Structure-function relationships were determined for L5 vertebral bodies from three inbred mouse strains. Genetic variability in whole bone mechanical properties could be explained by a combination of the traits specifying the amount, distribution, and quality of the cortical and trabecular bone tissue.
Introduction: Although phenotypically correlated with fracture, BMD may be disadvantageous to use in genetic and biomechanical analyses because BMD does not distinguish the contributions of the underlying morphological and compositional bone traits. Developing functional relationships between the underlying bone traits and whole bone mechanical properties should further our understanding of the genetics of bone fragility.
Materials and Methods: Microarchitecture and composition of L5 vertebral bodies (n = 10/strain) from A/J, C57BL/6J, and C3H/HeJ inbred mouse strains were determined using μCT with an isotropic voxel size of 16 μm3. Failure load, stiffness, and total deformation as a measure of ductility were measured in compression using a noncontact strain extensometer imaging system. A correlation analysis related morphological and compositional bone traits to whole bone mechanical properties. A multivariate analysis identified structure-function relationships for each genotype.
Results: No single bone trait accurately explained the genetic variation in mechanical properties. However, a combination of traits describing the amount, distribution, and quality of cortical and trabecular bone tissue explained >70% of the variation in vertebral mechanical properties. Importantly, structure-function relationships were unique among genotypes.
Conclusions: Different genetic backgrounds use different combinations of underlying bone traits to create mechanically functional structures. Using a single complex trait such as BMD or BV/TV as the sole phenotypic marker in genetic analyses may prove to be disadvantageous because of the complex relationship between mechanical properties and the underlying bone traits. Therefore, considering multiple bone traits and the interaction among these bone traits is necessary to understand the relationship between genetic background and complex whole bone mechanical properties.
OSTEOPOROSIS IS A systemic skeletal disease characterized by low BMD and microarchitectural deterioration of bone tissue, leading to enhanced bone fragility and an increased risk of fracture.(1) In the United States alone, there are >10 million cases of osteoporosis, and >1.5 million individuals suffer fractures annually.(2,3) One of the main sites of osteoporotic fractures is the spinal column, with ∼700,000 osteoporotic vertebral fractures occurring each year in the United States.(3) The loss of vertebral height and stability, risk of neurological injury, and pain that often result from vertebral fractures make osteoporosis a major clinical problem. With increasing life expectancy, the cost and number of patients with postmenopausal osteoporotic fractures is steadily increasing, driving the need for new preventative and diagnostic procedures.
Low peak bone mass, which is influenced by genetic and environmental factors,(4) is a trait that is correlated with fracture risk in osteoporosis patients. Bone mass is highly heritable, with up to 80% of the variation in BMD attributable to genetic background.(5) Although phenotypically correlated with fracture,(6) BMD may be disadvantageous to use in genetic and biomechanical analyses because it does not distinguish the contributions of the underlying morphological and compositional bone traits.(7,8) Identifying the individual bone traits that underlie BMD and fracture risk should lead to a better understanding of how adult trait values are determined by cellular processes, and ultimately, genetic and environmental factors.
Inbred mice provide a valuable resource to study the genetic basis of complex diseases including osteoporosis.(9) We previously studied the relationship between whole bone mechanical properties and the underlying morphological and compositional traits for femurs from various inbred mouse strains.(10) The data revealed that no single trait could explain variation in all whole bone mechanical properties. Instead, genetic variation in three traits—cortical area (describing the amount of bone), moment of inertia (distribution of bone), and mineral content (quality of bone)—explained 66-88% of the interstrain variability in four whole bone mechanical properties that describe all aspects of the failure process, including measures of fragility.(11) These structure-function relationships were consistent with the concept that mechanical properties of a structure depend on both the amount and quality of the constituent materials. Because the genes that affect the skeletal traits of the long bones may also affect the spine,(12,13) a similar multivariate approach has potential for understanding structure-function relationships in the mouse vertebra.
