## Materials and Methods
### Computation of Forearm \(R^{ca/ha}\) from Peripheral Cone Beam Computed Tomography (CBCT) Images  
Using forearm images obtained by peripheral CBCT, we first calculated the \(R^{ca/ha}\). We extracted the areas from both cortical radius and ulnar bones as shown in Figure 1b. The cortical bone compartment was segmented by an auto-contouring process, which generates a periosteal contour that delineates mineralized bone and extra-osseal soft tissue, and an endosteal contour that delineates the endocortical boundary from the cancellous compartment [19; 20]. To extract the periosteal surface, the thresholding which defined the cortical bone was applied to the CT image to obtain the contour of cortical bone. The endosteal surface was extracted by masking the periosteal surface with bone mask from an original image, and the periosteal contour was peeled to leave only the marrow pixels [21]. Subsequently, we subtracted the endosteal surface from periosteal surface to obtain the cortical bone segmentation. The areas of cortical radius and ulna bones were calculated by counting the number of pixels inside the extracted cortical bone segment. Finally, the total radius and ulna bone areas were calculated by counting the total number of pixels of periosteal surface, and defined by \(Ar^{c}(radius)\) and \(Ar^{c}(ulna)\), respectively [22; 23]. Next, we calculated the total radius and ulna bone areas by counting the total number of pixels within the cortical areas, as shown in Figure 1c. The total radius and ulna bone areas were defined by \(Ar^{t}(radius)\) and \(Ar^{t}(ulna)\), respectively. Each four-part area comprised of \(Ar^{c}(radius)\), \(Ar^{c}(ulna)\), \(Ar^{t}(radius)\), and \(Ar^{t}(ulna)\) was confirmed by two radiologists. Finally, we calculated \(R^{ca/ha}\) in four different ways, as shown in Equations (1)-(4).  
\[R^{ca/ha}(radius)\ =\ Ar^{c}(radius)/Ar^{t}(radius) \tag{1}\]  
\[R^{ca/ha}(ulna)\ =\ Ar^{c}(ulna)/Ar^{t}(ulna) \tag{2}\]  
\[R^{ca/ha}(total)\ =\ [Ar^{c}(radius)\ +\ Ar^{c}(ulna)]/[Ar^{t}(radius)\ +\ Ar^{t}(ulna)] \tag{3}\]  
\[R^{ca/ha}(average)\ =\ [R^{ca/ha}(radius)\ +\ R^{ca/ha}(ulna)]/2 \tag{4}\]  
For the general expression, we used \(R^{ca/ha}(type)\), where \(type\in\{radius,\ ulna,\ total,\ average\}\). The four ratio types of the cortical bone area to the total bone area of \(R^{ca/ha}(type)\) were repeatedly computed for all 797 slice images.  
During the post-processing of all 797 slice images, the radiologists first identified the 50-slice midshaft area (region \(M\)) as shown in Figure 2. Note that 50 slices are equivalent to 10.8 mm in length (e.g., 50 \(\times\) 0.2162 mm). Subsequently, the 50-slice image region in the proximal direction was defined as region \(P1\), and the other 50 slice image regions in the distal direction as \(D1\) to \(D8\). In this way, we classified into the 10 region with each 50 slice image region. More specifically, \(R_{G}{}^{ca/ha}(type)\) was defined as the mean value of \(R^{ca/ha}(type)\) in the region \(G\), where \(G\in\{D1,\ D2,\ D3,\ D4,\ D5,\ D6,\ D7,\)  
Figure 1: (**a**) Forearm images of the radius and ulna. (**b**) Separation of the cortical bones. (**c**) Total bone areas (red area + white area).  
\(D8\), \(M\), \(P1\)). For instance, \(R_{D1}{}^{\alpha/ta}\)(_radius_) represents the mean value of \(R^{\alpha/ta}\)(_radius_) in the region \(D1\), while \(R_{M}{}^{\alpha/ta}\)(_total_) is the mean value of \(R^{\alpha/ta}\)(_total_) in the region \(M\).