during endochondral ossification would be regulated by the adjacent bone tissue. We investigated this hypothesis with an established computational bone adaptation model. In this model, osteocytes stimulate osteoblastic bone formation in response to the mechanical bone tissue loading. Osteoclasts resorb bone near randomly occurring microcracks that are assumed to block osteocyte signals. We used finite element modeling to evaluate our hypothesis in a 2D-domain representing part of the growth plate and adjacent bone. Cartilage was added at a constant physiological rate to simulate growth. Simulations showed that osteocyte signals from neighboring bone were sufficient for successful cartilage turnover, since equilibrium between cartilage remodeling and growth was obtained. Furthermore, there was good agreement between simulated bone structures and rat tibia histology, and the development of the trabecular architecture resembled that of infant long bones. Additionally, prohibiting osteoclast invasion resulted in thickened mineralized cartilage, similar to observations in a knock-out mouse model. We therefore conclude that it is well possible that osteocytes regulate the turnover of mineralized growth plate cartilage.     

Trabecular architecture can remain intact for both disuse and overload enhanced resorption characteristics

The paradigm that bone metabolic processes are controlled by osteocyte signals have been the subject of investigation in many recent studies. One hypothesis is that osteoblast formation is enhanced by these signals, and that osteoclast resorption is enhanced by the lack of them. Reduced, or absent, osteocyte signaling can be an effect of reduced mechanical loading (disuse) or of defects in the canalicular network, due to microcracks. This would mean that bone is resorbed precisely there where it is mostly needed. In our study, we addressed this apparent contradiction. The purpose was to investigate how alternative strain-based local stimuli for osteoclasts to resorb bone would affect remodeling and adaptation of the trabecular architecture. For this purpose, a computer-simulation model was used, which couples morphological and mechanical effects of local bone metabolism to changes in trabecular architecture and density at large. Six resorption characteristics were studied in the model: (I) resorption occurs spatially random, (II) resorption is enhanced or (III) strongly enhanced where there is disuse, (IV) resorption is enhanced or (V) strongly enhanced where there are high strains, i.e. overload, and (VI) resorption is enhanced where there is disuse and where there are high strains. Results showed that the rates of structural adaptation to alternative loading were higher for disuse-controlled resorption than for overload-controlled resorption. Architecture and mass remained stable for all cases except (V) in which the structure deteriorated as in osteoporotic bone. We conclude that, given the potential of osteoblasts to form bone in highly strained areas, based on signals from osteocytes, osteoclast resorption can normally be compensated for.     

Skeletal adaptation to intramedullary pressure-induced interstitial fluid flow is enhanced in mice subjected to targeted osteocyte ablation

Interstitial fluid flow (IFF) is a potent regulatory signal in bone. During mechanical loading, IFF is generated through two distinct mechanisms that result in spatially distinct flow profiles: poroelastic interactions within the lacunar-canalicular system, and intramedullary pressurization. While the former generates IFF primarily within the lacunar-canalicular network, the latter generates significant flow at the endosteal surface as well as within the tissue. This gives rise to the intriguing possibility that loading-induced IFF may differentially activate osteocytes or surface-residing cells depending on the generating mechanism, and that sensation of IFF generated via intramedullary pressurization may be mediated by a non-osteocytic bone cell population. To begin to explore this possibility, we used the Dmp1-HBEGF inducible osteocyte ablation mouse model and a microfluidic system for modulating intramedullary pressure (ImP) to assess whether structural adaptation to ImP-driven IFF is altered by partial osteocyte depletion. Canalicular convective velocities during pressurization were estimated through the use of fluorescence recovery after photobleaching and computational modeling. Following osteocyte ablation, transgenic mice exhibited severe losses in bone structure and altered responses to hindlimb suspension in a compartment-specific manner. In pressure-loaded limbs, transgenic mice displayed similar or significantly enhanced structural adaptation to Imp-driven IFF, particularly in the trabecular compartment, despite up to ～50% of trabecular lacunae being uninhabited following ablation. Interestingly, regression analysis revealed relative gains in bone structure in pressure-loaded limbs were correlated with reductions in bone structure in unpressurized control limbs, suggesting that adaptation to ImP-driven IFF was potentiated by increases in osteoclastic activity and/or reductions in osteoblastic activity incurred independently of pressure loading. Collectively, these studies indicate that structural adaptation to ImP-driven IFF can proceed unimpeded following a significant depletion in osteocytes, consistent with the potential existence of a non-osteocytic bone cell population that senses ImP-driven IFF independently and potentially parallel to osteocytic sensation of poroelasticity-derived IFF.     

