## 3 Results
### VBQ Determination Methods' Results  
VBQ was determined for a mid-sagittal slice of six randomly selected series using three different methods: the hand-drawn ROI method, automated segmentation from T1-weighted images, and automated segmentation with an applied erosion algorithm. Figure 6 shows an example of the three VBQ determination methods on the same image.  
Table 2 shows the result of VBQ score determination using Equation (9).  
Four different methods were compared for VBQ determination (T1_VBQ, T1_VBQ, eroded, T2_VBQ and T2_VBQ_eroded). Examples of the segmentation with each method and the segmentation with the trained neural network model are shown in Figure 7 as a 3D rendering. The 3D rendering was performed with the ITK-SNAP software application (version 4.2.0.) [26].  
Table 3 shows the results of the four methods of VBQ determination, with average values and standard deviations for VBQ score, vertebra SI, and CSF signal intensity. These values were determined across the 83 studies randomly selected from the resident hospital database, with 166 series of images.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Series** & **Manually Drawn ROI VBQ** & **T1_VBQ** & **T1_VBQ_eroded** \\ \hline
1 & 3.37 & 2.80 & 3.01 \\ \hline
2 & 2.60 & 2.69 & 2.86 \\ \hline
3 & 3.52 & 3.29 & 3.46 \\ \hline
4 & 3.58 & 3.09 & 3.27 \\ \hline
5 & 4.22 & 3.59 & 3.84 \\ \hline
6 & 3.61 & 2.67 & 3.02 \\ \hline \end{tabular}
\end{table}
Table 2: Results of VBQ determination.  
Figure 6: **(a)** Hand-drawn ROIs for vertebra and CSF, shown as red circles. **(b)** ROIs generated by automatic segmentation from trained neural network model and CSF extraction algorithm (T1_VBQ). **(c)** Same as **(b)**, with erosion algorithm applied to vertebrae and CSF ROIs (T1_VBQ_eroded). In **(b,c)**, red color represents vertebrae segmentation, while green color represents CSF segmentation.  
Each set of VBQ scores obtained using one of the four different methods was compared using a one-way ANOVA statistic to determine if there were statistically significant differences between the four methods. The resulting \(p\)-value is \(p=0.00001<0.05\), which  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **T1\_VBQ** & **T1\_VBQ\_ eroded** & **T2\_VBQ** & **T2\_VBQ\_ eroded** \\ \hline VBQ score & 2.60 \(\pm\) 0.56 & 2.73 \(\pm\) 0.58 & 2.21 \(\pm\) 0.54 & 2.33 \(\pm\) 0.57 \\ \hline Vertebra SI & 127.50 \(\pm\) 31.84 & 133.94 \(\pm\) 34.48 & 124.68 \(\pm\) 30.52 & 131.61 \(\pm\) 33.19 \\ \hline CSF SI & 50.39 \(\pm\) 14.48 & 50.39 \(\pm\) 14.48 & 59.05 \(\pm\) 22.39 & 59.05 \(\pm\) 22.39 \\ \hline \end{tabular}
\end{table}
Table 3: Results of VBQ determination.  
Figure 7: (a) Upper: T1-weighted segmentation mask provided by trained neural network model (vertebrae and spinal canal). Lower: T2-weighted segmentation mask provided by trained neural network model. Different colors represent each of the 9 segmentation classes, which are labeled 1 – 9 in the segmentation masks. (b) Upper: T1_VBQ method. Lower: T2_VBQ method. (c) Upper: T1_VBQ_ eroded method. Lower: T2_VBQ_ eroded method. In (b,c) green regions represent segmented CSF, while red colored regions represent segmented vertebrae.  
means that there is a significant statistical difference between the datasets. A post hoc Tukey's Honest Significant Difference (HSD) test was applied to the same data to assess the significance of differences between pairs of VBQ scores obtained by the different methods. The results show that there is a statistically significant difference between the T1_VBQ and T2_VBQ methods (\(p\) = 0.00006), the T1_VBQ and T2_VBQ_eroded methods (\(p\) = 0.00907), the T1_VBQ_eroded and T2_VBQ methods (\(p\) = 0.000001), and the T1_VBQ_eroded and T2_VBQ_eroded methods (\(p\) = 0.00004).