The goal of this study was to assess the biomechanical properties of the vertebrae from three inbred mouse strains and identify combinations of intrinsic bone traits (e.g., morphology, composition) that contribute to genetic variation in vertebral mechanical properties. We examined A/J, C57BL/6J, and C3H/HeJ inbred mouse strains because the femurs of these three strains showed significantly different morphological and compositional bone traits.(11) We expected that the vertebrae of these mice would also show sufficient heterogeneity to establish a relationship between the intrinsic bone traits and the whole bone mechanical properties.
MATERIALS AND METHODS
Female A/J (A, n = 10), C57BL/6J (B6, n = 10), and C3H/HeJ (C3H, n = 10) inbred mice were purchased from Jackson Laboratory (Bar Harbor, ME, USA) at 4 weeks of age. Mice were fed a standard mouse chow (Purina Rodent Chow 5001; 4.5% fat, 23.4% protein, with 0.95% Ca, 0.67% P, and vitamin supplements; Purina Mills, St Louis, MO, USA) and water ad libitum, kept on a 12-h light/dark cycle, and housed with five mice per cage. The Committee on Animal Care and Use approved the handling and treatment of mice. Mice were killed at 15 weeks of age, and the L4-L6 lumbar vertebrae were harvested, cleaned of soft tissue, and stored frozen at −20°C before testing.
Bone morphology and microarchitecture measurements
Gross morphologic and microarchitectural traits for the L5 vertebra were determined from scans of lumbar motion segments containing three vertebrae (L4-L6) using a desktop μCT system (GE eXplore Locus SP Specimen Scanner; GE Medical Systems, London, Ontario, Canada). CT images bone by measuring the attenuation of the mineral phase. This attenuation is expressed as a “CT number” in Hounsfield units (HUs).(14)
The GE Medical Systems μCT system was engineered to reduce beam hardening and produce field-flatness, where the uniformity of the CT number within a uniform material is independent of spatial position. The linearity of the CT scanner was established by scanning a phantom containing several densities of a standard calibration material and met the American Association of Physicists in Medicine (AAPM) standards requiring that the CT number not vary >2 SD from the mean.
The samples were placed in an airtight cylindrical holder filled with PBS. The caudal end (L6) was fixed in the cylinder using putty. For each sample, scans were reconstructed at a 16-μm3 isotropic voxel size. A standard Feldkamp Conebeam algorithm was used to reconstruct the CT images. Image data were stored in 3D image arrays and later converted to 2D images.
Images were thresholded to differentiate bone from nonbone by setting the threshold level at 10.2% of the maximum gray value for each specimen.(14) Extraneous pixels were filtered using image analysis software (IMAQ Vision Builder 6.0; National Instruments, Austin, TX, USA). For each sample, 11 2D transverse slices were taken an equal distance apart over the entire height of the vertebral body, excluding the endplates. The first slice was taken approximately one slice (16 μm) superior to the caudal growth plate. The last slice was captured at approximately one slice (16 μm) inferior to the cranial growth plate.
The posterior elements were removed in each image manually; the new edge was determined to be continuous with the perimeter of the vertebral body, and all bone beyond this perimeter was removed. Using this method, accurate trabecular parameters of the entire vertebral body were measured for the isolated vertebral body. The cortex was manually separated from trabecular bone, and traits specifying the amount and distribution for each type of tissue were measured (Scion Corp., Frederick, MD, USA). Overall measures included the total cross-sectional area (TtAr = cortical bone + trabecular bone + marrow) and the total bone area (BAr = cortical bone + trabecular bone). Cortical bone traits included the area of cortical bone (CtAr) and the second area (polar) moment of inertia (CtJ). In addition, the 2D images were analyzed for trabecular microarchitectural traits that characterize the amount (BV/TV) and morphology of the trabecular tissue (TAS v.2.09; Biomedical Sciences, University of Leeds, Leeds, UK). Measures of trabecular morphology included trabecular number (TbN), trabecular thickness (TbTh), trabecular separation (TbSp), and connectivity (NNd:NTm).(15) All morphological parameters were averaged over the entire vertebral body (11 slices) and analyzed for variation along the height of the vertebral body. The vertebrae were split into three regions, with the middle region consisting of the middle 4 of the 11 total slices.