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.     

Computational study of Wolff's law with trabecular architecture in the human proximal femur using topology optimization

In the field of bone adaptation, it is believed that the morphology of bone is affected by its mechanical loads, and bone has self-optimizing capability; this phenomenon is well known as Wolff's law of the transformation of bone. In this paper, we simulated trabecular bone adaptation in the human proximal femur using topology optimization and quantitatively investigated the validity of Wolff's law. Topology optimization iteratively distributes material in a design domain producing optimal layout or configuration, and it has been widely and successfully used in many engineering fields. We used a two-dimensional micro-FE model with 50 microm pixel resolution to represent the full trabecular architecture in the proximal femur, and performed topology optimization to study the trabecular morphological changes under three loading cases in daily activities. The simulation results were compared to the actual trabecular architecture in previous experimental studies. We discovered that there are strong similarities in trabecular patterns between the computational results and observed data in the literature. The results showed that the strain energy distribution of the trabecular architecture became more uniform during the optimization; from the viewpoint of structural topology optimization, this bone morphology may be considered as an optimal structure. We also showed that the non-orthogonal intersections were constructed to support daily activity loadings in the sense of optimization, as opposed to Wolff's drawing.     

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.     

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.     

Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state

Two-dimensional simulation of trabecular surface remodeling was conducted for a human proximal femur to investigate the structural change of cancellous bone toward a uniform stress state. Considering that a local mechanical stimulus plays an important role in cellular activities in bone remodeling, local stress nonuniformity was assumed to drive trabecular structural change to seek a uniform stress state. A large-scale pixel-based finite element model was used to simulate structural changes of individual trabeculae over the entire bone. As a result, the initial structure of trabeculae changed from isotropic to anisotropic due to trabecular microstructural changes caused by surface remodeling according to the mechanical environment in the proximal femur. Under a single-loading condition, it was shown that the apparent structural property evaluated by fabric ellipses corresponded to the apparent stress state in cancellous bone. As is observed in the actual bone, a distributed trabecular structure was obtained under a multiple-loading condition. Through these studies, it was concluded that trabecular surface remodeling toward a local uniform stress state at the trabecular level could naturally bring about functional adaptation phenomenon at the apparent tissue level. The proposed simulation model would be capable of providing insight into the hierarchical mechanism of trabecular surface remodeling at the microstructural level up to the apparent tissue level.     

Poroelastic analysis of interstitial fluid flow in a single lamellar trabecula subjected to cyclic loading

Trabecula, an anatomical unit of the cancellous bone, is a porous material that consists of a lamellar bone matrix and interstitial fluid in a lacuno-canalicular porosity. The flow of interstitial fluid caused by deformation of the bone matrix is believed to initiate a mechanical response in osteocytes for bone remodeling. In order to clarify the effect of the lamellar structure of the bone matrix—i.e., variations in material properties—on the fluid flow stimuli to osteocytes embedded in trabeculae, we investigated the mechanical behavior of an individual trabecula subjected to cyclic loading based on poroelasticity. We focused on variations in the trabecular permeability and developed an analytical solution containing both transient and steady-state responses for interstitial fluid pressure in a single trabecular model represented by a multilayered two-dimensional poroelastic slab. Based on the obtained solution, we calculated the pressure and seepage velocity of the interstitial fluid in lacuno-canalicular porosity, within the single trabecula, under various permeability distributions. Poroelastic analysis showed that a heterogeneous distribution of permeability produces remarkable variations in the fluid pressure and seepage velocity in the cross section of the individual trabecula, and suggests that fluid flow stimuli to osteocytes are mostly governed by the value of permeability in the neighborhood of the trabecular surfaces if there is no difference in the average permeability in a single trabecula.     

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.     

