This study characterized the changes in fracture callus structure and composition that occur over time and with pharmacologic or genotypic modulation in order to relate these changes to the gradual restoration of bone stiffness and strength. The MANOVA results indicate that the temporal progression of healing in all three experiments was strongly linked to an increase in tissue mineral density (TMD) in the callus. Although temporal changes in the other measures of callus structure and composition were more subtle in comparison, these other measures did discriminate among treatments and genotypes. For example, BV/TV was strongly associated with differences between treatments or genotypes in Experiments 1 and 3, respectively.
The results of the principal components analysis indicate that the majority of the variability in callus structure and composition among all specimens, irrespective of experimental group, was captured by the outcome measures that quantify the absolute and relative amounts of mineralized tissue in the callus, i.e. BV, BMC, and BV/TV. Comparatively less variability was found among specimens in total callus size (TV), tissue mineral density (TMD), and the standard deviation in mineral density (σTMD). Thus, despite the importance of TMD in describing the time-dependent changes in the calluses, the greatest amount of diversity among the calluses was in the quantity of mineralized tissue present.
Importantly, however, the combination of μCT outcome measures that resulted in the best predictions of torsional strength and rigidity included descriptors of both the quantity and
mineral density of the mineralized tissue. Given that the maximum torque and torsional rigidity are extrinsic measures of strength and stiffness, this finding reflects the importance of both geometry and material properties for the mechanical behavior of the callus. Although significant relationships between callus mechanical properties and mineral density and between callus mechanical properties and the quantity of mineralized tissue have been shown previously [4
], the current results are notable in that the use of multiple regression analyses establishes the independent and respective contributions of each of these two factors. When viewed in conjunction with the MANOVA and PCA results, these regression results indicate that while the regain of bone strength and stiffness over time is due largely to a time-dependent increase in mineral density, this relationship between mechanical properties and mineral density can be modulated by factors that alter geometry.
Several aspects of the experimental design strengthen the findings of this study. First, multivariate statistical analyses were used in order to account for mutual correlations among the μCT outcome measures. For the specimens included in this study, Pearson correlation coefficients (r
) for pairs of the outcome measures ranged −0.64 to 0.95. Whereas the results of univariate comparisons of callus structure and composition among experimental groups would be confounded by these correlations, the multivariate analyses control for them such that the results identify the fundamental and most salient differences in callus structure and composition among experimental groups. Second, this study used a large sample size (188 bones) that provided not only a broad range of callus structure and composition but also greater power in the statistical analyses. The results of PCA can be sensitive to sample size when the ratio of the number of samples to number of variables is less than ten [29
]. Third, cross-validation was performed in conjunction with the stepwise regression analyses in order to test the validity of the resulting set of predictors for maximum torque and torsional rigidity. The robustness of the resulting set of predictors and the low cross- validation prediction errors indicated that meaningful regression models were obtained for the full data set. Given that stepwise regression is confounded by collinearity among the predictor variables, these analyses were performed excluding either BV or BMC, as these two variables were highly correlated (r
=0.95). With either of these two variables excluded from the set of candidate predictors, the maximum correlation coefficient was 0.75. Fourth, because the assessment of callus structure and composition was performed using non-invasive imaging techniques, the results have direct bearing on development of diagnostic indices of fracture healing. The parameters found to be most relevant to callus strength—BV (or BMC), TMD and σTMD
—can all be quantified in vivo
with μCT in small animals and with QCT in humans. Thus, these parameters could potentially be used in pre-clinical and clinical studies as surrogate measures of callus mechanical properties. This in turn would facilitate non-invasive and also longitudinal assessments of the extent and rate of healing. Although it remains to be seen whether the current results also hold for the lower resolution imaging afforded by QCT as compared to μCT, these results certainly indicate that such an investigation is warranted.
A final strength of this study is that specimens from three murine fracture healing experiments were included in order to investigate the effects of several, clinically relevant, biological perturbations on callus structure and mechanical properties. Intermittent PTH treatment has previously been shown to increase callus size [30
], largely by enhancing the endochondral phase of repair [32
]. The MANOVA results for the PTH experiment (Experiment 1) revealed that the effects of PTH on callus structure and composition at the peak of the endochondral phase (Day 14) and beyond were most strongly associated with an increase in BV/TV. In Experiment 2, the separation among treatment groups was greatest during the remodeling phase of repair (Day 42, ) and the treatment effect was due primarily to differences in TMD and callus size (TV and BV). The differences in callus size, particularly at late timepoints, are consistent with known effects of anti-resorptive treatments on osteoclast differentiation and function [33
]. Experiment 3, which investigated the consequences of a catabolic pathology on healing, also showed the greatest differences during callus remodeling (Day 35, ), and these differences were due primarily to lower BV/TV in the B6.MRL/FASlpr
calluses as compared to the C57BL/6 calluses. This difference in callus mineralized volume fraction most likely reflects the increased osteoclast count found in the B6.MRL/FASlpr
calluses as compared to controls [37
Some limitations of this study also warrant discussion. For example, because different genotypes and timepoints were used in the three experiments, it was not possible to make direct, quantitative comparisons among the different biological perturbations. Analyses of callus structure and composition in studies such as those investigating the combined effects of osteogenic and anti-resorptive agents on fracture healing [38
] are needed in order to make such comparisons. An additional limitation of this study is that the effective torsional constant was not computed and was instead estimated by the effective polar moment of inertia. Further, in relating the effective polar moment of inertia to the measured torsional rigidity, it was implicitly assumed that the tissue shear modulus was either constant throughout the callus (in the case of Jeff
) or was proportional to X-ray attenuation (in the case of Jeff,w
). These approximations and assumptions are likely the reason why the measured torsional rigidity was not more strongly predicted by the effective polar moment of inertia, even though Jeff,w
took into account spatial variations in attenuation. The relatively poor predictive capability of the polar moment of inertia agrees with the results of Shefelbine et al.
