The authors state that they have no conflicts of interest.
Published online on March 17, 2008;
Inbred strains of mice make useful models to study bone properties. Our aim was to compare bone competence and cortical morphometric parameters of two inbred strains to better determine the role of bone structure and geometry in the process of bone failure. Morphometric analysis was performed on 20 murine femora with a low bone mass (C57BL/6J; B6) and 20 murine femora with a high bone mass (C3H/HeJ; C3H) using desktop μCT. The bones were tested under three-point bending to measure their mechanical properties. Results showed that the C3H strain is a more reproducible model regarding bone morphometric and mechanical phenotypes than the B6 strain. Bone strength, stiffness, yield force, yield displacement, and toughness, as well as morphometric traits, were all significantly different between the two strains, whereas postyield displacement was not. It was found that bone volume, cortical thickness, and cross-sectional area predicted almost 80% (p < 0.05) of bone stiffness, strength, and yield force. Nevertheless, cortical bone postyield properties such as bone toughness could not be explained by morphometry, but postyield whitening was observed in that phase. In conclusion, we found that morphometric parameters are strong predictors of preyield but not postyield properties. The lack of morphometric influence on bone competence in the postyield phase in combination with the observed postyield whitening confirmed the important contribution of ultrastructure and microdamage in the process of overall bone failure behavior, especially in the postyield phase.
The number of osteoporosis-related hip fractures is expected to increase from 1.7 million in 1990 to 6.3 million in 2050. Given the mortality, disability, and cost associated with fragility fractures, identifying the factors that contribute to fracture risk has become increasingly important for improved diagnosis, treatment, and prevention. Peak bone mass, which is defined by genetic and environmental factors, has been postulated to be an important risk factor. However, measures of bone mass and BMD have been inconsistent predictors of fracture risk. Although altered bone quality has been recognized as an additional determinant of fracture risk, the genetic and environmental contributions to variations in bone quality, the correlation between bone quality and fracture risk, and the relationship between bone quality and bone mass are poorly understood. Bone quality is a generic term that refers to a wide spectrum of tissue mechanical properties such as elastic modulus, strength, toughness, creep, and brittleness. The specific tissue mechanical properties that contribute to bone strength are not completely understood.
With the exception of identical twins, the genetic background in humans varies significantly from one individual to another, making studies of genetic involvement in a given bone phenotype in humans difficult. The use of animal models with relevant biological phenotypes related to disease models may provide important genetic clues that will improve the efficiency of identifying genes underlying bone strength. Well-characterized animal lines with phenotypes related to certain aspects of human osteoporosis can be used as an approach to study more homogeneous populations in which isolation of candidate chromosomal regions and genetic loci should be faster and more efficient. Animal models complement and extend human studies by allowing close control of environmental factors by expanding the characterization of phenotypes underlying bone strength and by facilitating breeding strategies to identify genetic linkage. Of particular value are experimental approaches using inbred animals. Although individuals within an inbred strain are genetically identical, genetic differences exist between different inbred strains. Where there are differences in bone strength between two inbred strains, one can identify the genetic differences that are linked to the variation in bone strength phenotypes. Adult C3H/HeJ (C3H) and C57BL/6J (B6) mice are similar in body size and weight, and their bones are of similar external size, but show significantly different morphological and compositional bone traits, such as adult peak BMD and cross-sectional area. Most importantly, these two mouse strains have often been identified as a model system for high (C3H) and low (B6) bone mass phenotypes and with that as a model to study genetic factors in osteoporosis.
In this study, we evaluated the microstructure and mechanical properties of cortical bone in the femur of inbred strains B6 and C3H. We hypothesized that bone mechanical properties could be predicted by cortical bone morphometry. We asked the question of whether these predictions were influenced by genetic background and whether they were different for pre- and postyield mechanical properties. Our aim, therefore, was to compare bone competence and cortical morphometric parameters of both strains to better determine the role of bone structure and geometry in the process of bone failure behavior.
