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Age-related changes in trabecular bone microdamage initiation
Bone 40 (2007) 973 – 980 www.elsevier.com/locate/bone
Age-related changes in trabecular bone microdamage initiation Srinidhi Nagaraja, Angela S.P. Lin, Robert E. Guldberg ⁎ Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA Petit Institute for Bioengineering and Biosciences, Georgia Institute of Technology, Atlanta, GA 30332, USA Received 8 July 2006; revised 27 October 2006; accepted 31 October 2006 Available online 18 December 2006
Abstract With age, alterations occurring in bone quality, quantity, and microarchitecture affect the resistance of trabecular bone to local failure. The clinical implications of these changes are evident by the observed exponential increase in fracture incidence with age. Although age-related development of skeletal fragility is well established, it is unclear how the local failure properties of bone change with age. We previously reported a specimen-specific technique to assess microstructural stresses and strains associated with microdamage initiation but did not assess age-related changes. In this study, we compared younger (average age 2 years) and older (average age 10 years) bovine trabecular bone to evaluate how alterations in bovine bone quantity and quality with age affect the local mechanical environment associated with microdamage formation. The results show strong positive correlations between microdamage and local stresses and strains for both younger and older bovine trabecular bone. Correlation strength was slightly improved (< 8%) for some parameters by incorporating heterogeneous local material properties based on mineral density into the finite element models. Within individual trabeculae, average stresses and strains were significantly higher in microdamaged trabeculae compared to randomly selected undamaged trabeculae, regardless of age. However, damaged trabeculae in older bone were found to have higher stresses and lower strains than those from younger bone. Corresponding differences in mineral density, microarchitecture, and FEMdetermined local material properties were also observed between the two groups. Taken together, these data suggest marked age-related changes in the mechanics of microdamage initiation at the trabecular level. The combined experimental, computational, and histochemical approaches used in this study provide an improved understanding of microdamage initiation and bone quality. © 2006 Elsevier Inc. All rights reserved. Keywords: Trabecular bone; Microdamage; Microcomputed tomography; Finite element analysis; Aging
Introduction Regions of bone microdamage are formed during normal functional loading of the skeleton and then repaired through the coordinated process of bone remodeling, thus preserving bone's structural integrity. In fact, it has been suggested that bone microdamage is an important stimulus in providing spatial regulation of bone remodeling activity [1–3]. With age, however, alterations in bone quality (collagen, mineral, and water content), quantity (bone volume fraction), and microarchitecture (trabecular thickness, degree of anisotropy, structure model index, etc.) may alter the local failure properties of bone. Furthermore, age-related changes in remodeling ⁎ Corresponding author. Institute for Bioengineering and Biosciences 315 Ferst Drive Atlanta, GA 30332-0405, USA. Fax: +1 404 385 1397. E-mail address: [email protected] (R.E. Guldberg). 8756-3282/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.bone.2006.10.028
dynamics result in an accumulation of unrepaired microdamage that may play an important role in the development of skeletal fragility, particularly in trabecular bone [4–7]. Given its high clinical relevance, numerous studies have investigated age-related alterations in bone quantity and architecture. Micro-CT imaging of trabecular bone has identified architectural changes such as decreased bone volume fraction with associated thinning of trabeculae, altered trabecular shape from plates to rods, and increased anisotropy [8– 11]. Analysis of bone matrix properties revealed that aging results in increased mineralization, mineral crystal size, and non-enzymatic cross-linking with decreased collagen content and reducible/non-reducible cross-link ratio [12–17]. Therefore, variations in bone quantity and quality have major implications in the reported exponential increase in fracture incidence with age [18]. Although age-related development of skeletal fragility has been well documented, the contribution of
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local changes in failure properties is not clear. We previously reported a specimen-specific technique to assess microstructural stresses and strains associated with microdamage initiation in bovine trabecular bone [19]. In the current study, we analyzed how alterations in bone quantity and quality with age affect the local mechanical environment at microdamage initiation. Specifically, the objectives were to (1) analyze spatial correlations of tissue-level stresses and strains with microdamage in younger and older bovine trabecular bone and (2) evaluate age-related changes in the local stresses and strains, mineralization, and microarchitecture associated with microdamage initiation. Materials and methods Specimen preparation Trabecular bone specimens were harvested from the proximal tibia of skeletally mature bovines with average age of 2 years and 10 years old (Animal Technologies, Tyler, TX). Cores were extracted from a single tibia in each age group. Specimens 18 mm in length and 5 mm in diameter were extracted so that the principal material direction was approximately aligned with the loading axis. Stainless steel endcaps were attached to minimize the effects of end artifacts on mechanical testing data [20]. Cylindrical reduced-section samples were created from these cores to produce specimens with an 8 mm overall length and 4 mm diameter. The wasted specimens were wrapped in saline-soaked gauze and stored at − 20 °C until testing [21].
Micro-CT imaging and mechanical testing All specimens were micro-CT imaged (μCT 40, Scanco Medical, Basserdorf, Switzerland) at a voxel resolution of 20 μm. A threshold to distinguish trabecular bone from background was chosen through histogram analysis of grayscale images and remained consistent throughout all evaluations. Automated distance transformation algorithms calculated morphological parameters such as bone volume fraction, trabecular thickness, structure model index (SMI), and trabecular orientation [22]. Trabecular orientation was measured as the angle from the principal axis of the trabeculae to the loading axis. Trabecular bone mineralization (in mg/cm3 HA) was computed from attenuation values of grayscale micro-CT images based on hydroxyapatite (HA) calibration standards. Using a servo-hydraulic mechanical testing system (Mini Bionix 858, MTS Corp.), specimens were preconditioned for 3 cycles to 0.1% strain followed by a uniaxial compression ramp at a rate of 0.5% strain/s. Specimens (n = 6 per age group) were compressed either in the elastic region to 0.55% or to 1.1% strain (approximately the yield strain as determined by preliminary testing) and held at fixed strain for 3 h. In each age group, three specimens were used for each apparent strain endpoint. Apparent strain was calculated using an effective gauge length, defined as the exposed length plus half the length embedded in the endcaps [23]. Specimens were immersed in 0.9% physiologic saline throughout mechanical testing.
Labeling microdamage Microdamage was detected using a sequential fluorescent labeling technique. This technique was previously developed to differentiate preexisting damage from damage induced by in vitro mechanical testing [24,25]. Prior to mechanical testing, specimens were stained with 0.02% alizarin complexone for 8 h at atmospheric pressure to label preexisting microdamage. Preexisting microdamage included damage created from specimen extraction, exposed calcium in resorption cavities created during bone remodeling, and microdamage sustained in vivo prior to animal sacrifice. To improve stain penetration, marrow was removed from specimens prior to staining (WP-72W, WaterPik, USA) and the top endcap was attached only after staining with alizarin
complexone. Specimens were then rinsed in deionized water for 1 h to remove any unbound alizarin complexone stain. After mechanical testing, the endcap top was carefully removed from samples using a diamond saw (Isomet 1000, Buehler Ltd., USA) to improve stain penetration. The localized damage created from this process occurred outside the gauge length and therefore was not in the analysis region. Specimens were stained with 0.005% calcein for 8 h at atmospheric pressure to label microdamage incurred from mechanical testing. Specimens were then rinsed in deionized water for 1 h to remove any unbound calcein stain. After staining, specimens were dehydrated in a series of graded alcohols, cleared and embedded in methyl methacrylate (MMA). Prior to embedding, specimens were secured in custom alignment fixtures to facilitate registration of histological sections to corresponding micro-CT sections for the same specimen. MMA blocks were sectioned into 150–200 μm thick longitudinal slices on a diamond saw and mounted with Eukitt's mounting medium (EM Sciences, USA) onto glass slides. Microdamage in the form of linear and diffuse damage was assessed using a 4× objective (2.4 μm/pixel) in the central four histology sections from each sample. Preexisting microdamage was quantified with grayscale images taken under red epifluorescence. Test-induced microdamage was quantified with grayscale images taken under green epifluorescence. A threshold based on grayscale intensity was chosen to separate microdamaged pixels from undamaged pixels. A lower threshold was chosen to distinguish bone from background. Using image analysis software (Image-Pro Plus, Media Cybernetics, USA), damaged area and bone area were quantified. Damage area was then normalized by the total bone area in each section.
