Morphometry of bone. Are parameters from the iliac crest reliable indicators of renal-insufficiency osteopathy?

Bone samples from 25 autopsy cases with chronic renal insufficiency were analyzed stereologically. The findings in the iliac crest were found to be representative of those of the rib, femur condyle and lumbar vertebra for the following stereologic parameters: volume of osteoid seems related to total bone volume [VV(OID/BONE)], surface of osteoid seams related to total bone volume [SV(OID/BONE)] and surface of osteoid seams in relation to trabecular surface [SS(OID/TRAB)]. In addition, the value of various stereologic parameters for the classification of osteopathies was checked.     

Changes in the Fabric and Compliance Tensors of Cancellous Bone due to Trabecular Surface Remodeling,Predicted by a Digital Image-based Model

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.     

Changes in the fabric and compliance tensors of cancellous bone due to trabecular surface remodeling, predicted by a digital image-based model

Fabric and compliance tensors of a cube of cancellous bone with a complicated three-dimensional trabecular structure were obtained for trabecular surface remodeling by using a digital image-based model combined with a large-scale finite element method. Using mean intercept length and a homogenization method, the fabric and compliance tensors were determined for the trabecular structure obtained in the computer remodeling simulation. The tensorial quantities obtained indicated that anisotropic structural changes occur in cancellous bone adapting to the compressive loading condition. There were good correlations between the fabric tensor, bone volume fraction, and compliance tensor in the remodeling process. The result demonstrates that changes in the structural and mechanical properties of cancellous bone are essentially anisotropic and should be expressed by tensorial quantities.     

Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models

A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional adaptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcomputed tomography (microCT), and was uniaxially compressed. As a result, the apparent stiffness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investigation of the adaptive bone remodeling phenomenon.     

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.     

Analysis of microstructural and mechanical alterations of trabecular bone in a simulated three-dimensional remodeling process

Bone remodeling is a complex dynamic process, which modulates both bone mass and bone microstructure. In addition to bone mass, bone microstructure is an important contributor to bone quality in osteoporosis and fragility fractures. However, the quantitative knowledge of evolution of three-dimensional (3D) trabecular microstructure in adaptation to the external forces is currently limited. In this study, a new 3D simulation method of remodeling of human trabecular bone was developed to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to different external loading conditions. The morphological features of trabecular plate and rod, such as thickness and number density in different orientations were monitored during the remodeling process using a novel imaging analysis technique, namely Individual Trabecula Segmentation (ITS). We showed that the volume fraction and microstructures of trabecular bone including, trabecular type and orientation, were determined by the applied mechanical load. Particularly, the morphological parameters of trabecular plates were more sensitive to the applied load, indicating that they played the major role in the mechanical properties of the trabecular bone. Reducing the applied load caused severe microstructural deteriorations of trabecular bone, such as trabecular plate perforation, rod breakage, and a conversion from plates to rods.     

Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law

Ever since Julius Wolff proposed the law of bone transformation in the 19th century, it has been widely known that the trabecular structure of cancellous bone adapts functionally to the loading environment. To understand the mechanism of Wolff's law, a three-dimensional (3D) computer simulation of trabecular structural changes due to surface remodeling was performed for a human proximal femur. A large-scale voxel finite element model was constructed to simulate the structural changes of individual trabeculae over the entire cancellous region. As a simple remodeling model that considers bone cellular activities regulated by the local mechanical environment, nonuniformity of local stress was assumed to drive the trabecular surface remodeling to seek a uniform stress state. Simulation results demonstrated that cell-scale (～10 μm) remodeling in response to mechanical stimulation created complex 3D trabecular structures of the entire bone-scale (～10 cm), as illustrated in the reference of Wolff. The bone remodeling reproduced the characteristic anisotropic structure in the coronal cross section and the isotropic structures in other cross sections. The principal values and axes of a structure characterized by fabric ellipsoids corresponded to those of the apparent stress of the structure. The proposed large-scale computer simulation indicates that in a complex mechanical environment of a hierarchical bone structure of over 10⁴ length scale (from ～10 μm to ～10 cm), a simple remodeling at the cellular/trabecular levels creates a highly complex and functional trabecular structure, as characterized by bone density and orientation.     

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.     