As of today, there have been several studies on μCT of bones from C3H and B6 mice with emphasis on the importance of bone cross-sectional geometry as a determinant in bone mechanical properties. Our work distinguishes from these previous studies with the following specific aims. We examined in detail which mechanical parameters can or cannot be explained by bone geometry, distinguishing between preyield and postyield parameters. Furthermore, we looked at the relative degree of variations of mechanical and morphometric traits in both murine strains. Higher orders of variation in mechanical traits than morphometric traits would suggest that not only morphometry is responsible for variations in mechanical parameters. Finally, we performed a close observation with a high-speed and high-resolution camera of the postyield and failure behaviors, highlighting the whitening effect and monitoring microcrack accumulation until bone failure.
We expect that a better understanding of morphometric parameters, at different scales ranging from the organ level to bone ultrastructure, and their relative contribution to bone competence in animal models will provide helpful inputs for human research at the genetic and phenotypic levels.
MATERIALS AND METHODS
For this study, we used two inbred strains, where C57BL/6He (B6) represented the low bone mass strain and C3H/He (C3H) displayed the high bone mass phenotype. Twenty femora from 16-wk-old B6 and 20 femora from 16-wk-old C3H were imaged by means of μCT and tested in three-point bending. Each series of 20 bones was composed of 10 femora from male mice and 10 femora from female mice. The mice were raised and killed at the Jackson Laboratory. Bones were sized and prepared at the Jackson Laboratory and kept in alcohol for overseas travel. Use of mice in this research project was reviewed and approved by the local authorities.
Each bone was measured using desktop μCT (μCT 40; Scanco Medical, Bassersdorf, Switzerland) equipped with a 5-μm focal spot X-ray tube as a source. A 2D charge-coupled device, coupled to a thin scintillator as a detector, permitted acquisition of 20 tomographic images in parallel. The long axis of the femur was orientated orthogonal to the axis of the X-ray beam. The X-ray tube was operated at 50 kVp and 160 μA. The integration time was set to 100 ms. Scans were performed at a nominal resolution of 20 μm in all three spatial dimensions (medium resolution mode). 2D CT images were reconstructed in 1024 × 1024 pixel matrices from 1000 projections using a standard convolution-backprojection procedure with a Shepp and Logan filter. Images were stored in 3D arrays with an isotropic voxel size of 20 μm. Then they were rotated in a standard orientation and a constrained 3D gaussian filter was used to suppress partly the noise in the volumes (σ = 1.2 and support = 1). The images were segmented to distinguish bone voxels from nonbone voxels using a global threshold (22.4% of maximum possible grayscale value) as previously described. A 1-mm analysis region, situated at 55% of the length from the proximal side, was defined as the analysis region (Fig. 1). At this location, only cortical bone can be found. Morphometric traits were determined using a direct 3D approach. Fourteen morphometric parameters, including total volume (TV), cortical bone volume (BV), bone surface area (BS), bone volume density (BV/TV), bone surface density (BS/TV), bone surface to volume ratio (BS/BV), cortical average thickness (C.Th), anterior-posterior diameter (APD), and average cross-sectional area (T.Ar) were assessed in the 1-mm-thick cortical volume in the diaphysis. Bending moments of inertia were also computed: bending moment of inertia with respect to the anterior-posterior axis (IAP), bending moment of inertia with respect to the medial-lateral axis (IML), biaxial area moment of inertia (Ixy), polar moment of inertia (J), and principal moments of inertia (Imax and Imin).
The 40 bone specimens were kept in alcohol for 4 mo and rehydrated for 24 h in PBS solution before testing. Load was applied midway between two supports that were 6 mm apart, exactly in the region where the morphometric analysis was performed. The femora were positioned so that the loading pin was applying a force at a location on the shaft situated at 55% of the length from the proximal side. The femora were lying freely on the supports, and the 1-N preload oriented them so that the load was applied in the anterior-posterior direction (Fig. 2A). Load-displacement curves were recorded at a cross-head speed of 0.5 mm/s. Bone stiffness, strength, yield force, yield displacement, postyield displacement, and toughness were derived from these curves as described previously. To observe the fracture initiation, tests were imaged with a high-speed and high-resolution camera (AOS Technologies, Daetwil, Switzerland). The image size was set to 1280 × 1024 pixels and the frame rate to 62.5 frame/s. Between 200 and 300 high-resolution images were recorded per single test.