Finite element analysis Micro-CT images were used to create 3-D high-resolution finite element (FE) models for estimating the local stress and strain distributions (FEA software, Scanco Medical, Basserdorf, Switzerland). After thresholding microCT images, individual voxels within the images were directly converted into 1– 3 million hexahedral finite elements by assigning nodal connectivity and bone tissue properties. Approximately six voxels (20 μm/voxel) spanned the mean trabecular thickness, which provided accurate solution convergence [26,27]. A conjugate gradient solver with an element-by-element matrix vector multiplication scheme allowed for the estimation of tissue-level stresses and strains [28]. A homogeneous linear isotropic analysis was utilized. The tissue modulus was back-calculated to match the apparent modulus obtained during testing of the specimens [29]. The back-calculated tissue moduli were 11.5 GPa (2-yearold) and 25.2 GPa (10-year-old). A Poisson's ratio of 0.3 was assumed. A recent study has shown that FE models accounting for spatial variations in tissue properties within trabecular bone more accurately predict the apparent stiffness than analyses performed with homogeneous properties [30]. In order to determine whether intraspecimen mineral variations significantly affected the local stresses/strains initiating microdamage, specimens in both age groups underwent an additional FE analysis with inhomogeneous tissue moduli. Each voxel in the three-dimensional structure was assigned a tissue modulus based on its density and scaled according to the average density and back-calculated modulus. Due to the large number of elements in each model, every voxel was not assigned a unique tissue modulus. Rather, voxels were assigned to one of ten different tissue properties based on its tissue density. Using this approach each sample was scaled independently and tissue moduli ranged from 8.3 to 15.1 GPa for the 2-year-old and for 19.6 to 39.4 GPa for the 10-year-old. Boundary conditions replicating the mechanical test were imposed on the model. Von Mises equivalent stresses and strains, and maximum compressive principal stresses and strains were the mechanical parameters extracted from the FE analysis.
Image registration A two-dimensional automated registration program (MATLAB, MathWorks, USA) was developed to spatially correlate damage with stress or strain distributions within the same sample. This algorithm aligns bone structures between histology and micro-CT sections by implementing rigid registration techniques. In this program, histology images are iteratively rotated and translated with optimal alignment based on the lowest mean squared difference
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Fig. 1. Example of two-dimensional automated image registration. Histology section is iteratively rotated and translated to optimally align with micro-CT section. Gray circles indicate regions of histological processing and sectioning artifacts. image similarity measure. Although good alignment was observed, perfect registration was not possible due to thresholding and sectioning artifacts from histological processing (Fig. 1). Once registered, sections were divided into 3 horizontal subsections (top, middle, and bottom). The normalized damage area in each subsection was then compared to local stresses and strains for that particular region.
Statistics Tukey's pairwise comparisons and t-tests (Minitab, Minitab Inc., USA) were performed to determine statistical significance for microdamage, architecture, mineralization and mechanical parameters between different age groups. In addition, Spearman rank analysis was used to determine the strength of spatial correlations between microdamage and local stresses and strains. The Spearman correlation, a non-parametric measure, was chosen over regression analysis since (1) these data were not normally distributed (as measured by the Anderson–Darling normality test) and (2) stress and microdamage were independent observations that could not be controlled. A Spearman correlation coefficient, R, of 0 implies there is no correlation between the variables; whereas, an R value of 1 indicates a perfect positive correlation.
Results Global architecture and microdamage Bone volume fraction in young trabecular bone specimens (19.6 ± 1.1%, mean ± SE) was higher than in older specimens (15.0 ± 2.0%). Similarly, average trabecular thickness in younger specimens (146.4 ± 5.1 μm) was higher than in older trabecular bone (116.7 ± 1.2 μm). Younger specimens were more anisotropic (degree of anisotropy = 2.15 ± 0.04) than older (degree of anisotropy = 1.65 ± 0.08). Both age groups contained a mix of rod and plate like elements (SMIyoung = 1.63 ± 0.05 and SMIold = 1.71 ± 0.25). The amount of overall preexisting microdamage was not significantly different in younger trabecular bone specimens (0.0023 ± 0.0005 mm2/mm2) compared to older specimens (0.0018 ± 0.005 mm2/mm2). Similarly, there was no significant difference in test-induced microdamage in older specimens (0.0112 ± 0.0021 mm 2 /mm 2 ) than in younger specimens (0.0104 ± 0.0009 mm2/mm2). Although spatial correlations between preexisting damage and test-induced damage was not
possible, approximately 25% of trabeculae with test-induced damage also contained preexisting damage in both younger and older bovine bone specimens. In older samples loaded within the elastic region (0.55%), microdamage was evident on the surface of trabeculae; whereas, in younger specimens no appreciable microdamage was observed. In both younger and older samples loaded to yield, moderate levels of microdamage occurred with cracks extending into the trabecular thickness. Microfractured trabeculae were not detected in any of the loaded samples. The elastic region tests qualitatively suggested differences between the younger and older groups. However, quantitative analysis of the local stresses and strains associated with microdamage initiation were only possible for specimens loaded to apparent yield since this loading protocol produced microdamaged trabeculae in both groups. Correlations of microdamage to local stresses/strains Significant positive correlations between microdamage and compressive principal stress and strain were found for both younger and older specimens (p < 0.05). Age comparisons revealed that the principal strain correlation strength was slightly higher for older (R = 0.65) bone compared to younger (R = 0.52) bone (Table 1). When accounting for mineral density variations within the trabecular bone tissue, inhomogeneous
Table 1 Spatial correlations between microdamage and local compressive stresses and strains Homogeneous
Principal strain Principal stress
Inhomogeneous
2-year-old
10-year-old
2-year-old
10-year-old
0.52 0.49
0.65 0.64
0.56 0.51
0.64 0.63
Spearman rank correlation coefficient for homogeneous and inhomogeneous analyses. Homogeneous FE analysis used a constant bone tissue modulus; whereas inhomogeneous FE analysis utilized a range of bone tissue moduli based on tissue density. Principal stress and strain were significantly correlated to microdamage (p < 0.04).
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FE analyses produced little to no change in correlation strength. For principal stress and strain, correlation strength increased marginally (4–8%) compared to homogenous models in younger bone only (Table 1).
5.7 MPa and 89.2 ± 18.6 MPa for the 2- and 10-year-old groups, respectively. The average von Mises effective stresses and strains followed the same trends as maximum compressive principal stresses and strains, respectively (data not shown).
Local stress/strain homogeneous modeling Local stress/strain inhomogeneous modeling To identify ranges of local stress and strain associated with microdamage initiation, individual microdamaged and undamaged trabeculae were randomly sampled (n = 20 per group) from histology sections. Microdamaged and undamaged trabeculae were identified from thresholded images taken under green epifluorescence. Corresponding trabeculae were then identified within the finite element models (Fig. 2), and the average stress and strain within each extracted trabeculae was determined from boundary conditions that simulated compressive loading to the apparent yield point. In both younger and older samples, damaged trabeculae exhibited significantly higher (p < 0.001) stresses and strains than undamaged trabeculae (Fig. 3). The maximum compressive principal strain in microdamaged trabeculae of 2year-old specimens (1.24 ± 0.06%) was significantly higher compared to microdamaged trabeculae in the 10-year-old samples (0.86 ± 0.08%, p < 0.001) (Fig. 3a). Similarly, maximum compressive principal strain for undamaged trabeculae in the 2-year-old specimens (0.86 ± 0.05%) was significantly greater than in the 10-year-old samples (0.34 ± 0.07%, p < 0.001). The opposite effect was observed for maximum compressive principal stress. The maximum compressive principal stress in microdamaged trabeculae from younger bone was significantly lower (144.1 ± 7.2 MPa) compared to microdamaged trabeculae from older bone (219.2 ± 20.5 MPa, p < 0.001) (Fig. 3b). Maximum compressive principal stresses in undamaged trabeculae were not significantly different (p = 0.60) between age groups. Average maximum compressive principal stresses for undamaged trabeculae were 99.6 ±
Inhomogeneous FE models were employed in order to better represent the variations in local density occurring throughout the trabecular structure. Using inhomogeneous material properties, there were small (< 5%) changes in local stresses and strains for both age groups compared to homogenous analyses (Table 2). For the 2-year-old group, the average maximum compressive principal stress for microdamaged and undamaged trabeculae decreased to 141.7 ± 7.3 MPa and 98.8 ± 5.7 MPa, respectively. For the 10-year-old group, the average maximum compressive principal stresses for microdamaged and undamaged trabeculae slightly increased to 223.9 ± 20.5 MPa and 92.5 ± 18.9 MPa, respectively. These differences in stress from homogeneous estimates showed trends towards significance (p ≤ 0.10) for damaged and undamaged trabeculae in both age groups. There was less than a 2% change in the local principal strains for damaged and undamaged trabeculae in 2-year-old specimens when applying inhomogeneous material properties (Table 2). The average maximum compressive principal strains for microdamaged and undamaged trabeculae decreased to 1.25 ± 0.06% and 0.85 ± 0.04%, respectively. This decrease was only significant in undamaged trabeculae (p = 0.02). In 10-year-old specimens, there was a larger increase (6–9%) in principal strains for damaged and undamaged trabeculae. The average maximum compressive principal strains for microdamaged and undamaged trabeculae increased to 0.91 ± 0.08% and 0.37 ± 0.07%, respectively. This increase was a trend in microdamaged trabeculae (p = 0.06), but significant in undamaged trabeculae (p = 0.02).
