A comparison of the fatigue behavior of human trabecular and cortical bone tissue

The fatigue properties of trabecular bone tissue (single trabeculae) and similarly sized cortical bone specimens from human tibia were experimentally determined on a microstructural level using four-point bending cyclic tests, and they were compared based on modulus, mineral density, and microstructural characteristics. The results showed that trabecular specimens had significantly lower moduli and lower fatigue strength than cortical specimens, despite their higher mineral density values. Fracture surface and microdamage analyses illustrated different fracture and damage patterns between trabecular and cortical bone tissue, depending upon their microstructural characteristics. Based on the results from mechanical tests and qualitative observations, a possible mechanical role of the cement lines in trabecular tissue microfracture was suggested.     

The effect of age, sex, and physical activity on entheseal morphology in a contemporary Italian skeletal collection

Entheseal changes are traditionally included in a large array of skeletal features commonly referred to as "skeletal markers of activity." However, medical studies and recent anthropological analyses of identified skeletal series suggest a complex combination of physiological and biomechanical factors underlying the variability of such "markers." The aim of this study is to examine the relationship between age, sex, physical activity, and entheseal variability. To this end, 23 postcranial entheses are examined in a large (N = 484) Italian contemporary skeletal series using standardized scoring methods. The sample comprises subjects of known age, sex and, mostly, occupation. Results show a strong relationship between age and entheseal changes. Differences between sexes are also highlighted, while the effects of physical activity appear moderate. Altogether, our study indicates that entheseal morphology primarily reflects the age of an individual, while correlation with lifetime activity remains ambiguous.     

Regional,ontogenetic, and sex‐related variations in elastic properties of cortical bone in baboon mandibles

Understanding the mechanical features of cortical bone and their changes with growth and adaptation to function plays an important role in our ability to interpret the morphology and evolution of craniofacial skeletons. We assessed the elastic properties of cortical bone of juvenile and adult baboon mandibles using ultrasonic techniques. Results showed that, overall, cortical bone from baboon mandibles could be modeled as an orthotropic elastic solid. There were significant differences in the directions of maximum stiffness, thickness, density, and elastic stiffness among different functional areas, indicating regional adaptations. After maturity, the cortical bone becomes thicker, denser, and stiffer, but less anisotropic. There were differences in elastic properties of the corpus and ramus between male and female mandibles which are not observed in human mandibles. There were correlations between cortical thicknesses and densities, between bone elastic properties and microstructural configuration, and between the directions of maximum stiffness and bone anatomical axes in some areas. The relationships between bone extrinsic and intrinsic properties bring us insights into the integration of form and function in craniofacial skeletons and suggest that we need to consider both macroscopic form, microstructural variation, and the material properties of bone matrix when studying the functional properties and adaptive nature of the craniofacial skeleton in primates. The differences between baboon and human mandibles is at variance to the pattern of differences in crania, suggesting differences in bone adaption to varying skeletal geometries and loading regimes at both phylogenetic and ontogenetic levels. Am J Phys Anthropol, 2010. © 2009 Wiley‐Liss, Inc.     

A Comparison of Micro-CT and Dental CT in Assessing Cortical Bone Morphology and Trabecular Bone Microarchitecture

Objective

The objective of this study was to evaluate the relationship between the trabecular bone microarchitecture and cortical bone morphology by using micro-computed tomography (micro-CT) and dental cone-beam computed tomography (dental CT).

Materials and Methods

Sixteen femurs and eight fifth lumbar vertebrae were collected from eight male Sprague Dawley rats. Four trabecular bone microarchitecture parameters related to the fifth lumbar vertebral body (percent bone volume [BV/TV], trabecular thickness [TbTh], trabecular separation [TbSp], and trabecular number [TbN]) were calculated using micro-CT. In addition, the volumetric cancellous bone grayscale value (vCanGrayscale) of the fifth lumbar vertebral body was measured using dental CT. Furthermore, four cortical bone morphology parameters of the femoral diaphysis (total cross-sectional area [TtAr], cortical area [CtAr], cortical bone area fraction [CtAr/TtAr], and cortical thickness [CtTh]) were calculated using both micro-CT and dental CT. Pearson analysis was conducted to calculate the correlation coefficients (r) of the micro-CT and dental CT measurements. Paired-sample t tests were used to compare the differences between the measurements of the four cortical bone morphology parameters obtained using micro-CT and dental CT.