Both strains were compared at the mechanical and morphometric levels using Student's unpaired t-tests. Relationships between mechanical and morphometric parameters were computed using single and multiple linear regression analyses. Significance level for all analyses was set to p < 0.05.
For multiple linear regression, we pooled both strains. This sometimes resulted in clustered clouds around the average values in each strain. To reduce the gap separating the clusters in the multiple linear regression plots and correct the error in correlation caused by the clustering effect, we applied a simplified version of the cluster linear regression method developed by Henning to our data set. A factor for each multiple linear regression was computed. In short, the factor (f) was calculated dividing the x-coordinate of the point in the C3H cluster with the smallest x-coordinate by the x-coordinate of the point in the B6 cluster with the highest x-coordinate. Because the slope of the plots was equal to 1, the factor for y-coordinates was the same as for the x-coordinates. Both x and y values of each C3H points were divided by f. Thus, a more homogenous population was generated, and the contribution of the clustering effect to the high correlation coefficients previously obtained was removed (Fig. 4).
All statistical analyses were performed with Excel 2003 (Microsoft, Redmond, WA, USA) and the GNU statistical package R (version 2.4.0, http://www.r-project.org).
The CV of all morphometric traits was smaller for C3H than for B6 (Table 1). Furthermore, our measurements showed that both strains were significantly different for all the parameters except postyield displacement. Comparison between the mechanical and morphometric parameters showed that the morphometric parameters typically varied less than the mechanical ones within each inbred strain. CV's were smaller (<12%) for morphometric parameters, whereas those for moments of inertia and mechanical parameters ranged from 10% to 47%, except for the postyield parameters, which were between 40% and 93%.
Table Table 1.. Morphometric Parameters
The information gained from the high-resolution and high-speed camera showed the way fractures occurred. The images showed well how bone fractures initiated at the posterior, tensile, side of the bone (Fig. 2B). The fracture pattern did not differ between femurs of the two breeds. Other relevant information delivered by this visualization technique was the exact positioning of the femora in three-point bending after preload. It provided an easy and elegant way to ascertain that bones, simply put on supports, were positioned correctly and that they rotated in a very reproducible way after preload. Furthermore, imaging helped to discriminate outliers and permitted to determine whether variability in the results was caused by problems in the experimental set-up. Even if a reasonable force versus displacement curve was measured, visualization of the failure process could sometimes identify measurement errors. Indeed, two tests on B6 and one test on C3H were excluded because the samples slipped or did not position appropriately after preloading. The high resolution images recorded also permitted to visualize a whitening effect found in bone as a consequence of overloading (Fig. 2C).
The average curves of the three-point bending tests were computed (Fig. 3). Results from female and male bones were pooled, because there was no significant difference between sexes. All CVs were smaller for C3H than for B6 (Table 2), as was the case for the morphometric parameters. Our experiments also showed that both models were significantly different for stiffness, strength, yield force, yield displacement, and toughness. Only for postyield displacement, the two strains did not show significant differences. In both strains, the results were much more reproducible for strength, stiffness, yield force, and yield displacement than for the postyield parameters, such as postyield displacement and toughness.
Table Table 2.. Biomechanical Parameters of the Three-Point Bending Tests
Computing intrastrain correlations of mechanical parameters and morphometric indices, it was found that morphometry was only a poor predicator within each strain; correlations to mechanical parameters were <50%. We therefore pooled both strains. Although mechanical and morphometric parameters were often highly strain dependent and therefore clustered around the mean value of each strain, an interstrain multiple regression analysis showed that the least clustered morphometric traits, such as BV, C.Th, and T.Ar, could predict 87% of stiffness, 85% of yield force, and 88% of strength (Figs. 4A–4C). To reduce the gap separating the clusters in the multiple linear regression plots and correct the error in correlation caused by the clustering effect, we applied, as mentioned earlier, a simplified version of the cluster linear regression method. As expected, the correlation coefficients decreased but were still significantly high: r2 = 0.79, r2 = 0.76, and r2 = 0.77 for stiffness, yield force, and strength, respectively (Figs. 4D–4F). Finally, morphometry was only a poor predicator for yield displacement and postyield parameters, such as postyield displacement and toughness (r2 < 0.50).