The same transverse sections analyzed for histomorphometry were used to assess tissue mineral content of the vertebral body. The slices were extracted from the nonthresholded data and used to calculate a threshold for each specimen.(16) The lowest threshold value for any specimen was 1209 HUs. Therefore, a threshold of 1200 was used for all specimens. This value was consistent with the threshold used to quantify morphological traits using the technique in the previous step. A calibration phantom equivalent to hydroxyapatite with a density of 1130 mg/cm3 was included in each scan. Mineral content was calculated on a voxel-by-voxel basis as the voxel Hounsfield unit divided by the phantom Hounsfield unit multiplied by 1130 mg/cm3. The resulting data were an average value of the mineral content of the bone tissue. In addition, the apparent mineral content was determined by normalizing the tissue mineral content for total cross-sectional area for each section.
Whole bone mechanical properties of L5 vertebrae were measured by compressing the vertebral body with a 3-mm-diameter platen. Samples were compressed at a cross-head speed of 0.05 mm/s using a servohydraulic materials testing machine (Instron model 8872; Instron Corp., Canton, MA, USA). Posterior elements were left intact, and the endplates of the vertebrae were minimally shaved flat (Fig. 1). Samples were kept from slipping during the test by precoating the platens with a thin film of cyanoacrylate; the glue was allowed to gel to prevent diffusion into the specimen. Samples were aligned vertically, relative to the loading axis, using an alignment pin that was attached to the lower platen and placed through the spinal column. The specimens were kept wet with PBS, and tests were conducted at room temperature. Mechanical properties measured were failure load (Fu), stiffness (S), and total deflection (ΔT) as a measure of ductility. Failure load was defined as the highest load preceding a rapid decrease in the measured load.
Deformation was measured using a high-resolution digital video camera (RH1100; Duncan Tech, Auburn, CA, USA) and a video zoom microscope lens (Edmund Industrial Optics, Barrington, NJ, USA). Using the methods of Derwin et al.,(17) two series of calibration tests were done on the optical system to assess uniaxial displacement accuracy and optical errors caused by translation perpendicular to the axis of displacement. The results of all tests confirmed that the optical errors were associated with pixel resolution (4.05 μm/pixel), and optical displacement measurements were accurate to approximately one pixel. The image acquisition sequence and the mechanical data acquisition were synchronized with computer software (LabView 6i; National Instruments). Randomly placed stone filings were used as markers for optical deformation measurement on the anterior surface of the vertebral body. Two unique particle patterns were identified that were spaced over 90% of the vertebral body height (Fig. 1). Deformation measurements were automated by pattern recognition software (IMAQ Vision Builder 6.0). The selection of the patterns away from the platen-specimen interface also minimized errors associated with system compliance and potential local crushing of the sample immediately below the platen.(18,19)
Differences in morphological, compositional, and mechanical properties between A, B6, and C3H were determined using a one-way ANOVA and a Tukey's posthoc test (GraphPad Prism). Structure-function relationships were determined by calculating correlation coefficients between each whole bone mechanical property (FU, S, ΔT) and each morphological and compositional trait (BV/TV, TtAr, CtAr, mineral content, etc.; Minitab, State College, PA, USA). This analysis was conducted for each genotype separately. Because several traits could be varying simultaneously, stepwise multiple regression models were also used to identify combinations of traits that contributed significantly to the variation in whole bone mechanical properties within each genotype. An α level of 0.5 to enter and leave the regression was used. For each strain, traits and properties varying significantly with body weight were adjusted to an average weight of 20.65 g using a linear regression-based method.(20) All multivariate analyses used the weight-corrected trait and property values for each mouse genotype.
