Synchrotron radiation imaging
The reconstruction images from different sites of the same rat in the sham group were shown in Fig. 1. Compared with conventional CT, the synchrotron radiation images had higher resolution and more details. There were obvious differences in the bone microstructure of different sites.
Fig. 2 showed the reconstructed images of the femoral head of rats in each group. For the same site, compared with the reconstruction images of rats treated with different intensities of swimming, the cancellous bone in the sham group was the most compact, the number of trabeculae was the largest, and the spacing between trabeculae was the smallest. Compared with the sham group, rats in the control group had obvious bone loss, which was characterized by less number of trabeculae and large bone spacing. After the swimming exercise treatment, the bone microstructure of each exercise group was improved, the number of trabeculae was larger, and the bone spacing was smaller compared with the control group. However, it was difficult to judge the difference between the exercise groups simply based on images. Therefore, further quantitative analysis of bone microstructure was necessary.
Bone microstructure analysis
To quantitatively compare the therapeutic effects of different swimming intensities on osteoporosis and the response of different sites to treatment, we calculated the bone microstructure parameters of each group and showed them in Table 1. Regardless of being femoral head, lumbar vertebrae or distal femur, when compared with the sham group, the bone volume fraction (BV/TV), bone surface area to tissue volume ratio (BS/TV), trabecular number (Tb.N) and other parameters which could reflect bone mass were significantly decreased. On the contrary, trabecular separation (Tb.Sp), structural model index (SMI) and other parameters which could reflect the trabecular bone structure and the degree of osteoporosis were significantly increased, indicating that the osteoporosis rat models established in this study was successful.
Compared with the control group, the bone mass of each exercise group was increased and the bone microstructure was improved, which could be seen from the increase of BV/TV, BS/TV, Tb.N and the decrease of Tb.Sp and SMI. These results indicated that swimming exercise had a certain therapeutic effect on osteoporosis. Additionally, different intensity of swimming exercises have different therapeutic effects.
Compared with the femoral head, lumbar vertebrae and distal femur, we found that although the data of different sites showed that the bone microstructure of rats after ovariectomy was degenerated, swimming exercise could improve the bone microstructure. Among the exercise groups, the treatment effect of moderate-intensity exercise group (MIE group) was the best, with the largest BV/TV, BS/TV and Tb.N and the smallest Tb.Sp and SMI, but the range of changes in different sites was different, that is, the degree of osteoporosis in different sites after ovariectomy was different, and the degree of response to treatment was also different.
A one-way ANOVA was performed on the data of each group, and the bone microstructural parameters with significant differences between the groups were retained. The percentage changes of the structural parameters of the femur, distal femur and lumbar vertebrae before and after ovariectomy were compared, as shown in Fig. 3. Except for the structural parameter SMI, which had the largest change in the femoral head, the variation range of bone microstructure parameters in the distal femur was the largest, and the variation range of femoral head was similar to that
of the lumbar vertebrae and slightly higher than that of the lumbar vertebrae. It showed that after ovariectomy, the bone microstructure degeneration of femur (especially the distal femur) was more obvious, and the degree of osteoporosis was higher. Choosing the femur as the diagnostic site could reflect the degeneration of bone microstructure earlier and improv the sensitivity of osteoporosis diagnosis.
For the femoral head, compared with the control group, the BV/TV and BS/TV were significantly increased in all exercise groups, but only in the MIE group they showed a slight but statistically significant increase; the Tb.N was increased in all exercise groups, but only in the MIE and high-intensity exercise group (HIE groups), it was statistically different from that of the control group; the Tb.Sp was decreased in each exercise group, but only in the MIE group it reached a statistically significant level; Similarly, the SMI showed a decreasing trend in the exercise groups, but it was only statistically significant in the MIE group and the HIE group. Overall, the difference between the MIE group and the control group was the largest, indicating that moderate intensity swimming exercise had the most significant effect on bone mass improvement, and the best therapeutic effect on osteoporosis.
In summary, morphological characteristics can reflect the changes of bone microstructure to some certain extent, but careful selection of certain index or site will improve the accuracy of diagnosis and efficacy evaluation of osteoporosis. The change of femur was more sensitive, suggesting that the femur (especially the distal femur) might be more suitable for the diagnosis and efficacy evaluation of osteoporosis than lumbar vertebrae. Therefore, it is necessary and meaningful to select the appropriate site and introduce more bone microstructure features besides bone mass to evaluate bone strength.
Correlation between bone microstructure and bone strength
The diagnostic significance of osteoporosis is to predict the risk of fracture. We are more concerned about the ability of bone not to fracture under external force, that is, the strength of the bone. Combined with bone microstructure imaging and histomorphological analysis, the structural information of bone can be obtained quantitatively, which is helpful for early identification and detection of bone microstructure degradation. However, how bone microstructure affects bone strength and the relationship between bone microstructure and mechanical properties still need further study.
Pearson correlation coefficient (R) was used for univariate regression analysis to explore the correlation between bone mineral density, trabecular structure parameters and bone strength. The linear regression model between bone microstructure parameters and failure load was shown in Fig. 5. From the results, there was a significant correlation between the parameters and the failure load (P < 0.05). The failure load was positively correlated with trabecular bone density (Tb.vBMD), BV/TV, BS/TV and Tb. N, and negatively correlated with Tb.Sp and SMI. That is, the higher bone
density, the larger BV/TV, the larger BS/BV, the larger Tb.N, the smaller Tb.Sp and the smaller SMI, the fracture resistance ability of the bone would be greater and less prone to fracture.
The parameters closely related to failure load were BV/TV and SMI (| R | = 0.81, 0.82, Fig. 5 (b), (f) ). In contrast, Tb. vBMD showed only a moderate linear correlation with bone strength (| R | = 0.73, Fig. 5 (a) ). In addition, BS/TV, Tb. N and Tb. Sp were moderately correlated with bone strength (| R | = 0.62, 0.75, 0.7, Fig. 5 (c), (d), (e) ).
Bone strength prediction model
The FEM analysis can obtain the mechanical characteristics of bone noninvasively, but the complicated process of modeling and analysis limit its clinical application.
The above research showed that bone microstructure was a more important parameter than BMD in the assessment of bone strength. Bone microstructure imaging could detect the changes of fine spatial structure of bone earlier and more accurately. Therefore, we proposed a machine learning model for calculating the strength of trabecular bone, which predicted bone strength by fusing more bone microstructure parameters than bone mass, hoping to be an alternative to the FEM.
Elastic net regression includes L1 regularization and L2 regularization, which not only has the sparsity of lasso regression, but also has the regularization ability of ridge regression, and can deal with groups of highly correlated variables more effectively. In this study, through 5-fold nested cross-validation, the average coefficient of determination (R2) and average root mean square error (RMSE) between the predicted value of the model and the calculated value of the finite element method were 0.774 and 0.110. Figure 7 showed the correlation between each bone microstructure parameter and the predicted bone strength. The best predictive model integrated 5 features of BV/TV, BS/BV, Tb.Sp, Tb.N and SMI, and was superior to the results of using any single variable to predict bone strength. The comparison of the results of each model was shown in Table 2. Figure 8 depicted the scatter plot of the model's results on the test set. Figure 9 further compared the consistency of the two bone strength assessment methods of FEM analysis and predictive model by Bland-Altman diagram. The mean ± variance between the bone strength calculated based on EFA and the model prediction was 0 ± 0.23, which indicated that there was no significant statistical difference between the two methods,
and there was no systematic bias. The method of predicting bone strength through the predictive model can be a good alternative to the FEM.