In this study, femoral cortical bone morphometry in two characteristic murine strains was performed. Femora were tested under three-point bending to study their mechanical competence. To better understand the bone failure behavior, analyses of bone competence were conducted combining mechanical and morphometric results.
High-resolution imaging of common mechanical tests drastically increased the informative output of the mechanical tests. In an earlier study, we showed that, by using a proper image-based aligning procedure and exclusion of unsuccessful tests, the variability was reduced to one half compared with conventional approaches. This is of great value in experimental studies, because reduced variability means increased power in the results. This also indicates that fewer samples and therefore fewer animals are needed to obtain significant results. In our study, these bad samples were evident, and their exclusion did not appeal to our subjective judgment. We removed three samples: two misaligned samples after the preload and another one slipped from the loading device while loading.
Using this image-guided approach, we noticed that bone surfaces whitened with increasing strain in the postyield phase (Fig. 2C), similar to work on trabecular bone recently reported by Thurner et al. We hypothesized that the effect seen was caused by microcrack formation in these areas, comparable to stress whitening seen in synthetic polymers. Thurner et al. showed that the whitened areas were also of high deformation. They suggested that the detected whitening and also microdamage appeared at points of highest strain, which would be consistent with failure initiation in compact bone, at the point of highest local strain. Therefore, visually investigating typical failure locations and fracture propagation, using high-speed video, could give first insight into the bone failure behavior. A further step would be to quantify the whitening effect and to relate it directly to the fracture initiation and propagation, but this would require specific devices and software as used by Thurner et al.
In recent years, there has been a considerable emphasis placed on the detailed mechanism whereby the skeleton provides mechanical support for the organism. Extrinsic bone strength is the pivotal parameter describing this aspect of skeletal function. In terms of the determinants of mechanical support, BMD is well recognized, whereas cross-sectional geometry, which is equally important as BMD, has only achieved recognition of its importance in the last few years. Now, there are multiple studies that have emphasized the importance of bone cross-sectional geometry as a determinant in bone mechanical properties. In this study, we investigated BMD and 14 cross-sectional morphometric parameters in cortices of the murine femoral mid-diaphysis. They were all significantly different for the two observed strains. As showed previously, B6 and C3H are well characterized with regard to differences in BV/TV and T.Ar. These strains seem to be very good models for high and low bone mass, respectively. Our study completed these findings with further significantly different parameters including intrinsic geometrical traits and computed moments of inertia (Table 1).
Looking at the results of mechanical testing, these experiments showed that both models were significantly different for stiffness, strength, yield force, yield displacement, and toughness. Nevertheless, the 8% difference in postyield displacement was not significantly different between the two strains, because of the large SDs found for this parameter. Similar to previous studies, this indicated that these two inbred mice do not only show different morphometrical phenotypes but also different mechanical phenotypes. Furthermore, it was found that all the mechanical parameters for C3H were more reproducible than for B6 (Table 2), also indicating more homogeneous bone mechanical properties for C3H.
As mentioned above, postyield displacement showed large variations within each strain (Table 2). Several components of the bone material influenced the postyield displacement. First, the inorganic phase might play a role in the deformation ability of bone until failure. Indeed, the level of mineralization directly contributed to the ductility level of the material. The organic phase also determined the ductility of bone. Because the failure occurred under tension in three-point bending, the collagen fibers, which can only bear load under tension, resisted against the external loading. The way they resist and the way they break also determined the ductility of bone. Finally and, we believe, most importantly, the way microdamage accumulated directly influenced the way bone fails; hence, it directly affects the ductility and its reciprocal bone brittleness. The critical influence of microdamage initiation and accumulation was also already mentioned by Jepsen et al. In this study, none of these three components of bone material properties were directly analyzed or quantified, because they were not the focus of the study. We could only visualize microcrack accumulation through whitening. Our results clearly identified the importance of these material components because geometry failed in explaining postyield behavior.
A closer study of the morphometric traits showed that C3H parameters were less variable than B6, as was the case for mechanical properties, confirming that C3H is a strain with more precise traits than the B6, both mechanically and morphometrically. This finding can be of great help when selecting mice inbred strains for phenotyping purposes. In such studies, large populations of mice are usually experimented within the same strain or between different strains. Comparing results between predefined groups and showing significant differences between treated or untreated animals, between different strains, or between different models is often the main goal of these studies. Reduced variability in the results within each group makes the results more powerful and increases the significance of the study and therefore its impact. It also reduces the number of animals needed for significant outcomes.