Anatomic variation in bone morphology and mineral content
Each strain showed a nonuniform distribution of cortical and trabecular bone along the axial height of the vertebral body (Figs. 2A-2C). To determine how morphologic measures varied along the height of the vertebral body, the amount of cortical bone plus trabecular bone (BAr/TtAr) and trabecular bone alone (BV/TV) were plotted as a function of anatomic position (Figs. 2D-2F). The area fraction of cortical (BAr/TtAr) and trabecular (BV/TV) tissue reached minimum values in the mid-cranial region and reached maximum values near the endplates. This inhomogeneity was particularly apparent for C3H, which showed nearly zero BV/TV in the middle region. The μCT analysis also revealed that the distribution of mineral content varied nonuniformly along the height of the vertebral body (Figs. 2G-2I). For all three strains, this nonuniform distribution was inversely related to the magnitude of BV/TV. The middle region of the vertebral body, which had the smallest trabecular bone volume values, had the highest levels of mineral content. This anatomical variation of mineral content did not change when mineral content was normalized for total cross sectional area (data not shown).
Genetic variation in bone morphology and mineral content
When the gross morphologic measures were averaged over all transverse sections (Table 1), the A vertebral body exhibited a smaller total cross-sectional area (TtAr) compared with B6 (p < 0.05), which was smaller than C3H (p < 0.05). There was only an 11% difference in the bone area (BAr) among the three inbred strains. BAr was significantly smaller in A mice compared with B6 and C3H mice (p < 0.01). The vertebrae of C3H mice showed larger cortical area values compared with A and B6 mice (p < 0.001). The cortical shell had an important anatomical presence in the mouse vertebral body, particularly for C3H mice. Cortical bone area accounted for 53% and 44% of the bone area for A and B6 mice, respectively. In contrast, cortical area accounted for 64% of the bone area for C3H mice. Importantly, cortical bone accounted for nearly 80% of the bone area in the middle region of the C3H vertebral body. The spatial distribution of the cortical tissue also varied significantly among the strains. C3H mice had a higher cortical polar moment of inertia (CtJ) than B6 mice (p < 0.001), which had a higher CtJ than A mice (p < 0.01).
Table Table 1.. Variation in Morphological and Compositional Traits Among Three Inbred Mouse Strains
The amount of trabecular tissue varied significantly among the inbred strains. B6 mice showed larger trabecular BV/TV values compared with A and C3H mice (p < 0.001). Furthermore, there were significant differences in the microarchitectural traits underlying the variation in BV/TV among the three inbred strains. Most trabecular microarchitectural traits for C3H vertebrae were different than A and B6 vertebrae. C3H trabeculae showed greater trabecular thickness (TbTh), lower trabecular number (TbN), and greater trabecular separation (TbSp) than A and B6 trabeculae (p < 0.001), but similar connectivity as A. In terms of thickness and separation, A and B6 trabecular traits were similar, but B6 trabeculae were more numerous (p < 0.001) and showed greater connectivity (p < 0.01) than A trabeculae.
When averaged over the height of the vertebral body, C3H vertebrae had 6.7% more mineral content than A vertebrae (p < 0.001), which in turn was 4.8% higher than B6 vertebrae (p < 0.001). However, when mineral content was normalized for total cross-sectional area (mineral content/TtAr), A was 13.3% greater than C3H (p < 0.001) and 19.2% greater than B6 (p < 0.001).
Genetic variation in vertebral mechanical properties
Biomechanical data (Table 2) revealed that the C3H vertebrae exhibited more than double the stiffness (263%) of both A and B6 vertebrae (p < 0.001). The A vertebral body had a 34% smaller failure load (Fu) compared with B6 and C3H vertebral bodies (p < 0.001). The total deflection (ΔT) of the A vertebrae was slightly lower than B6 vertebrae (p < 0.05), and C3H vertebrae had a dramatically lower ΔT than B6 vertebrae (p < 0.001). Thus, the data revealed that the failure mode varied significantly among the three inbred strains, with B6 being the most ductile and C3H being the least ductile.