Results

High correlations between the vCanGrayscale measured using dental CT and the trabecular bone microarchitecture parameters (BV/TV [r = 0.84] and TbTh [r = 0.84]) measured using micro-CT were observed. The absolute value of the four cortical bone morphology parameters may be different between the dental CT and micro-CT approaches. However, high correlations (r ranged from 0.71 to 0.90) among these four cortical bone morphology parameters measured using the two approaches were obtained.

Conclusion

We observed high correlations between the vCanGrayscale measured using dental CT and the trabecular bone microarchitecture parameters (BV/TV and TbTh) measured using micro-CT, in addition to high correlations between the cortical bone morphology measured using micro-CT and dental CT. Further experiments are necessary to validate the use of dental CT on human 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.     

A comparative analysis of the microarchitecture of cortical membranous and cortical endochondral onlay bone grafts in the craniofacial skeleton

Previous work in this laboratory established that an onlay bone graft's survival is determined primarily by its relative cortical and cancellous composition rather than its embryologic origin. A volumetric analysis of external bone graft resorption, however, does not explain the internal microarchitectural changes that may be occurring as these grafts become incorporated. To expand the knowledge of bone graft dynamics beyond volumetric parameters, a better understanding of the internal processes of bone graft remodeling is needed. In this comparative study of cortical onlay bone graft microarchitecture, the authors propose to show that cortical onlay bone grafts undergo measurable internal microarchitectural changes as they become incorporated into the surrounding craniofacial skeleton. In addition, the authors propose to further demonstrate similarities between the internal microarchitecture of cortical onlay bone grafts of different embryologic origin over time. Twenty-five adult New Zealand White rabbits were used for this study. They were divided into two groups of eight animals and one group of nine. The groups were killed at 3, 8, and 16 weeks. Cortical membranous and endochondral bone grafts were placed subperiosteally onto each rabbit's cranium. In addition, five ungrafted cortical endochondral and membranous bone specimens were used as controls. Microcomputed tomography (MCT) scanning and histomorphometric analysis were performed on all of the specimens to obtain detailed information regarding the microarchitecture of the cortical bone grafts. The parameters of bone volume fraction, bone surface area to volume, mean trabecular number, and anisotropy were used to give quantitative information about a bone's micro-organization. The results showed that there is no statistically significant difference between the cortical endochondral and the cortical membranous bone grafts for bone volume fraction, bone surface to volume, mean trabecular number, and anisotropy measurements for all time points. There were, however, statistically significant differences when comparing the control and 3-week groups to the 16-week group for all parameters. The advanced MCT technology and histomorphometric techniques proved to be effective in providing a qualitative and quantitative ultrastructural comparison of cortical endochondral and membranous onlay bone grafts over time. In this study, a statistically significant change in the internal microarchitecture of cortical onlay bone grafts of different embryologic origins was seen as they were remodeled and resorbed at all time points. Specifically, the onlay cortical bone grafts developed a less dense, more trabecular, and less organized internal ultrastructure. In addition, no difference in the three-dimensional ultrastructure of cortical endochondral and membranous bone was found. These results challenge some of the currently accepted theories of bone-graft dynamics and may eventually lead to a change in the way clinicians approach bone-graft selection for craniofacial surgery.     

Functional plasticity of the human humerus: Shape,rigidity, and muscular entheses

The relationship between the mechanical loading undergone by a bone and its form has been widely assumed as a premise in studies aiming to reconstruct behavioral patterns from skeletal remains. Nevertheless, this relationship is complex due to the existence of many factors affecting bone structure and form, and further research combining structural and shape characteristics is needed. Using two‐block PLS, which is a test to analyze the covariance between two sets of variables, we aim to investigate the relationship between upper‐limb entheseal changes, cross‐sectional properties, and contour shape of the humeral diaphysis. Our results show that individuals with strongly marked entheseal changes have increased diaphyseal rigidities. Bending rigidities are mainly related to entheseal changes of muscles that cross the shoulder. Moreover, the entheseal changes of muscles that participate in the rotation of the arm are related to mediolaterally flatter and ventrodorsally broader humeral shapes in the mid‐proximal diaphysis. In turn, this diaphyseal shape is related to diaphyseal rigidity, especially to bending loadings. The shape of the diaphysis of the rest of the humerus does not covary either with rigidity or with entheseal changes. The results indicate that large muscular scars, such as those found in the mid‐proximal diaphyses, seem to be related to diaphyseal shape, whereas this relationship is not seen for areas with less direct influences of powerful muscles. Am J Phys Anthropol 150:609–617, 2013. © 2013 Wiley Periodicals, Inc.     

