## 4 Discussion  
Automatic segmentation of vertebrae and the spinal canal from T1- and T2-weighted MRI data was achieved by training a hybrid CNN-transformer neural network, BRAU-Net++, using a publicly available dataset. The resulting model achieved good accuracy, precision and DSC values. Compared to the DSC scores of the state-of-the-art nnU-Net neural network, BRAU-Net++ achieves comparable results for vertebral segmentation and poorer results for spinal canal segmentation. This is also in line with a review of modern deep learning architectures for lumbar spine imaging, which reports DSC values between 84.9 and 93 for different U-Net-based architectures [27]. The accuracy values approach 99% for each class, which can be explained by the relative number of TP and TN pixels in the segmentation images [27]. As is common in medical image segmentation, the segmented area comprises only a small part of the image, while the background contains all other pixels. For this reason, the number of TP pixels is much smaller than the number of TN pixels. Consequently, the accuracy of Equation (5) yields large values for each segmentation class [27].  
The spinal canal class has the lowest DSC and accuracy values, which can be explained by the different pixel intensities of the CSF in T1-weighted and T2-weighted images. In T1-weighted images, the CSF is dark and has low intensity values. Conversely, the CSF in T2-weighted images is bright, i.e., it contains high pixel intensity values. Since the network was trained simultaneously with T1- and T2-weighted image data, the difference in pixel values in only one part of the segmented region (spinal canal) could influence the training and the resulting neural network model.  
Although the evaluation metrics obtain good results, in some of the 166 data series selected for VBQ determination, label mixing is present in the resulting segmentation. The cause of this is not apparent, but should be investigated further. Fortunately, the mixing of labels does not affect the VBQ determination, as this only requires a mean vertebral ROI SI across all lumbar vertebrae.  
Automatic VBQ determination was successfully achieved by using the segmentations from the trained neural network model with the addition of analytical CSF segmentation using a connected threshold algorithm. Four different VBQ determination methods were presented. Interestingly, the mean and standard deviation of the VBQ score for each of the four methods appear to be relatively close to each other. However, the result of the one-way ANOVA shows that there is a significant statistical difference between the datasets, which means that the choice of VBQ determination method is not straightforward. The results of the post hoc [PERSON]'s HSD test show statistically significant differences between the methods using T1-weighted images and those using T2-weighted images for segmentation. The average VBQ scores of all four methods are in the range reported in [12]. The results of the manually drawn ROI method are also in the range cited by [12], except for the VBQ score for series 5, as shown in Table 2. The automatic VBQ determination method obtained plausible results for the same series, which, although only a single data point is involved, illustrates how useful a consistent automatic method can be. The main difficulty in the practical implementation of this method is the co-registration of T1- and T2-weighted images, which is required for two of the four proposed methods as it uses an additional program, FSL. The challenges of neural network training, data curation and preparation do not affect the practical implementation, as once a neural network model is trained, it can be easily shared and used for the segmentation task.