# A Linkage Representation of the Human Hand Skeletal System Using CT Hand Scan Images
## 4 Discussion
Our models provide longer link lengths for Segment 1 of the five fingers and Segment 4 of the four fingers and shorter link lengths for the remaining finger segments than those of [PERSON] et al. 's models, indicating that the CoRs of the interphalangeal (IP) and CMC joints of the thumb and the MCP joints of the four fingers estimated by our method are further away from the wrist joint center than those estimated by [PERSON] et al. 's method; the CoRs of the  
Figure 6: Variation of finite joint centers (**green**) with the change of flexion–extension of a hand joint. DIP joints of the four fingers estimated by our method are closer to the wrist joint center than those estimated by [PERSON] et al. 's method. The differences in the locations of joint centers between our study and [PERSON] et al. 's study could be caused by several factors. First, [PERSON] et al. [8] anatomically estimated joint centers as the curvature center of the proximal bone head of a given joint, whereas we kinematically estimated joint centers as the centroid of all finite joint centers using 3D hand skeleton motions reconstructed from CT scans. Second, they used cadaver hands to estimate joint centers, whereas we did in vivo. Lastly, [PERSON] et al. used 2D radiographic images taken from the sagittal view to estimate joint centers, whereas we used 3D hand skeletons. The present study built regression models to estimate the \(z\)-coordinates of the CMC joint center of the thumb and the MCP joint centers of the ring and little fingers as a linear function of hand breadth or hand length rather than hand thickness. Regression models based on hand thickness (HT; \(z\) = E \(\times\) HT \(\pm\) error) were constructed but found inferior to those based on hand length or hand breadth. Coefficients of these models (mean \(\pm\) standard error and \(R^{2}\)) were -0.666 \(\pm\) 0.020 (0.987) for the CMC joint center of the thumb, -0.187 \(\pm\) 0.018 (0.889) for the MCP joint center of the ring finger, and -0.360 \(\pm\) 0.035 (0.886) for the MCP joint center of the little finger. These models showed slightly higher \(R^{2}\) values for the ring finger but lower \(R^{2}\) values for the thumb and little finger and much higher standard errors than the models based on hand length or hand breadth. The Pearson correlation analysis showed that the correlation between hand thickness and hand length or hand breadth was weak and not statistically significant. The Pearson correlation coefficients were 0.337 (\(p\) = 0.220) for hand thickness and hand length, 0.368 (\(p\) = 0.177) for hand thickness and hand breadth, and 0.703 (\(p\) = 0.003) for hand length and hand breadth. The weak correlation between hand thickness and hand length or hand breadth could be caused by the obesity level of a participant's hand. For example, a relatively small hand could have a relatively large hand thickness if the obesity level of the participant's hand is relatively high, and vice versa. Thus, hand thickness is not preferred for estimating the \(z\)-coordinates of the CMC joint center of the thumb and the MCP joint centers of the ring and little fingers. The major concern of the present study is the use of a CT scan. Magnetic resonance imaging (MRI) that has no ionizing radiation is an alternative to a CT scan. However, we chose a CT scan instead of an MRI scan in our study after carefully considering several aspects. First, we need to sequentially capture ten hand postures in a short period of time to make sure natural hand motions are captured. A CT scan takes less than one minute (3 to 5 s per scan) to capture the ten postures, whereas an MRI scan takes five hours (30 min per scan), which is practically infeasible. Second, a CT scan performs better in bony structure imaging than an MRI scan that is more suitable for soft tissue imaging. Lastly, the total exposure to radiation of a CT scan could be 5 to 40 mSv (0.5 to 4.0 mSv per scan \(\times\) 10 trials), which is lower than the dose limit of 500 mSv for the hand in a year recommended by Ionizing Radiation Regulations [20].