Over-expression of fibroblast growth factor-2 causes defective bone mineralization and osteopenia in transgenic mice

Over-expression of human FGF-2 cDNA linked to the phosphoglycerate kinase promoter in transgenic (TgFGF2) mice resulted in a dwarf mouse with premature closure of the growth plate and shortening of bone length. This study was designed to further characterize bone structure and remodeling in these mice. Bones of 1-6 month-old wild (NTg) and TgFGF2 mice were studied. FGF-2 protein levels were higher in bones of TgFGF2 mice. Bone mineral density was significantly decreased as early as 1 month in femurs from TgFGF2 mice compared with NTg mice. Micro-CT of trabecular bone of the distal femurs from 6-month-old TgFGF2 mice revealed significant reduction in trabecular bone volume, trabecular number (Tb.N), and increased trabecular separation (Tb.Sp). Osteoblast surface/bone surface, double-labeled surface, mineral apposition rate, and bone formation rates were all significantly reduced in TgFGF2 mice. There were fewer TRAP positive osteoclasts in calvaria from TgFGF2 mice. Quantitative histomorphometry showed that total bone area was similar in both genotypes, however percent osteoclast surface, and osteoclast number/bone surface were significantly reduced in TgFGF2 mice. Increased replication of TgFGF2 calvarial osteoblasts was observed and primary cultures of bone marrow stromal cells from TgFGF2 expressed markers of mature osteoblasts but formed fewer mineralized nodules. The data presented indicate that non-targeted over-expression of FGF-2 protein resulted in decreased endochondral and intramembranous bone formation. These results are consistent with FGF-2 functioning as a negative regulator of postnatal bone growth and remodeling in this animal model.     

Age-related changes in microarchitecture and mineralization of cancellous bone in the porcine mandibular condyle

The mandibular condyle is considered a good model for developing cancellous bone because of its rapid growth and high rate of remodeling. The aim of the present study was to analyze the simultaneous changes in microarchitecture and mineralization of cancellous bone during development in a three-dimensional fashion. Eight mandibular condyles of pigs aged 8 weeks prepartum to 108 weeks postpartum were scanned using microCT with an isotropic spatial resolution of 10 microm. The number of trabeculae decreased during development, whereas both the trabecular thickness and the distance between the trabeculae increased. The bone surface to volume ratio decreased during development, possibly limiting the amount of (re)modeling. Both the mean degree of mineralization and intratrabecular differences in mineralization between the surfaces and cores of trabecular elements increased during development. The trabecular surfaces were more highly mineralized in the older condyles compared to the younger ones. Together with the observed decrease in the relative size of trabecular surface, this finding suggests a decrease in (re)modeling activity during development. In accordance with the general growth and development of the pig, it was concluded that most developmental changes in cancellous bone occur until the age of 40 weeks postpartum.     

Amelioration of type I diabetes-induced osteoporosis by parathyroid hormone is associated with improved osteoblast survival

Type 1 diabetic osteoporosis results from impaired osteoblast activity and death. Therefore, anti-resorptive treatments may not effectively treat bone loss in this patient population. Intermittent parathyroid hormone (PTH) treatment stimulates bone remodeling and increases bone density in healthy subjects. However, PTH effects may be limited in patients with diseases that interfere with its signaling. Here, we examined the ability of 8 and 40 μg/kg intermittent PTH to counteract diabetic bone loss. PTH treatment reduced fat pad mass and blood glucose levels in non-diabetic PTH-treated mice, consistent with PTH-affecting glucose homeostasis. However, PTH treatment did not significantly affect general body parameters, including the blood glucose levels, of type 1 diabetic mice. We found that the high dose of PTH significantly increased tibial trabecular bone density parameters in control and diabetic mice, and the lower dose elevated trabecular bone parameters in diabetic mice. The increased bone density was due to increased mineral apposition and osteoblast surface, all of which are defective in type 1 diabetes. PTH treatment suppressed osteoblast apoptosis in diabetic bone, which could further contribute to the bone-enhancing effects. In addition, PTH treatment (40 μg/kg) reversed preexisting bone loss from diabetes. We conclude that intermittent PTH may increase type 1 diabetic trabecular bone volume through its anabolic effects on osteoblasts.     