Fig. 2. Representative microdamaged and undamaged trabeculae extracted from histology sections and homogeneous finite element models for 2- and 10-year-old age groups. Test-induced microdamaged and undamaged trabeculae were selected after thresholding grayscale images under green epifluorescence.
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Fig. 3. Mechanical parameters for undamaged and test-induced microdamaged trabeculae for 2- and 10-year-old age groups (homogeneous analysis). (a) Microstructural compressive principal strain. (b) Microstructural compressive principal stress. Pairwise comparisons: asterisk symbol (*) indicates significant difference between damaged and undamaged trabeculae within an age group (p < 0.001). Double asterisk symbol (**) indicates significant difference between damaged trabeculae across age groups (p < 0.001).
Local mineralization Once individual trabeculae were extracted, local density was compared between damaged and undamaged trabeculae as well as across age groups (Fig. 4). For 2-year-old specimens, average mineralization for microdamaged trabeculae (896.4 ± 9.5 mg/ cm3 HA) was lower (p = 0.06) than undamaged trabeculae (920.7 ± 8.1 mg/cm3 HA). For 10-year-old specimens, there was no difference in mineralization between damaged (998.6.4 ± 7.9 mg/cm3 HA) and undamaged trabeculae (999.6 ± 6.5 mg/ cm3 HA). Comparing across age groups, local density in the 10year-old group was approximately 100 mg/cm3 HA greater than microdamaged trabeculae in the 2-year-old group (p < 0.001).
age groups, microdamaged trabeculae were significantly thinner in 10-year-old specimens (p < 0.001). Similar analysis of SMI demonstrated that damaged trabeculae were more rodlike than undamaged trabeculae in the younger bovine (p < 0.001). However, there were no differences in SMI between damaged and undamaged trabeculae from older specimens. Finally, trabecular orientation was assessed to determine whether trabeculae oriented at particular angles from the loading axis were preferentially damaged. There were no differences between damaged and undamaged trabeculae for either the 2-year-old (p = 0.96) or 10-year-old groups (p = 0.31). Discussion
Local architecture Trabecular thickness, SMI, and trabecular orientation were analyzed to determine whether damaged trabeculae possessed different microarchitecture than trabeculae that did not sustain damage (Fig. 5). A script written within micro-CT software was used to calculate local SMI, thickness, and orientation of individual trabeculae previously extracted for stress/strain analyses. For 2-year-old specimens, microdamaged trabeculae (131.3 ± 6.0 μm) were significantly thinner than undamaged trabeculae (156.9 ± 7.2 μm, p = 0.01). However, there were no differences in thickness between damaged (98.9 ± 4.9 μm) and undamaged trabeculae (93.2 ± 5.6 μm, p = 0.45) in 10-year-old samples. Comparing between
Degradations in trabecular bone quality may lead to reduced local resistance to microdamage formation. In turn, accelerated microdamage accumulation may be one factor contributing to fractures of the hip, wrist and spine [31,32]. Although the agerelated development of skeletal fragility has been well characterized, the contribution of local changes in failure
Table 2 Inhomogeneous FE analyses had only minor effects on local stresses and strains for damaged and undamaged trabeculae compared to homogeneous FE analyses 2-year-old
Principal strain Principal stress
10-year-old
Damaged
Undamaged
Damaged
Undamaged
0.54% − 1.69%
− 1.18% − 0.78%
6.34% 2.13%
8.70% 3.69%
Values are percentage change between inhomogeneous and homogeneous model estimates. Positive percentage indicates that inhomogeneous analysis resulted in higher stress or strain than homogeneous model estimates.
Fig. 4. Local mineralization for test-induced microdamaged and undamaged trabeculae in 2- and 10-year-old bovine trabecular bone. Pairwise comparisons: asterisk symbol (*) indicates significant difference between damaged trabeculae across age groups (p < 0.001). Cross symbol (†) indicates trend (p = 0.06) between damaged and undamaged trabeculae in younger bovine age group.
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Fig. 5. Local trabecular thickness, structural model index (SMI), and orientation from the loading axis for 2- and 10-year-old bovine trabecular bone. A script was used to calculate local SMI, thickness, and orientation of individual trabeculae previously extracted for stress/strain analyses. SMI values of 3 indicate a rod-like structure; whereas an SMI value of 0 implies a plate-like structure. Pairwise comparisons: asterisk symbol (*) indicates significant difference between test-induced damaged and undamaged trabeculae within an age group (p < 0.02).