Table Table 2.. Variation in Whole Bone Mechanical Properties Among Three Inbred Mouse Strains
Genetic variation in structure-function relationships
When the partial correlation coefficients were determined for each genotype separately, the univariate analysis revealed that the mechanical properties were significantly correlated with only a few physical bone traits (Table 3). For A mice, ΔT correlated with mineral content (R2 = 0.50), TbN (R2 = 0.48), and TbSp (R2 = 0.48). For B6 mice, FU correlated with TbSp (R2 = 0.36), and ΔT correlated with TbSp (R2 = 0.36) and TbN (R2 = 0.34). For C3H mice, S correlated with mineral content (R2 = 0.46). These data suggest that one trait accounted for a small fraction of the overall variation in mechanical properties.
Table Table 3.. Correlation Coefficients for A (top line of each cell), B6 (middle line), and C3H (bottom line) Taking Body Weight into Consideration
The univariate analysis conducted within each inbred strain also showed that there were significant correlations among the physical bone traits themselves (Table 3). Relationships between traits that were anticipated based on geometric scaling (e.g., TtAr versus BAr) and mathematical dependency (e.g., TbN versus TbSp) were as expected. Unexpected significant relationships were also observed between parameters describing cortical bone and trabecular architecture (e.g., CtAr versus TbTh) and between mineral content and trabecular architecture (e.g., mineral content versus TbN). However, the correlation analysis does not convey the nature of the relationships. Although all three strains may have shown similar correlation coefficients for most trait-trait relationships, the regressions varied with respect to slope and/or intercept. For the relationships between traits where two or more strains showed significant correlations, an analysis of covariance (ANCOVA) was performed, and the resulting relationships were segregated into three categories based on differences in slope and intercept (Table 4). Correlations such as those between TbN and mineral content (Fig. 3A) had similar slopes and intercepts for the three inbred strains, suggesting that the relationship between variables was consistent across genotypes (Table 4A). However, other relationships were unique to each genotype. For example, the relationship between BV/TV and TbTh (Fig. 3B) had similar slopes but different intercepts for each inbred strain (Table 4B). Also, correlations such as those between TbSp and mineral content (Fig. 3C) had significantly different slopes and intercepts (Table 4C). Together, these results clearly showed that each inbred mouse strain constructed vertebrae differently.
Table Table 4.. Relationships Between Bone Traits Were Segregated Into Three Categories by ANCOVA
The stepwise regression (Table 5) revealed that, for each genotype, two to four traits were needed to achieve >70% explanatory power for each mechanical property. Failure load for A mice and total deflection for C3H mice, however, were not well predicted by the stepwise regression with any combination of traits. After an exhaustive search of all possible combinations of traits, including those that were not identified by the stepwise regression, no specific trait combination accurately predicted stiffness, failure load, or deflection for all three strains simultaneously. Most trait combinations accounted for >70% of the variability in mechanical properties for two of the three strains. However, the trait combinations explained <20% of the variability in the third strain. In general, variability in the whole bone mechanical properties of the lumbar vertebral body for each of the inbred strains depended on a combination of multiple traits that specified the morphology and composition of cortical and trabecular tissue, and the structure-function relationships varied among the three strains for each of the three mechanical properties.
Table Table 5.. Stepwise Multivariate Regression Analysis Within Genotypes
In this study, a biomechanical evaluation of vertebral bodies from three inbred mouse strains was conducted to identify morphological and compositional bone traits that contribute to genetic variation in whole bone mechanical properties. The principal finding of this study was that structure-function relationships (i.e., the correlation between whole bone mechanical properties and the underlying physical bone traits) varied with genetic background. The data clearly indicated that mechanically functional structures were achieved in significantly different ways. Each of the inbred strains showed different combinations of adult physical bone trait values that were associated with a particular repertoire of whole bone stiffness, failure load, and ductility. The mean structural and compositional trait values as well as the anatomic variation in morphology were consistent with previous studies.(21–23) The fact that many trait-trait correlations varied among the mouse strains (Fig. 3; Table 4) may be one reason why structure-function relationships varied with genotype. Presumably, the variation in adult trait combinations was caused by differences in genetic and environmental factors that occurred during growth and development. It is expected that other inbred strains will show different trait combinations and, consequently, different repertoires of whole bone stiffness, failure, load, and ductility. Cluster analyses, such as that used previously for mouse femora,(11) could be used to determine how these traits differ from A, B6, and C3H.
