Partial gravity unloading inhibits bone healing responses in a large animal model

The reduction in mechanical loading associated with space travel results in dramatic decreases in the bone mineral density (BMD) and mechanical strength of skeletal tissue resulting in increased fracture risk during spaceflight missions. Previous rodent studies have highlighted distinct bone healing differences in animals in gravitational environments versus those during spaceflight. While these data have demonstrated that microgravity has deleterious effects on fracture healing, the direct translation of these results to human skeletal repair remains problematic due to substantial differences between rodent and human bone. Thus, the objective of this study was to investigate the effects of partial gravitational unloading on long-bone fracture healing in a previously-developed large animal Haversian bone model. In vivo measurements demonstrated significantly higher orthopedic plate strains (i.e. load burden) in the Partial Unloading (PU) Group as compared to the Full Loading (FL) Group following the 28-day healing period due to inhibited healing in the reduced loading environment. DEXA BMD in the metatarsus of the PU Group decreased 17.6% (p<0.01) at the time of the ostectomy surgery. Four-point bending stiffness of the PU Group was 4.4 times lower than that of the FL Group (p<0.01), while µCT and histomorphometry demonstrated reduced periosteal callus area (p<0.05), mineralizing surface (p<0.05), mineral apposition rate (p<0.001), bone formation rate (p<0.001), and periosteal/endosteal osteoblast numbers (p<0.001/p<0.01, respectively) as well as increased periosteal osteoclast number (p<0.05). These data provide strong evidence that the mechanical environment dramatically affects the fracture healing cascade, and likely has a negative impact on Haversian system healing during spaceflight.     

Impact loading history modulates hip fracture load and location: A finite element simulation study of the proximal femur in female athletes

Sideways falls impose high stress on the thin superolateral cortical bone of the femoral neck, the region regarded as a fracture-prone region of the hip. Exercise training is a natural mode of mechanical loading to make bone more robust. Exercise-induced adaptation of cortical bone along the femoral neck has been previously demonstrated. However, it is unknown whether this adaption modulates hip fracture behavior. The purpose of this study was to investigate the influence of specific exercise loading history on fall-induced hip fracture behavior by estimating fracture load and location with proximal femur finite element (FE) models created from magnetic resonance images (MRI) of 111 women with distinct exercise histories: 91 athletes (aged 24.7 ± 6.1 years, >8 years competitive career) and 20 women as controls (aged 23.7 ± 3.8 years). The athletes were divided into five groups based on typical loading patterns of their sports: high-impact (H-I: 9 triple-jumpers and 10 high jumpers), odd-impact (O-I: 9 soccer and 10 squash players), high-magnitude (H-M: 17 power-lifters), repetitive-impact (R-I: 18 endurance runners), and repetitive non-impact (R-NI: 18 swimmers). Compared to the controls, the H-I, O-I, and R-I groups had significantly higher (11–26%, p < 0.05) fracture loads. Also, the fracture location in the H-I and O-I groups was significantly more proximal (7–10%) compared to the controls. These results suggest that an exercise loading history of high impacts, impacts from unusual directions, or repetitive impacts increases the fracture load and may lower the risk of fall-induced hip fracture.     

Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements

The mechanical properties of cancellous bone and the biological response of the tissue to mechanical loading are related to deformation and strain in the trabeculae during function. Due to the small size of trabeculae, their motion is difficult to measure. To avoid the need to measure trabecular motions during loading the finite element method has been used to estimate trabecular level mechanical deformation. This analytical approach has been empirically successful in that the analytical models are solvable and their results correlate with the macroscopically measured stiffness and strength of bones. The present work is a direct comparison of finite element predictions to measurements of the deformation and strain at near trabecular level. Using the method of digital volume correlation, we measured the deformation and calculated the strain at a resolution approaching the trabecular level for cancellous bone specimens loaded in uniaxial compression. Smoothed results from linearly elastic finite element models of the same mechanical tests were correlated to the empirical three-dimensional (3D) deformation in the direction of loading with a coefficient of determination as high as 97% and a slope of the prediction near one. However, real deformations in the directions perpendicular to the loading direction were not as well predicted by the analytical models. Our results show, that the finite element modeling of the internal deformation and strain in cancellous bone can be accurate in one direction but that this does not ensure accuracy for all deformations and strains.     