properties is unclear. Using a specimen-specific technique, we analyzed younger (average age 2 years) and older (average age 10 years) bovine trabecular bone to evaluate how alterations in bone quantity and quality with age affect the local mechanical environment at microdamage formation. To put the chosen age groups in perspective, 2 years is approximately the age of skeletal maturity and the average life span of a cow is approximately 20 years. Because of the limited age range examined and the fact that cows do not develop skeletal fragility, the results of this study cannot be directly extrapolated to human bone quality, aging, and disease. However, the significant differences observed in microdamage initiation between young and older bovine bone suggests that changes in bone quality may occur with age and warrant future studies on human trabecular bone. Using an automated two-dimensional image registration algorithm, significant positive correlations between microdamage and local stresses and strains were observed for both younger and older bone samples. Although there were significant positive correlations between microdamage and local stresses and strains, several factors may be important in obtaining stronger correlations. First, once microdamage has initiated, non-linear behavior is expected to occur and would decrease the constant tissue properties assumed throughout the linear finite element analysis. Second, sectioning and alignment artifacts during histological processing prevent perfect registration between micro-CT and histology images. Also, spatial correlations were performed without differentiating between linear and diffuse microdamage. Distinguishing between different mechanisms of failure may provide improved correla-
tions. Finally, submicron flaws can not be detected with microCT imaging. These flaws may result in microcrack initiation in regions of estimated low stress, thus reducing the correlation strength. Models created from higher resolution systems, such as synchrotron imaging, may further improve spatial correlations between microdamage and local stresses and strains. Compared to homogeneous models, inhomogeneous FE models are more accurate representations of the heterogeneous distribution of tissue properties observed in trabecular bone. Therefore, it was expected that using inhomogeneous FE analysis would provide improvements in correlation strength between microdamage and local stresses/strains. Although correlation strength improved, these improvements were modest (< 8%) compared to homogeneous FE analysis. The small improvements in correlation strength may be due to averaging within the subsections used for analysis. Refinement of spatial correlations to smaller subsections or a pixel by pixel approach may show a greater effect of accounting for local tissue heterogeneity. In addition, inhomogeneous FE analyses were expected to provide more precise estimates of local stresses and strains in microdamaged and undamaged trabeculae than homogenous model estimates. However, there was less than a 9% difference in stresses and strains in both microdamaged and undamaged trabeculae compared to homogeneous analysis. This result may be due to the voxel resolution used in this study. Models created from higher resolution imaging systems may provide more sensitive distribution of mineral within trabeculae. Significant age-related differences were found in the estimated average local stresses in strains within microdamaged
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trabeculae. Microdamaged trabeculae from younger specimens were found to have higher strain (1.24%) compared to older bone (0.86%). Conversely, the average local stresses in younger microdamaged bone (144.1 MPa) were lower than in older microdamaged bone (219.2 MPa). The higher local stresses are not surprising given that mineralization was significantly higher in the older bone resulting in a greater back-calculated tissue modulus. To assess microdamage initiation, it is necessary to differentiate the stresses and strains observed in damaged and undamaged trabeculae. The initiation of microdamage was assumed to occur in the range between the average stress/strain for undamaged trabeculae and damaged trabeculae. Although the average stress for damaged trabeculae in older bone was significantly higher than in younger bone, the principal stress ranges at which microdamage initiated for younger bone (99– 144 MPa) and older bone (89–219 MPa) overlapped. As a result, an age-related change in the local stress associated with microdamage initiation was not clearly demonstrated. However, the threshold of microdamage initiation in younger trabecular bone occurred between 0.86% and 1.24% principal strain, which did not overlap with the 0.34–0.86% range observed in older bone. These data therefore indicate that bone tissue from the younger specimen was able to sustain larger local strains prior to microdamage formation than bone tissue from the older specimen. However, the use of a linear FE analysis in this study did not capture material softening occurring during microdamage formation or the subsequent stress redistribution to surrounding undamaged elements. As a result, the reported local stresses were overestimated in microdamaged trabeculae and underestimated in surrounding undamaged elements when compared to an FE analysis allowing for material softening. More sophisticated non-linear FE analyses may narrow the ranges of microdamage initiation. Although this is a limitation of the current study, it is important to note that only approximately 1% of the bone is damaged under the pre-failure loading conditions applied, thus limiting the amount of load redistribution that occurs. This study confirmed that strong positive correlations exist between microdamage and local stresses and strains for both younger and older bovine trabecular bone. Within individual trabeculae, microdamage initiated in more mineralized bone tissue from the older bovine at lower strains compared to bone tissue from the younger bovine, suggesting an increasingly brittle local damage behavior with age. The age-related alterations in local mechanics at microdamage formation observed in this study may be a consequence of recently reported changes in bone extracellular matrix with aging. For example, Wang et al. showed that with age, increased nonenzymatic glycation-mediated cross-links reduced the toughness of bone [33]. Also, Nalla et al. speculated that changes in the integrity of the collagen network may weaken crack bridging, a primary mechanism of crack-growth toughness [34]. Consistent with this hypothesis, Paschalis et al. recently used FTIR analysis to demonstrate that the pyridinium (nonreducible)/reducible collagen cross-link ratio is different in patients with osteoporotic fractures compared to normal
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controls [16]. This was found to be true even for a population of premenopausal women with a history of multiple spontaneous fractures, despite normal bone mineral density levels. These data suggest that abnormalities in bone collagen may contribute to skeletal fragility and highlight the important function of local bone material properties. Our study adds to the growing body of knowledge on the role of bone quality occurring with age and lays the foundation for future studies focused on an improved understanding of the relationship between the local mechanical environment, matrix properties, and microdamage in human trabecular bone. Acknowledgments This work made use of ERC Shared Facilities supported by the National Science Foundation under Award Number EEC9731643. The micro-CT system was provided by an NSF Major Research Instrumentation Award (9977551). The authors would like to thank Raymond P. Vito, Andres Laib, Mario D. Ball, and Tracey L. Couse for assistance in this study. References [1] Hansson T, Roos B. Microcalluses of the trabeculae in lumbar vertebrae and their relation to the bone mineral content. Spine 1981;6(4):375–80. [2] Mosekilde L. Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). Bone Miner 1990;10(1):13–35. [3] Fazzalari NL. Trabecular microfracture. Calcif Tissue Int 1993;53(Suppl 1):S143–6 (discussion S146–7). [4] Frost H. Presence of microscopic cracks in vivo in bone. Henry Ford Hosp Med Bull 1960. [5] Turner CH. Biomechanics of bone: determinants of skeletal fragility and bone quality. Osteoporos Int 2002;13(2):97–104. [6] Schaffler MB. Role of bone turnover in microdamage. Osteoporos Int 2003;14(Suppl 5):73–80. [7] O'Brien FJ, Taylor D, Lee TC. Microcrack accumulation at different intervals during fatigue testing of compact bone. J Biomech 2003;36 (7):973–80. [8] Bergot C, et al. Measurement of anisotropic vertebral trabecular bone loss during aging by quantitative image analysis. Calcif Tissue Int 1988;43 (3):143–9. [9] Mosekilde L. Age-related changes in vertebral trabecular bone architecture— assessed by a new method. Bone 1988;9(4):247–50. [10] Mosekilde L. Sex differences in age-related loss of vertebral trabecular bone mass and structure—biomechanical consequences. Bone 1989;10 (6):425–32. [11] Preteux F, Bergot C, Laval-Jeantet AM. Automatic quantification of vertebral cancellous bone remodeling during aging. Anat Clin 1985;7 (3):203–8. [12] Bailey AJ, et al. Age-related changes in the biochemical properties of human cancellous bone collagen: relationship to bone strength. Calcif Tissue Int 1999;65(3):203–10. [13] Boskey AL. Bone mineral crystal size. Osteoporos Int 2003;14 (Suppl 5):16–21. [14] Paschalis EP, et al. FTIR microspectroscopic analysis of normal human cortical and trabecular bone. Calcif Tissue Int 1997;61(6):480–6. [15] Paschalis EP, et al. FTIR microspectroscopic analysis of human iliac crest biopsies from untreated osteoporotic bone. Calcif Tissue Int 1997;61 (6):487–92. [16] Paschalis EP, et al. Bone fragility and collagen cross-links. J Bone Miner Res 2004;19(12):2000–4. [17] Wang X, et al. Age-related changes in the collagen network and toughness of bone. Bone 2002;31(1):1–7.
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[18] Melton 3rd LJ. Epidemiology of hip fractures: implications of the exponential increase with age. Bone 1996;18(3 Suppl):121S–5S. [19] Nagaraja S, Couse TL, Guldberg RE. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech 2005;38 (4):707–16. [20] Keaveny TM, et al. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J Biomech 1994;27(9):1137–46. [21] Linde F, Sorensen HC. The effect of different storage methods on the mechanical properties of trabecular bone. J Biomech 1993;26 (10):1249–52. [22] Hildebrand T, et al. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Miner Res 1999;14(7):1167–74. [23] Keaveny TM, et al. Systematic and random errors in compression testing of trabecular bone. J Orthop Res 1997;15(1):101–10. [24] Lee TC, et al. Sequential labelling of microdamage in bone using chelating agents. J Orthop Res 2000;18(2):322–5. [25] O'Brien FJ, Taylor D, Lee TC. An improved labelling technique for monitoring microcrack growth in compact bone. J Biomech 2002;35 (4):523–6.
[26] Guldberg RE, Hollister SJ, Charras GT. The accuracy of digital imagebased finite element models. J Biomech Eng 1998;120(2):289–95. [27] Niebur GL, et al. Convergence behavior of high-resolution finite element models of trabecular bone. J Biomech Eng 1999;121(6):629–35. [28] Van Rietbergen B, Weinans H, Huiskes R. Computational strategies for iterative solutions of large FEM applications employing voxel data. Int J Numer Methods Eng 1996;39:2743–67. [29] Van Rietbergen B, et al. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 1995;28(1):69–81. [30] Bourne BC, van der Meulen MC. Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CTattenuation. J Biomech 2004;37(5):613–21. [31] Burr D. Microdamage and bone strength. Osteoporos Int 2003;14(Suppl 5):67–72. [32] Martin RB. Fatigue microdamage as an essential element of bone mechanics and biology. Calcif Tissue Int 2003;73(2):101–7. [33] Wang X, Puram S. The toughness of cortical bone and its relationship with age. Ann Biomed Eng 2004;32(1):123–35. [34] Nalla RK, et al. Effect of aging on the toughness of human cortical bone: evaluation by R-curves. Bone 2004;35(6):1240–6.