Trabecular eccentricity and bone adaptation

It is well established that bones functionally adapt by mechanisms that control tissue density, whole bone geometry, and trabecular orientation. In this study, we propose the existence of another such powerful mechanism, namely, trabecular eccentricity, i.e. non-central placement of trabecular bone within a cortical envelope. In the human femoral neck, trabecular eccentricity results in a thicker cortical shell on the inferior than superior aspect. In an overall context of expanding understanding of bone adaptation, the goal of this study was to demonstrate the biomechanical significance of, and provide a mechanistic explanation for, the relationship between trabecular eccentricity and stresses in the human femoral neck. Using composite beam theory, we showed that the biomechanical effects of eccentricity during a habitual loading situation were to increase the stress at the superior aspect of the neck and decrease the stress at the inferior aspect, resulting in an overall protective effect. Further, increasing eccentricity had a stress-reducing effect equivalent to that of increasing cortical thickness or increasing trabecular modulus. We conclude that an asymmetric placement of trabecular bone within a cortical bone envelope represents yet another mechanism by which whole bones can adapt to mechanical demands.     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

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.     

A Novel 3D Microstructural Model for Trabecular Bone: II. The Relationship Between Fabric and the Yield Surface

A novel 3D microstructural model was proposed and validated in part I of this publication. In part II, the model was used to identify the yield surface of a representative volume element of human trabecular bone as a function of volume fraction and degree of anisotropy. Finite element models of open and closed cells geometries were used to calculate effective yield stresses for a variety of loading cases with periodic boundary conditions. The postyield behaviour of the trabecular tissue was assumed from data available for cortical tissue. The yield stresses defined by a 0.2% offset in the global stress-strain curve were fit to an orthotropic Hill criterion and the parameters of the surface calculated. Similarly to the previous elastic analysis, distinct but strong relationships were obtained between volume fraction, fabric and the yield surface parameters for both the open and closed cell geometries. This finding suggests that volume fraction and fabric may be used to predict the initiation of mechanical damage in human trabecular bone at the continuum level.     

A novel in vivo mouse model for mechanically stimulated bone adaptation--a combined experimental and computational validation study

To facilitate the investigation of bone formation, in vivo, in response to mechanical loading a caudal vertebra axial compression device (CVAD) has been developed to deliver precise mechanical loads to the fifth caudal vertebra (C5) of the C57BL/6 female mouse. A combined experimental and computational approach was used to quantify the micro-mechanical strain induced in trabecular and cortical components following static and dynamic loading using the CVAD. Cortical bone strains were recorded using micro-strain gages. Finite element (FE) models based on micro-computed tomography were constructed for all C5 vertebrae. Both theoretical and experimental cortical strains correlated extremely well (R(2)>0.96) for a Young's modulus of 14.8 GPa, thus validating the FE model. In this study, we have successfully applied mechanical loads to the C5 murine vertebrae, demonstrating the potential of this model to be used for in vivo loading studies aimed at stimulating both trabecular and cortical bone adaptation.     

Cortical Bone Morphological and Trabecular Bone Microarchitectural Changes in the Mandible and Femoral Neck of Ovariectomized Rats

ObjectiveThis study used microcomputed tomography (micro-CT) to evaluate the effects of ovariectomy on the trabecular bone microarchitecture and cortical bone morphology in the femoral neck and mandible of female rats.ResultsRegarding the trabecular bone microarchitectural parameters, the BV/TV of the trabecular bone microarchitecture in the femoral necks of the control group (61.199±11.288%, median ± interquartile range) was significantly greater than that of the ovariectomized group (40.329±5.153%). Similarly, the BV/TV of the trabecular bone microarchitecture in the mandibles of the control group (51.704±6.253%) was significantly greater than that of the ovariectomized group (38.486±9.111%). Furthermore, the TbSp of the femoral necks in the ovariectomized group (0.185±0.066 mm) was significantly greater than that in the control group (0.130±0.026mm). Similarly, the TbSp of the mandibles in the ovariectomized group (0.322±0.047mm) was significantly greater than that in the control group (0.285±0.041mm). However, the TbTh and TbN trends for the mandibles and femoral necks were inconsistent between the control and ovariectomized groups. Regarding the cortical bone morphology parameters, the TtAr of the femoral necks in the ovariectomized group was significantly smaller than that in the control group. There was no significant difference in the TtAr, CtAr, or CtTh of the femoral necks between the control and ovariectomized groups, and no significant difference in the CtTh of the mandibles between the control and ovariectomized groups. Moreover, the BV/TV and TbSp of the mandibles were highly correlated with those of the femurs (r_s = 0.874 and r_s = 0.755 for BV/TV and TbSp, respectively). Nevertheless, the TbTh, TbN, and CtTh of the mandibles were not correlated with those of the femoral necks.ConclusionAfter the rats were ovariectomized, osteoporosis of the trabecular bone microarchitecture occurred in their femurs and mandibles; however, ovariectomy did not influence the cortical bone morphology. In addition, the parametric values of the trabecular bone microarchitecture in the femoral necks were highly correlated with those of the trabecular bone microarchitecture in the mandibles.     