Computational simulation of simultaneous cortical and trabecular bone change in human proximal femur during bone remodeling

In this study, we developed a numerical framework that computationally determines simultaneous and interactive structural changes of cortical and trabecular bone types during bone remodeling, and we investigated the structural correlation between the two bone types in human proximal femur. We implemented a surface remodeling technique that performs bone remodeling in the exterior layer of the cortical bone while keeping its interior area unchanged. A micro-finite element (μFE) model was constructed that represents the entire cortical bone and full trabecular architecture in human proximal femur. This study simulated and compared the bone adaptation processes of two different structures: (1) femoral bone that has normal cortical bone shape and (2) perturbed femoral bone that has an artificial bone lump in the inferomedial cortex. Using the proposed numerical method in conjunction with design space optimization, we successfully obtained numerical results that resemble actual human proximal femur. The results revealed that actual cortical bone, as well as the trabecular bone, in human proximal femur has structurally optimal shapes, and it was also shown that a bone abnormality that has little contribution to bone structural integrity tends to disappear. This study also quantitatively determined the structural contribution of each bone: when the trabecular adaptation was complete, the trabecular bone supported 54% of the total load in the human proximal femur while the cortical bone carried 46%.     

The role of mineral content in determining the micromechanical properties of discrete trabecular bone remodeling packets

In trabecular bone, each remodeling event results in the resorption and/or formation of discrete structural units called ‘packets’. These remodeling packets represent a fundamental level of bone’s structural hierarchy at which to investigate composition and mechanical behaviors. The objective of this study was to apply the complementary techniques of quantitative backscattered electron microscopy (qBSEM) and nanoindentation to investigate inter-relationships between packet mineralization, elastic modulus, contact hardness and plastic deformation resistance. Indentation arrays were performed across nine trabecular spicules from 3 human donors; these spicules were then imaged using qBSEM, and discretized into their composite remodeling packets (127 in total). Packets were classified spatially as peripheral or central, and mean contact hardness, plastic deformation resistance, elastic modulus and calcium content calculated for each. Inter-relationships between measured parameters were analysed using linear regression analyses, and dependence on location assessed using Student’s t-tests. Significant positive correlations were found between all mechanical parameters and calcium content. Elastic modulus and contact hardness were significantly correlated, however elastic modulus and plastic deformation resistance were not. Calcium content, contact hardness and elastic modulus were all significantly higher for central packets than for peripheral, confirming that packet mineral content contributes to micromechanical heterogeneity within individual trabecular spicules. Plastic deformation resistance, however, showed no such regional dependence, indicating that the plastic deformation properties in particular, are determined not only by mineral content, but also by the organic matrix and interactions between these two components.     

Capturing microscopic features of bone remodeling into a macroscopic model based on biological rationales of bone adaptation

To understand Wolff’s law, bone adaptation by remodeling at the cellular and tissue levels has been discussed extensively through experimental and simulation studies. For the clinical application of a bone remodeling simulation, it is significant to establish a macroscopic model that incorporates clarified microscopic mechanisms. In this study, we proposed novel macroscopic models based on the microscopic mechanism of osteocytic mechanosensing, in which the flow of fluid in the lacuno-canalicular porosity generated by fluid pressure gradients plays an important role, and theoretically evaluated the proposed models, taking biological rationales of bone adaptation into account. The proposed models were categorized into two groups according to whether the remodeling equilibrium state was defined globally or locally, i.e., the global or local uniformity models. Each remodeling stimulus in the proposed models was quantitatively evaluated through image-based finite element analyses of a swine cancellous bone, according to two introduced criteria associated with the trabecular volume and orientation at remodeling equilibrium based on biological rationales. The evaluation suggested that nonuniformity of the mean stress gradient in the local uniformity model, one of the proposed stimuli, has high validity. Furthermore, the adaptive potential of each stimulus was discussed based on spatial distribution of a remodeling stimulus on the trabecular surface. The theoretical consideration of a remodeling stimulus based on biological rationales of bone adaptation would contribute to the establishment of a clinically applicable and reliable simulation model of bone remodeling.     

The skeleton in primary hyperparathyroidism: a review focusing on bone remodeling, structure, mass, and fracture.