] who found that estimates of torsional rigidity obtained from finite element models of the calluses were more accurate than those obtained from the polar moment of inertia. Finally, we note that the choice of threshold used in the present study was based on qualitative inspection of the images. The wide spectrum of mineralization, and hence attenuation, contained in the fracture callus presents difficulties for devising an automated method to identify a suitable threshold (). To test the sensitivity of our results to the threshold, we repeated the MANOVA, PCA, and regression analyses for two different thresholds () and found nearly identical results. The only notable discrepancy was in the principal components analysis: σTMD
also contributed heavily to the first and second principal components for the highest and lowest thresholds, respectively. These findings, together with previous findings of good agreement between μCT- and histomorphometry-derived measures of bone volume and bone volume fraction in bone healing studies [39
], demonstrate that the results of this study are not an artifact of the choice of threshold.
Figure 5 The distribution of grayvalues throughout the fracture callus presents difficulties in devising an automated method for identifying a suitable threshold for distinguishing mineralized tissue from unmineralized tissue. (A) Histogram for a specimen from (more ...)
Interestingly, both maximum torque and torsional rigidity were found to depend on the standard deviation in mineral density (σTMD), with larger values of σTMD associated with higher strength and rigidity. Although the mechanistic basis of this relationship is not clear at this time, there are several possible explanations. First, this result may be a consequence of differences in tissue composition among genotypes. Larger values of σTMD, strength, and rigidity were observed in the specimens from Experiment 2, which was conducted on C57BL/6 human RANKL knock-in transgenic mice, as compared to the other two experiments that were conducted on C57BL/6 wild type mice. Second, larger values of σTMD could occur when both mineralized cartilage and mineralized bone tissue are present in the callus, as the former is expected to have somewhat lower mineral density than the latter. Both of these types of mineralized tissue are present in significant amounts towards the end of the endochondral phase, which typically coincides with an increase in callus stiffness and strength. Further investigation of the specific X-ray attenuation values for mineralized cartilage vs. mineralized bone tissue and of the spatial distribution of mineral density throughout the callus are needed to understand more fully the contribution of σTMD to callus mechanical properties.
Given that several of the results of this study indicate the importance of TMD and σTMD
for callus mechanical properties and for describing the variation among calluses, it is necessary to consider factors such as beam hardening and partial volume effects that can confound μCT measurements of tissue mineralization. Although two-voxel “peeling” was used when calculating TMD and σTMD
, it was not possible to ensure that all partial volume effects were excluded. With respect to beam hardening, a correction algorithm based on a 200-mgHA/cc wedge phantom was used in reconstructing the μCT image data in this study. Recent reports have indicated that the use of a 1200-mgHA/cc correction algorithm can reduce the beam hardening artifact, particularly for specimens of high bone volume fraction (BV/TV) [41
]. For the experiment and timepoint that contained specimens with the highest BV/TV and greatest variations in callus size (Experiment 3, day 42), we repeated the μCT analyses on image data reconstructed using the higher density correction algorithm and also repeated the multivariate statistical analyses. The values of TMD and σTMD
changed by 9.7% and 16.1%, respectively (paired -tests, p<0.001), t
indicating that additional work is needed to fully validate measurements of tissue mineralization obtained by μCT. However, the conclusions drawn from the MANOVA, PCA, and regression analyses were unchanged, leading us to conclude that the outcomes of this study were not specific to the beam hardening correction used.
In summary, the results of this study have identified subsets of μCT-derived metrics that describe the time-dependent changes in callus structure and composition and that are significant predictors of callus mechanical properties. These results were obtained through analyses of a diverse set of specimens representing investigations of specific anabolic and catabolic perturbations on healing, and as such, the findings generate a broad picture of how alterations to different biological processes can modulate callus structure, composition, and mechanical function. Taken together, the results demonstrate the use of μCT-based assessments to relate the biology of fracture healing to the gradual regain of bone stiffness and strength and to identify potential surrogate measures of healing.