Mechanics of linear microcracking in trabecular bone

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

Wing and leg bone microstructure reflects migratory demands in resident and migrant populations of the Dark-eyed Junco (Junco hyemalis)

Migration is the primary strategy that temperate birds use to avoid overwintering under harsh conditions. As a consequence, migratory birds have evolved specific morphological features in their wings and skeleton. However, in addition to varying in overall shape and size, bone can also change at the microstructural level by, for example, increasing its thickness. Such changes are critical to preventing fracture and damage under repeated loading (fatigue), yet it is not known whether migratory behaviour influences bone microstructure. To address this gap in the literature, we performed micro-computed tomography on skeletons of resident and migrant subspecies of the Dark-eyed Junco Junco hyemalis. We investigated the differences in the major wing bone, the humerus, and the major leg bone, the femur. In each bone, we studied the microarchitecture of the two types of bone tissue: cortical bone, the thick outer layer of bone; and trabecular bone, which is the porous network of bone tissue at the ends of long bones. We used linear models to quantify morphological features with respect to body mass and migratory behaviour. Humeri from migratory birds were thinner, wider and had higher overall geometric stiffness, i.e. a higher polar moment of inertia, relative to humeri from resident birds. These features may help keep their bones stiff to maintain their increased body mass during migration. In contrast, migrant femora were shorter, thinner and had lower geometric stiffness than femora of residents, potentially to reduce total body mass. Tissue mineral density was lower in both the humerus and the femur of migratory birds. In addition, migratory subspecies had less trabecular bone (lower bone volume fraction) due primarily to a loss of trabecular thickness. Migratory behaviour may thus select for improved stiffness and fatigue resistance in the wing bones and reduced mass of leg bones. Our work demonstrates how important insights into morphological adaptation can be obtained by investigating bone microstructure.     

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.     

Experimental and finite element analysis of the mouse caudal vertebrae loading model: prediction of cortical and trabecular bone adaptation

In this study, we attempt to predict cortical and trabecular bone adaptation in the mouse caudal vertebrae loading model using knowledge of bone’s local mechanical environment at the onset of loading. In a previous study, we demonstrated appreciable 25.9 and 11% increases in both trabecular and cortical bone volume density, respectively, when subjecting the fifth caudal vertebrae (C5) of C57BL/6 (B6) mice to an acute loading regime (amplitude of 8N, 3000 cycles, 10 Hz, 3 times a week for 4 weeks). We have also established a validated finite element (FE) model of the C5 vertebra using micro-computed tomography (micro-CT), which characterizes, in 3D, the micro-mechanical strains present in both cortical and trabecular compartments due to the applied loads. To investigate the relationship between load-induced bone adaptation and mechanical strains in-vivo and in-silico data sets were compared. Using data from the previous cross-sectional study, we divided cortical and trabecular compartments into 15 subregions and determined, for each region, a bone formation parameter ΔBV/BS (a cross-sectional measure of the bone volume added to cortical and trabecular surfaces following the described loading regime). Linear regression was then used to correlate mean regional values of ΔBV/BS with mean values of mechanical strains derived from the FE models which were similarly regionalized. The mechanical parameters investigated were strain energy density (SED), the orthogonal strains (e _x , e _y , e _z ) and the three shear strains (e _xy , e _yz , e _zx ). For cortical regions, regression analysis showed SED to correlate extremely well with ΔBV/BS (R ² =?0.82) and e _z (R ²?=?0.89). Furthermore, SED was found to predict expansion of the cortical shell correlating significantly with the regional percentage increases in cortical tissue volume (R ² = 0.92), cortical marrow volume (R ² =?0.91) and cortical thickness (R ² = 0.56). For trabecular regions, FE parameters were found not to correlate with load-induced trabecular bone morphology. These results indicate that load-induced cortical morphology can be predicted from population data, whereas the prediction of trabecular morphology requires subject-specific micro- architecture.     

