## 2 Methods and Materials
### Bone-Density Observation by Micro-CT Analysis  
The bone densities of the artificial bones were those specified for the product, which are 5, 10, 12, 20, and 30 pcf, respectively. On the other hand, the bone density of the cadaveric bone was determined using micro-CT. Figure 1 shows an example of a micro-CT image of a cadaveric bone. Bone-density estimation using micro-CT image data extracted from digital imaging and communications in medicine (DICOM) data consists of preprocessing for image noise removal, bone region extraction based on thresholding and morphology processing, and a comparative analysis of the bone region volume and high-intensity region volume inside the bone region. DICOM, which was initially developed in the 1980s, provides a unified format for storing, transmitting, and sharing medical images and associated patient information across different healthcare systems and devices. DICOM has become the de facto standard for medical imaging because of its comprehensive specifications and support for a wide range of imaging modalities, including X-rays, CT, magnetic resonance imaging (MRI), ultrasound, and nuclear medicine. Preprocessing uses a mid-value filtering process with a spherical kernel of radius one voxel. The bone region extraction procedure consisted of binarization at luminance values of 4000 or higher, extraction of the connected component of the largest volume, and filling of the extracted region. The connected component of the maximum volume was obtained based on the results of the 3D labeling process for the area obtained by binarization (3D labeled image). Bone regions were extracted by closing and hole-filling processes to obtain the maximum volume component. First, a 3D morphological closing process using a spherical kernel with a radius of 4.5 voxels was applied to the extracted maximum volume component region. Next, 2D hole-filling of the region was performed on each axial slice. The same 3D morphological closure process was repeated to determine the final bone region. Finally, the volume of the extracted bone region and the high-intensity region within the bone region with a luminance value of 4000 or higher were measured, and the volume ratio of the high-intensity region to the bone region was calculated. Each parameter employed in the above process was experimentally optimized.  
The percentage of luminance values greater than 4000 obtained from micro-CT scans ranged from 0.486 to 0.664, with a mean value of 0.537 and a standard deviation of 0.0513. The absolute value of the bone density was determined from the proportions obtained from phantom measurements [25] in previous studies. In this study, an approximation was made by fitting a high coefficient of determination of the peak torque and bone density at the time of implantation obtained from the simulated bones, as shown by the circular plot in Figure 2. The percentage of the peak torque evaluation results for each cadaveric bone with a luminance value of 4000 or higher was used as the bone density to determine the bone density shown in the square plots to minimize the squared error with fitting. As a result, the bone density of the cadaveric bones was estimated to be equivalent to 7.73 pcf to 10.5 pcf. The bone density was included into the dataset as a clinical parameter, yielding a total of 65 variables and utilizing a dataset standardized by each explanatory variable.  
For bone-density information in this study, only the value averaged over the entire bone was used as a feature. In the future, accuracy may be improved by introducing information on the fine reticular structure and structure of the cortical and trabecular bones. However, because the information to be used in clinical practice will be obtained from multislice CT, it is expected to be more convenient to use the overall average value, as in the present study. It is also possible to introduce values measured using dual-energy X-ray absorptiometry (DEXA).