## 4 Discussion  
Our proposed method is simple and easily reproducible because of the simple steps for BMD estimation. There are three main steps for the femoral neck BMD estimation. Firstly, the forearm bone CT images, especially for midshaft area, are obtained using CBCT. Secondly, cortical bone ratio of the forearm bone is measured automatically based on the cortices thickness to the amount of total bone. Figure 4: Bland–Altman plot: the mean of \(e\)-\(BMD_{M}\)(_average_) and \(BMD^{\prime}\)_versus_ the difference of \(e\)-\(BMD_{M}\)(_average_) and \(BMD^{\prime}\). Area bone mineral density derived from dual-energy X-ray absorptiometry (BMD\({}_{\text{DXA}}\)) and computed tomographic images (BMD\({}_{\text{CBR}}\)). \(e\)-\(BMD_{M}\)(_average_) systematically underestimates \(BMD^{\prime}\). The circle represents the difference of \(e\)-\(BMD_{M}\)(_average_) and \(BMD^{\prime}\) for each sample. Solid and dash lines represent mean\(\pm\)1.96\(\times\)standard deviation of the differences of \(e\)-\(BMD_{M}\)(_average_) and \(BMD^{\prime}\). Figure 5: (**a**) Regression plot of \(R_{M}\)\({}^{\alpha\)/\(\alpha\)(_average_) _versus BMD\({}^{\prime}\)_. (**b**) Correlation plot of \(e\)-BMD\({}_{M}\)_versus BMD\({}^{\prime}\)_.  
Lastly, the femoral neck BMD is estimated using the established equation between femur neck BMD and the measured ratio. We further investigated the correlations of lumbar spine BMD (\(BMD^{ls}\)) and total femur BMD (\(BMD^{lf}\)) with \(R_{M}{}^{\alpha/Na}\)(_Average_), respectively. \(BMD^{ls}\) and \(BMD^{lf}\) were obtained in the same manner as for \(BMD^{f}\) from DXA. Figure 6 shows the correlation of \(R_{M}{}^{\alpha/Na}\)(_average_) with \(BMD^{ls}\) and \(BMD^{lf}\), respectively. The correlation coefficients were \(r\) = 0.647 and 0.792, respectively, as summarized in Table 4. Note that the correlation of \(BMD^{f}\) corresponded to \(r\) = 0.857. \(R_{M}{}^{\alpha/Na}\)(_average_) was also correlated with BMDs of the lumbar spine and total femur. The higher correlation from femoral neck can be interpreted that the structure of femoral neck is similar with that of radius and ulna in forearm, which is cortical and trabecular bone structure. Bone strength is determined by several factors of cortical thickness, bone size, trabecular bone density, and architecture. All these facts change with age as a result of the remodeling process. The cortical bone in a forearm and a femoral neck BMD also change with age [17; 18]. However, there is a report that forearm BMD with DXA provides inadequate accuracy and very low predictive ability for identifying hip osteoporosis or femoral neck BMD [24]. Even though the femoral neck and the forearm bones are not directly associated with each other, similar research effort has been conducted on the relationship between BMDs from different sites. In [25; 26; 27], the results showed that that some parameters from the cortical bone in distal radius and ulnar on anteroposterior radiograph could reflect the femoral neck BMD. In [25], the distal radius BMD was correlated with the ratio of the outside cortical shell diameter to the inside cortical shell diameter at the metaphyseal/diaphyseal junction. In [26], radiologic density of dental structure from CBCT imaging could provide information of lumbar vertebra and femoral neck. In [27], the radial bicortical widths were measured at 50 and 70 mm proximal to the distal ulnar articular surface, and the mean bicortical width was compared with each patient's femoral BMD. The results showed that bicortical thickness of the distal radius was positively correlated with femoral neck BMD. It reflects similarity in quality and loading properties of the femur and radius as appendicular bones. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Correlation Coefficients** & \(BMD^{ls}\) & \(BMD^{lf}\) & \(BMD^{lf}\) \\ \hline \(R_{M}{}^{\alpha/Na}\)(_average_) & 0.647 & 0.792 & 0.857 \\ \hline \hline \end{tabular}
\end{table}