Age-related changes in trabecular bone microdamage initiation Srinidhi Nagaraja, Angela S.P. Lin, Robert E. Guldberg ⁎ Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA Petit Institute for Bioengineering and Biosciences, Georgia Institute of Technology, Atlanta, GA 30332, USA Received 8 July 2006; revised 27 October 2006; accepted 31 October 2006 Available online 18 December 2006
Abstract With age, alterations occurring in bone quality, quantity, and microarchitecture affect the resistance of trabecular bone to local failure. The clinical implications of these changes are evident by the observed exponential increase in fracture incidence with age. Although age-related development of skeletal fragility is well established, it is unclear how the local failure properties of bone change with age. We previously reported a specimen-specific technique to assess microstructural stresses and strains associated with microdamage initiation but did not assess age-related changes. In this study, we compared younger (average age 2 years) and older (average age 10 years) bovine trabecular bone to evaluate how alterations in bovine bone quantity and quality with age affect the local mechanical environment associated with microdamage formation. The results show strong positive correlations between microdamage and local stresses and strains for both younger and older bovine trabecular bone. Correlation strength was slightly improved (< 8%) for some parameters by incorporating heterogeneous local material properties based on mineral density into the finite element models. Within individual trabeculae, average stresses and strains were significantly higher in microdamaged trabeculae compared to randomly selected undamaged trabeculae, regardless of age. However, damaged trabeculae in older bone were found to have higher stresses and lower strains than those from younger bone. Corresponding differences in mineral density, microarchitecture, and FEMdetermined local material properties were also observed between the two groups. Taken together, these data suggest marked age-related changes in the mechanics of microdamage initiation at the trabecular level. The combined experimental, computational, and histochemical approaches used in this study provide an improved understanding of microdamage initiation and bone quality. © 2006 Elsevier Inc. All rights reserved. Keywords: Trabecular bone; Microdamage; Microcomputed tomography; Finite element analysis; Aging
Introduction Regions of bone microdamage are formed during normal functional loading of the skeleton and then repaired through the coordinated process of bone remodeling, thus preserving bone's structural integrity. In fact, it has been suggested that bone microdamage is an important stimulus in providing spatial regulation of bone remodeling activity [1–3]. With age, however, alterations in bone quality (collagen, mineral, and water content), quantity (bone volume fraction), and microarchitecture (trabecular thickness, degree of anisotropy, structure model index, etc.) may alter the local failure properties of bone. Furthermore, age-related changes in remodeling ⁎ Corresponding author. Institute for Bioengineering and Biosciences 315 Ferst Drive Atlanta, GA 30332-0405, USA. Fax: +1 404 385 1397. E-mail address: [email protected] (R.E. Guldberg). 8756-3282/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.bone.2006.10.028
dynamics result in an accumulation of unrepaired microdamage that may play an important role in the development of skeletal fragility, particularly in trabecular bone [4–7]. Given its high clinical relevance, numerous studies have investigated age-related alterations in bone quantity and architecture. Micro-CT imaging of trabecular bone has identified architectural changes such as decreased bone volume fraction with associated thinning of trabeculae, altered trabecular shape from plates to rods, and increased anisotropy [8– 11]. Analysis of bone matrix properties revealed that aging results in increased mineralization, mineral crystal size, and non-enzymatic cross-linking with decreased collagen content and reducible/non-reducible cross-link ratio [12–17]. Therefore, variations in bone quantity and quality have major implications in the reported exponential increase in fracture incidence with age [18]. Although age-related development of skeletal fragility has been well documented, the contribution of
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local changes in failure properties is not clear. We previously reported a specimen-specific technique to assess microstructural stresses and strains associated with microdamage initiation in bovine trabecular bone [19]. In the current study, we analyzed how alterations in bone quantity and quality with age affect the local mechanical environment at microdamage initiation. Specifically, the objectives were to (1) analyze spatial correlations of tissue-level stresses and strains with microdamage in younger and older bovine trabecular bone and (2) evaluate age-related changes in the local stresses and strains, mineralization, and microarchitecture associated with microdamage initiation. Materials and methods Specimen preparation Trabecular bone specimens were harvested from the proximal tibia of skeletally mature bovines with average age of 2 years and 10 years old (Animal Technologies, Tyler, TX). Cores were extracted from a single tibia in each age group. Specimens 18 mm in length and 5 mm in diameter were extracted so that the principal material direction was approximately aligned with the loading axis. Stainless steel endcaps were attached to minimize the effects of end artifacts on mechanical testing data [20]. Cylindrical reduced-section samples were created from these cores to produce specimens with an 8 mm overall length and 4 mm diameter. The wasted specimens were wrapped in saline-soaked gauze and stored at − 20 °C until testing [21].
Micro-CT imaging and mechanical testing All specimens were micro-CT imaged (μCT 40, Scanco Medical, Basserdorf, Switzerland) at a voxel resolution of 20 μm. A threshold to distinguish trabecular bone from background was chosen through histogram analysis of grayscale images and remained consistent throughout all evaluations. Automated distance transformation algorithms calculated morphological parameters such as bone volume fraction, trabecular thickness, structure model index (SMI), and trabecular orientation [22]. Trabecular orientation was measured as the angle from the principal axis of the trabeculae to the loading axis. Trabecular bone mineralization (in mg/cm3 HA) was computed from attenuation values of grayscale micro-CT images based on hydroxyapatite (HA) calibration standards. Using a servo-hydraulic mechanical testing system (Mini Bionix 858, MTS Corp.), specimens were preconditioned for 3 cycles to 0.1% strain followed by a uniaxial compression ramp at a rate of 0.5% strain/s. Specimens (n = 6 per age group) were compressed either in the elastic region to 0.55% or to 1.1% strain (approximately the yield strain as determined by preliminary testing) and held at fixed strain for 3 h. In each age group, three specimens were used for each apparent strain endpoint. Apparent strain was calculated using an effective gauge length, defined as the exposed length plus half the length embedded in the endcaps [23]. Specimens were immersed in 0.9% physiologic saline throughout mechanical testing.
Labeling microdamage Microdamage was detected using a sequential fluorescent labeling technique. This technique was previously developed to differentiate preexisting damage from damage induced by in vitro mechanical testing [24,25]. Prior to mechanical testing, specimens were stained with 0.02% alizarin complexone for 8 h at atmospheric pressure to label preexisting microdamage. Preexisting microdamage included damage created from specimen extraction, exposed calcium in resorption cavities created during bone remodeling, and microdamage sustained in vivo prior to animal sacrifice. To improve stain penetration, marrow was removed from specimens prior to staining (WP-72W, WaterPik, USA) and the top endcap was attached only after staining with alizarin
complexone. Specimens were then rinsed in deionized water for 1 h to remove any unbound alizarin complexone stain. After mechanical testing, the endcap top was carefully removed from samples using a diamond saw (Isomet 1000, Buehler Ltd., USA) to improve stain penetration. The localized damage created from this process occurred outside the gauge length and therefore was not in the analysis region. Specimens were stained with 0.005% calcein for 8 h at atmospheric pressure to label microdamage incurred from mechanical testing. Specimens were then rinsed in deionized water for 1 h to remove any unbound calcein stain. After staining, specimens were dehydrated in a series of graded alcohols, cleared and embedded in methyl methacrylate (MMA). Prior to embedding, specimens were secured in custom alignment fixtures to facilitate registration of histological sections to corresponding micro-CT sections for the same specimen. MMA blocks were sectioned into 150–200 μm thick longitudinal slices on a diamond saw and mounted with Eukitt's mounting medium (EM Sciences, USA) onto glass slides. Microdamage in the form of linear and diffuse damage was assessed using a 4× objective (2.4 μm/pixel) in the central four histology sections from each sample. Preexisting microdamage was quantified with grayscale images taken under red epifluorescence. Test-induced microdamage was quantified with grayscale images taken under green epifluorescence. A threshold based on grayscale intensity was chosen to separate microdamaged pixels from undamaged pixels. A lower threshold was chosen to distinguish bone from background. Using image analysis software (Image-Pro Plus, Media Cybernetics, USA), damaged area and bone area were quantified. Damage area was then normalized by the total bone area in each section.