Three-dimensional micro-level computational study of Wolff's law via trabecular bone remodeling in the human proximal femur using design space topology optimization

The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. The goal of the current study was to utilize an advanced structural optimization algorithm, called design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The result is a "fully stressed" structure with minimized compliance and increased stiffness. The large-scale computational simulation utilized a 175 μm mesh resolution and the routine daily loading activities of walking and stair climbing. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using a variety of visualization techniques, including radiography and computed tomography (CT). The results qualitatively revealed several anisotropic trabecular regions, that were comparable to the natural human femurs. Quantitatively, the various regional bone volume fractions from the computational results were consistent with quantitative CT analyses. The global strain energy proceeded to become more uniform during optimization; implying increased mechanical efficiency was achieved. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as the Wolff hypothesized.     

Phenotypic plasticity and mechano‐transduction in the teleost skeleton

The proper formation, growth and maintenance of many bones depends on the mechanical loads generated by gravity and muscles. Mechanical loading by muscle forces does not only affect bone growth and maintenance in adult and juvenile vertebrates, but also affects larval and embryonic bone development. We have reviewed the current understanding of mechanotransduction in birds and mammals and compared it to teleosts. The major mechanosensing cells in the adult mammalian and avian skeleton are osteocytes. They are interconnected via cell processes and are contained within a canalicular network. Basal teleosts have osteocytes but their connectivity is questionable and the presence of a functional canalicular network is unlikely. Advanced teleosts have acellular bone and therefore lack osteocytes. Yet the skeleton of teleosts does show adaptive responses to changes in mechanical load. In these animals it is likely that osteoblasts, bone surface cells and chondrocytes act as mechanosensors. The factors expressed by osteocytes upon mechanical stimulation have been extensively investigated in vitro and in vivo in adult mammals and birds. Less is, however, known about the mechanotransduction pathway during embryonic bone development. The zebrafish presents new opportunities to analyze the mechanotransduction pathway during early (larval) bone formation due to the ex utero development and genetic analyses.     

Mechanosensation and fluid transport in living bone

The mechanosensory mechanisms in bone include (i) the cell system that is stimulated by external mechanical loading applied to the bone; (ii) the system that transduces that mechanical loading to a communicable signal; and (iii) the systems that transmit that signal to the effector cells for the maintenance of bone homeostasis and for strain adaptation of the bone structure. The effector cells are the osteoblasts and the osteoclasts. These systems and the mechanisms that they employ have not yet been unambiguously identified. The candidate systems will be reviewed. It will be argued that the current theoretical and experimental evidence suggests that osteocytes are the principal mechanosensory cells of bone, that they are activated by shear stress from fluid flowing through the osteocyte canaliculi, and that the electrically coupled three-dimensional network of osteocytes and lining cells is a communications system for the control of bone homeostasis and structural strain adaptation. The movement of bone fluid from the region of the bone vasculature through the canaliculi and the lacunae of the surrounding mineralized tissue accomplishes three important tasks. First, it transports nutrients to the osteocytes in the lacunae buried in the mineralized matrix. Second, it carries away the cell waste. Third, the bone fluid exerts a force on the cell process, a force that is large enough for the cell to sense. This is probably the basic mechanotransduction mechanism in bone, the way in which bone senses the mechanical load to which it is subjected. The mechanisms of bone fluid flow are described with particular emphasis on mechanotransduction. Also described is the cell to cell communication by which higher frequency signals might be transferred, a potential mechanism in bone by which the small whole tissue strain is amplified so the bone cells can respond to it. One of the conclusions is that higher frequency low amplitude strains can maintain bone as effectively as low frequency high amplitude strains. This conclusion leads to a paradigm shift in how to treat osteoporosis and how to cope with microgravity.     