Adaptive changes in micromechanical environments of cancellous and cortical bone in response to in vivo loading and disuse

The skeleton accommodates changes in mechanical environments by increasing bone mass under increased loads and decreasing bone mass under disuse. However, little is known about the adaptive changes in micromechanical behavior of cancellous and cortical tissues resulting from loading or disuse. To address this issue, in vivo tibial loading and hindlimb unloading experiments were conducted on 16-week-old female C57BL/6J mice. Changes in bone mass and tissue-level strains in the metaphyseal cancellous and midshaft cortical bone of the tibiae, resulting from loading or unloading, were determined using microCT and finite element (FE) analysis, respectively. We found that loading- and unloading-induced changes in bone mass were more pronounced in the cancellous than cortical bone. Simulated FE-loading showed that a greater proportion of elements experienced relatively lower longitudinal strains following load-induced bone adaptation, while the opposite was true in the disuse model. While the magnitudes of maximum or minimum principal strains in the metaphyseal cancellous and midshaft cortical bone were not affected by loading, strains oriented with the long axis were reduced in the load-adapted tibia suggesting that loading-induced micromechanical benefits were aligned primarily in the loading direction. Regression analyses demonstrated that bone mass was a good predictor of bone tissue strains for the cortical bone but not for the cancellous bone, which has complex microarchitecture and spatially-variant strain environments. In summary, loading-induced micromechanical benefits for cancellous and cortical tissues are received primarily in the direction of force application and cancellous bone mass may not be related to the micromechanics of cancellous bone.     

The effects of tensile-compressive loading mode and microarchitecture on microdamage in human vertebral cancellous bone

The amount of microdamage in bone tissue impairs mechanical performance and may act as a stimulus for bone remodeling. Here we determine how loading mode (tension vs. compression) and microstructure (trabecular microarchitecture, local trabecular thickness, and presence of resorption cavities) influence the number and volume of microdamage sites generated in cancellous bone following a single overload. Twenty paired cylindrical specimens of human vertebral cancellous bone from 10 donors (47–78 years) were mechanically loaded to apparent yield in either compression or tension, and imaged in three dimensions for microarchitecture and microdamage (voxel size 0.7×0.7×5.0 μm³). We found that the overall proportion of damaged tissue was greater (p=0.01) for apparent tension loading (3.9±2.4%, mean±SD) than for apparent compression loading (1.9±1.3%). Individual microdamage sites generated in tension were larger in volume (p<0.001) but not more numerous (p=0.64) than sites in compression. For both loading modes, the proportion of damaged tissue varied more across donors than with bone volume fraction, traditional measures of microarchitecture (trabecular thickness, trabecular separation, etc.), apparent Young?s modulus, or strength. Microdamage tended to occur in regions of greater trabecular thickness but not near observable resorption cavities. Taken together, these findings indicate that, regardless of loading mode, accumulation of microdamage in cancellous bone after monotonic loading to yield is influenced by donor characteristics other than traditional measures of microarchitecture, suggesting a possible role for tissue material properties.     

The discrete nature of trabecular bone microarchitecture affects implant stability

Small endosseous implants, such as screws, are important components of modern orthopedics and dentistry. Hence they have to reliably fulfill a variety of requirements, which makes the development of such implants challenging. Finite element analysis is a widely used computational tool used to analyze and optimize implant stability in bone. For these purposes, bone is generally modeled as a continuum material. However, bone failure and bone adaptation processes are occurring at the discrete level of individual trabeculae; hence the assessment of stresses and strains at this level is relevant. Therefore, the aim of the present study was to investigate how peri-implant strain distribution and load transfer between implant and bone are affected by the continuum assumption. We performed a computational study in which cancellous screws were inserted in continuum and discrete models of trabecular bone; axial loading was simulated. We found strong differences in bone-implant stiffness between the discrete and continuum bone model. They depended on bone density and applied boundary conditions. Furthermore, load transfer from the screw to the surrounding bone differed strongly between the continuum and discrete models, especially for low-density bone. Based on our findings we conclude that continuum bone models are of limited use for finite element analysis of peri-implant mechanical loading in trabecular bone when a precise quantification of peri-implant stresses and strains is required. Therefore, for the assessment and improvement of trabecular bone implants, finite element models which accurately represent trabecular microarchitecture should be used.     