Finite element analysis Micro-CT images were used to create 3-D high-resolution finite element (FE) models for estimating the local stress and strain distributions (FEA software, Scanco Medical, Basserdorf, Switzerland). After thresholding microCT images, individual voxels within the images were directly converted into 1– 3 million hexahedral finite elements by assigning nodal connectivity and bone tissue properties. Approximately six voxels (20 μm/voxel) spanned the mean trabecular thickness, which provided accurate solution convergence [26,27]. A conjugate gradient solver with an element-by-element matrix vector multiplication scheme allowed for the estimation of tissue-level stresses and strains [28]. A homogeneous linear isotropic analysis was utilized. The tissue modulus was back-calculated to match the apparent modulus obtained during testing of the specimens [29]. The back-calculated tissue moduli were 11.5 GPa (2-yearold) and 25.2 GPa (10-year-old). A Poisson's ratio of 0.3 was assumed. A recent study has shown that FE models accounting for spatial variations in tissue properties within trabecular bone more accurately predict the apparent stiffness than analyses performed with homogeneous properties [30]. In order to determine whether intraspecimen mineral variations significantly affected the local stresses/strains initiating microdamage, specimens in both age groups underwent an additional FE analysis with inhomogeneous tissue moduli. Each voxel in the three-dimensional structure was assigned a tissue modulus based on its density and scaled according to the average density and back-calculated modulus. Due to the large number of elements in each model, every voxel was not assigned a unique tissue modulus. Rather, voxels were assigned to one of ten different tissue properties based on its tissue density. Using this approach each sample was scaled independently and tissue moduli ranged from 8.3 to 15.1 GPa for the 2-year-old and for 19.6 to 39.4 GPa for the 10-year-old. Boundary conditions replicating the mechanical test were imposed on the model. Von Mises equivalent stresses and strains, and maximum compressive principal stresses and strains were the mechanical parameters extracted from the FE analysis.
Image registration A two-dimensional automated registration program (MATLAB, MathWorks, USA) was developed to spatially correlate damage with stress or strain distributions within the same sample. This algorithm aligns bone structures between histology and micro-CT sections by implementing rigid registration techniques. In this program, histology images are iteratively rotated and translated with optimal alignment based on the lowest mean squared difference
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Fig. 1. Example of two-dimensional automated image registration. Histology section is iteratively rotated and translated to optimally align with micro-CT section. Gray circles indicate regions of histological processing and sectioning artifacts. image similarity measure. Although good alignment was observed, perfect registration was not possible due to thresholding and sectioning artifacts from histological processing (Fig. 1). Once registered, sections were divided into 3 horizontal subsections (top, middle, and bottom). The normalized damage area in each subsection was then compared to local stresses and strains for that particular region.
Statistics Tukey's pairwise comparisons and t-tests (Minitab, Minitab Inc., USA) were performed to determine statistical significance for microdamage, architecture, mineralization and mechanical parameters between different age groups. In addition, Spearman rank analysis was used to determine the strength of spatial correlations between microdamage and local stresses and strains. The Spearman correlation, a non-parametric measure, was chosen over regression analysis since (1) these data were not normally distributed (as measured by the Anderson–Darling normality test) and (2) stress and microdamage were independent observations that could not be controlled. A Spearman correlation coefficient, R, of 0 implies there is no correlation between the variables; whereas, an R value of 1 indicates a perfect positive correlation.
Results Global architecture and microdamage Bone volume fraction in young trabecular bone specimens (19.6 ± 1.1%, mean ± SE) was higher than in older specimens (15.0 ± 2.0%). Similarly, average trabecular thickness in younger specimens (146.4 ± 5.1 μm) was higher than in older trabecular bone (116.7 ± 1.2 μm). Younger specimens were more anisotropic (degree of anisotropy = 2.15 ± 0.04) than older (degree of anisotropy = 1.65 ± 0.08). Both age groups contained a mix of rod and plate like elements (SMIyoung = 1.63 ± 0.05 and SMIold = 1.71 ± 0.25). The amount of overall preexisting microdamage was not significantly different in younger trabecular bone specimens (0.0023 ± 0.0005 mm2/mm2) compared to older specimens (0.0018 ± 0.005 mm2/mm2). Similarly, there was no significant difference in test-induced microdamage in older specimens (0.0112 ± 0.0021 mm 2 /mm 2 ) than in younger specimens (0.0104 ± 0.0009 mm2/mm2). Although spatial correlations between preexisting damage and test-induced damage was not
possible, approximately 25% of trabeculae with test-induced damage also contained preexisting damage in both younger and older bovine bone specimens. In older samples loaded within the elastic region (0.55%), microdamage was evident on the surface of trabeculae; whereas, in younger specimens no appreciable microdamage was observed. In both younger and older samples loaded to yield, moderate levels of microdamage occurred with cracks extending into the trabecular thickness. Microfractured trabeculae were not detected in any of the loaded samples. The elastic region tests qualitatively suggested differences between the younger and older groups. However, quantitative analysis of the local stresses and strains associated with microdamage initiation were only possible for specimens loaded to apparent yield since this loading protocol produced microdamaged trabeculae in both groups. Correlations of microdamage to local stresses/strains Significant positive correlations between microdamage and compressive principal stress and strain were found for both younger and older specimens (p < 0.05). Age comparisons revealed that the principal strain correlation strength was slightly higher for older (R = 0.65) bone compared to younger (R = 0.52) bone (Table 1). When accounting for mineral density variations within the trabecular bone tissue, inhomogeneous
Table 1 Spatial correlations between microdamage and local compressive stresses and strains Homogeneous
Principal strain Principal stress
Inhomogeneous
2-year-old
10-year-old
2-year-old
10-year-old
0.52 0.49
0.65 0.64
0.56 0.51
0.64 0.63
Spearman rank correlation coefficient for homogeneous and inhomogeneous analyses. Homogeneous FE analysis used a constant bone tissue modulus; whereas inhomogeneous FE analysis utilized a range of bone tissue moduli based on tissue density. Principal stress and strain were significantly correlated to microdamage (p < 0.04).
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FE analyses produced little to no change in correlation strength. For principal stress and strain, correlation strength increased marginally (4–8%) compared to homogenous models in younger bone only (Table 1).
5.7 MPa and 89.2 ± 18.6 MPa for the 2- and 10-year-old groups, respectively. The average von Mises effective stresses and strains followed the same trends as maximum compressive principal stresses and strains, respectively (data not shown).
Local stress/strain homogeneous modeling Local stress/strain inhomogeneous modeling To identify ranges of local stress and strain associated with microdamage initiation, individual microdamaged and undamaged trabeculae were randomly sampled (n = 20 per group) from histology sections. Microdamaged and undamaged trabeculae were identified from thresholded images taken under green epifluorescence. Corresponding trabeculae were then identified within the finite element models (Fig. 2), and the average stress and strain within each extracted trabeculae was determined from boundary conditions that simulated compressive loading to the apparent yield point. In both younger and older samples, damaged trabeculae exhibited significantly higher (p < 0.001) stresses and strains than undamaged trabeculae (Fig. 3). The maximum compressive principal strain in microdamaged trabeculae of 2year-old specimens (1.24 ± 0.06%) was significantly higher compared to microdamaged trabeculae in the 10-year-old samples (0.86 ± 0.08%, p < 0.001) (Fig. 3a). Similarly, maximum compressive principal strain for undamaged trabeculae in the 2-year-old specimens (0.86 ± 0.05%) was significantly greater than in the 10-year-old samples (0.34 ± 0.07%, p < 0.001). The opposite effect was observed for maximum compressive principal stress. The maximum compressive principal stress in microdamaged trabeculae from younger bone was significantly lower (144.1 ± 7.2 MPa) compared to microdamaged trabeculae from older bone (219.2 ± 20.5 MPa, p < 0.001) (Fig. 3b). Maximum compressive principal stresses in undamaged trabeculae were not significantly different (p = 0.60) between age groups. Average maximum compressive principal stresses for undamaged trabeculae were 99.6 ±
Inhomogeneous FE models were employed in order to better represent the variations in local density occurring throughout the trabecular structure. Using inhomogeneous material properties, there were small (< 5%) changes in local stresses and strains for both age groups compared to homogenous analyses (Table 2). For the 2-year-old group, the average maximum compressive principal stress for microdamaged and undamaged trabeculae decreased to 141.7 ± 7.3 MPa and 98.8 ± 5.7 MPa, respectively. For the 10-year-old group, the average maximum compressive principal stresses for microdamaged and undamaged trabeculae slightly increased to 223.9 ± 20.5 MPa and 92.5 ± 18.9 MPa, respectively. These differences in stress from homogeneous estimates showed trends towards significance (p ≤ 0.10) for damaged and undamaged trabeculae in both age groups. There was less than a 2% change in the local principal strains for damaged and undamaged trabeculae in 2-year-old specimens when applying inhomogeneous material properties (Table 2). The average maximum compressive principal strains for microdamaged and undamaged trabeculae decreased to 1.25 ± 0.06% and 0.85 ± 0.04%, respectively. This decrease was only significant in undamaged trabeculae (p = 0.02). In 10-year-old specimens, there was a larger increase (6–9%) in principal strains for damaged and undamaged trabeculae. The average maximum compressive principal strains for microdamaged and undamaged trabeculae increased to 0.91 ± 0.08% and 0.37 ± 0.07%, respectively. This increase was a trend in microdamaged trabeculae (p = 0.06), but significant in undamaged trabeculae (p = 0.02).
