# Three-Dimensional Anatomical Analysis of Muscle-Skeletal Districts
## 4 Results
### Single Exam Evaluation: Vertebral Spine Characterisation
Figure 9a shows the results of the thresholding of the distance distribution, which leads to the shape segmentation. The red part of the surface represents the vertebral body, the blue one the vertebral arch, and the green one the transverse and spinous processes. Applying the segmentation to all the vertebrae represented in the image, we obtained the segmentation of the whole vertebral spine (Figure 9b). On a pathological subject, the shape and morphology of the vertebra can change drastically as a result of different processes that damage the tissue; thus, the 3D surface models highlight such morphological changes. Applying our segmentation to a pathological case that presented a vertebral fracture due to osteoporosis, the fractured vertebra was identified among the others by a clear change in the segmentation result (Figure 9c). Indeed, a change in the distance from the vertebral centroid distribution, in turn, modifies the vertebra's probability distribution curve, as well as the position of the inflexion points. Figure 10 highlights how the inflexion points' location on the probability distribution has changed due to the osteoporosis processes that brought the vertebral fracture. Figure 8: Probability density curve of a vertebra and resulting segmentation associated with the inflexion points. Distances from the centroid values (\(x\)-axis) and probability density value (\(y\)-axis). The distance values corresponding to an inflexion point on the curve are considered as thresholds for the vertebral shape segmentation: \(T_{1}\) and \(T_{2}\) create the distinction between the three functional parts, where \(T_{1}\) is considered the reference value of the distance for the vertebral body, \(T_{2}\) for the vertebral arch, and \(T_{3}\) for the spinous and transverse processes region. Figure 9: Spine segmentation result: (**a**) single vertebra shape segmentation, (**b**) in a healthy subject, and (**c**) in a pathological subject. The application of the grey-level mapping algorithm to the vertebral surface model produces a 3D textured representation of the spine, where the texture corresponds to the HU values of the original 3D CT. Depending on the mapping criteria, we can investigate the tissues inside, across, or outside the vertebral surface. As a texture feature, we evaluated the mean HU values of the vertebra's functional region. At this point, we link the texture information obtained through the texture mapping method to the geometrical parameter that permitted the segmentation in functional regions. Thus, we correlated the geometrical thresholds localising the vertebral region (i.e., \(T_{1}\), \(T_{2}\), and \(T_{3}\) in Figure 8a), with the mean HU value of the region in all three mapping method criteria. In this way, we characterised the district considering both tissue and geometrical information, and we evaluated which of the mapping criteria is best suited for this characterisation. Figure 11 shows the results obtained in the comparison of the geometrical and tissue information. In each different mapping criterion, the graphs show various clusters. In the internal mapping case, the clusters could be associated with the varying percentage of cortical bone in the different vertebral components. Indeed, the body is composed mainly of cancellous bone, a spongy type of bony tissue. This cancellous bone is covered by a thin coating of cortical bone (or compact bone), which is a hard and dense type of bony tissue. The vertebral arch and processes have thicker coverings of cortical bone. The clusters identified in the external mapping results can be related to the tissue surrounding the vertebra from the outside. The vertebral body is confined by cartilaginous tissues (intervertebral disc), while the other parts of the vertebral border by ligaments and tendons (e.g., vertebral arch with the foramen). The slightly different values of HU between the Euclidean and external mapping results can be explained by the ligament insertion distribution on the vertebral arch and body.