Multi-deformation Model

This section assesses the performance of the complete method developed in this work. Here, a rigid transformation is used along with a poly-rigid deformation model to han- dle articulated motion of the pelvis and femurs and approximate the deformation that articulation causes to nearby tissue and three deformation models which handle de- formation of the skin, PBR, and any residual transformation. The raw data for these models is a set of spatially varying weights for the poly-rigid transformation and a set of transformations from each patient to the atlas image for each of the three non-rigid stages. Dimensionality reduction is then performed on the transformations to develop the deformation models. Here, two variants are assessed, differing only in how the dimensionality reduction is performed. The first variant is the PGA method. The group-wise symmetric Log demons method used in this produces transformations in the Log domain, that is, VVFs. PCA is performed directly on these Log domain trans- formations. The resulting modes of variation can then be linearly combined, and the resulting Log domain transformation is then Exponentiated to provide a transformation

in the typical DVF form. In the PCA method, the Log domain VVFs are first expo- nentiated prior to performing PCA. The linear modes of variation are then combined to directly produce a DVF.

Placing these two variants on equal footing requires the introduction of an additional element that has the potential to introduce additional error. As described in section 3.4, the models are developed such that the transformations map from the training im- ages to the atlas space. In order to use the models to segment new images, an inverse transformation must be calculated. Recall that the inverse of a Log domain transfor- mation can be computed cheaply and with high precision by negating the VVF. The composite transformation can then be determined by composing each of the inverses in reverse order. This is not the case for the PCA variant, and an explicit inverse must be computed. To address this and ensure that any error from the inverse affects both methods similarly, the inverse method found in [13] is used for both the PGA and PCA cases. This method is simple to implement, fast, and, typically, accurate.

Figure 5.12 shows the results from the PGA variant, and figure 5.13 shows the results from the PCA variant. The mean and median of the DSC values are shown in figure 5.14. Both methods performed well in the AP direction, having mean DSCs comparable to inter-expert variation. Noting that there is greater contrast in MR than in CT, [77] found that the mean inter-expert DSC when segmenting the prostate from preoperative 1.5 T MR images was 0.883 and from intraoperative 0.5 T MR images was 0.838. Based on the available limited angle data, this method likely generates better segmentations than human experts because the prostate is nearly invisible in the reconstructions from the limited angle projection images used for 3D/2D registration. This is shown in figure 5.15.

It was expected that both these variants would perform similarly because the modes of variation that they produce are so similar. However, the PGA variant did not perform

Figure 5.12: Differences in the DSC between the rigid method and the full method proposed in this work. In the AP orientation, the full method provided significant improvement for all organs except the prostate in patient 3115. Performance in the LR orientation was much worse, only providing significant improvement for the bladder in patient 3101.

Figure 5.13: Differences in the DSC between the rigid method and the full method proposed in this work using the PCA variants. The method using linear geodesics produced significantly better segmentations than the rigid method for all patients in both orientations except for the prostate in patient 3115 in both orientations and the bladder in patient 3115 in the LR orientations.

Prostate Bladder Rectum PGA AP 0.851 (0.863) 0.879 (0.905) 0.826 (0.836) PGA LR 0.726 (0.753) 0.738 (0.763) 0.570 (0.592) PCA AP 0.850 (0.859) 0.882 (0.907) 0.822 (0.845) PCA LR 0.835 (0.855) 0.848 (0.870) 0.792 (0.797)

Figure 5.14: Summary of the DSC values (mean with median in parentheses) for each of the organs and both variants and orientations. The variants performed similarly for each of the variants and orientations with the exception of the PGA variant in the LR direction.

Figure 5.15: Coronal slices of the source CT with prostate indicated in red. The coronal plane being the preferred viewing plane for limited angle images with projections pri- marily in the AP direction. The CT is then used to simulate limited angle projections for the NST geometry in the AP orientation. These projections are then reconstructed using 10 iterations of the SART reconstruction algorithm. The corresponding slices show the difficulty of identifying the prostate in these limited angle images.

well in the LR direction. Despite their similar performance in the AP orientation and because of this failure, it appears that the use of PGA variant does not provide any advantages over PCA variant in this instance. The parameters of the PCA variant can also be determined faster because it does not require exponentiation during the optimization.

This method is intended to be used as part of an ART protocol. A treatment- time CT (or CT-like image) is necessary to perform dose accumulation for treatment monitoring, which is the central component of ART. However, figure 5.15 demonstrates that limited angle images do not provide reconstructed images of sufficient quality to perform dose accumulation. This method is a deformable segmentation method; it generates a deformation between an atlas image and the treatment space that is used to transfer the atlas segmentation to the treatment space. If this deformation is used to warp the atlas image to the planning space, that warped atlas can serve as an approximation to a CT at treatment-time. The success of this method in segmenting the PBR suggests that the deformed planning image is a good approximation of the patient’s actual anatomy because it generates projections that are similar enough to the projections from the actual patient to segment the low contrast PBR structures. Figure 5.16 provides further evidence of this.