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.     

Mechanical significance of femoral head trabecular bone structure in Loris and Galago evaluated using micromechanical finite element models

Work on the interspecific and intraspecific variation of trabecular bone in the proximal femur of primates demonstrates important architectural variation between animals with different locomotor behaviors. This variation is thought to be related to the processes of bone adaptation whereby bone structure is optimized to the mechanical environment. Micromechanical finite element models were created for the proximal femur of the leaping Galago senegalensis and the climbing and quadrupedal Loris tardigradus by converting bone voxels from high-resolution X-ray computed tomography scans of the femoral head to eight-noded brick elements. The resulting models had approximately 1.8 million elements each. Loading conditions representing takeoff phase of a leap and more generalized load orientations were applied to the models, and the models were solved using the iterative "row-by-row" matrix-vector multiplication algorithm. The principal strain and Von Mises stress results for the leaping model were similar for both species at each load orientation. Similar hip joint reaction forces in the range of 4.9 x to 12 x body weight were calculated for both species under each loading condition, but the hip reaction values estimated for Loris were higher than predicted based on locomotor behavior. These results suggest that functional adaptation to hip joint loading may not fully explain the differences in femoral head trabecular bone structure in Galago and Loris. The finite element method represents a unique and useful tool for analyzing the functional adaptation of trabecular bone in a diversity of animals and for reconstructing locomotor behavior in extinct taxa.     

Material Changes in Osteoporotic Human Cancellous Bone Following Infiltration with Acrylic Bone Cement for a Vertebral Cement Augmentation

Bone cement infiltration can be effective at mechanically augmenting osteoporotic vertebrae. While most published literature describes the gain in mechanical strength of augmented vertebrae, we report the first measurements of viscoelastic material changes of cancellous bone due to cement infiltration. We infiltrated cancellous core specimen harvested from osteoporotic cadaveric spines with acrylic bone cement. Bone specimen before and after cement infiltration were subjected to identical quasi-static and relaxation loading in confined and free compression. Testing data were fitted to a linear viscoelastic model of compressible material and the model parameters for cement, native cancellous bone, and cancellous bone infiltrated (composite) with cement were identified. The fitting demonstrated that the linear viscoelastic model presented in this paper accurately describes the mechanical behaviour of cement and bone, before and after infiltration. Although the composite specimen did not completely adopt the properties of bulk bone cement, the stiffening of cancellous bone due to cement infiltration is considerable. The composite was, for example, 8.5 times stiffer than native bone. The local stiffening of cancellous bone in patients may alter the load transfer of the augmented motion segment and may be the cause of subsequent fractures in the vertebrae adjacent to the ones infiltrated with cement. The material model and parameters in this paper, together with an adequate finite-element model, can be helpful to investigate the load shift, the mechanism for subsequent fractures, and filling patterns for ideal cement infiltration.     

An in vivo model of a mechanically-induced bone marrow lesion

Bone marrow lesions (BMLs) are radiologic abnormalities in magnetic resonance images of subchondral bone that are correlated with osteoarthritis. Little is known about the physiologic processes within a BML, although BMLs are associated with mechanical stress, bone tissue microdamage and increased bone remodeling. Here we establish a rabbit model to study the pathophysiology of BMLs. We hypothesized that in vivo loads that generate microdamage in cancellous bone would also create BMLs and increase bone remodeling. In vivo cyclic loading (0.2–2.0 MPa in compression for 10,000 cycles at 2 Hz) was applied to epiphyseal cancellous bone in the distal femurs of New Zealand white rabbits (n = 3, right limb loaded, left limb controls experienced surgery but no loading). Magnetic resonance images were collected using short tau inversion recovery (STIR) and T1 weighted sequences at 1 and 2 weeks after surgery/loading and histological analysis of the BML was performed after euthanasia to examine tissue microdamage and remodeling. Loaded limbs displayed BMLs while control limbs showed only a small BML-like signal caused by surgery. Histological analysis of the BML at 2 weeks after loading showed increased tissue microdamage (p = 0.03) and bone resorption (p = 0.01) as compared to controls. The model described here displays the hallmarks of load-induced BMLs, supporting the use of the model to examine changes in bone during the development, progression and treatment of BMLs.     