Articular structure and function in Hylobates,Colobus, and Papio

It has been demonstrated in clinical and experimental studies that subarticular trabecular bone responds to mechanical loads transmitted across joints through changes in mass and structural organization. We investigated differences in mass, volume, and density of subarticular trabecular bone of the humeral and femoral head in Hylobates syndactylus, Colobus guereza, and Papio cynocephalus. Our hypothesis was that variations in trabecular properties between taxa may reflect differences in mechanical loading associated with different locomotor repertoires. A nondestructive method for measuring trabecular properties using optical luminance data measured from radiographs was developed. We also examined the relationship between internal trabecular properties and the external size and surface area of the humeral and femoral heads in these taxa. Our results suggest that internal and external articular structure are relatively independent of each other and may be adapted to different aspects of the mechanical environment. Differences in trabecular mass between taxa appear to correspond to differences in the magnitudes of mechanical loads borne by the joint, whereas aritcular volume and surface area are related primarily to differences in joint mobility. Because of the apparent physiological “de-coupling” of articular mass and volume, variations in articular density (mass/volume) are difficult to interpret in isolation. Comparisons of internal and external articular structure may provide new ways to reconstruct the locomotor/positional behavior of extinct taxa. © 1994 Wiley-Liss, Inc.     

Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation

The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level) and macroscopic (whole bone level) to simulate the process of bone remodelling. As whole bone simulation, including the 3D reconstruction of trabecular level bone, is time consuming, finite element calculation is only performed at the macroscopic level, whilst trained neural networks are employed as numerical substitutes for the finite element code needed for the mesoscale prediction. The bone mechanical properties are updated at the macroscopic scale depending on the morphological and mechanical adaptation at the mesoscopic scale computed by the trained neural network. The digital image-based modelling technique using μ-CT and voxel finite element analysis is used to capture volume elements representativeof 2 mm³ at the mesoscale level of the femoral head. The input data for the artificial neural network are a set of bone material parameters, boundary conditions and the applied stress. The output data are the updated bone properties and some trabecular bone factors. The current approach is the first model, to our knowledge, that incorporates both finite element analysis and neural network computation to rapidly simulate multilevel bone adaptation.     

Osteoprotegerin (OPG) and RANKL expression and distribution in developing human craniomandibular joint

During embryogenesis the bone tissue of craniomandibular joint (CMJ) is formed through two pathways: intramembranous ossification and endochondral ossification. The development process is under the control of regulatory factors.The osteoprotegerin (OPG) and the receptor activator of nuclear factor (NF)-kappaB ligand are key regulators of osteoclastogenesis. The aim of this study is the localization of OPG and RANKL mRNA and protein in the foetal CMJ by immunohistochemistry (IHC) and in situ hybridization (ISH). The main results were: OPG and RANKL mRNA and protein were co-localized in the same cell types; OPG and RANKL were specially immunolocated in osteogenic cells; immunolabeling was often seen in the nucleus and cytoplasm of otherwise negative hypertrophic chondrocytes; IHC and ISH labeling decreased from proliferative to hypertrophic chondrocytes; early osteocytes showed dual protein expression and some of the mature osteocytes were ISH-negative; periosteal osteoclasts and chondroclasts were mostly stained by IHC and variably labeled by ISH; the new bone matrix and trabecular borders showed intense immunolabeling. The co-expression of OPG and RANKL in the same bone cell types confirms their strictly coupled action in the regulation of bone metabolism in the CMJ development and their extracellular presence in the new bone matrix and trabecular borders suggests a local regulatory role.     

A microstructural finite element simulation of mechanically induced bone formation.

A finite element method to simulate the formation of an interconnected trabectular bone microstructure oriented with respect to applied in vivo mechanical forces is introduced and quantitatively compared to experimental data from a hydraulic bone chamber implant model. Randomly located 45 microm mineralized nodules were used as the initial condition for the model simulations to represent an early stage of intramembranous bone formation. Boundary conditions were applied consistent with the mechanical environment provided by the in vivo bone chamber model. A two-dimensional repair simulation algorithim that incorporated strain energy density (SED), SED gradient, principal strain, or principal strain gradient as the local objective criterion was utilized to simulate the formation of an oriented trabecular bone microstructure. The simulation solutions were convergent, unique, and relatively insensitive to the assumed initial distribution of mineralized nodules. Model predictions of trabecular bone morphology and anisotropy were quantitatively compared to experimental results. All simulations produced structures that qualitatively resembled oriented trabecular bone. However only simulations utilizing a gradient objective criterion yielded results quantitatively similar to in vivo observations. This simulation approach coupled with an experimental model that delivers controlled in vivo mechanical stimuli can be utilized to study the relationship between physical factors and microstructural adaptation during bone repair.