The concept that each genotype constructs mechanically functional bones in very different ways seems to be a common theme underlying genetic variation in whole bone mechanical function for most skeletal structures(24,25) and is entirely consistent with the structure-function relationships observed for the mouse femur.(11) In addition to genetic variation directly affecting bone traits, part of the variability could be caused by differences in genes that influence behavioral traits that affect how mice interact with their environment and thus indirectly influence bone traits.(26,27) This study, which examined genetic variability among three inbred strains, indicated that there are more similarities between appendicular and axial bones than previously reported.(21,22) Axial and appendicular bones of A mice were generally slender and had a high mineral content, whereas B6 bones were wider and had a lower mineral content. These trait combinations led to similar stiffness values but significantly different failure modes, with B6 being more ductile. C3H femurs and vertebrae showed a significantly greater cortical area and mineral content, which manifested grossly as increased stiffness, but a brittle failure mode. Previous studies have also shown that differences in the shape of axial and appendicular bones including the ulna, radius, clavicle, femur, mandible, os coxa, tibia-fibula, scapula, and humerus can be used to successfully discriminate among different inbred mouse strains.(12,13,28–30) Thus, the complex relationships between morphology and composition that exist in the mouse femur may also exist in the vertebra, and these genetically determined combinations of traits seem to be responsible for the mechanical variation observed in the bones of inbred mouse strains. Taken together, the genes controlling the morphological and compositional traits of the vertebral body may also affect additional bones even if these bones come through different developmental processes.
The data emphasized the importance of taking a multivariate approach to understand how variability in vertebral whole bone mechanical function arises from variability in the underlying physical bone traits. Silva et al.(23) used a multivariate approach and found that the combination of cortical thickness and trabecular BV/TV explained ∼50% of the variation in failure load for SAMP6 and SAMR1 vertebrae. Based on the current data for the spine, multiple physical bone traits encompassing trabecular, cortical, and compositional elements were needed to account for >70% of the variation in whole bone mechanical properties within each inbred mouse strain (Table 5). Importantly, the identity of the traits that contributed to whole bone mechanical properties varied among the inbred mouse strains. For example, a combination of BV/TV, TtAr, and connectivity explained 76.4% of the variation in A whole bone stiffness; a combination of BAr, CtJ, and TbTh explained 96.0% of the variation in B6 stiffness; a combination of CtAr, CtJ, and TbTh explained 90.1% of the variation in C3H stiffness. Understanding how these whole bone mechanical properties relate to the physical bone traits should provide insight into the underlying biological processes responsible for these genetic variations. However, genotype-phenotype relationships are complex, as shown by comparing A and B6 stiffness. A and B6 mice achieved similar stiffness values, but this came about from different trait combinations and thus, for different genetic and biological reasons. Consequently, the differences in underlying physical bone traits between the two strains led to differences in other mechanical properties because each mechanical property had a unique relationship with the underlying physical bone traits. Thus, a systems approach is needed to fully understand how complex traits or mechanical properties are related to the underlying biology.
The correlations observed among the physical bone traits (Table 3) provided new insight into the way biological processes create mechanically functional structures. Previous research examining the mouse femoral diaphysis suggested that biological processes were capable of balancing physical bone traits that specify the amount (cortical area), distribution (cortical moment of inertia), and quality (mineral content) of bone to achieve stiffness and strength.(11) The current results showed novel correlations among the traits specifying trabecular architecture and mineral content, trabecular architecture and cortical morphology, and cortical morphology and mineral content. Lower trabecular BV/TV seemed to be matched with higher mineral content values. Low BV/TV was also coupled with higher cortical area in the C3H vertebrae. Mineral content was negatively correlated with trabecular number and connectivity and positively correlated with trabecular separation and thickness. Thus, variation in the architecture of the trabecular tissue seemed to be coupled to the amount of mineral within the tissue. This suggested that the relative magnitudes of each trait are subject to biological (adaptive) control mechanisms during growth that ensure an appropriate trait combination is achieved in adulthood to satisfy in vivo loading demands.(31–33) Thus, a systems approach to better understand the relationship between genotype and phenotype revealed two important factors: (1) Multiple traits are needed to explain the genetic variation in whole bone mechanical properties, and (2) the physical bone traits may be coordinately regulated.(34–36) These results provide a potential framework to understand the biological basis for pleiotropic effects as well as to help differentiate how the same or different genetic loci influence these complex mechanical properties. Because of inherent differences in biology and scaling, it is unclear whether these specific relationships identified in mice also exist in the human skeleton. However, this study using inbred mice provided an approach that can be used to study similar biological issues in the human skeleton.