In this study, we showed that variations in mechanical properties are on average higher than variations in morphometric traits. A reason for this is the higher inaccuracies induced by the mechanical setup. Indeed, the small size of murine bones makes them difficult to test with perfectly reproducible boundary conditions. Therefore, a part of the variation in mechanical results is inherent to the testing setup. This part is much reduced in morphometric analyses, where a very high reproducibility of <1% has been shown for cortical bone parameters. A further explanation could come from bone material properties. Bone tissue is a composite material comprised of an organic matrix reinforced with an inorganic mineral phase. The inorganic phase is composed of mineral microcrystals and the organic matrix of protein (principally collagen) fibers. Because bone is a composite material, its mechanical properties are dependent not only on its cross-sectional geometry but also on its diverse material components and on its ultrastructure. Here, we mean mostly bone porosity including cortical bone vasculature, osteocytic lacunae and the canalicular network, and bone microdamage, when referring to cortical bone ultrastructure. It has been shown that bone ultrastructure also has a contribution to failure behavior. In a recent study, Schneider et al. showed that bone capacity can only be partly explained by bone geometry. Nevertheless, in this study, we tried to quantify the geometric influence on bone mechanical properties. We performed two types of studies: an intrastrain (within each strain) and an interstrain (merging both strains results) analysis. It was found that, intrastrain, morphometry is a poor predictor of bone mechanical properties. The best predictions we could compute using multiple linear regression were <50% in each strain. In the case of strength, stiffness, yield force, and yield displacement, this was to be expected, because variations in mechanical and morphometric parameters were relatively small. In other words, these bone phenotypes were well characterized in each strain. For the postyield parameters, which showed large variations, the lack of correlation indicated that these parameters were mostly independent from bone geometry.
Computing interstrain multiple linear regression, BV, C.Th, and T.Ar were good predictors for stiffness, yield force, and strength. No prediction was found for postyield displacement and toughness. As mentioned previously, multiple linear regression on clustered data can be biased by the cluster effect. The larger the two populations differ for the analyzed parameters, the higher will be the correlation because of the cluster effect. To prevent this problem, we selected those parameters that clustered the least. When values were linearly distributed, we were able to compute high correlations between preyield mechanical parameters (stiffness, yield force, and strength) and BV, C.Th, and T.Ar (r2 = 0.85–0.88; Figs. 4A–4C). However, a small gap between both strains could be seen in the linear regression curves. To prove that the cluster effect did not act a major influence on the computed correlation coefficients and to correct for this influence, we reduced the gap between both strains using statistical normalization (Figs. 4D–4F) and verified that the obtained correlation factors were still high (r2 = 0.76–0.79).
In both strains, the mechanical results were more reproducible for strength, stiffness, yield force, and yield displacement than for postyield displacement and toughness. Furthermore, multiple linear regression analysis showed no correlation between the morphometric traits and yield displacement or postyield mechanical parameters (postyield displacement and toughness). This also indicated that postyield behavior is only poorly predicted by microstructural bone morphometry. Comparing the mechanical data with the recorded movies of the tests, whitening and fracture initiation happened in the postyield phase. Whitening indicated that bone failure behavior is governed in its plastic phase by ultrastructural changes including microdamage initiation and propagation. Thus, our study confirmed that microcracking plays an important role in the postyield failure behavior. It is of great interest to further study microdamage to better understand the whole failure behavior and to try explaining the large variance in postyield behavior within each strain. Recent studies have explored microdamage initiation and propagation, the relation between ultrastructure and microdamage, and the contribution of microdamage to overall fracture initiation and propagation. There was no conclusive finding from these studies and therefore the overall bone failure behavior is still poorly understood and needs further study at microscopic and nanoscopic scales to uncover properties determining postyield behavior.