Mechanical effects of load speed on the human colon

The aim of this study was to examine the mechanical behavior of the colon using tensile tests under different loading speeds.Specimens were taken from different locations of the colonic frame from refrigerated cadavers. The specimens were submitted to uniaxial tensile tests after preconditioning using a dynamic load (1 m/s), intermediate load (10 cm/s), and quasi-static load (1 cm/s).A total of 336 specimens taken from 28 colons were tested. The stress-strain analysis for longitudinal specimens indicated a Young’s modulus of 3.17 ± 2.05 MPa under dynamic loading (1 m/s), 1.74 ± 1.15 MPa under intermediate loading (10 cm/s), and 1.76 ± 1.21 MPa under quasi-static loading (1 cm/s) with p < 0.001. For the circumferential specimen, the stress-strain curves indicated a Young’s modulus of 3.15 ± 1.73 MPa under dynamic loading (1 m/s), 2.14 ± 1.3 MPa under intermediate loading (10 cm/s), and 0.63 ± 1.25 MPa under quasi-static loading (1 cm/s) with p < 0.001. The curves reveal two types of behaviors of the colon: fast break behavior at high speed traction (1 m/s) and a lower break behavior for lower speeds (10 cm/s and 1 cm/s). The circumferential orientation required greater levels of stress and strain to obtain lesions than the longitudinal orientation. The presence of taeniae coli changed the mechanical response during low-speed loading.Colonic mechanical behavior varies with loading speeds with two different types of mechanical behavior: more fragile behavior under dynamic load and more elastic behavior for quasi-static load.     

Predicting bone remodeling around tissue- and bone-level dental implants used in reduced bone width

The objective of this study was to predict time-dependent bone remodeling around tissue- and bone-level dental implants used in patients with reduced bone width. The remodeling of bone around titanium tissue-level, and titanium and titanium–zirconium alloy bone-level implants was studied under 100 N oblique load for one month by implementing the Stanford theory into three-dimensional finite element models. Maximum principal stress, minimum principal stress, and strain energy density in peri-implant bone and displacement in x- and y- axes of the implant were evaluated. Maximum and minimum principal stresses around tissue-level implant were higher than bone-level implants and both bone-level implants experienced comparable stresses. Total strain energy density in bone around titanium implants slightly decreased during the first two weeks of loading followed by a recovery, and the titanium–zirconium implant showed minor changes in the axial plane. Total strain energy density changes in the loading and contralateral sides were higher in tissue-level implant than other implants in the cortical bone at the horizontal plane. The displacement values of the implants were almost constant over time. Tissue-level implants were associated with higher stresses than bone-level implants. The time-dependent biomechanical outcome of titanium–zirconium alloy bone-level implant was comparable to the titanium implant.     

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.     

A theoretical model to predict distribution of the fabric tensor and apparent density in cancellous bone

 The adaptation of cancellous bone to mechanical forces is well recognized. Theoretical models for predicting cancellous bone architecture have been developed and have mainly focused on the distribution of trabecular mass or the apparent density. The purpose of this study was to develop a theoretical model which can simultaneously predict the distribution of trabecular orthotropy/orientation, as represented by the fabric tensor, along with apparent density. Two sets of equations were derived under the assumption that cancellous bone is a biological self-optimizing material which tends to minimize strain energy. The first set of equations provide the relationship between the fabric tensor and stress tensor, and have been verified to be consistent with Wolff’s law of trabecular architecture, that is, the principal directions of the fabric tensor coincide with the principal stress trajectories. The second set of equations yield the apparent density from the stress tensor, which was shown to be identical to those obtained based on local optimization with strain energy density of true bone tissue as the objective function. These two sets of equations, together with elasticity field equations, provide a complete mathematical formulation for the adaptation of cancellous bone. Received: 25 February 1997/Revised version: 23 September 1997     

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

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

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.     