One limitation of this study was that mineral content was assessed noninvasively using μCT as an alternative to the invasive method of ashing. The μCT system that was designed by GE Medical Systems (GEMS) minimized error associated with nonlinearity and beam hardening by equalizing the beam path throughout the field of view using a Lexan equilibration “bath.” Beam hardening would have the effect of cupping, which is an artifact that manifests as lower grayscale values in the middle of a uniformly dense object. For the GEMS μCT system, complete spatial uniformity (field flatness) was observed across a 5-mm homogeneous plug of a cortical bone mimicker. Because the 5-mm cortical bone plug did not generate cupping, a smaller, less dense object such as mouse bone would not be subjected to beam hardening. Therefore, the variation in mineral content along the height of the vertebral body and among inbred strains, which was consistent with previous studies,(24,25) could not be explained as an artifact of imaging technology.
The number of mice used and the large number of physical bone traits and whole bone mechanical properties examined presented a limitation for the correlation matrix. When a large number of tests that are not independent are conducted, the likelihood increases that at least one correlation will achieve statistical significance on the basis of chance alone. Permutation tests can be used to establish a threshold for statistical significance to correct for multiple comparisons.(37) A copy of the analytical program used for this study is available at http://www.jax.org/staff/churchill/labsite under the data sets link.(38) The average threshold values for all three strains were r = 0.85 for p < 0.10 and r = 0.87 for p < 0.05. Thus, after correcting for multiple comparisons, some correlations fail to satisfy this threshold, but many correlations remained significant. Although 10 mice were sufficient to achieve significance for ANOVA and for single trait-trait correlations, 10 mice may not be sufficient when multiple comparisons are examined.
Limitations with the testing methodology may have contributed to poor structure-function relationships for the failure load of A mice and the total deflection of C3H mice. One contributing factor was that not all bone traits were measured, and additional physical traits assessed by destructive means may contribute to the variation in these two examples. Mechanical testing was done by compression and may not be representative of in vivo vertebral loading. In vivo, the mouse vertebral body may experience other modes of loading in addition to compression. Fracture of the vertebral body is also complex because of factors such as hoop stress effects, damage accumulation, and a small height to width ratio. The decreased ductility of C3H vertebrae, which may have led to premature (brittle) failure of the vertebral body, could also explain why this genotype did not show a failure load that was proportionally greater than the other two strains, similar to that observed for stiffness. Furthermore, the structure-function relationships were established using physical trait values that were averaged over the height of the vertebral body. Anatomic variability (Fig. 2) will be important to incorporate in future analyses.
The results of this study provided new insight into the contribution of genetically determined bone traits to variation in whole bone mechanical function. Different genetic backgrounds use different combinations of underlying bone traits to create mechanically functional structures. Using a single complex trait such as BMD or BV/TV as the sole phenotypic marker in genetic analyses may prove to be disadvantageous because of the complex relationship between mechanical properties and the underlying bone traits. Therefore, considering multiple bone traits and the biological, mechanical, and mathematical interaction among these bone traits is necessary to understand the relationship between genetic background and complex whole bone mechanical properties.
The authors thank Philip Nasser for help in developing the mechanical testing protocol and the National Institutes of Health (AR44927, NCRR 1S10RR014801) for support.