Effects of reproduction on sexual dimorphisms in rat bone mechanics

Osteoporosis most commonly affects postmenopausal women. Although men are also affected, women over 65 are 6 times more likely to develop osteoporosis than men of the same age. This is largely due to accelerated bone remodeling after menopause; however, the peak bone mass attained during young adulthood also plays an important role in osteoporosis risk. Multiple studies have demonstrated sexual dimorphisms in peak bone mass, and additionally, the female skeleton is significantly altered during pregnancy/lactation. Although clinical studies suggest that a reproductive history does not increase the risk of developing postmenopausal osteoporosis, reproduction has been shown to induce long-lasting alterations in maternal bone structure and mechanics, and the effects of pregnancy and lactation on maternal peak bone quality are not well understood. This study compared the structural and mechanical properties of male, virgin female, and post-reproductive female rat bone at multiple skeletal sites and at three different ages. We found that virgin females had a larger quantity of trabecular bone with greater trabecular number and more plate-like morphology, and, relative to their body weight, had a greater cortical bone size and greater bone strength than males. Post-reproductive females had altered trabecular microarchitecture relative to virgins, which was highly similar to that of male rats, and showed similar cortical bone size and bone mechanics to virgin females. This suggests that, to compensate for future reproductive bone losses, females may start off with more trabecular bone than is mechanically necessary, which may explain the paradox that reproduction induces long-lasting changes in maternal bone without increasing postmenopausal fracture risk.     

Loading Mode Interactions in Simulations of Long Bone Cross-Sectional Adaptation

Although many bone adaptation theories have been formulated to address both trabecular and cortical adaptation, most applications have focused on trabecular adaptation. Thus far, no thorough investigations of the influence of different types of loading on predicted patterns of long bone cross-sectional adaptation have been reported. In the current study, we present a new model for long bone cross-sectional adaptation that incorporates axial, bending and torsional loading components. We found that bending moments have a strong potential to modulate cross-sectional geometry, but can produce unforseen (and unrealistic) geometric instabilities. Torsional moments have the ability to suppress these instabilities, suggesting that torsion may play a more significant role in guiding long bone development than previously recognized. Our results also call into question the concept of strict "remodeling equilibrium," suggesting that long bones do not necessarily approach a state of uniform mechanical stimulation. This modeling approach provides an additional perspective on experimental studies, and may lead to a greater understanding of the interaction between mechanics and biology in long bone adaptation.     

Quantification of a rat tail vertebra model for trabecular bone adaptation studies

A feedback controlled loading apparatus for the rat tail vertebra was developed to deliver precise mechanical loads to the eighth caudal vertebra (C8) via pins inserted into adjacent vertebrae. Cortical bone strains were recorded using strain gages while subjecting the C8 in four cadaveric rats to mechanical loads ranging from 25 to 100 N at 1 Hz with a sinusoidal waveform. Finite element (FE) models, based on micro computed tomography, were constructed for all four C8 for calculations of cortical and trabecular bone tissue strains. The cortical bone strains predicted by FE models agreed with strain gage measurements, thus validating the FE models. The average measured cortical bone strain during 25-100 N loading was between 298 +/- 105 and 1210 +/- 297 microstrain (muepsilon). The models predicted average trabecular bone tissue strains ranging between 135 +/- 35 and 538 +/- 138 mu epsilon in the proximal region, 77 +/- 23-307 +/- 91 muepsilon in the central region, and 155 +/- 36-621 +/- 143 muepsilon in the distal region for 25-100 N loading range. Although these average strains were compressive, it is also interesting that the trabecular bone tissue strain can range from compressive to tensile strains (-1994 to 380 mu epsilon for a 100 N load). With this novel approach that combines an animal model with computational techniques, it could be possible to establish a quantitative relationship between the microscopic stress/strain environment in trabecular bone tissue, and the biosynthetic response and gene expression of bone cells, thereby study bone adaptation.