Our study suffers some limitations. The bones were stored in alcohol before mechanical testing. It is controversial how alcohol conservation influences bone biomechanical properties. Beaupied et al. showed that alcohol conservation did not affect the tensile properties of rat cortical bone. In the same way, Linde and Sorensen showed that the mechanical properties of human trabecular bone under compression were not affected by alcohol storage. Furthermore, previous highly referenced studies already used bones stored in alcohol before performing three-point bending tests. Hence, there is substantial evidence that alcohol storage was not a crucial issue for our biomechanical findings. On the other hand, Burr stated that an altered organic matrix contributed to reduced bone postyield properties. Alcohol storage does affect postyield properties. Because the bones that we tested were stored in alcohol for the same period, we assume that if the bones were affected by storage, this would have had similar effects on both inbred strains. Nevertheless, this cannot be quantified.
Another limitation of this study was that some biomechanical parameters were very different in B6 and C3H (although this was also one of the reasons to chose these two strains in other studies), but the aforementioned parameters (BV, Ct.Th, T.Ar, stiffness, yield force, and strength) were not so different and permitted interstrain computation of multiple linear regression. When pooling together both strains, some mechanical and morphometric parameters were clustered for each strain. This clustering effect biased the correlation factors of multiple linear regression. All the parameters that were much clustered (high correlation caused by separated and clustered clouds of dots) were not considered in our analyses. Nevertheless, there were some morphometric parameters, such as BV, C.Th, and T.Ar, and mechanical parameters, such as stiffness, yield force, and strength, that were significantly less clustered. These parameters even considered within only one strain showed clear trends (see single cloud of dots in Figs. 4A–4C). Looking at such different behaviors of morphometric and mechanical parameters (clustered and less clustered), we decided to consider only the poorly clustered parameters. To remove the remaining clustering effect, we artificially and linearly approached the two clouds and closed the gap along the diagonal axis (same coefficient for mechanical and morphometric parameters). This process only slightly reduced the correlation coefficients.
Finally, the three-point bending test is a complex mode of loading with a combination of tensile, compressive, and shear loads. The reader must keep in mind that that results of mechanical testing vary according to the type of forces producing the fracture. Notably, bone fractures are usually caused by multiaxial forces. Our work only considered one type of loading, and our results may vary for other loading modes, especially for physiological modes.
In conclusion, our work showed that the C3H strain is a more reproducible model regarding bone morphometrical and mechanical phenotypes than the B6 strain. This finding is important when selecting mouse models for phenotyping purposes.
Strength, stiffness, yield force, toughness, and morphometric traits were significantly different between each strain, whereas postyield displacement was not. Intrastrain mechanical predictions from morphometry were not possible, because bone phenotypes were well characterized in each strain. Interstrain analyses showed that the morphometric parameters BV, Ct.Th, and T.Ar are strong predictors of preyield parameter. They predicted almost 80% of the preyield parameters such as stiffness, strength, and yield force, whereas bone postyield behavior could not be explained by morphometry.
Furthermore, a higher order of variation in mechanical parameters than in morphometry was shown for both strains. This also indicated that, in many cases, bone geometry is not sufficient to fully explain bone biomechanics.
A close observation of the failure behavior evidenced the whitening effect and therefore microcrack accumulation in the postyield phase. These observations, together with the lack of correlation between morphometry and postyield parameters, clearly indicated that a better understanding of postyield and failure behaviors will only be possible with a better understanding of bone quality, in particular of the intrinsic bone ultrastructure and microcracking as a consequence of overloading.
Our study together with the findings of Schneider et al., where they provided strong evidence for a significant influence of the canal network on murine bone mechanics, suggest that the morphometric analysis of the ultrastructural phenotypes and the study of the relationships between phenotypes of bone at different hierarchy levels will provide new insights in the assessment of bone quality on all levels of bone hierarchy. Although murine bone is lacking the osteonal structures seen in larger mammals and humans, its ultrastructural features such as osteocyte lacunae and blood vessels are present in osteonal bone as well. There is no reason to believe that these features would have a differential effect in osteonal bone. Nevertheless, this will need experimental confirmation.
This work was supported through ETH Intramural Funding (TH 00124/41–2631.5) and the Swiss National Science Foundation (FP 620–58097.99, PP-104317/1). The authors thank Paul Lüthi for machining several parts indispensable for our loading device and Leah Rae Donahue for providing the murine bones.