The mechanisms behind the influence of PHPT on the skeleton are closely connected with bone turnover. Throughout life, the skeleton is continuously renewed by bone remodeling, a process which serves the purpose of repairing damaged bone and adapting the skeleton to changes in physical load. In this process, old bone is removed by osteoclastic resorption and new bone is laid down by osteoblastic formation. Bone mass increases with growth in the first decades of life, and around the age of 30 years the peak bone mass is reached. Thereafter, as a result of mechanisms involving bone remodeling, a net bone loss is seen: 1) A reversible bone loss because of increase in the remodeling space, i.e., the amount of bone resorped but not yet reformed during the remodeling cycle. This mechanism leads to decrease in average trabecular thickness and cortical width, and to increase in cortical porosity. 2) An irreversible bone loss caused by negative bone balance, where the amount of bone formed by the osteoblasts is exceeded by the amount of bone resorbed by the osteoclasts at the same remodeling site. Consequently, progressive thinning of trabecular elements, reduced cortical width and increased cortical porosity is seen. 3) Finally, perforation of trabecular plates by deep resorption lacunae leads to complete irreversible removal of structural bone components. Parathyroid hormone, together with vitamin D, are the principal modulators in calcium homeostasis. The main actions of PTH are executed in bone and kidneys. In the kidneys, PTH increases the tubular re-absorption of calcium, thereby tending to increase serum calcium. PTH also induces increased conversion of 25(OH)-D to 1,25(OH)2-D. This last action, enhances intestinal calcium absorption and increased skeletal calcium mobilization, which further adds to the circulating calcium pool. In bone, the "acute" regulatory actions of PTH on serum calcium are probably accompliced via activation of osteocytes and lining cells. A second mechanism of PTH in bone is the regulation of bone remodeling. The action seems to be an increased recruitment from osteoblastic precursor cells and activation of mature osteoclasts. It is supposed that these responses are predominantly mediated indirectly through actions on osteoblast-like or nonosteoblast-like stromal cells, as osteoclasts themselves to not have PTH receptors. Bone metabolism and bone mass are studied by biochemical bone markers, bone histomorphometry, and densitometry. As bone markers and bone histomorphometry give information on bone metabolism from different points of view, these methods are preferably combined. Histomorphometry gives detailed information about bone turnover on cellular level, the whole remodeling sequence is described, and the bone balance can be calculated. However, they focus on a small volume, and may, therefore, not be representative for the whole skeleton. On the other hand, studies of bone markers supply general information about turnover in the whole skeleton, but they do not give facts on the bone turnover on the cellular or tissue level and bone balance. Bone densitometry is the principal method in studying bone mass, but valuable information concerning bone structure also comes from histomorphometry. Bone remodeling is considerably increased in PHPT. Studies of bone markers show increase in both resorptive and formative markers, and the increases seem to be of equivalent size. This is in agreement with histomorphometric findings and shows that the coupling between resorption and formation is preserved. By histomorphometry on iliac crest biopsies, trabecular bone remodeling is found increased by 50%, judged by the increase in activation frequency; a measure of how often new remodeling is initiated on the trabecular bone surface. In PHPT, such remodeling activity is repeated about once every year. Reconstruction of the whole remodeling sequence does not show major deviations in lengths of the resorptive and formative periods compared to normal. Furthermore, the amount of bone removed by the osteoclasts during the resorptive phase is matched by the amount of new bone formed by the osteoblasts leading to a bone balance very close to zero. Compared with trabecular bone, the turnover rate in cortical bone is considerably lower, around 10%. Remodeling of the cortical bone takes place at the endocortical, the pericortical, and the Haversian surfaces. Endocortical bone remodeling activities are very similar to trabecular remodeling activities with good correlation between individual parameters. Periosteal remodeling activity is negligible in PHPT, as it is in the normal state. Cortical porosity, which reflects the remodeling activity on the Haversian surface, is increased by 30-65% in PHPT. (ABSTRACT TRUNCATED)     

Possible case of hyperparathyroidism in a Roman period skeleton from the Dakhleh Oasis, Egypt, diagnosed using bone histomorphometry

A histomorphometric study of thin femoral head sections of a skeletal sample from the Dakhleh Oasis, Egypt, dated from circa 36 B.C. to 400 A.D., identified an adult female (Dk31-A1) in her mid-50s with a high percentage resorption surface with tunneling resorption as is typically found in hyperparathyroidism. Five static histomorphometric bone parameters were measured with the following results for this individual: 1) mean wall thickness, 41.94 micron, 2) trabecular bone volume, 18.54%, 3) surface volume, 4,070 mm2/cm3, 4) mean trabecular diameter, 132 microns, and 5) total resorption surface, 12.31%. The overall histomorphometric features and differential diagnosis support the diagnosis of hyperparathyroidism. We conclude that histomorphometry of dried bone, particularly in this case where preservation is ideal, is a valuable investigative technique for paleopathology.     