Fig. 2. Representative microdamaged and undamaged trabeculae extracted from histology sections and homogeneous finite element models for 2- and 10-year-old age groups. Test-induced microdamaged and undamaged trabeculae were selected after thresholding grayscale images under green epifluorescence.
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Fig. 3. Mechanical parameters for undamaged and test-induced microdamaged trabeculae for 2- and 10-year-old age groups (homogeneous analysis). (a) Microstructural compressive principal strain. (b) Microstructural compressive principal stress. Pairwise comparisons: asterisk symbol (*) indicates significant difference between damaged and undamaged trabeculae within an age group (p < 0.001). Double asterisk symbol (**) indicates significant difference between damaged trabeculae across age groups (p < 0.001).
Local mineralization Once individual trabeculae were extracted, local density was compared between damaged and undamaged trabeculae as well as across age groups (Fig. 4). For 2-year-old specimens, average mineralization for microdamaged trabeculae (896.4 ± 9.5 mg/ cm3 HA) was lower (p = 0.06) than undamaged trabeculae (920.7 ± 8.1 mg/cm3 HA). For 10-year-old specimens, there was no difference in mineralization between damaged (998.6.4 ± 7.9 mg/cm3 HA) and undamaged trabeculae (999.6 ± 6.5 mg/ cm3 HA). Comparing across age groups, local density in the 10year-old group was approximately 100 mg/cm3 HA greater than microdamaged trabeculae in the 2-year-old group (p < 0.001).
age groups, microdamaged trabeculae were significantly thinner in 10-year-old specimens (p < 0.001). Similar analysis of SMI demonstrated that damaged trabeculae were more rodlike than undamaged trabeculae in the younger bovine (p < 0.001). However, there were no differences in SMI between damaged and undamaged trabeculae from older specimens. Finally, trabecular orientation was assessed to determine whether trabeculae oriented at particular angles from the loading axis were preferentially damaged. There were no differences between damaged and undamaged trabeculae for either the 2-year-old (p = 0.96) or 10-year-old groups (p = 0.31). Discussion
Local architecture Trabecular thickness, SMI, and trabecular orientation were analyzed to determine whether damaged trabeculae possessed different microarchitecture than trabeculae that did not sustain damage (Fig. 5). A script written within micro-CT software was used to calculate local SMI, thickness, and orientation of individual trabeculae previously extracted for stress/strain analyses. For 2-year-old specimens, microdamaged trabeculae (131.3 ± 6.0 μm) were significantly thinner than undamaged trabeculae (156.9 ± 7.2 μm, p = 0.01). However, there were no differences in thickness between damaged (98.9 ± 4.9 μm) and undamaged trabeculae (93.2 ± 5.6 μm, p = 0.45) in 10-year-old samples. Comparing between
Degradations in trabecular bone quality may lead to reduced local resistance to microdamage formation. In turn, accelerated microdamage accumulation may be one factor contributing to fractures of the hip, wrist and spine [31,32]. Although the agerelated development of skeletal fragility has been well characterized, the contribution of local changes in failure
Table 2 Inhomogeneous FE analyses had only minor effects on local stresses and strains for damaged and undamaged trabeculae compared to homogeneous FE analyses 2-year-old
Principal strain Principal stress
10-year-old
Damaged
Undamaged
Damaged
Undamaged
0.54% − 1.69%
− 1.18% − 0.78%
6.34% 2.13%
8.70% 3.69%
Values are percentage change between inhomogeneous and homogeneous model estimates. Positive percentage indicates that inhomogeneous analysis resulted in higher stress or strain than homogeneous model estimates.
Fig. 4. Local mineralization for test-induced microdamaged and undamaged trabeculae in 2- and 10-year-old bovine trabecular bone. Pairwise comparisons: asterisk symbol (*) indicates significant difference between damaged trabeculae across age groups (p < 0.001). Cross symbol (†) indicates trend (p = 0.06) between damaged and undamaged trabeculae in younger bovine age group.
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Fig. 5. Local trabecular thickness, structural model index (SMI), and orientation from the loading axis for 2- and 10-year-old bovine trabecular bone. A script was used to calculate local SMI, thickness, and orientation of individual trabeculae previously extracted for stress/strain analyses. SMI values of 3 indicate a rod-like structure; whereas an SMI value of 0 implies a plate-like structure. Pairwise comparisons: asterisk symbol (*) indicates significant difference between test-induced damaged and undamaged trabeculae within an age group (p < 0.02).