Stress intensity variations in bone microcracks during the repair process

Microscopic cracks form and grow in compact bone in vivo due to cyclic loading. Their growth can cause stress fractures and has been implicated in the processes of remodelling and adaptation. These cracks are repaired by the actions of BMUs which are mobile resorption cavities. In this work, we studied the interaction between cracks and BMUs by making finite element models representing different stages in the repair process. The tendency of the crack to grow was measured by its stress intensity factor, K. We found that K changes in a complex manner during the repair process, both decreasing and increasing depending on the size of the crack and the type of loading applied. For loading conditions similar to those that exist in vivo, the presence of the BMU can cause K to rise significantly, in some cases by more than 20%, implying a substantial increase in crack growth rate. This information is important for our general understanding of the complexities of the repair process, and especially for the development of theoretical models to simulate damage and repair in bone.     

Relationship between nutrition factors and osteopenia: Effects of experimental diets on immature bone quality

To investigate the influence of experimental diets on morphological and mechanical characteristics of immature bone, this study thoroughly examined the nutrition–bone connection. A non-destructive evaluation method involving high-resolution in-vivo micro-computed tomography and finite element (FE) analysis was used to investigate the relationship between obesity and osteopenia—two disorders of body composition. Correlation of nutritional deficiency with bone characteristics was also investigated. Some recent studies have shown that both obesity and osteopenia share several common genetic and environmental factors. However, there have been few studies correlating these pathologies in-vivo from a structural and biomechanical point of view. In the present study, detailed changes in morphological and mechanical characteristics of trabecular bone architecture were detected and tracked by longitudinal studies of morphometric parameters and simulated compression testing. Rats were randomized into three groups: overeaten diet (OD) for formation of obesity, normal diet (ND), and restricted diet (RD) in which rats received 65% of the normal diet. In the OD and ND groups, all structural parameters changed significantly (p<0.05). The degree of alteration in the structural parameters of the ND group was similar to that of the RD group (p<0.05). In simulated compression tests using FE models, the effective modulus of the OD group significantly decreased, depending on measuring time (p<0.05), whereas that of the ND and RD groups significantly increased (p>0.05). The key finding of the present study is that fat mass is morphologically and mechanically inversely correlated with bone mass when the mechanical loading effects of greater body weight on bone mass are applied.     

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.     

The influence of mechanical stimulation on osteoclast localization in the mouse maxilla: bone histomorphometry and finite element analysis

The mechanism of traumatic bone resorption in the denture-bearing bone has not yet been established with regard to the osteoclastic activity in relation to the mechanical stimulus. The purpose of this study was to clarify whether osteoclast appearance in maxilla depends on the strain intensity, using the murine loading model. The maxillary palate of thirteen-week-old male C57BL/6 mice was subjected to continuous pressure of 2 kPa (low stimulation, n = 4) or 7 kPa (high stimulation, n = 4) for 30 min/day for 7 consecutive days, and the mice were sacrificed after the last loading. The control group underwent the same protocol without load (n = 4). An animal-specific finite element model was constructed based on morphology and characteristics obtained from the micro-CT data and used to calculate the strain intensity of the bone. The bone histomorphometric technique revealed significant reduction of cortical bone volume and significant increase of bone resorption parameters such as osteoclast number in the bone tissue under the loading contact in comparison to the control (p < 0.05). The osteoclasts were observed in the subsurface region adjacent to the loading contact and the peripheral region of the marrow space in the intracortical region of the cortical bone in the mouse maxilla in both stimulation groups. An average of more than 90 % of the osteoclasts was observed in the areas with strain intensity higher than 85.0μ strain for the high stimulation group. The result suggests that the osteoclastic resorption is location-dependent and is also sensitive to the local strain intensity.