A cellular solid criterion for predicting the axial-shear failure properties of bovine trabecular bone.

In a long-term effort to develop a complete multi-axial failure criterion for human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai-Wu, Principal Strain, and von Mises phenomenological criteria--all normalized to minimize effects of interspecimen heterogeneity of strength--to predict the on-axis axial-shear failure properties of bovine trabecular bone. The Cellular Solid criterion that was developed here assumed that vertical trabeculae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, respectively. Twenty-seven bovine tibial trabecular bone specimens were destructively tested on-axis without end artifacts, loaded either in combined tension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6). For compression-shear, the mean (+/- S.D.) percentage errors between measured values and criterion predictions were 7.7 +/- 12.6 percent, 19.7 +/- 23.2 percent, 22.8 +/- 18.9 percent, and 82.4 +/- 64.5 percent for the Cellular Solid, Tsai-Wu, Principal Strain, and von Mises criteria, respectively; corresponding mean errors for tension-shear were -5.2 +/- 11.8 percent, 14.3 +/- 12.5 percent, 6.9 +/- 7.6 percent, and 57.7 +/- 46.3 percent. Statistical analysis indicated that the Cellular Solid criterion was the best performer for compression-shear, and performed as well as the Principal Strain criterion for tension-shear. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More importantly, the results firmly establish the importance of cellular solid analysis for understanding and predicting the multiaxial failure behavior of trabecular bone.     

Trabecular bone remodeling around smooth and porous implants in an equine patellar model

The objective of this investigation was to examine the stress-morphology relationships for trabecular bone around implants with different surface characteristics. Stainless steel spheres with either a polished surface or a sintered-bead porous coating were implanted unilaterally into equine patellae and maintained for a 6 month period. Stereological methods were used to quantify the trabecular bone morphology and finite element analyses were performed to predict the trabecular bone stresses. In general, the remodeling response around the smooth implants was greater than that around those porous implants that exhibited bone ingrowth. In accordance with these differences, the finite element models predicted greater changes in the stresses adjacent to the smooth implants due to the nonlinear boundary conditions. However, it did not appear that the trajectorial theory, in its simplest form, was applicable to the remodeling induced by the implants. A linear relationship between the change in bone areal density and the change in von Mises effective stress provides support for the hypothesis that the architecture of trabecular bone corresponds to an optimal structure. The results also demonstrated that, under certain circumstances, small changes in the stress state may result in large changes in the principal material orientation.     

Predicting changes in mechanical properties of trabecular bone by adaptive remodeling

Because changes in the mechanical properties of bone are closely related to trabecular bone remodeling, methods that consider the temporal morphological changes induced by adaptive remodeling of trabecular bone are needed to estimate long-term fracture risk and bone quality in osteoporosis. We simulated bone remodeling using simplified and pig trabecular bone models and estimated the morphology of healthy and osteoporotic cases. We then displayed the fracture risk of the remodeled models based on a cumulative histogram from high stress. The histogram showed more elements had higher stresses in the osteoporosis model, indicating that the osteoporosis model had a greater risk.     

The effect of surface roughness on the stress adaptation of trabecular architecture around a cylindrical implant

The effect of implant-bone bonding and the effect of implant surface roughness on bone remodeling near the bone-implant interface were studied by using a surface remodeling theory and the boundary element method. The study has shown that implant attachment plays an important role in bone remodeling near the implant. It has been observed in animal experiments and in clinical situations that the remodeled trabecular bone architecture around a cylindrical implant could vary, on one hand, from a hub surrounding the implant with a set of external spokes to, on the other hand, a hubless situation in which a set of spokes attach directly to the implant. It is shown here that the difference in these structures may be attributed to differences in implant attachment. The results show that the bone with perfect bonding or roller boundary condition without a gap remodeled to a hubless spoke trabecular bone architecture. On the other hand, the roller boundary condition with a specified gap yielded a spoke trabecular architecture with a hub or ring surrounding the implant. These quantitative results mirror the experimental and clinical observations. It is concluded that the hub is a consequence of the gap and not a consequence of the lack of friction between the implant and the bone.