properties is unclear. Using a specimen-specific technique, we analyzed younger (average age 2 years) and older (average age 10 years) bovine trabecular bone to evaluate how alterations in bone quantity and quality with age affect the local mechanical environment at microdamage formation. To put the chosen age groups in perspective, 2 years is approximately the age of skeletal maturity and the average life span of a cow is approximately 20 years. Because of the limited age range examined and the fact that cows do not develop skeletal fragility, the results of this study cannot be directly extrapolated to human bone quality, aging, and disease. However, the significant differences observed in microdamage initiation between young and older bovine bone suggests that changes in bone quality may occur with age and warrant future studies on human trabecular bone. Using an automated two-dimensional image registration algorithm, significant positive correlations between microdamage and local stresses and strains were observed for both younger and older bone samples. Although there were significant positive correlations between microdamage and local stresses and strains, several factors may be important in obtaining stronger correlations. First, once microdamage has initiated, non-linear behavior is expected to occur and would decrease the constant tissue properties assumed throughout the linear finite element analysis. Second, sectioning and alignment artifacts during histological processing prevent perfect registration between micro-CT and histology images. Also, spatial correlations were performed without differentiating between linear and diffuse microdamage. Distinguishing between different mechanisms of failure may provide improved correla-
tions. Finally, submicron flaws can not be detected with microCT imaging. These flaws may result in microcrack initiation in regions of estimated low stress, thus reducing the correlation strength. Models created from higher resolution systems, such as synchrotron imaging, may further improve spatial correlations between microdamage and local stresses and strains. Compared to homogeneous models, inhomogeneous FE models are more accurate representations of the heterogeneous distribution of tissue properties observed in trabecular bone. Therefore, it was expected that using inhomogeneous FE analysis would provide improvements in correlation strength between microdamage and local stresses/strains. Although correlation strength improved, these improvements were modest (< 8%) compared to homogeneous FE analysis. The small improvements in correlation strength may be due to averaging within the subsections used for analysis. Refinement of spatial correlations to smaller subsections or a pixel by pixel approach may show a greater effect of accounting for local tissue heterogeneity. In addition, inhomogeneous FE analyses were expected to provide more precise estimates of local stresses and strains in microdamaged and undamaged trabeculae than homogenous model estimates. However, there was less than a 9% difference in stresses and strains in both microdamaged and undamaged trabeculae compared to homogeneous analysis. This result may be due to the voxel resolution used in this study. Models created from higher resolution imaging systems may provide more sensitive distribution of mineral within trabeculae. Significant age-related differences were found in the estimated average local stresses in strains within microdamaged
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trabeculae. Microdamaged trabeculae from younger specimens were found to have higher strain (1.24%) compared to older bone (0.86%). Conversely, the average local stresses in younger microdamaged bone (144.1 MPa) were lower than in older microdamaged bone (219.2 MPa). The higher local stresses are not surprising given that mineralization was significantly higher in the older bone resulting in a greater back-calculated tissue modulus. To assess microdamage initiation, it is necessary to differentiate the stresses and strains observed in damaged and undamaged trabeculae. The initiation of microdamage was assumed to occur in the range between the average stress/strain for undamaged trabeculae and damaged trabeculae. Although the average stress for damaged trabeculae in older bone was significantly higher than in younger bone, the principal stress ranges at which microdamage initiated for younger bone (99– 144 MPa) and older bone (89–219 MPa) overlapped. As a result, an age-related change in the local stress associated with microdamage initiation was not clearly demonstrated. However, the threshold of microdamage initiation in younger trabecular bone occurred between 0.86% and 1.24% principal strain, which did not overlap with the 0.34–0.86% range observed in older bone. These data therefore indicate that bone tissue from the younger specimen was able to sustain larger local strains prior to microdamage formation than bone tissue from the older specimen. However, the use of a linear FE analysis in this study did not capture material softening occurring during microdamage formation or the subsequent stress redistribution to surrounding undamaged elements. As a result, the reported local stresses were overestimated in microdamaged trabeculae and underestimated in surrounding undamaged elements when compared to an FE analysis allowing for material softening. More sophisticated non-linear FE analyses may narrow the ranges of microdamage initiation. Although this is a limitation of the current study, it is important to note that only approximately 1% of the bone is damaged under the pre-failure loading conditions applied, thus limiting the amount of load redistribution that occurs. This study confirmed that strong positive correlations exist between microdamage and local stresses and strains for both younger and older bovine trabecular bone. Within individual trabeculae, microdamage initiated in more mineralized bone tissue from the older bovine at lower strains compared to bone tissue from the younger bovine, suggesting an increasingly brittle local damage behavior with age. The age-related alterations in local mechanics at microdamage formation observed in this study may be a consequence of recently reported changes in bone extracellular matrix with aging. For example, Wang et al. showed that with age, increased nonenzymatic glycation-mediated cross-links reduced the toughness of bone [33]. Also, Nalla et al. speculated that changes in the integrity of the collagen network may weaken crack bridging, a primary mechanism of crack-growth toughness [34]. Consistent with this hypothesis, Paschalis et al. recently used FTIR analysis to demonstrate that the pyridinium (nonreducible)/reducible collagen cross-link ratio is different in patients with osteoporotic fractures compared to normal
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controls [16]. This was found to be true even for a population of premenopausal women with a history of multiple spontaneous fractures, despite normal bone mineral density levels. These data suggest that abnormalities in bone collagen may contribute to skeletal fragility and highlight the important function of local bone material properties. Our study adds to the growing body of knowledge on the role of bone quality occurring with age and lays the foundation for future studies focused on an improved understanding of the relationship between the local mechanical environment, matrix properties, and microdamage in human trabecular bone. Acknowledgments This work made use of ERC Shared Facilities supported by the National Science Foundation under Award Number EEC9731643. The micro-CT system was provided by an NSF Major Research Instrumentation Award (9977551). The authors would like to thank Raymond P. Vito, Andres Laib, Mario D. Ball, and Tracey L. Couse for assistance in this study. References [1] Hansson T, Roos B. Microcalluses of the trabeculae in lumbar vertebrae and their relation to the bone mineral content. Spine 1981;6(4):375–80. [2] Mosekilde L. Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). Bone Miner 1990;10(1):13–35. [3] Fazzalari NL. Trabecular microfracture. Calcif Tissue Int 1993;53(Suppl 1):S143–6 (discussion S146–7). [4] Frost H. Presence of microscopic cracks in vivo in bone. Henry Ford Hosp Med Bull 1960. [5] Turner CH. Biomechanics of bone: determinants of skeletal fragility and bone quality. Osteoporos Int 2002;13(2):97–104. [6] Schaffler MB. Role of bone turnover in microdamage. Osteoporos Int 2003;14(Suppl 5):73–80. [7] O'Brien FJ, Taylor D, Lee TC. Microcrack accumulation at different intervals during fatigue testing of compact bone. J Biomech 2003;36 (7):973–80. [8] Bergot C, et al. Measurement of anisotropic vertebral trabecular bone loss during aging by quantitative image analysis. Calcif Tissue Int 1988;43 (3):143–9. [9] Mosekilde L. Age-related changes in vertebral trabecular bone architecture— assessed by a new method. Bone 1988;9(4):247–50. [10] Mosekilde L. Sex differences in age-related loss of vertebral trabecular bone mass and structure—biomechanical consequences. Bone 1989;10 (6):425–32. [11] Preteux F, Bergot C, Laval-Jeantet AM. Automatic quantification of vertebral cancellous bone remodeling during aging. Anat Clin 1985;7 (3):203–8. [12] Bailey AJ, et al. Age-related changes in the biochemical properties of human cancellous bone collagen: relationship to bone strength. Calcif Tissue Int 1999;65(3):203–10. [13] Boskey AL. Bone mineral crystal size. Osteoporos Int 2003;14 (Suppl 5):16–21. [14] Paschalis EP, et al. FTIR microspectroscopic analysis of normal human cortical and trabecular bone. Calcif Tissue Int 1997;61(6):480–6. [15] Paschalis EP, et al. FTIR microspectroscopic analysis of human iliac crest biopsies from untreated osteoporotic bone. Calcif Tissue Int 1997;61 (6):487–92. [16] Paschalis EP, et al. Bone fragility and collagen cross-links. J Bone Miner Res 2004;19(12):2000–4. [17] Wang X, et al. Age-related changes in the collagen network and toughness of bone. Bone 2002;31(1):1–7.
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[18] Melton 3rd LJ. Epidemiology of hip fractures: implications of the exponential increase with age. Bone 1996;18(3 Suppl):121S–5S. [19] Nagaraja S, Couse TL, Guldberg RE. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech 2005;38 (4):707–16. [20] Keaveny TM, et al. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J Biomech 1994;27(9):1137–46. [21] Linde F, Sorensen HC. The effect of different storage methods on the mechanical properties of trabecular bone. J Biomech 1993;26 (10):1249–52. [22] Hildebrand T, et al. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Miner Res 1999;14(7):1167–74. [23] Keaveny TM, et al. Systematic and random errors in compression testing of trabecular bone. J Orthop Res 1997;15(1):101–10. [24] Lee TC, et al. Sequential labelling of microdamage in bone using chelating agents. J Orthop Res 2000;18(2):322–5. [25] O'Brien FJ, Taylor D, Lee TC. An improved labelling technique for monitoring microcrack growth in compact bone. J Biomech 2002;35 (4):523–6.
[26] Guldberg RE, Hollister SJ, Charras GT. The accuracy of digital imagebased finite element models. J Biomech Eng 1998;120(2):289–95. [27] Niebur GL, et al. Convergence behavior of high-resolution finite element models of trabecular bone. J Biomech Eng 1999;121(6):629–35. [28] Van Rietbergen B, Weinans H, Huiskes R. Computational strategies for iterative solutions of large FEM applications employing voxel data. Int J Numer Methods Eng 1996;39:2743–67. [29] Van Rietbergen B, et al. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 1995;28(1):69–81. [30] Bourne BC, van der Meulen MC. Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CTattenuation. J Biomech 2004;37(5):613–21. [31] Burr D. Microdamage and bone strength. Osteoporos Int 2003;14(Suppl 5):67–72. [32] Martin RB. Fatigue microdamage as an essential element of bone mechanics and biology. Calcif Tissue Int 2003;73(2):101–7. [33] Wang X, Puram S. The toughness of cortical bone and its relationship with age. Ann Biomed Eng 2004;32(1):123–35. [34] Nalla RK, et al. Effect of aging on the toughness of human cortical bone: evaluation by R-curves. Bone 2004;35(6):1240–6.