## 3 Results  
The detection accuracy of the trained models, which involved a careful comparison between the bounding boxes identified by the trained model and the labeled bounding boxes annotated by expert physicians, was a robust 0.969 for mAP (50) and 0.573 for mAP (50-95). The best score for precision was 0.953, and for recall was 0.956. These analyses were  
Figure 3: (a) The detection of the center coordinate of the bounding box. The X-axis indicates radial–ulnar direction and the Y-axis indicates dorsal-palmar direction. (b) The trajectory plot. The maximum distance of MN movement was shown as the X distance on the X-axis and as the Y distance on the Y-axis.  
Figure 2: Images of the CTS detection model showed that it could detect MN by being surrounded by the bounding box.  
performed using 20% of our basic input data of 5000 US images derived from 100 hands as test data.  
The characteristics of the MN dynamics analysis participants from the remaining 40 hands are shown in Table 1. The control group consisted of twelve males and eight females with a mean age of 55.2 \(\pm\) 4.52 years, ranging from 32 to 75 years. The CTS group consisted of eight males and twelve females. The mean age was 67.9 \(\pm\) 2.82 years, ranging from 28 to 80 years. There was no significant age difference between the two groups.  
The X distance was 3.56 \(\pm\) 0.39 mm in the control group and 2.04 \(\pm\) 0.21 mm in the CTS group. The Y distance was 1.06 \(\pm\) 0.14 mm in the control group and 0.96 \(\pm\) 0.29 mm in the CTS group (Figure 4). The X distance was significantly shorter in the CTS group than in the control group (\(p\) = 0.0002), and the Y distance was shorter in the CTS group (not significant). The X distance for each stage of CTS was 2.03 mm (Stage 2), 2.22 mm (Stage 3), 2.08 mm (Stage 4, 5); the Y distance was 1.11 mm (Stage 2), 0.82 mm (Stage 3), 0.80 mm (Stage 4, 5); and there were no significant differences between CTS stage.  
When analyzing the MN velocity, the X velocity was 3.74 \(\pm\) 0.71 mm/s in the control group and 2.71 \(\pm\) 0.18 mm/s in the CTS group. The Y velocity was 1.39 \(\pm\) 0.33 mm/s in the control group and 1.02 \(\pm\) 0.10 mm/s in the CTS group. The magnitude velocity was 4.22 \(\pm\) 0.81 mm/s in the control group and 3.14 \(\pm\) 0.22 mm/s in the CTS group. The velocity of Y did not show significant differences between the two groups, and both the  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Control Group** & **CTS Group** \\  & **(n = 20)** & **(n = 20)** \\ \hline Age & 55.2 (4.52) & 67.9 (2.82) \\ Sex & & \\ Male & 12 & 8 \\ Female & 8 & 12 \\ NCS & & \\ Healthy volunteer & 11 & - \\ Stage 1 & 9 & - \\ Stage 2 & - & 5 \\ Stage 3 & - & 7 \\ Stage 4 & - & 7 \\ Stage 5 & - & 1 \\ \hline \hline \end{tabular} Data were presented as the mean value (standard deviation). Abbreviations: CTS, carpal tunnel syndrome; NCS, nerve conduction study.  
\end{table}
Table 1: The participant’s characteristics.  
Figure 4: The X distance and Y distance in each group. The X distance in the CTS group was significantly shorter than that of the control group.  
X velocity (\(p\) = 0.03) and magnitude velocity (\(p\) = 0.03) showed statistically significant differences (Figure 5). The X velocity for each stage of CTS was 2.46 mm/s (Stage 2), 2.40 mm/s (Stage 3), 2.83 mm/s (Stage 4, 5); the Y velocity was 1.05 mm/s (Stage 2), 0.94 mm/s (Stage 3), 0.96 mm/s (Stage 4, 5); the magnitude velocity was 2.68 mm/s (Stage 2), 2.59 mm/s (Stage 3), 3.01 mm/s (Stage 4, 5); and there were no significant differences between the CTS stages.